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Simulation of the cardiotocogram during labor : towardsmodel-based understanding of fetal physiologyCitation for published version (APA):Jongen, G. J. L. M. (2016). Simulation of the cardiotocogram during labor : towards model-based understandingof fetal physiology. Eindhoven: Technische Universiteit Eindhoven.

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Simulation of the cardiotocogram during labor

Towards model-based understanding of fetal physiology

Germaine Jongen

A catalogue record is available from the Eindhoven University of Technology Library.ISBN: 978-90-386-4123-2

Copyright © 2016 by G.J.L.M. JongenAll rights reserved. No part of this publication may be reproduced, stored in a retrievalsystem, or transmitted, in any form or by any means, electronically, mechanically, by print,photo print, recording or any other means, without the prior written permission from theauthor.

Printed by Gildeprint, Enschede, The Netherlands

The research described in this thesis was funded by Stichting De Weijerhorst and performedwithin the IMPULS perinatology framework.

Simulation of the cardiotocogram during labor

Towards model-based understanding of fetal physiology

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven,op gezag van de rector magni�cus prof.dr.ir. F.P.T. Baaijens,

voor een commissie aangewezen door het College voor Promoties,in het openbaar te verdedigen op dinsdag 13 september 2016 om 16:00 uur

door

Germaine Josefa Lucienne Maria Jongen

geboren te Maastricht

Dit proefschrift is goedgekeurd door de promotoren en de samenstelling van de promotiecom-missie is als volgt:

voorzitter:1e promotor:2e promotor:copromotor:leden:

adviseur:

prof.dr. P.A.J. Hilbersprof.dr.ir. F.N. van de Vosseprof.dr. S.G. Oeidr.ir. P.H.M. Bovendeerdprof.dr. M. Ursino (Università di Bologna)prof.dr. F.P.H.A. Vandenbussche (RUN)prof.dr.ir. J.W.M. Bergmansdr.ir. M.B. van der Hout

Het onderzoek of ontwerp dat in dit proefschrift wordt beschreven is uitgevoerd in overeenstem-ming met de TU/e Gedragscode Wetenschapsbeoefening.

Contents

Summary ix

1 Background and aim of the thesis 1

1.1 General introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Mathematical models in a clinical setting . . . . . . . . . . . . . . . . . . . . 3

1.3 The cardiotocogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3.1 Clinical evaluation of the CTG . . . . . . . . . . . . . . . . . . . . . . 41.3.2 Physiological background . . . . . . . . . . . . . . . . . . . . . . . . . 51.3.3 Mathematical models for CTG simulation . . . . . . . . . . . . . . . . 7

1.4 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 A mathematical model to simulate the cardiotocogram during laborPart A: Model setup and simulation of late decelerations 11

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Material and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2.1 Feto-maternal hemodynamics . . . . . . . . . . . . . . . . . . . . . . 142.2.2 Oxygenation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.3 Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.4 Model simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

v

Contents

3 A mathematical model to simulate the cardiotocogram during laborPart B: Parameter estimation and simulation of variable decelerations 31

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.2 Material and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.2.1 Model extension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.2.2 Parameter estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.2.3 Model simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4 Simulation of fetal heart rate variability with a mathematical model 45

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2 Material and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.2.1 Mathematical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.2.2 Model extension with FHRV . . . . . . . . . . . . . . . . . . . . . . . . 504.2.3 Spectral analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.2.4 Model simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5 Hypoxia-induced catecholamine feedback on fetal heart rate:A mathematical model study 63

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.2 Material and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665.2.1 Physiological background . . . . . . . . . . . . . . . . . . . . . . . . . 665.2.2 Mathematical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.2.3 Parameter estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 705.2.4 Model simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6 General discussion 83

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

6.2 Main achievements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

6.3 Application of the CTG simulation model . . . . . . . . . . . . . . . . . . . . 86

6.4 Future perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

vi

Bibliography 91

Samenvatting 105

Dankwoord 109

About the author 113

vii

Contents

viii

Summary

ix

Summary

Simulation of the cardiotocogram during labor: towards model-basedunderstanding of fetal physiology

During labor and delivery, it is important to monitor fetal well-being to enable timely andadequate intervention in case of fetal discomfort. Ideally, fetal monitoring should includeassessment of oxygen status, but reliable oxygen measurements can only be performedduring labor, after rupture of membranes, and then are only available at a limited number oftime points. In current clinical practice, cardiotocography is therefore mainly used to estimatefetal well-being. The cardiotocogram (CTG) represents the simultaneous registration of thefetal heart rate (FHR) and uterine contractions. The underlying physiology, relating uterinecontractions to the �nal e�ect on FHR, involves a complex chain of events. This chainincludes the baro- and chemore�ex, as a response to variations in blood and oxygen pressure.Humoral feedback is also thought to be part of this response. Due to the complexity of thissystem, assessment of fetal well-being on the basis of the CTG is a challenging task.

Mathematical models can be used to gain more insight into the complex chain through whichuterine contractions lead to changes in fetal blood and oxygen pressure that �nally result intochanges in FHR. Previously, a mathematical model for simulation of the CTG was developed.This model describes feto-maternal hemodynamics, oxygenation, fetal regulation and uterinecontraction generation, and can be used to simulate early, late and variable decelerations ascaused by head compression, uterine blood �ow reduction, and umbilical cord compressionfollowing uterine contractions.

The �rst step of this work was to reduce model complexity of the submodels where pa-rameter estimation was complicated or where less detailed model output was su�cient. Inaddition, the physical description of other submodels was improved. In the next step, fetalheart rate variability (FHRV), which is an important indicator of fetal distress, was added tothe model. Finally, the contribution of humoral feedback in the cardiovascular response torepetitive severe episodes of hypoxia was investigated with the model.

The improved model, resulting from the �rst step, was used to investigate the cascadefrom uterine contractions resulting in decreased uterine and/or umbilical blood �ow, to FHRchanges. Uterine contractions a�ect fetal blood and oxygen pressures, which stimulate thebaro- and chemoreceptor, and �nally change FHR via the sympathetic and parasympatheticnervous system. The faster and more severe FHR decrease during uterine contractions caus-ing combined uterine and umbilical blood �ow reduction, compared to contractions leadingto uterine �ow reduction alone, can be explained by the oxygen bu�er function of the in-tervillous space. During the latter scenario, this oxygen bu�er is still available for the fetus,resulting in a delayed and slower drop in fetal oxygen pressure. As a consequence, thechemoreceptor-mediated FHR reduction is also delayed and less severe. If the umbilical cord

x

becomes occluded, this bu�er is no longer available for the fetus. During both scenarios,fetal blood �ow was redistributed from the peripheral to the cerebral circulation in order tomaintain oxygen transport to the brain. The initial FHR increase, observed during umbilicalcord occlusions, can be explained by a blood volume shift from the fetus to the fetal placenta.This results in a fetal blood pressure decrease and a baroreceptor-mediated increase in FHR.The volume shift can be attributed to the delay between the closure of the umbilical veinand arteries. The model was evaluated with data from sheep experiments: similar trends inblood pressure, oxygen pressure and FHR were obtained, showing the ability of the model todescribe realistic decelerations.

Since the exact source of FHRV is not known, in the model we investigated the e�ect ofthree possible sources of variability on FHRV: autoregulation of the peripheral blood vessels,in�uence of higher brain centers on the processing of the baroreceptor output in the nucleustractus solitarius of the medulla oblongata, and in�uence of a�erent systems, such as theheart, lungs and muscles, on the vagal center. Simulations were performed by superimposingeither 1/f noise or white noise on the peripheral vascular resistance, baroreceptor output, andvagal e�erent nervous system output. We evaluated FHR tracings by both visual inspectionand spectral analysis. All power spectra showed a physiological 1/f character, irrespectiveof the noise source and type used. Since the clinically observed peak near 0.1 Hz was onlyobtained when white noise was superimposed on each of the di�erent sources of variability, itis hypothesized that white noise is more likely to resemble physiological input. In accordancewith clinical data, sympathetic control predominantly in�uenced the low frequency power,while vagal control a�ected both low and high frequency power. Addition of FHRV improvedthe capability of the model to generate realistic FHR signals, which is of importance if themodel is used in clinical education.

During serious hypoxic episodes, induced by repeated severe contractions, secondary FHR re-sponses, such as FHR baseline increase and FHR overshoots, are often observed. Presumably,these FHR responses involve di�erent mechanisms, including stress hormone feedback andattenuation of the vagal tone. We extended the model to describe secondary FHR responsesvia a simple catecholamine feedback submodel. Simulation results of repeated severe uterineblood �ow reductions showed a similar trend as observed in sheep experiments: an initialdecrease of inter-occlusion FHR, followed by a gradual increase. Simulations of repeated se-vere umbilical blood �ow reductions showed FHR overshoots, following the FHR decelerations.However, these overshoots were less sharp than observed in sheep experiments. It is shownthat catecholamines play a role in the origin of secondary FHR responses, however othermechanisms, such as vagal inhibition or hypoxic myocardial depression, cannot be excluded.

xi

Summary

The improved and extended CTG simulation model is considered more suitable for use asa tool for hypothesis formation and testing and for educational purposes than our previousmodel. The new model contributes to understanding of the cascade of events betweenuterine contractions and FHR variations.

xii

Chapter 1

Background and aim of the thesis

Chapter 1

1.1 General introduction

Childbirth is a harzardous event for mother and child. Although fetal, neonatal, and infantmortality rates in Europe have declined between 2004 and 2010, these rates are still high[52]. In the 29 countries that participated in Euro-Peristat 2010 [52], fetal mortality ratesranged from 2.6 to 9.2 per 1000 total births. Neonatal mortality rates (until the 28th dayafter birth) ranged from 1.2 to 5.5 per 1000 live births. The infant mortality (0-364 days afterbirth) ranged from 2.3 to 9.8 per 1000 live births.

One of the main concerns during labor and delivery is fetal oxygenation. If oxygen transportfrom mother to child is reduced, this may result in fetal acidosis, which is related to devel-opment of neonatal morbidity, including neurological, respiratory and cardiovascular compli-cations [99, 158, 176]. In order to reduce the number of complications and to enable timelyintervention in case of fetal distress, it is important to monitor fetal well-being during laborand delivery. Ideally, assessment of fetal well-being is based on fetal oxygen status. However,since in current clinical practice reliable continuous oxygen measurement techniques are notavailable, the cardiotocogram (CTG) is used to estimate fetal condition. The CTG representsthe simultaneous registration of fetal heart rate (FHR) and uterine contractions. The relationbetween uterine contractions and changes in FHR is rather complex. Apart from variationsin oxygen pressure, also changes in e.g. blood pressure and stress hormone concentrationsplay a role. Although the CTG is widely used to monitor fetal well-being, the intra- and inter-observer variability is high [27, 110, 125]. Unfortunately, the use of cardiotocography has notlead to a reduction of perinatal death compared to intermittent auscultation, yet it is associ-ated with a reduction of neonatal seizures [7]. However, introduction of the CTG did result inan increased number of cesarean sections and instrumented vaginal births [7]. In addition tothe CTG, fetal blood sampling, ST-waveform analysis, and pulse oximetry, can be used duringdelivery to gain more insight into the fetal condition. However, the added value of thesetechniques in the detection of fetal distress is limited [164]. Furthermore, these techniqueswill not replace the CTG and thus interpretation of the CTG still remains an important taskof the clinician.

Due to the complex physiology involved in the cascade from uterine contractions to FHRvariations, interpretation of the CTG is not an easy task. Mathematical models might helpto gain insight into the di�erent mechanisms involved in FHR regulation, and thus improveunderstanding of the CTG. Moreover, a CTG simulation model will not only provide the clinicallymeasured signals –FHR and uterine contractions– but will also give an estimate of otherclinically relevant signals such as fetal oxygenation and blood pressure. These models canbe used for research and educational purposes, and in the longer term might be used tosupport clinical decision making.

2


Aim of this thesis is to optimize and extend the existing CTG simulation model of Van derHout-van der Jagt et al. [161–163] in order to enhance model applicability for research andeducation. As a �rst step, model complexity of submodels was reduced where possible. Inaddition, the physical description of other submodels was improved. In subsequent steps,fetal heart rate variability (FHRV), which is an important indicator of fetal distress, as wellas the contribution of humoral feedback in the cardiovascular response to repetitive severeepisodes of hypoxia, were investigated with the model.

In this chapter, �rst the use of mathematical models in clinic is discussed, whereafter twoexamples of such models are given. Thereafter, the CTG and the physiological aspects relatedto FHR changes are brie�y explained. Furthermore, mathematical models available for CTGsimulation are discussed. This chapter is concluded with an outline of the thesis.

1.2 Mathematical models in a clinical setting

In the clinic, many patient measurements are performed. However, the motto ‘the numberstell the tale’ does not always hold for these kind of measurements. Often clinicians have touse data obtained via indirect measurements, since direct measurements usually are inva-sive or not possible at all. Besides, these measurements are often related to large measuringinaccuracies. Nevertheless, clinicians are expected to estimate patient well-being and deter-mine a treatment plan based on these data. This is where mathematical models come in.Mathematical models can be used to gain insight into the complex physiology and supporthypothesis testing and formation. They can be made patient-speci�c in order to estimatethe e�ect of medical interventions and as such play a large role in clinical decision making.

An example is an existing model designed to support clinical decision-making concerningvascular access surgery in patients on hemodialysis therapy [18]. The model can help theclinician to choose the optimal location for creation of an arteriovenous �stula (AVF), a directconnection between an artery and vein in the arm of patients su�ering from kidney disease,by predicting the patient-speci�c postoperative blood �ow for di�erent AVF con�gurations.To be able to use the AVF-model in clinic, the model has �rst been tested, both in vivo asexperimentally. Presently, the feasibility of the model to support decision-making in AVFsurgery is being investigated via a randomized controlled trial. Since the computer model issoftware speci�cally designed for intervention planning, it will be considered a medical deviceby the medical ethics committee. Therefore, a computer model has to be certi�ed like othermedical devices.

3

Chapter 1

Another model, used to calculate the ‘virtual fractional �ow reserve’ (vFFR) in patients withcoronary artery disease based on coronary CT-angiography [111], has already obtained suchcerti�cation [53]. The FFR assesses the ratio of �ow across a stenosis to putative �ow in theabsence of a stenosis. It is an index of the physiological signi�cance of a coronary stenosisand an indication for percutaneous coronary intervention [151]. The FFR, which is normallyassessed via invasive cardiac catheterization, can now be computed non-invasively by use ofthe vFFR-model on the basis of CT images, for a large patient population.

These examples show that the idea to use a model for simulation of human physiology isnot new. Both models discussed are currently used, or will likely be used in future as adiagnostic modality. Inherently, these models only partly represent reality and can thus beused for decision support. Obviously, the �nal decision-making is in hands of the clinician.

This section is based on publications in ‘Medisch Journaal’ [79] and ‘MT Integraal’ [80].

1.3 The cardiotocogram

1.3.1 Clinical evaluation of the CTG

The CTG contains the simultaneous registration of FHR and uterine contractions. An exampleis shown in �gure 1.1. The clinical evaluation of the CTG is based on contraction strength,duration and frequency, in relation to FHR characteristics like FHR baseline, baseline variabil-ity, accelerations and decelerations. Fetal heart rate variability is described as �uctuationsin the FHR baseline, which are irregular in shape and frequency [115, 152]. Accelerations arede�ned as abrupt increases of more than 15 bpm above baseline, lasting longer than 15 s[100, 126], and are associated with fetal movements or may result from mild compressionof the umbilical vein [109, 177]. Fetal asphyxia is unlikely in the presence of accelerations.Decelerations are FHR reductions, which often are related to contractions. There are threetypes of decelerations which have di�erent shapes and vary in timing with respect to theuterine contraction: early, late and variable decelerations. Early decelerations, are gradualFHR reductions whose nadirs coincide with the uterine contraction peaks [100, 126]. Theyare caused by head compression, stimulating the vagal nerve via direct vagal hypoxia and/orstimulation of mechanoreceptors in the fetal head [102]. The clinical relevance of early de-celerations is limited. Late decelerations are also characterized by a gradual decrease in FHR,however, these decelerations are delayed with respect to the uterine contractions [100, 126].They can be caused by a re�ex pathway via the chemoreceptor, activated by low oxygenpressures caused by uterine contractions, or by hypoxic myocardial depression when oxygendelivery to the heart is not su�cient [63, 103, 114]. The presence of late decelerations is in-dicative for fetal distress, hence clinical interventions to advance labor and delivery are often

4


0 1 2 3 4 5 6 7 8 9 10 11 12 1360

80

100

120

140

160

180

200

time [min]

FH

R [bpm

]CTG

0 1 2 3 4 5 6 7 8 9 10 11 12 130

255075

100

time [min]

UP

[m

mH

g]

Figure 1.1: Example of a CTG. The upper signal represents fetal heart rate and the lowersignal represents the uterine contractions. This �gure is taken from [160] with permissionfrom the author.

indicated. Variable decelerations result from umbilical cord compression, which during labormostly occur during uterine contractions [57]. This type of decelerations is characterized byan abrupt FHR decrease, and by a varying shape between successive contractions [100, 126].A variable deceleration by itself is no indicator for fetal asphyxia. However, acidosis maydevelop if variable decelerations continue for a longer period. Additional information of fetalwell-being is often needed in order to determine if intervention is required.

1.3.2 Physiological background

The cascade from uterine contractions to the �nal e�ect on FHR depends on several path-ways, with a prominent role for the chemore�ex, barore�ex, and humoral re�exes, which willbe discussed in this section.

The maternal and fetal cardiovascular systems are separated, meaning that the maternalblood will not be in contact with the fetal blood (see �gure 1.2). Oxygen and nutrients aretransported to the fetus via the placenta, while metabolic waste products are removed fromthe fetal circulation. In the mother, about 10% [55, 115, 171] of the cardiac output is directed tothe uterine circulation, of which 70-90% [115, 131] enters the intervillous space to participatein gas exchange. Oxygen-rich blood enters the intervillous space via spiral arteries, branchingfrom the uterine arteries. Oxygen-poor blood is collected in the uterine veins. On the fetalside, oxygen-poor blood enters the placenta via two umbilical arteries, which branch intothe villous capillaries. The fetal placental villi actually bathe within the maternal blood in the

5

Chapter 1

fetal side

oxygen-rich blood

to umbilical vein

placental membrane

IVS with

villous capillaries

with fetal blood

oxygen-poor blood

from umbilical arteries

maternal side

to uterine vein

IVS with

maternal blood

from uterine artery

Figure 1.2: Schematic overview of the placenta. Maternal blood enters the placenta via theuterine artery and leaves the placenta via the uterine vein. Fetal blood enters the placentavia the umbilical arteries and leaves the placenta via the umbilical vein. Exchange of oxygen,waste products, and nutrients takes place between the maternal blood in the intervillousspace (IVS) and the fetal blood in the villous capillaries. This illustration is taken from [160]with permission from the author.

intervillous space. Here oxygen di�uses from the mother to the fetus. Oxygen-rich bloodleaves the fetal placenta and enters the fetal circulation via the umbilical vein. Umbilicalblood �ow comprises about 25% of the fetal cardiac output [3, 87, 97, 115, 133].

During uterine contractions, the oxygen transport between mother and fetus might be dis-turbed. First of all, the vessels running through the uterine wall will be squeezed, resulting inreduced uterine blood �ow [109]. Second, depending on its location, the umbilical cord mightbecome compressed, reducing transport of oxygen-rich blood from the fetal placental villito the fetus itself [109]. Both of these scenarios result in changes in fetal oxygen pressureand blood pressure [68, 69, 117], thus activating the chemo- and baroreceptor. Signals fromthese receptors are transmitted to the autonomic nervous system: the sympathetic nervoussystem is stimulated by the chemoreceptor and inhibited by the baroreceptor; the parasym-pathetic nervous system is stimulated by both chemo- and baroreceptor. Via the autonomicnervous system, several cardiovascular e�ectors are a�ected, including FHR, which is in-creased by activation of the sympathetic nervous system and decreased via the parasympa-thetic nervous system. As a net result, the FHR tracing shows decelerations. During hypoxia,the sympathetically-induced increase of the peripheral resistance results in a reduced per-fusion of the peripheral tissues. Concurrently, decreased cerebral vascular resistance results

6


in an increased blood �ow to the fetal brain (cerebral autoregulation). Due to this blood �owredistribution, oxygen transport to the most vital organs is maintained at the expense of theperipheral circulation [115].

Progression of hypoxic insults often results in FHR baseline increase [115, 152], and develop-ment of FHR overshoots [138, 177]. Catecholamines are thought to at least partly play a rolein the development of these secondary FHR variations [115, 136, 179]. Catecholamines enterthe blood stream via over�ow of neurotransmitters from the nervous system to the circu-lation, or via secretion by the adrenal medulla [49, 88]. In the fetus, adrenal catecholaminesecretion can be increased by nervous stimulation or by a direct e�ect of hypoxia on theadrenal medulla, known from several animal species [31–34, 141]. In adults, catecholaminesare removed from the circulation via neuronal and extra-neuronal uptake [47]. In the fetus,the placenta also plays an important role in the elimination of catecholamines [23, 47, 119].Catecholamines a�ect the cardiovascular system by increasing heart rate and blood pressure[88, 109, 115]. However, many uncertainties concerning the catecholamine feedback systemin the fetus remain.

1.3.3 Mathematical models for CTG simulation

In �gure 1.3, an overview is given of the di�erent subsystems contributing to the cascadebetween uterine contractions and FHR changes. Mathematical computer models do not onlyprovide these two CTG signals, but also give an estimate of other clinically important, butimmeasurable signals such as fetal oxygen pressure and blood pressure.

There are several submodels available that describe parts of the required model as shownin �gure 1.3. For example, models focusing on uterine contractions [9, 14], circulation [21, 61,66, 107, 134], oxygenation [67, 135], or regulation [154, 178]. However, models that describeall required submodels are scarce and most of these models are designed to simulate adultphysiology and thus have to be adapted for the fetus.

At the start of the project, there was only one model available containing all submodelsrequired to investigate the whole cascade from uterine contraction to FHR variations, namelythe model of Van der Hout-van der Jagt et al. [161–163]. This model is designed to simulatenon-asphyxiated fetuses and is used to investigate the in�uence of caput compressions[162], uterine �ow reductions [163] and umbilical cord compressions on FHR [161]. The modelpresented in this thesis is based on the model of Van der Hout-van der Jagt and describesfetal circulation, oxygenation, and regulation in a similar fashion. The model of Van derHout-van der Jagt was critically evaluated and simpli�ed, improved and extended in order toenhance applicability for educational and research purposes.

7

Chapter 1

uterine pressure

cardiovascular

system mother O2 distribution

mother

cardiovascular

system fetus

catecholamine

O2 distribution

fetusoxygen pressure

placentacontraction

generator

blood pressure

cardiovascular

parameters

baroreflex

chemoreflex

NS fetus

feedback

Monitor

FHR

contractions

oxygen pressure

Figure 1.3: Overview of all components of the CTG simulation model. The cardiovascularsystem of mother and fetus are separated and describe blood �ows and volumes in di�erentparts of the circulation. Changes of the cardiovascular parameters will lead to changes inthe oxygen distribution models. In the placenta, oxygen di�uses from mother to child. Fromthe fetal cardiovascular model a blood pressure signal can be obtained. Oxygen pressuresare obtained from the fetal oxygenation model. The blood and oxygen pressure variationsare input for the baro- and chemoreceptors, which via the nervous system (NS) result intochanges of several cardiovascular parameters, including FHR. A reduced oxygen pressurewill also increase the production of catecholamines, which has an additional e�ect on FHR.Uterine contractions are modeled via increases of uterine pressure, which a�ect the fetaland maternal cardiovascular systems and so initiate the whole cascade from contractionsto FHR changes. From the model, not only the two CTG signals can be obtained (FHR anduterine contractions), but it also gives an estimate of other clinically relevant signals such asoxygen pressure. Adapted from [160].

1.4 Outline of the thesis

In this thesis, the model of Van der Hout-van der Jagt [161–163] has been used as a startingpoint. Critical evaluation of the model setup showed room for improvement. In chapter 2,the updated model is introduced. In order to enhance model applicability for educationaland research purposes, the complexity of some submodels is reduced, while the physicaldescription of other submodels is improved. Furthermore, the model is used to investigateFHR variations induced by uterine contractions causing uterine blood �ow reduction.

Parameter estimation remains di�cult, despite a reduction in the number of model param-eters. Estimation of all model parameter values is extensively described in chapter 3. Inaddition, the model is used to gain insight into the mechanism through which umbilical cord

8


compressions lead to variable FHR decelerations.

Since fetal heart rate variability is an important indicator of fetal distress [181], this FHRfeature is also included in the model. In chapter 4, three possible sources of variability areadded to the model: autoregulation of the peripheral blood vessels, in�uence of higher braincenters on the processing of the baroreceptor output in the nucleus tractus solitarius of themedulla oblongata, and in�uence of other a�erent systems on the vagal center. The e�ecton the FHR tracings is investigated for each of these sources of variability, as well as for thetype of noise applied to these sources.

During prolonged hypoxia, secondary FHR e�ects might develop, such as increased FHRbaseline and FHR overshoots. In chapter 5, a simple catecholamine model is proposed andadded to the model in order to investigate the role of catecholamines in the development ofthese FHR e�ects.

The thesis concludes with a general discussion in chapter 6 in which all �ndings are putinto a broader perspective. As chapter 2 to 5 are written to be self-contained, some overlapbetween these chapters will be present.

9

Chapter 1

10

Chapter 2

A mathematical model to simulate thecardiotocogram during labor

Part A: Model setup and simulation of latedecelerations

The contents of this chapter have been published in Journal of BiomechanicsJongen GJLM, van der Hout-van der Jagt MB, van de Vosse FN, Oei SG and Bovendeerd PHM

Available online: http://dx.doi.org/10.1016/j.jbiomech.2016.01.036

Chapter 2

Abstract

The cardiotocogram (CTG) is commonly used to monitor fetal well-being during labor anddelivery. It shows the input (uterine contractions) and output (fetal heart rate, FHR) of acomplex chain of events including hemodynamics, oxygenation and regulation. Previouslywe developed a mathematical model to obtain better understanding of the relation betweenCTG signals and vital, but clinically unavailable signals, such as fetal blood pressure andoxygenation.

The aim of this study is to improve this model by reducing complexity of submodels whereparameter estimation is complicated (e.g. regulation) or where less detailed model outputis su�cient (e.g. cardiac function), and by using a more realistic physical basis for thedescription of other submodels (e.g. vessel compression).

Evaluation of the new model is performed by simulating the e�ect of uterine contractionson FHR as initiated by reduction of uterine blood �ow, mediated by changes in oxygen andblood pressure, and e�ected by the chemore�ex and barore�ex. Furthermore the ability ofthe model to simulate uterine artery occlusion experiments in sheep is investigated.

With the new model a more realistic FHR decrease is obtained during contraction-inducedreduction of uterine blood �ow, while the reduced complexity and improved physical basisfacilitate interpretation of model results and thereby make the model more suitable for useas a research and educational tool.

12

Uterine blood �ow reduction

2.1 Introduction

In current clinical practice the cardiotocogram (CTG), the combined registration of fetal heartrate (FHR) and uterine contractions, is used to monitor fetal well-being during labor and de-livery. The CTG signals show the input (uterine contractions) and output (FHR) of a complexregulation mechanism, in which amongst others variations in fetal blood pressure and oxy-genation play a role. To better understand the underlying physiology, mathematical modelscan be used. Previously a model for CTG simulation was presented [161–163]. This modelincluded feto-maternal hemodynamics, oxygen distribution, and regulation and was used tosimulate di�erent clinical scenarios following uterine �ow reduction and umbilical cord com-pression as induced by uterine contractions. While model results were in line with clinicalobservations, critical evaluation of the model setup showed room for improvement. Forexample, since the description of regulation and cardiac function was very detailed whilethe availability of experimental data was limited, estimation of the many parameter valueswas ambiguous. Furthermore, the model of hemodynamics focused on the detailed changeof arterial pressure during the cardiac cycle, whereas baroreceptor feedback was based onaverage arterial pressure only, allowing for a less complex model of cardiac function. Also,closure of the uterine and umbilical blood vessels due to uterine contractions was depen-dent on external vascular pressure, whereas it would be physically more realistic to make itdependent on vascular transmural pressure.

The aim of this study is to improve our previous model for simulation of the CTG, by reducingthe complexity of some submodels (e.g. regulation and cardiac function) and thus reducingerrors related to ambiguity in parameter estimation, and by improving the physical basis forthe description of other submodels (e.g. vessel compression).

In this chapter an overview of the new CTG simulation model is given. Functionality of themodel is tested by simulating the e�ect of uterine �ow reduction on FHR in term preg-nancy, resulting in FHR changes being known as late decelerations. Late decelerations arecharacterized as a gradual FHR decrease, meaning that it takes more than 30 s from onsetof the deceleration to the FHR nadir, with the nadir of the deceleration occurring after thecontraction peak [100, 126]. Two di�erent mechanisms are known to be responsible for latedecelerations: hypoxic myocardial depression, which plays a role when oxygen delivery to theheart is insu�cient, and re�ex feedback, which acts via activation of the chemo- and barore-ceptor as a result of reduced oxygen pressures induced by uterine contractions [63, 103, 114].In this study we focus on the re�ex induced late decelerations only. We tested the ability ofthe model to reproduce experimental data on arterial oxygen pressure, blood pressure andFHR from sheep experiments, in which late decelerations were evoked by means of in�ationof a balloon catheter to reduce uterine blood �ow [68, 117]. In chapter 3 we focus on theestimation of all model parameters and we investigate the e�ect of combined uterine and

13

Chapter 2

umbilical �ow reduction on FHR, resulting in so-called variable decelerations. Furthermore,in chapter 3 model limitations will be discussed.

2.2 Material and methods

The model consists of several submodels which describe feto-maternal hemodynamics, oxy-genation, fetal regulation, and uterine contractions. Although the general structure of theprevious model is maintained [161–163], changes are applied to the di�erent submodels inorder to simplify and enhance the CTG simulation model. Below we describe the setup ofthe new model. A detailed description of the parameter estimation is given in chapter 3.

2.2.1 Feto-maternal hemodynamics

The model of hemodynamics is composed of compartments, representing the storage ofblood and oxygen, which are connected via segments that represent convective transport.The fetal circulation consists of a combined ventricle (CV) from where blood �ows into thecerebral, umbilical, and tissue circulation (�gure 2.1). In the latter circulation, all tissues apartfrom the brain and fetal placenta (villi) are lumped. In the mother, the heart is representedby the left ventricle (LV) and the uterine circulation is modeled explicitly, while the remainderis lumped into the tissues.

2.2.1.1 Vascular function

To describe blood storage in the vascular system, we use a linear approximation of thepressure-volume relation around the working pressure of the blood vessel:

ptm =V – V0

C(2.1)

where C represents the compliance of the vessel, V the actual volume, and V0 the unstressedvolume of the vessel at zero transmural pressure. The transmural pressure ptm is de�nedas:

ptm = p – pext (2.2)

where p represents the absolute pressure in the compartment, and pext the external pressureacting on the outside. Fetal external pressure is equal to uterine pressure (put), while maternalexternal pressure is set to zero, except for the placental intervillous space (IVS) which is alsosubjected to put, see �gure 2.1.

14


For the IVS, that may undergo large volume changes during uterine contractions, a nonlinearpressure-volume relation is used:

Vivs(ptm) = Vmax · f (ptm) with f (ptm) = 12 + 1

π· tan–1

(ptm–p0

p1

)(2.3)

where Vivs represents the IVS blood volume, Vmax the maximal IVS blood volume, and ptm thetransmural blood pressure of the compartment, while p0 and p1 are constants. The functionf (ptm) was based on a relation between vessel cross-sectional area and transmural pressure[92].

In each compartment, the change in blood volume in time is determined by:

dVdt

= qin – qout (2.4)

where qin and qout represent in�ow and out�ow, respectively.

Blood �ow q in between compartments is generally described by:

q =∆pR

(2.5)

where R represents the resistance of the segment and ∆p the (absolute) pressure di�erenceover a segment. The resistance Rutv of the uterine vein, which is exposed to large changesin transmural pressure during uterine contractions, is modeled as function of transmuralpressure. Assuming as a �rst approximation that the �ow in this segment follows Poiseuille’slaw, we model the resistance to be inversely proportional to the square of the vessel area:

R(ptm) = max(

R0 ·(

1f (ptm)

)2,Rref

)(2.6)

where Rref is the resistance in steady state, R0 is a constant, and f (ptm) is de�ned by eq. 2.3.The transmural pressure of the uterine veins (ptm,utv) is determined as the mean absolutepressure of the two neighboring blood compartments (see �gure 2.1) minus the externaluterine pressure put:

ptm,utv = pivs+pven2 – put (2.7)

During uterine contractions, uterine pressure put increases above the resting pressure prest

[162]:

put = prest +

{pcon · sin2

(π(t–tcon)

Tcon

), tcon < t < tcon + Tcon

0, else(2.8)

with pcon peak pressure, tcon moment of contraction initiation, and Tcon contraction duration.See section 2.2.4 for parameter values.

15

Chapter 2

put

putput

put

put

villi umaumv

tisatisv

ceracerv

artven

tis

cer

putqout

CV

qin

QM,tis,f

artven

qin qout

LV

tisatisv

utautv

tis

ivs

put

QM,tis,m

QD,plac

QD,lung

mother

fetus

QM,cer,f

Figure 2.1: Schematic overview of the model of feto-maternal hemodynamics and oxygendistribution. The circles represent compartments where storage of blood and oxygen cantake place, while rectangles represent segments where blood �ows from one compartmentto the next. Metabolic and di�usional oxygen �ows are indicated with dashed arrows. In themother, blood �ows from the left ventricle (LV), via the systemic arteries (art) and the tissuemicrocirculation arteries (tisa) into the tissue microcirculation (tis). Blood �ow into the inter-villous space (ivs) takes place via the uterine spiral arteries (uta). Via the microcirculationveins (tisv) and the intramural veins in the uterus (utv) blood �ows into the systemic veins(ven), back to the heart. In the fetus, blood �ows from the combined ventricle (CV) into thesystemic arteries (art). Via the microcirculation arteries (tisa and cera) blood reaches thetissue and cerebral microcirculation (tis and cer, respectively), while blood leaves the mi-crocirculation compartments via the microcirculation veins (tisv and cerv). Via the umbilicalarteries (uma) blood �ows into the placental villi (villi), and via the umbilical vein (umv) backinto the systemic veins (ven). From the veins, blood �ows back into the heart. Uterine veinresistance (utv), and umbilical artery and vein resistance (uma and umv, respectively) arevariable and change as function of transmural blood pressure as described in eq. 2.6. In bothmother and fetus, qin represents in�ow of blood into the heart, while qout represents car-diac out�ow. The intervillous space and all fetal compartments experience external uterinepressure put. In the mother, oxygen di�uses from the air into the lungs (QD,lung) (modeledas oxygen di�usion into the systemic veins), while oxygen metabolism takes place in thetissues (QM,tis,m). In the placenta, oxygen di�uses from the mother to the fetus (QD,plac). Inthe fetus, oxygen is consumed in the tissues (QM,tis,f ) and the brain (QM,cer,f ).

16


Table 2.1: Cardiovascular parameters. Parameter estimation and sources are extensivelydescribed in chapter 3.

Fetal parameters

Parameter Value Unit Parameter Value UnitT* 60/135 s EF 0.67 -Vart,0 35.2 ml Rtisa* 2.81 mmHg·s/mlVven,0* 153.4 ml Rtisv 0.15 mmHg·s/mlVtis,0 15.9 ml Rcera* 7.24 mmHg·s/mlVcer,0 2.6 ml Rcerv 0.38 mmHg·s/mlVvilli,0 35.9 ml Ruma 3.84 mmHg·s/mlCart 0.33 ml/mmHg Rumv 2.56 mmHg·s/mlCven 21.91 ml/mmHg Emax* 7.71 mmHg/mlCtis 0.35 ml/mmHg Emin 0.26 mmHg/mlCcer 0.06 ml/mmHg V0,max 0 mlCvilli 2.40 ml/mmHg V0,min 5.8 ml

Maternal parameters

Parameter Value Unit Parameter Value UnitT 60/80 s Rtisv 0.04 mmHg·s/mlVart,0 721 ml Ruta 5.71 mmHg·s/mlVven,0 3604 ml Rutv 1.43 mmHg·s/mlVtis,0 504 ml R0,utv 0.358 mmHg·s/mlVivs,0 163 ml p0,utv -2.5 mmHgCart 3.9 ml/mmHg p1,utv 25 mmHgCven 308.9 ml/mmHg Emax 1.83 mmHg/mlCtis 6.4 ml/mmHg Emin 0.06 mmHg/mlCivs,max 2.4 ml/mmHg V0,max 0 mlEF 0.67 - V0,min 44 mlRtisa 0.67 mmHg·s/ml

*Denotes a reference parameter for the regulation submodel.

2.2.1.2 Cardiac function

Since only mean blood pressure values are used as input for the regulation submodel, wereplaced the dynamic one-�ber model of cardiac function [11, 20] by a two-state elastancemodel [65, 148]. This model relates the end diastolic volume Ved and the end ejection volumeVee to the transmural end diastolic pressure ptm,ed and end ejection pressure ptm,ee accordingto:

ptm,ed = Emin(Ved – Vmin,0) ; ptm,ee = Emax(Vee – Vmax,0) (2.9)

where the elastances Emin and Emax represent the slopes of the pressure-volume relations,and Vmin,0 and Vmax,0 the intercepts at zero pressure. We assume that the ventricle �lls atthe average venous blood pressure pv and ejects at the average arterial blood pressure pa.The average �ow from the heart, the cardiac output qCO, is described by:

qCO =VstrokeTcycle

=Ved – Vee

Tcycle(2.10)

17

Chapter 2

with stroke volume Vstroke and cardiac cycle time Tcycle.

The variation of the cycle-averaged cardiac volume with time is accounted for by:

qout = qCO ; qin = qCO + qV with qV = ddt

(Ved+Vee

2

)(2.11)

where qout and qin represent cardiac out�ow and in�ow, respectively. Parameter values forthe hemodynamic model can be found in table 2.1.

2.2.2 Oxygenation

For a schematic representation of the oxygen model see �gure 2.1. While we adopted thestructure of our previous model [162], we modi�ed several details. For completeness, wedescribe the new model below.

2.2.2.1 Oxygen content

In each compartment, oxygen concentration cO2 is determined by the sum of the oxygenbound to hemoglobin and the oxygen dissolved in blood:

cO2 =αHb · sO2

100+ βpO2 (2.12)

Here α represents the maximum binding capacity of hemoglobin, Hb the hemoglobin con-centration and β the content of dissolved oxygen per unit of partial pressure pO2. Oxygensaturation sO2 is related to oxygen partial pressure by:

sO2 =100

1 + c1/(pO32 + c2 ·pO2)

(2.13)

where c1 and c2 are constants. Since fetal blood has a higher oxygen a�nity than maternalblood, for the fetus this curve is steeper and shifted to the left compared to an adult [108],as determined by a lower value of c1 (see table 2.2).

2.2.2.2 Oxygen transport

In each compartment the rate of change of oxygen amount (oxygen concentration cO2 mul-tiplied by compartment blood volume V ) is determined by the sum of convective transportQC , di�usive exchange QD and metabolic uptake QM :

d(cO2V)dt

= QC + QD – QM (2.14)

18


where the change in volume is determined from the hemodynamic model. Whereas the actualsign of the di�usive and convective transport may vary depending on the compartment,metabolic uptake always leads to a reduction of oxygen content.

Table 2.2: Oxygen distribution parameters. See chapter 3 for estimation and sources.

Parameter Value Unit Parameter Value UnitDplac 0.082 ml O2/(s·mmHg) α 1.34 ml O2/g HbDlung 0.169 ml O2/(s·mmHg) β 3.1 ·10–5 ml O2/(ml blood·mmHg)QM,0,tis,f 3.36·10–1 ml O2/s Hbf 17 ·10–2 g Hb/ml bloodQM,0,cer,f 1.31·10–1 ml O2/s Hbm 12 ·10–2 g Hb/ml bloodQM,0,tis,m 10 ml O2/s c1f 1.04 ·104 mmHg3

pO2,th,cer,f 5 mmHg c1m 2.34 ·104 mmHg3

pO2,th,tis,f 10 mmHg c2f 150 mmHg2

pO2,air 160 mmHg c2m 150 mmHg2

f indicates a fetal parameter, and m indicates a maternal parameter.

Convection describes the blood �ow related transport of oxygen through the cardiovascularsystem. For each compartment convection is described by:

QC = ∑i

qiincOi

2,in –∑j

qjoutcO2 (2.15)

The �rst term represents the sum of all oxygen in�ows of the current compartment, where iruns across all segments with a blood in�ow qi

in into the compartment, with oxygen concen-tration of the in�ow compartment cOi

2,in. The second term represents the sum of all oxygenout�ows with oxygen concentration of the current compartment cO2, where j runs acrossall segments with a blood out�ow qj

out from the compartment.

In the model, oxygen di�usion takes place both in the placenta (QD,plac) from the maternalIVS into the fetal placental villi, and in the maternal lungs (QD,lung) from the air into thematernal veins (see �gure 2.1):

QD,plac = Dplac(pO2,ivs – pO2,villi) ; QD,lung = Dlung(pO2,air – pO2,mat,ven) (2.16)

with Dplac and Dlung the di�usion coe�cient in the placenta and the lung, respectively, andpO2 the partial oxygen pressure in a compartment. Since we did not explicitly model thematernal pulmonary circulation, we introduced pulmonary oxygen uptake at the in�ow of theLV, in the maternal veins.

Oxygen metabolism is modeled in the fetal and maternal tissues and fetal brain. Metabolicuptake is constant (QM,0) as long as the oxygen level in the compartment is above a certain

19

Chapter 2

threshold pO2,th and will decrease linearly if the oxygen level becomes lower:

QM =

{QM,0, pO2 ≥ pO2,th

QM,0 + QM,0pO2,th

· (pO2 – pO2,th), else(2.17)

Parameter values of the oxygen model can be found in table 2.2.

2.2.3 Regulation

The cardiovascular regulation submodel describes cerebral autoregulation as well as centralregulation in the fetus.

2.2.3.1 Cerebral autoregulation

The model for cerebral autoregulation increases oxygen transport to the brain in case ofhypoxemia. It is adapted with respect to Van der Hout-van der Jagt [163], to better re�ectthe limited capability of the cerebral autoregulation submodel to completely compensate fora reduced oxygen supply, via parameter γ in eq. 2.19. Cerebral autoregulation is includedvia decrease of cerebral artery resistance Rcera if oxygen levels drop. The limited ability ofthe actual resistance Rcera to instantaneously follow a desired resistance R∗cera is describedthrough a low pass �lter with time constant τRcera :

dRcera

dt=

1τRcera

(R∗cera – Rcera) (2.18)

The value of the desired resistance R∗cera is based on [120], who found a hyperbolic relationbetween arterial oxygen content and cerebral blood �ow in fetal lambs:

R∗cera =Rcera,ref

(1 – γ) + γ · cO2,a,refcO2,a

(2.19)

where cO2,a represents the oxygen concentration in the fetal arteries, and Rcera,ref andcO2,a,ref represent the reference value of Rcera and cO2,a respectively (table 2.1 and 2.3). Theterm γ [-] determines how well Rcera can adapt to variations in arterial oxygen concentrationcO2,a. A value of 1 means that a decrease in cO2,a is completely compensated by an increaseof blood �ow (modeled via a decrease of R∗cera) to keep up oxygen delivery to the brain. Inour model a value of 0.5 is chosen for γ based on Peeters [120]. The minimal value of R∗cerawas set to half of its reference value.

20


ΔpO2,a

Δptm,a rb

rc

Rtisa

Emax

Vven,0

T

ΔputRutv

Rcera

effectorsreceptors

cardiovascular and oxygen model

NS

+

+

+-

+

pO2,aptm,a

cO2,a,ref

pO2,a,ref

ptm,a,ref

cO2,a

-

G

G

zx k

z x Emax,refx k

z x Vven,0,refx k

zx Rtisa,refx k

z

x Tref

x kev

+

+

÷

-

+

+

+

Rumv & Ruma

-

+

uterine and umbilical flow reduction

cerebral autoregulation

D

D

D

D

D

Rcera

rc

rb

x Rcera,ref

es

+1

+1

+1

+1

Figure 2.2: Schematic overview of the e�ect of uterine contractions on the cardiovasculare�ectors via the regulation submodel. Uterine contractions result in changes in uterinepressure put , and a�ect uterine vein resistance (Rutv) and possibly umbilical vein and arteryresistance (Rumv and Ruma, respectively). This will lead to changes in mean transmural arterialblood pressure ptm,a and oxygen pressure pO2,a. Via a Gompertz relation G and a lowpass �lter τ , these variations are translated into the normalized baro- and chemoreceptoroutputs, rb and rc respectively, which in turn in the nervous system (NS) are combinedinto a normalized vagal ev, and sympathetic es e�erent output. Via a delay D, another lowpass �lter, and a multiplication factor k, these outputs lead to relative changes z of thefour cardiovascular e�ectors: heart period T (composed of a sympathetic and a vagal heartrate response), cardiac contractility Emax, venous unstressed volume Vven,0, and peripheralvascular resistance Rtisa. Addition of the value 1, followed by multiplication with the referencevalue of each e�ector, results into the �nal e�ector values. For the cerebral autoregulation,arterial oxygen content cO2,a is derived from pO2,a by use of the fetal saturation curve. Anonlinear function, a low pass �lter, and multiplication with the reference resistance value,determine the relation between cO2,a and cerebral resistance Rcera.

2.2.3.2 Central regulation

The model for central regulation describes the e�ect of baro- and chemoreceptor regulationon four cardiovascular e�ectors: heart period T , cardiac contractility Emax, peripheral vascu-lar resistance Rtisa, and venous unstressed volume Vven,0. We replaced our previous modelbased on Ursino [154] by a simpler model based on Wesseling [178]. Our new regulation modelonly contains a baro- and chemoreceptor and does no longer include the responses of vagalnerve hypoxia or central nervous system (CNS) hypoxia. Furthermore, the two sympatheticpathways (α and β ) were combined into one sympathetic e�erent signal (see �gure 2.2).

21

Chapter 2

In the receptor model, deviations of transmural arterial blood pressure ptm,a and oxygenpressure pO2,a are translated into normalized deviations of the baroreceptor output rb andchemoreceptor output rc, with respect to their steady-state value of 0. The actual receptoroutput r (where r may represent rb or rc) responds to variations in input y (representing ptm,a

or pO2,a) via a low pass �lter with time constant τr:

dr(y)dt

=1τr

(r∗(y) – r(y)) (2.20)

Here r∗ represents the desired output, which is described by an asymmetric sigmoid relation(Gompertz function):

r∗(y) = rmin + (rmax – rmin) · eη1·eη2 ·(y–yref )

(2.21)

with yref a reference value for ptm,a or pO2,a, and rmin [-] and rmax [-] the minimum andmaximum receptor value, respectively (table 2.3). Derivation of η1 and η2 is described inchapter 3.

The e�erent pathways e in the model consist of a vagal and a sympathetic signal (ev andes, respectively), which both are a function of the a�erent information from the baro- andchemoreceptor. The e�erent pathways also represent normalized deviations from steadystate in which ev = es = 0:

ev = wb,v · rb + wc,v · rc, with wb,v + wc,v = 1es = –wb,s · rb + wc,s · rc, with wb,s + wc,s = 1

(2.22)

The weighting parameters w are all positive (table 2.3). Since an increase in transmural arterialblood pressure has an inhibiting e�ect on the sympathetic output, the contribution of thebaroreceptor output rb to the sympathetic signal es is taken negative.

The e�erent vagal and sympathetic signal determine the setting of the four cardiovasculare�ectors. The e�ectors Rtisa, Vven,0, and Emax are sympathetically-mediated. For T wedistinguish between a vagally- and sympathetically-induced change in heart period. In general,for each e�ector �rst the corresponding e�erent signal (ev or es) is delayed with a time delayD. The resulting intermediate output x∗(t) passes a low pass �lter characterized by its speci�ctime constant τ to yield a signal x(t), that in turn is multiplied by an e�ector gain k [-] toobtain an e�ector signal z(t):

x∗(t) = e(t – D) ;dx(t)

dt=

1τ

(x∗(t) – x(t)) ; z(t) = kx(t) (2.23)

22


Table 2.3: Regulation parameters. See chapter 3 for estimation and sources.

Model component Parameter Value Unit Parameter Value UnitCerebral cO2,a,ref 0.107 ml O2/ml blood γ 0.5 -

autoregulation τRcera 10 sη1,b -0.69 - η1,c -6.91 -η2,b -0.06 mmHg–1 η2,c 0.52 mmHg–1

rb,min -1 - rc,min -0.001 -Central regulation: rb,max 1 - rc,max 1 -

receptors τrb 8 s τrc 2 syref ,b 45 mmHg yref ,c 18.1 mmHgwb,s 1/4 - wc,s 3/4 -wb,v 1/4 - wc,v 3/4 -DTv 0.2 s kEmax 1.2 -τTv 1.5 s DRtisa 2 skTv 2.4 - τRtisa 6 s

Central regulation: DTs 2 s kRtisa 4.2 -e�ectors τTs 2 s DVven,0 5 s

kTs 1.2 - τVven,0 20 sDEmax 2 s kVven,0 -1.2 -τEmax 8 s

The signal z(t) represents the relative change of the e�ector value. For Rtisa, Vven,0, and Emax

the new e�ector values are computed via:

Rtisa(t) = Rtisa,ref · (1 + zRtisa (t))Vven,0(t) = Vven,0,ref · (1 + zVven,0 (t))Emax(t) = Emax,ref · (1 + zEmax (t))

(2.24)

where Rtisa,ref , Vven,0,ref , and Emax,ref represent the reference e�ector values (table 2.1). ForT the e�ector value is computed through:

T(t) = Tref · (1 + zTv (t) – zTs (t)) (2.25)

where zTv and zTs represent the vagally- and sympathetically-induced relative change in heartperiod and are determined using eq. 2.23 and Tref represents the reference heart period.The minus sign in eq. 2.25 indicates the inhibitory e�ect of the sympathetic feedback onT(t). Parameter values for the regulation model can be found in table 2.3.

2.2.4 Model simulations

The model was implemented in MATLAB R2013a (The MathWorks, Inc., USA). Di�erentialequations were evaluated by forward Euler time integration with a time step of 0.02 s. Sce-narios described below were initiated from a steady-state situation at which variation of ptm,a

and pO2,a was less than 1 ·10–4 mmHg/s, respectively.

23

Chapter 2

We simulated uterine �ow reduction in term pregnancy (full term fetus of 3.5 kg) during areference contraction de�ned by a duration (Tcon) of 60 s and a uterine pressure amplitude(pcon) of 70 mmHg with respect to the reference pressure (prest), which was set at 15 mmHg[109, 115], (i.e. a maximum uterine pressure of 85 mmHg is reached). Furthermore, moresevere contractions, with a contraction amplitude of 110 mmHg or a contraction duration of120 s, were simulated.

We also simulated sheep experiments in which uterine blood �ow was blocked for 20 s by useof a balloon catheter in the descending aorta [68, 117]. We assumed that the balloon catheterwas in�ated and de�ated over a time span of 5 s [69]. We linearly increased uterine arteryresistance Ruta over 5 s to a maximum value of 100 times the reference resistance, then keptthe resistance at maximum level for 20 s, and subsequently decreased the resistance backto steady-state level over another 5 s. To investigate the e�ect of compression duration,simulations of 30 s compression were performed as well.

Simulation results of combined uterine and umbilical �ow reduction are presented in chapter3 of this paper.

2.3 Results

Figure 2.3 shows simulation results of isolated uterine �ow reduction caused by a referenceuterine contraction of 60 s with a pressure amplitude of 70 mmHg. In steady state, uterinepressure (panel A1) is equal to the resting pressure of 15 mmHg. Fetal arterial blood pressureis 45 mmHg (panel A2), arterial oxygen pressure is 18.5 mmHg (panel A3), and fetal heartrate is about 135 bpm (panel A4). Uterine blood �ow is about 630 ml/min (panel B1) andIVS blood volume is 175 ml (panel B2). Oxygen pressure both in fetal tissues and brainis 15.4 mmHg (panel B3). Blood �ow through the fetal tissues and brain equals 850 and330 ml/min, respectively (panel B4). Note that blood pressures mentioned in this sectionrepresent transmural blood pressures.

Column A shows the CTG signals (uterine pressure and FHR) and vital signals (arterial bloodpressure and oxygen pressure). During a standard uterine contraction, modeled via an in-crease in uterine pressure (panel A1), only a slight increase in arterial blood pressure is ob-served (panel A2), while arterial oxygen pressure is reduced by about 1.5 mmHg (panel A3).FHR only shows a small deceleration of 3 bpm (panel A4). If we look into more detail (col-umn B) we observe an initial increase of IVS out�ow and decrease of IVS in�ow (panel B1),due to compression of the IVS. As uterine pressure increases, IVS venous out�ow decreasesbecause the uterine veins become compressed. Due to the pressure build-up in the IVS, thepressure di�erence between the maternal arteries and IVS reduces, decreasing IVS in�ow via

24


0 1 2 3 40

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]

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qutv

quta

pO2,tispO2,cer

qtis

qcer

ivs

Figure 2.3: Simulation results for a standard uterine contraction of 60 s with an amplitudeof 70 mmHg and for contraction variations. From top to bottom, signals in column A repre-sent: uterine pressure (put); mean arterial transmural blood pressure (ptm,a); arterial oxygenpressure (pO2,a); and FHR. In column B, signals represent: blood �ow through the uterineintramural veins and uterine spiral arteries (qutv and quta, respectively); IVS blood volume(Vivs); tissue and cerebral oxygen pressure (pO2,tis and pO2,cer , respectively); and fetal tissueand cerebral blood �ow (qtis and qcer , respectively). In column C, similar signals as in columnA are shown for the standard contraction (light gray), for a contraction with an increasedamplitude of 110 mmHg (dark gray), and for a contraction with an increased duration of 120s (black). Signals are described brie�y in the main text.

the uterine arteries. Since IVS out�ow is larger than IVS in�ow, IVS blood volume drops (panelB2). When uterine pressure decreases, the uterine veins open again, causing an increase ofvenous out�ow. IVS pressure decreases as well, causing an increase in arterial in�ow. Finally,IVS blood volume is restored. During the contractions fetal oxygen levels drop (panel B3), thedrop in the brain being less deep than that in the tissues. This di�erence is caused by theredistribution of fetal blood �ow from the tissues to the brain, since peripheral resistanceincreases due to central re�ex regulation, and cerebral resistance decreases due to cerebralautoregulation (panel B4). As shown in column C, more severe contractions result in a largerreduction of oxygen pressure, a larger increase of blood pressure, and a larger decelerationof FHR.

25

Chapter 2

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A: Simulation results.

-20

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]

Parer 20 s

Itskovitz 20 s

Model 20 s

Model 30 s

pO2,a [mmHg] ptm,a [mmHg] FHR [bpm]

ns

B: Comparison with sheep data.

Figure 2.4: Results from simulations of uterine artery block. A) Model response to uterineartery occlusions of 20 (gray) and 30 s (black). From top to bottom: arterial oxygen pressure(pO2,a); transmural arterial blood pressure (ptm,a); and FHR. The rectangles in the bottomindicate the uterine artery occlusion times. B) Comparison of model results to experimentalresults from sheep studies [68, 117]. From left to right: relative maximum variations inarterial oxygen pressure (pO2,a), transmural arterial blood pressure (ptm,a), and FHR. N.B.:‘ns’ indicates that uterine artery block does not result in a signi�cant variation with respectto the steady-state value.

Figure 2.4 shows the simulation results of uterine artery block of 20 and 30 s. From thesesignals the relative changes of arterial oxygen pressure, blood pressure and FHR were ob-tained and compared to relative changes as obtained from sheep experiments [68, 117]. Inboth sheep experiments uterine blood �ow was blocked for 20 s. In the model, 20 s of uter-ine �ow reduction caused qualitatively correct changes in oxygen pressure, blood pressureand FHR, although these changes were quantitatively reduced as compared to those obtainedfrom the sheep experiments. A �ow block of 30 s was required to obtain results more similarto sheep data.

26


2.4 Discussion

Mathematical model. In comparison to our previous model [161–163], we replaced the dy-namic one-�ber model [11, 20], that enabled computation of the change of blood pressuresand blood �ows during a heart beat, by a two-state elastance model [65, 148] that gener-ates average blood �ows and pressures. This simpli�cation did reduce the number of modelparameters, but did not a�ect input for the regulation model: the baroreceptor only usesaverage blood pressure as input, and computed oxygen concentrations vary at a time scalethat exceeds that of one cardiac cycle.

The central regulation submodel used in our previous model [161, 163] was based on an adultmodel [154], extended with the e�ect of vagal nerve hypoxia. While the model could beused to simulate early, late and variable decelerations in FHR, critical review showed severalshortcomings. Parameter estimation in the complex model was di�cult because of lackof experimental data. Furthermore, model response in simulations of contraction-induceduterine and umbilical �ow reductions was dominated by the response to vagal nerve hypoxia,and a reference contraction of 60 s with a pressure amplitude of 70 mmHg causing uterine�ow reduction alone, would lead to an FHR deceleration of 15 bpm. This response wasconsidered not representative for an uncompromised fetus.

In the current study, we drastically reduced the complexity of the central regulation modelto reduce the number of input parameters and facilitate interpretation of the model results.The central regulation submodel was based on Wesseling [178], while still maintaining someaspects of Ursino [154]. The new model only contains the baro- and chemore�ex and doesnot describe the response to vagal nerve and CNS hypoxia. Whereas literature data suggest ahyperbolic relation between arterial oxygen pressure and chemoreceptor discharge frequency[17, 90], we used a Gompertz relation (an asymmetrical S-curve) to prevent chemoreceptoroutput to go to in�nity at very low oxygen pressures. The baroreceptor response was alsomodeled through a Gompertz relation. The description of the central regulation, in whicha�erent baro- and chemoreceptor signals are combined into e�erent vagal and sympatheticsignals, was simpli�ed as well by replacing the nonlinear transfer functions in the previousmodel by constant weighting factors. We also chose not to di�erentiate between sympathetice�erent signals to the blood vessels and to the heart (α- and β -sympathetic pathways, re-spectively), because of lack of experimental data on these pathways in the fetus. This impliesthat it is impossible in the model to activate α- and β -sympathetic pathways separately. Asshown in the results, these simpli�cations did not limit the ability of the model to describevariation of FHR or clinically vital signals such as blood and oxygen pressure.

As in the previous model, uterine contractions are implemented through a transient increaseof uterine pressure. However, we now model the e�ect of the changes in uterine pressure onvessel volume and resistance in terms of vascular transmural pressure instead of external

27

Chapter 2

uterine pressure. This is physically more realistic, since it is the pressure di�erence acrossthe vessel wall that determines the cross sectional area of the vessel lumen, and therebyvessel volume and resistance. Also, compression of the uterine circulation leads to closureof the uterine veins rather than of the uterine artery, which is more realistic as well.

Results. In the scenario of contraction-induced uterine �ow reduction, the FHR decelerationis delayed with respect to the contraction peak. This can be explained from the fact thatduring uterine �ow reduction, oxygen in the IVS is still available to the fetus. Consequentlyit will take some time before fetal oxygen pressure, and accordingly FHR will drop (�gure2.3). Therefore these decelerations are referred to as ‘late’ decelerations. In our model thedelay between the onset of the FHR deceleration and FHR nadir is about 40 s, which is inaccordance with the guidelines of late decelerations, stating that the delay should be at least30 s [100, 126]. The decelerations, however, are not symmetrical as is usually observed inthe clinic [100, 126]. Presumably this is caused by the relative slow return of arterial oxygenpressure to baseline levels. The primary cardiovascular response is chemoreceptor-mediated.As a secondary response the mean arterial blood pressure will increase, thereby activatingthe baroreceptor. The steady-state values correspond with values found in literature asindicated in chapter 3.

If we compare predicted variations in FHR for the current and the previous model [163], weobserve that for uterine �ow reduction more realistic FHR decelerations of 3 bpm are ob-tained, even though the oxygen and blood pressure signals show the same characteristics.We think that this response is more realistic, since a standard contraction in an uncompro-mised full term fetus does not lead to fetal distress that is considered clinically signi�cant.Simulations of increased contraction amplitude (110 mmHg) or duration (120 s) showed thatlarger FHR deceleration depths (about 14 bpm and 21 bpm, respectively) can be obtainedduring severe contractions, see �gure 2.3.

Due to the limited measurements that can be performed in a human fetus, sheep exper-iments from literature were simulated in order to test our model. Trends in variation ofarterial oxygen pressure, blood pressure and FHR were similar to the trends obtained fromsheep experiments. To obtain results quantitatively similar to sheep data, occlusion time hadto be prolonged with 10 s (�gure 2.4). The temporal variations in �gure 2.4 show a delayedresponse with respect to experimental data [68, 117]. The drop in fetal oxygen levels couldbe accelerated by increasing fetal oxygen metabolism or decreasing IVS blood volume. Thiswould also lead to a better correspondence of the results of the 20 s occlusion with theexperimental data in �gure 2.4. However, we did not perform such model adaptations sincethen values for these parameters would no longer be consistent with values found in litera-ture. Moreover, it is unclear whether the response of the sheep fetus would quantitativelymatch that of the human fetus described in our model.

28


Conclusion. A new CTG model was presented, which in comparison to our previous modelwas improved by reducing complexity of some submodels and by using a better physicalbasis for the description of other submodels. The model shows a more realistic FHR responseduring uterine �ow reduction. Due to the reduced complexity and improved physical basis,the model is more suitable for use as a research and educational tool.

29

Chapter 2

30

Chapter 3

A mathematical model to simulate thecardiotocogram during labor

Part B: Parameter estimation and simulation ofvariable decelerations

The contents of this chapter have been published in Journal of BiomechanicsJongen GJLM, van der Hout-van der Jagt MB, van de Vosse FN, Oei SG and Bovendeerd PHM

Available online: http://dx.doi.org/10.1016/j.jbiomech.2016.01.046

Chapter 3

Abstract

During labor and delivery the cardiotocogram (CTG), the combined registration of fetal heartrate (FHR) and uterine contractions, is used to monitor fetal well-being. In chapter 2 weintroduced a new mathematical computer model for CTG simulation in order to gain insightinto the complex relation between these signals. By reducing model complexity and by usingphysically more realistic descriptions, this model was improved with respect to our previousmodel.

Aim of this chapter is to gain insight into the cascade of events from uterine contractionscausing combined uterine �ow reduction and umbilical cord compression, resulting in bloodand oxygen pressure variations, which lead to changes in FHR via the baro- and chemore�ex.In addition, we extensively describe and discuss the estimation of model parameter values.

Simulation results are in good agreement with sheep data and show the ability of the modelto describe variable decelerations. Despite reduced model complexity, parameter estimationstill remains di�cult due to limited clinical data.

32

Umbilical blood �ow reduction

3.1 Introduction

In chapter 2, we gave an overview of a new cardiotocogram (CTG) simulation model. Com-pared to our previous model [161–163] the complexity of some submodels was reduced andthe physical basis for the description of other submodels was enhanced. It was shown thatthe model was able to simulate realistic FHR decrease in response to uterine �ow reductionas induced by uterine contractions.

In this chapter the model is used to gain insight into the mechanism of variable FHR decel-erations which are caused by umbilical cord compressions, that mostly occur during uterinecontractions during labor [57]. Variable decelerations are de�ned as an abrupt FHR decreaseof more than 15 bpm, with a maximum time delay of 30 s between onset of the decelerationand FHR nadir, and a duration of less than 2 min [100, 126]. In addition, the e�ect of varyingamplitude and duration of uterine contractions on the CTG is investigated. We also comparemodel output with data of sheep experiments in which the umbilical cord was temporarilyblocked by use of an occluder [69]. Although model complexity is reduced, parameter esti-mation is di�cult due to the limited clinical data. Therefore, we will extensively describe anddiscuss estimation of these parameter values.

The new model is intended to be used to gain insight into the regulation of FHR during laborand delivery. For use as a clinical decision support tool, the model should be made patient-speci�c. This is a challenging task in view of the limited availability of clinical data and thelimited time span for model analysis during labor. Use as an educational tool would be amore realistic next step.


The model is extensively described in chapter 2. In this chapter we extend the model in orderto simulate combined uterine blood �ow reduction and umbilical cord compression inducedby contractions. Besides, an overview of model parameter estimation is given.

3.2.1 Model extension

Since during cord compression the umbilical vein and arteries are exposed to large changes intransmural pressure, the corresponding resistances, Rumv and Ruma respectively, are modeledas function of transmural pressure ptm, as described in eq. 2.6. Parameter values are chosensuch that �rst the umbilical vein will be closed, followed by the umbilical arteries at higherexternal umbilical pressures, see table 3.1.

33

Chapter 3

Table 3.1: Umbilical vein and artery resistance parameters.

Parameter Value UnitR0,umv 2.05 mmHg·s/mlp0,umv -17 mmHgp1,umv 10 mmHgR0,uma 2.34 mmHg·s/mlp0,uma -27 mmHgp1,uma 16 mmHg

The transmural pressure of the umbilical vein ptm,umv and umbilical arteries ptm,uma is deter-mined as the mean absolute pressure of the two neighboring blood compartments minusthe external pressure:

ptm,umv = pvilli+pven2 – (put + pum)

ptm,uma = pvilli+part2 – (put + pum)

(3.1)

where the external pressure consists of the uterine pressure put, that acts on the wholefetus, plus an extra pressure pum, caused by umbilical cord compression.

The degree of cord compression depends on the contraction intensity, fetal position, stageof labor, etc. The e�ect of these random variables is modeled through a weighting factorwum [-], relating put to the external pressure on the umbilical cord pum:

pum = wum(put – prest), wum ≥ 0 (3.2)

with prest uterine resting pressure.

3.2.2 Parameter estimation

Due to the limited available human fetal data, parameter estimation is di�cult. For thisreason parameter estimation is extensively described. Fetal cardiovascular parameters wereobtained from literature and set to values of a 3.5 kg term human fetus. If human data werenot available, fetal sheep data were used to derive the parameters. Some parameter valueswere set to obtain the desired model responses. Parameter choices are brie�y explainedbelow, all parameter values can be found in table 2.1 to 2.3.

3.2.2.1 Feto-maternal hemodynamics

Fetal combined ventricular output qCO was aimed at 450 ml/min/kg [87, 115, 133, 168], ejec-tion fraction EF at 0.67 [137], and heart rate at 135 bpm (table 2.1). Mean arterial transmu-ral blood pressure ptm,a and mean transmural venous blood pressure ptm,v were set to 45mmHg [69, 147, 150, 153] and 3 mmHg [74, 133, 150] respectively. Fetal blood volume wasreported to be about 75 ml/kg [96, 156, 182], which is about two third of total feto-placental

34


blood volume [182]. Therefore, the latter volume was set to 110 ml/kg, which is in accordancewith Schwarz [139]. Total microcirculation blood volume was computed from Guyton et al.[62] and set to 8% of fetal body blood volume, which was distributed over cerebral (14%)[26, 64] and tissue microcirculation (86%). Average cardiac cavity volume follows from qCO,EF and FHR and equals 11.7 ml. The remainder of the body blood volume was distributedover the systemic fetal arteries (1/6) and veins (5/6). Based on geometric considerations[43, 97, 172], blood volume of the umbilical circulation was divided between the placental villi(65%), umbilical arteries (10%) and vein (25%). Since for the umbilical arteries and vein noseparate compartments were included in the model, these blood volumes were added to thesystemic arteries and veins respectively.

Maternal cardiovascular parameters were based on pregnancy-related changes as describedin literature (table 2.1). Target values for ptm,a and ptm,v were set to 80 mmHg [29, 59, 84] and5 mmHg [109] respectively. During pregnancy, heart rate HR increases up to a target valueof 80 bpm [29, 59, 84, 132], while the cardiac output [1, 29, 84, 98] and blood volume [1, 98]both increase by 40%. In our model cardiac output and total blood volume were set to 7l/min and 7 l, respectively. EF was set to a value of 0.67 [29, 59, 84]. Intervillous space (IVS)volume was chosen to be 175 ml [15, 105, 123], while the volume of the tissue microcirculationwas chosen to be 8% of total maternal blood volume [62]. Average left ventricular bloodvolume follows from qCO, EF and HR and equals 87.5 ml. Like in the fetus, the remainder ofthe blood volume was distributed over systemic arteries (1/6) and veins (5/6). Parameters p1

and Vmax, de�ning the relation between IVS volume Vivs and transmural blood pressure asdescribed by eq. 2.3, were determined by assuming that p0 = pref , where pref is the referencetransmural IVS blood pressure in steady state. Then it follows that:

Vmax = 2 ·Vivs(pref )

Finally p1 was determined by assuming that IVS compliance is maximal at pref , meaning that:

p1 =Vmax

π ·Civs,max

For Civs,max we chose a similar value as for the placental villi (2.4 ml/mmHg).

For both fetus and mother, target values of blood �ows and pressures were used to estimateresistances and compliances. We chose umbilical cord �ow to be 25% of qCO, in agreementwith literature data that range from 15 to 34% of qCO [3, 87, 97, 115, 133]. The fraction ofcardiac output going to the fetal brain was estimated by use of a fractional brain mass of14% [26, 64] and by the estimation that oxygen metabolism per gram tissue, and thus alsoblood �ow per gram tissue, should be twice as high in brain tissue compared to peripheraltissues. This means that 21% of total cardiac output goes to the brain and 54% to the fetaltissues, which is in accordance with Rudolph [133]. In the mother about 10% of the cardiac

35

Chapter 3

output is directed to the uterine circulation [55, 115, 171], of which 70-90% is directed to theIVS [115, 131, 174]. Hence we chose 9% of qCO to be directed to the IVS, while 91% is directedto the other maternal tissues.

For the fetal and maternal tissues and fetal brain, 95% of the total resistance was assignedto the microcirculation arteries, while 5% was assigned to the microcirculation veins. Inthe umbilical circulation, the arterial resistance fraction was set to 60%, to obtain a bloodpressure of about 20 mmHg in the placental villi [66]. In the uterine circulation this fractionwas set to 80%, in order to obtain an IVS pressure of about 60-70 mmHg below mean arterialpressure [124]. Except for the placental villi and IVS, compliances were estimated assumingthat 70% of the volume in the reference state contributes to the unstressed volume. Forthe cerebral and tissue microcirculation, unstressed volume fraction was set to 90%. Thecompliance in the placental villi was set to 2.4 ml/mmHg [12, 66].

Initial values of Ved and Vee were calculated from target values of qCO, EF and FHR. Vmin,0

was chosen to be equal to Vee, while Vmax,0 was set to 0. Finally, Emax could be calculatedas the slope of a line through the data points (Vee, ptm,a) and (Vmax,0, 0), while Emin wascalculated as the slope of a line through (Ved , ptm,v) and (Vmin,0, 0).

3.2.2.2 Oxygen distribution

The oxygen di�usion coe�cient in the placenta was set to 0.082 ml O2/(s·mmHg) (table2.2) such that in steady state a fetal umbilical arterial oxygen pressure of 18.5 mmHg wasobtained [2, 97, 140]. Fetal oxygen metabolism was set to be 8 ml O2/(min·kg) [2, 19] anddivided over cerebral metabolism (28%) and tissue metabolism (72%). We chose a thresholdvalue of 5 mmHg for cerebral oxygen metabolism (pO2,th,cer,f ) [77] and 10 mmHg for theperipheral tissues (pO2,th,tis,f ), where the latter value corresponds to about 50% of the steady-state oxygen concentration, based on Sá Couto [135].

Maternal oxygen consumption was set to 600 ml O2/min. The oxygen pressure in the airwas set to 160 mmHg, while target maternal arterial oxygen pressure was set to 98 mmHg.Combination of this oxygen pressure di�erence and total feto-maternal oxygen metabolismyielded a pulmonary oxygen di�usion coe�cient of 0.169 ml O2/(s·mmHg). Since in thecurrent study maternal oxygenation was kept constant, an oxygen metabolism threshold wasirrelevant for the maternal model.

Fetal and maternal parameter values de�ning the relation between cO2 and pO2 were chosenas described by Sá Couto [135].

36


3.2.2.3 Regulation

Cerebral autoregulationFor the cerebral autoregulation the value of γ , indicating how well the cerebral resistancecan adapt to variations in arterial oxygen content, was estimated by use of Peeters [120] andset to a value of 0.5. The cerebral resistance can maximally decrease by 50%, which meansthat cerebral blood �ow can increase with a factor of 2. Finally, the time constant τRcera waschosen to be 10 s according to Ursino [154].

Central regulationFor the baroreceptor and chemoreceptor outputs, as described in eq. 2.21, the parametersη1 and η2 follow from the condition that r(y = yref ) = 0 and from the (desired) slope at thereference point (y = yref ):

η1 = ln(–rmin

rmax – rmin) (3.3)

dr∗(y)dy

∣∣∣∣y=yref

= η2 ·η1eη1 (rmax – rmin) (3.4)

Baroreceptor parameters were obtained by scaling the relation as described by Ursino [154]to fetal values and normalizing it to a range between -1 and 1 (table 2.3). Baroreceptorsensitivity in the fetus is reduced by a factor two as compared to the adult [38]. Parametervalues of the Gompertz function were chosen such that the relation between baroreceptorinput ptm,a and output rb closely resembled the scaled response of Ursino. Parameter valuesfor the chemoreceptor response were chosen such that a reference contraction of 60 s witha pressure amplitude of 70 mmHg would lead to a maximum FHR deceleration of about 3bpm for uterine �ow reduction alone and about 50 bpm for combined uterine �ow reductionand umbilical cord compression. The values of the e�ector gains k and e�erent weightingfactors w were also chosen to obtain the desired e�ects in FHR (table 2.3). For all e�ectorstime delays D and low pass �lter time constants τ were obtained from Ursino [154] (table2.3).

3.2.2.4 Uterine and umbilical blood vessel compressions

In the relation between transmural blood pressure and vessel resistance, as described in eq.2.6, R0 was chosen such that R(pth) = Rref , with pth the transmural pressure below which theblood vessel resistance starts to increase and Rref the reference resistance in steady state.For the uterine vein p0 and p1 were chosen such that a contraction with a uterine pressureamplitude of 60 mmHg and a duration of 60 s would result in a 60% blood �ow reductionthrough the uterine artery [70] (table 2.1). In our model, the uterine arteries are not subjectedto increasing uterine pressure. Parameter settings for the umbilical cord resistances werefound by simulating the sheep experiments in which initial fetal blood volume changes were

37

Chapter 3

measured during umbilical cord compressions with increasing external pressures [35]. Theumbilical vein is totally closed if the external pressure exceeds 40 mmHg, while the umbilicalarteries are compressed over a pressure range of 40 to 90 mmHg (see table 3.1).


We simulated combined uterine �ow reduction and umbilical cord compression in term preg-nancy by setting wum = 1 in eq. 3.2. A reference contraction with a duration (Tcon) of 60 sand a pressure amplitude (pcon) of 70 mmHg with respect to the reference pressure (prest)of 15 mmHg was used. To illustrate the e�ect of regulation, simulations with and withoutcentral regulation and autoregulation were performed. In addition, the e�ect of contractionintensity was investigated by changing contraction amplitude from 70 mmHg to 30 and 110mmHg respectively, or contraction duration from 60 s to 30 and 120 s respectively.

The model was evaluated by use of sheep experiments in which umbilical cord blood �owwas temporarily reduced by use of an occluder [69]. The sheep experiments were simulatedby linearly increasing the external pressure (pum) on the cord over 5 s to a maximum level,which was maintained for 35 s, and reduced to zero over another 5 s, while keeping put atthe resting level. In order to obtain umbilical �ow reductions of 25%, 50%, 75% or 100%, aspresented by Itskovitz, maximum external pressure was set to a value of 25, 33, 41, or 90mmHg, respectively. Umbilical vein and artery resistance, Rumv and Ruma respectively, werecalculated by use of eq. 2.6.

3.3 Results

Figure 3.1 shows the scenario of combined uterine �ow reduction and umbilical cord com-pression induced by a reference contraction of 60 s with a pressure amplitude of 70 mmHg.Initial values for this scenario are the same as for the scenario of uterine �ow reductionalone, as described in chapter 2. In addition, �gure 3.1 shows that umbilical blood �ow isabout 394 ml/min (panel B1) and that villous volume is 83 ml (panel B2). Note that bloodpressures described in this section represent transmural blood pressures.

We �rst consider the simulation without regulation, indicated by the gray lines. During cordcompression the external umbilical pressure rises (panel A1) and fetal blood pressure (panelA2) and arterial oxygen pressure (panel A3) decrease. Without regulation, FHR will not bea�ected (panel A4). If we now look into more detail (column B), we observe that �rst umbilicalvenous �ow reduces to near zero (panel B1) and that the placental villi are �lled via theumbilical arteries (panel B2). Once the umbilical arteries are compressed as well, villousvolume remains more or less constant. This blood volume shift from fetus to placenta

38


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ZTvZTsZTv-ZTs

ZRtisaZVven,0ZEmaxauto

Figure 3.1: Simulation results for a standard uterine contraction of 60 s with an amplitudeof 70 mmHg. Results for the simulation with regulation are indicated in black, results for thesimulation without regulation are indicated in gray. From top to bottom signals in column Arepresent external umbilical pressure (pum); mean arterial transmural blood pressure (ptm,a);arterial oxygen pressure (pO2,a); and FHR. In column B, signals represent blood �ow throughthe umbilical vein and arteries (qumv and quma, respectively); villous blood volume (Vvilli);tissue and cerebral oxygen pressure (pO2,tis and pO2,cer , respectively); and fetal tissue andcerebral blood �ow (qtis and qcer , respectively). Dimensionless signals in column C representbaro- and chemoreceptor outputs (rb and rc, respectively); sympathetic and vagal e�erentsignals (es and ev, respectively); relative e�ector changes z for peripheral vascular resistance(Rtisa), venous unstressed volume (Vven,0), and cardiac contractility (Emax), while the ‘auto’signal represents the relative change of the autoregulated cerebral resistance (Rcera); and�nally relative vagally- and sympathetically-induced heart period changes (zTv and zTs , re-spectively), and the di�erence between both (zTv – zTs ). (Note the change in axes comparedto �gure 2.3.)

39

Chapter 3

explains the drop in blood pressure (panel A2) that in turn causes a drop of blood �ow throughthe fetal tissues and brain (panel B4). The reduction of umbilical blood �ow decreases arterial,cerebral, and tissue oxygen levels (panel A3 and B3). Initially, no di�erence is observedbetween the cerebral and tissue oxygen pressures. Later, cerebral oxygen pressure dropsdeeper than tissue oxygen pressure, which is due to the lower oxygen metabolism thresholdvalue in the brain, as described in eq. 2.17. At the end of the occlusion umbilical cord vesselsopen again and all values will return back to normal levels. The regulation signals, as shownin column C, do not change if regulation is switched o�.

In the situation with cardiovascular regulation, indicated by the black lines, the initial decreasein arterial blood pressure results in a decreased baroreceptor output (panel C1) that in turncauses an increase of the sympathetic, and decrease of the vagal e�erent signal. This changeis modi�ed by the chemoreceptor-mediated increase of both e�erent signals. The resultinge�erent signals (panel C2) cause an initial drop of heart period (panel C4) and consequently aninitial increase in FHR (panel A4). The ongoing decrease in oxygen pressure further increaseschemoreceptor output (panel C1), stimulating both e�erent signals (panel C2). The increasedsympathetic response results in an increase of peripheral vascular resistance and cardiaccontractility, while venous unstressed volume is reduced (panel C3). This leads to an increaseof arterial blood pressure (panel A2) and baroreceptor output (panel C1). The weighted averageof the chemoreceptor and baroreceptor outputs now results in a similar time course ofthe vagal and sympathetic e�erent signal (panel C2). Since vagal feedback on heart periodis twice as strong as sympathetic feedback, FHR responds with a deceleration (panel A4).Comparison of panels A4 and C1 shows that the timing of the minimum FHR at about 1.3 minis dominated by the chemoreceptor response, while the timing of the second dip at 1.6 minis caused by the baroreceptor response. Finally, cerebral autoregulation decreases cerebralvascular resistance (panel C3), thereby increasing cerebral blood �ow (panel B4). Togetherwith �ow reduction in the tissues caused by the increased peripheral resistance, this resultsin �ow redistribution in favor of the fetal brain. As a consequence, the drop in cerebraloxygen pressure is reduced compared to the unregulated case (panel B3).

In �gure 3.2 the e�ect of variation in contraction amplitude and duration is shown. In gen-eral an increased or decreased contraction duration has a similar but opposite e�ect onpressures and FHR, while variation of amplitude has a nonlinear e�ect. When contractionamplitude is increased to 110 mmHg (column A), only minor changes are seen compared tothe reference contraction. When contraction amplitude is reduced to 30 mmHg (column B),umbilical vessels do not become fully blocked, hence less blood is stored in the villi, andthus the drop of arterial blood pressure is reduced. The drop of oxygen pressure is reducedsince oxygen supply through venous umbilical �ow continues. FHR remains rather constant,because of the reduced baroreceptor and chemoreceptor response. If contraction durationis increased to 120 s (column C), the drop in arterial blood pressure is similar to that during

40


0 1 2 3

time [min]0 1 2 3

time [min]0 1 2 3

time [min]

0

100

pu

m[m

mH

g]

35

55

75

ptm

,a[m

mH

g]

5

10

15

20

pO

2[m

mH

g]

0 1 2 350

100

150

time [min]

FH

R [b

pm

]

pO2,a

A1

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A4

A3

B1

B2

B4

B3

C1

C2

C4

C3

D1

D2

D4

D3

pO2,cer

Figure 3.2: Simulation results for uterine contractions with varying contraction amplitudeand duration. With respect to the reference contraction with a duration of 60 s and anamplitude of 70 mmHg, indicated in light gray, contraction amplitude was set to 110 mmHg(column A) or 30 mmHg (column B), or contraction duration was set to 120 s (column C),or 30 s (column D). The signals shown in each column are similar to the signals shown incolumn A of �gure 3.1.

the reference contraction. The increased FHR deceleration is mainly caused by the increasedchemoreceptor feedback, in response to the lower oxygen levels. Finally, if contraction du-ration is decreased to 30 s, less blood is stored in the villi, and the initial arterial pressuredrop is reduced. Arterial oxygen pressure drops less deep, due to the shortened durationof umbilical cord compression. FHR drops less deep because of reduced baroreceptor andchemoreceptor feedback.

Figure 3.3 shows the relative variations in arterial oxygen pressure, blood pressure and FHRduring di�erent degrees of umbilical cord block as obtained from sheep data [69] and frommodel simulations. Quantitatively, the simulation results agree well with the experimentaldata.

41

Chapter 3

-80

-60

-40

-20

0

20

40

60

Va

ria

tio

n f

rom

ste

ad

y s

tate

[%

]

Itskovitz

Model

pO2,a [mmHg] ptm,a [mmHg] FHR [bpm]

ns

ns nsns

25% 50% 75% 100%

25% 50% 75% 100%

25% 50% 75% 100%

Figure 3.3: Results from simulations of umbilical cord occlusion, in comparison to exper-imental results from sheep studies [69]. From left to right: relative variations in arterialoxygen pressure (pO2,a), transmural arterial blood pressure (ptm,a), and FHR. N.B.: ‘ns’ indi-cates that the relative �ow reduction does not result in a signi�cant variation with respectto the steady-state value.

3.4 Discussion

Parameter estimation. Parameter estimations were described in section 3.2.2. The mostimportant choices will be discussed here.

It has been reported that the baroreceptor sensitivity in the fetus is two to eight timeslower than that in the adult [38]. In the model, we used a two-fold decrease with respect tosettings for the adult, used by Ursino [154]. With this setting, we observed an initial increaseof FHR (clinically referred to as ‘shoulders’) when simulating variable decelerations, whichdisappeared when further lowering baroreceptor sensitivity.

Clinically, most contractions that a�ect uterine blood �ow alone, lead to reductions in FHR(‘late decelerations’) that do barely exceed the noise level of the FHR signal in a healthy fetus.In the model, we tuned parameter settings such that simulation of our reference contractionwith uterine �ow reduction alone yields an FHR deceleration of about 3 bpm. Due to thevariable character of the FHR decelerations caused by combined uterine and umbilical �owreduction, there is no typical response for this ‘variable deceleration’ scenario. We chose atarget value of 50 bpm during a reference contraction. Deeper decelerations can be reached

42


if contraction duration or amplitude increases (�gure 3.2).

Since oxygen pressure dropped by 1.5 mmHg in the former scenario, and by 6 mmHg in thelatter scenario, chemoreceptor output had to increase steeply over a small arterial oxygenpressure interval. Finally, to obtain the desired results, the e�ector gains k were multiplied bya factor 6 with respect to Wesseling [178]. This adaptation can partly be explained from thefact that in our regulation model the chemoreceptor was added and a larger reduction of FHRwas desired. Simulation of other scenarios is needed to test the validity of these parametersettings. However, the clinical or experimental data to validate the model is limited.

Results. Simulation results show that oxygen levels drop more quickly during combineduterine and umbilical �ow reduction (�gure 3.1) compared to uterine �ow reduction alone(�gure 2.3). This can be explained by the fact that during cord compression the fetus has noaccess to the IVS oxygen bu�er, since oxygen cannot be transported from the placental villiinto the fetus. Until the oxygen threshold is reached below which metabolic rate decreases,oxygen content drops linearly in time. Since the oxygen pressures reached are still in thelinear range of the saturation curve, oxygen pressure also drops linearly. We observed thatFHR increases before onset of the decelerations. This increase is clinically referred to as‘shoulder’ [50, 109, 115]. In the clinic these shoulders are often also observed at the end ofthe deceleration, however this e�ect was not obtained in the model, presumably due to thedominant sympathetically-induced blood pressure increase in our model. During a standardcontraction, the FHR decreases from baseline to nadir in about 26 s, which is in accordancewith the clinical guidelines de�ning an abrupt decrease in FHR to occur within 30 s [100, 126].Furthermore, FHR reaches baseline levels again within 2 minutes. This is in accordance withliterature [100, 126], although the �nal part of FHR return seems somewhat slow.

Simulation results of contraction variations (�gure 3.2) show that oxygen pressure reductiondepends on the duration and amplitude of the contraction, which will both increase duringprogression of labor. The time delay between onset and nadir of the FHR deceleration in-creases with increasing contraction amplitude or duration. The wide variation in the shapesof the FHR decelerations corresponds well with the clinical observation that umbilical cordocclusions have a variable character and are therefore called ‘variable decelerations’. Clini-cally, these variations are also caused by variation in the position of the umbilical cord withinthe uterus. In the model this could be simulated by variation of the weighting factor wum ineq. 3.2. However, since random variation of this factor would complicate comparison of theresults in the various scenarios, we kept this factor constant.

If we compare FHR signals obtained with the current model with the results of our previousmodel [161], we see that FHR decelerations are now preceded by a shoulder, which was notobserved in the previous model. This shoulder can partly be attributed to increased �lling ofthe villi, due to the fact that the umbilical arteries remain patent, and partly to the stronger

43

Chapter 3

baroreceptor response in the current model.

The model generates estimates of many physiological signals, while in clinical practice onlyFHR can be measured continuously. To gain more insight into the complex pathway fromuterine contractions to FHR changes, we also show signals that cannot be measured in theclinic. Since these intermediate signals cannot be compared to human data, we used sheepdata on oxygen pressure and blood pressure to evaluate the model, noting that quantitativecomparison with sheep data is di�cult due to the di�erences between the ovine and humanfetus. For example, in fetal lambs about 40-45% of the cardiac output is directed to theumbilical circulation [73, 115, 133], while in the human fetus this is only 25%. Despite thedi�erences between human and sheep fetuses, for the simulations of umbilical cord blocking,results were quantitatively in accordance with sheep experiments (�gure 3.3).

Limitations. Although we reduced the number of model parameters to be estimated, it is stilldi�cult to arrive at a unique set of model parameter settings from the limited experimentaldata presented in literature. Consequently, there may be di�erent combinations of parameterchoices which will lead to similar results. In future, a sensitivity analysis should be performedin order to investigate which parameters dominate model response and should be determinedvery precisely and for which parameters a more general value can be used.

The model lacks the ability to describe FHR variability, which is an important indicator of fetaldistress in clinical practice. Addition of this variability would further improve applicability ofthe model for training purposes and clinical diagnosis and decision making.

The current model is intended to describe CTG signals during short-term hypoxia and toprovide additional information on fetal oxygen status. To be able to describe the e�ectscaused by stronger and longer contractions, humoral feedback has to be added to the model[109], and the shift of the fetal oxygen dissociation curve due to the changes in pH (Bohre�ect) should be taken into account. Furthermore, cardiac metabolism and the e�ect ofmyocard hypoxia on FHR might be included in the model.

In the hemodynamic model of the fetus, the fetal heart is represented by a combined ven-tricle. To describe improved oxygen supply to the brain due to preferential blood �ows, thecombined ventricle might be replaced by a separate left and right ventricle.

Conclusion. With the improved model we were able to generate realistic variable deceler-ations for the scenario of combined uterine and umbilical �ow reduction. Parameter esti-mation of the simpli�ed model remains di�cult due to the limited availability of clinical andexperimental data.

44

Chapter 4

Simulation of fetal heart rate variability with amathematical model

The contents of this chapter are under review for Medical Engineering & PhysicsJongen GJLM, van der Hout-van der Jagt MB, Oei SG, van de Vosse FN, and Bovendeerd PHM

Chapter 4

Abstract

In the clinic, the cardiotocogram (CTG), the combined registration of fetal heart rate (FHR)and uterine contractions, is used to predict fetal well-being. Amongst others, fetal heart ratevariability (FHRV) is an important indicator of fetal distress. In this study we add FHRV to ourpreviously developed CTG simulation model, in order to improve its use as a research andeducational tool.

We implemented three sources of variability by applying either 1/f or white noise to theperipheral vascular resistance, baroreceptor output, or e�erent vagal signal. Simulated FHRtracings were evaluated by visual inspection and spectral analysis.

All power spectra showed a 1/f character, irrespective of noise type and source. The clini-cally observed peak near 0.1 Hz was only obtained by applying white noise to the di�erentsources of variability. Similar power spectra were found when peripheral vascular resistanceor baroreceptor output was used as source of variability. Sympathetic control predominantlyin�uenced the low frequency power, while vagal control in�uenced both low and high fre-quency power. In contrast to clinical data, model results did not show an increase of FHRVduring FHR decelerations. Still, addition of FHRV improves the applicability of the model asan educational and research tool.

46

Fetal heart rate variability

4.1 Introduction

The cardiotocogram (CTG) is a commonly used technique to monitor fetal well-being duringlabor and delivery. The CTG represents the combined registration of fetal heart rate (FHR)and uterine contractions. In clinical practice, fetal condition is based on evaluation of di�er-ent characteristics of the FHR signal during rest and in response to uterine contractions, suchas baseline level, accelerations, decelerations, and baseline variability. The relation betweenuterine contractions and changes in FHR is very complex. Therefore, previously we developeda mathematical CTG simulation model, describing hemodynamics, oxygenation, and cardio-vascular regulation [81, 82] (chapter 2 and 3). We successfully used the model to investigatethe e�ect of uterine vein and/or umbilical cord occlusions, initiated by uterine contractions,on fetal hemodynamic and oxygen pressures, which via the baro- and chemore�ex lead tochanges in FHR. However, the model lacked a description of fetal heart rate variability (FHRV),that is considered to be an important indicator of fetal well-being [181]. FHRV is describedas �uctuations in the FHR baseline, which are irregular in amplitude and frequency [115, 152].The presence of FHRV is highly associated with the absence of signi�cant metabolic acidemia,even if the FHR tracing shows decelerations [116]. Decreased FHRV is related to lower Apgarscores and fetal acidosis [118]. Furthermore, loss of FHRV was found to be the most consis-tent FHR characteristic preceding antepartum fetal death, despite of a usually normal FHRbaseline level [128].

In the autonomic control of heart rate (HR), the medulla oblongata of the brain stem, whichis part of the central nervous system (CNS), plays an important role [88]. It receives inputfrom baroreceptors, chemoreceptors and respiratory stretch receptors as well as from thehypothalamus and higher brain centers, and a�ects HR via the sympathetic and parasym-pathetic nerve system [88]. Sympathetic activation increases HR, while parasympatheticactivation decreases HR. In the adult, di�erent frequency bands can be de�ned. Very lowfrequencies (up to 0.04 Hz) are supposed to originate from thermoregulation and humoralsystems, and high frequency variations (0.15 to 0.4 Hz) are related to respiration [146]. Lowfrequency variations (0.04 to 0.15 Hz) are in�uenced by cardiac sympathetic and parasympa-thetic nerve activity [146], however, no consensus is reached about the relative contributionof these two pathways [149]. Many questions about the source and interpretation of heartrate variability (HRV) remain, and the underlying physiological mechanisms are not completelyknown [106]. Autonomic control of heart rate in the fetus is even less well understood due tochanges in baroreceptor sensitivity [38], cardiovascular sensitivity to neurotransmitters [13],and relative strength of the parasympathetic nervous system with respect to the sympatheticnervous system [13, 112] during fetal life.

Since FHRV is an important indicator of fetal distress, aim of this study is to add FHRVto the CTG simulation model to enhance the realism of the model-generated CTG tracings.

47

Chapter 4

In order to shed more light on the possible sources of FHRV, we investigate the e�ect ofthree sources of variability as described by Van Roon et al. [169, 170] and Wesseling et al.[178]: autoregulation of the peripheral blood vessels, in�uence of higher brain centers onthe processing of the baroreceptor output in the nucleus tractus solitarius of the medullaoblongata, and the in�uence of other a�erent systems like the heart, lungs and muscles,on the vagal center [169, 170, 178]. The enhanced model would be more suitable as aneducational tool, both as stand-alone screen-based training of CTG evaluation, and as anintelligent addition to manikins used in team-training, in order to have them automaticallyrespond to the interventions performed by the trainees.

The three sources of variability were implemented in a similar fashion as described by Wes-seling et al. [178] by applying a noise source on the peripheral resistance, baroreceptor outputand e�erent vagal signal. We focus on a normal full term fetus and simulate FHR tracingsbefore labor and during uterine contractions resulting in umbilical cord compression. Thesimulated FHR tracings are assessed by use of spectral analysis and on FHR bandwidth (BW),de�ned as the di�erence between the highest and lowest cardiac frequency in the FHR signal.Spectral analysis gives a quantitative representation of FHRV, and is often used in literature[166]. FHR BW is commonly assessed by visual inspection in the clinic.


4.2.1 Mathematical model

FHRV is added to our mathematical CTG simulation model, that describes feto-maternalhemodynamics, oxygen distribution and fetal regulation [81, 82] (chapter 2 and 3).

In �gure 4.1 a simpli�ed schematic overview of the CTG simulation model is shown. A moreelaborate description can be found in [81] (chapter 2). The maternal circulation contains aheart (left ventricle) from which blood �ows into the arteries. From here blood �ows into theintervillous space (IVS), which is modeled explicitly, and into the remainder of the tissues,which are lumped together. Blood �ows back into the heart via the veins. In the fetus theheart is modeled as a combined ventricle, the umbilical and cerebral circulation are modeledexplicitly, and the remainder is lumped into the tissues. Oxygenation in the mother takesplace in the veins, since the pulmonary circulation is not explicitly modeled. Oxygen is con-sumed in the maternal tissues and di�uses to the fetus in the IVS of the placenta. In thefetus, oxygen consumption takes place in the brain and tissues. During hypoxia, cerebralartery resistance Rcera is reduced via autoregulation in order to increase oxygen transportto the brain. Uterine contractions are modeled through an increase of uterine pressure put,acting on the IVS compartment and on all fetal compartments. Additionally, the externalpressure on the umbilical cord pum increases during cord compression. These pressure vari-

48


Figure 4.1: Schematic overview of the CTG simulation model. In the mother, blood �owsfrom the heart into the arteries, via the tissues and intervillous space (IVS), into the veins,and back to the heart. In the fetus, the umbilical cord and brain circulation are modeledexplicitly. Oxygen �ow is indicated with dashed arrows. The IVS compartment and all fe-tal compartments are exposed to the uterine pressure put. Furthermore, during umbilicalcord occlusion an additional external pressure pum acts on the umbilical cord, resulting inchanges in fetal oxygenation and blood pressure. Via autoregulation, cerebral resistanceRcera is decreased during hypoxia. Changes in mean arterial transmural blood pressure ptm,aand arterial oxygen pressure pO2,a, result in changes of normalized baro- and chemorecep-tor output, rb and rc, respectively. Via weighting factors, in the nervous system (NS), theseoutputs are combined into normalized e�erent vagal and sympathetic signals, ev and es,respectively, �nally resulting in variations of the four cardiovascular e�ectors (heart periodT , cardiac contractility Emax, venous unstressed volume Vven,0, and peripheral resistanceRtisa). These e�ector variations will again induce changes in the hemodynamic and oxygena-tion submodel. The three sources of variability are indicated by dashed circles. A detaileddescription is given in the main text.

ations result in changes of the resistances of the IVS vein and umbilical blood vessels, causingvariations in fetal mean arterial transmural blood pressure ptm,a and arterial oxygen pressurepO2,a. These changes are input for the fetal central regulation model. Via the baro- andchemoreceptor these variations are translated into a normalized baro- and chemoreceptoroutput, rb and rc, respectively. Baroreceptor output increases with increasing blood pres-

49

Chapter 4

sure, while chemoreceptor output increases with decreasing oxygen pressure. Via weightingfactors these baro- and chemoreceptor outputs are combined into normalized e�erent vagaland sympathetic signals, ev and es, respectively. Baro- and chemoreceptor activation bothhave a stimulating e�ect on the vagal nervous system. The sympathetic nervous systemis stimulated by the chemoreceptor, but inhibited via the baroreceptor (indicated with theminus sign). Stimulation of the vagal pathway leads to increase of heart period T , while stim-ulation of the sympathetic pathway will decrease T and venous unstressed volume Vven,0,but increase cardiac contractility Emax and peripheral artery resistance Rtisa. The changede�ectors are input for the cardiovascular and oxygen model.

For the purpose of the present study, we modi�ed the model [81, 82] (chapter 2 and 3) byremoving the baroreceptor low pass �lter. We will illustrate the need and the consequencesof this modi�cation in the results section.

4.2.2 Model extension with FHRV

Following Van Roon et al. [170] and Wesseling et al. [178], temporal variations are applied toeither the peripheral vascular arterial resistance Rtisa, to the baroreceptor output rb, or tothe e�erent vagal signal ev, see �gure 4.1. We test the model by using either 1/f noise orwhite noise as temporal variations. We used 1/f noise because it is considered physiologicallyrealistic [178]. White noise is used to better investigate the transfer function of the system.The noise signal N(t) [-] has a mean of 0 and a standard deviation of 1 and is describedaccording to Van Roon et al. [169]:

N(t) =

n∑

k=1A · sin(2πfkt + φk)√

12

n∑

k=1A2

,

{A = 1 white noiseA = 1√

fk1/f noise

(4.1)

with fk = k ·∆f and ∆f = fmaxn

Here, fmax [Hz] represents the maximum frequency taken into account and n the number ofharmonics, which in our model is set to 2 Hz and 2000 harmonics, respectively. The phaseshift φk is di�erent for each frequency fk, and has a uniformly distributed random valuebetween 0 and 2π .

50


The three sources of variability are obtained by superimposing noise on the correspondinge�ector or output signal, resulting in new values for the e�ector Rtisa,N or signal rb,N andev,N :

Rtisa,N(t) = Rtisa(t) + mRtisa ·N(t) ·Rtisa,0

rb,N(t) = rb(t) + mrb ·N(t)ev,N(t) = ev(t) + mev ·N(t)

(4.2)

where m [-] is a multiplication factor de�ning the standard deviation of the changes appliedto each of the sources of variability and Rtisa,0 [mmHg] is the reference peripheral resistance.For each combination of noise type and source, the value of m was chosen such to obtainan FHR BW (de�ned as 4 times standard deviation) of 15 ± 1 bpm in steady state, which is inthe normal range for a healthy full term fetus, while setting m of the other sources to 0.

4.2.3 Spectral analysis

Simulated FHR signals with a length of 30 min are sampled with a frequency of 4 Hz, allowingreliable spectral information for frequencies up to 2 Hz, according to the Nyquist criterion.The FHR tracings are converted into heart period tracings, representing the R-R intervalsin ms. Spectral analysis is performed by use of short-time Fourier transformation (STFT),as described by Peters et al. [121, 122]. Similar to Van Laar et al. [165, 167], the STFT isperformed using a moving window with a width of 64 s, providing a spectrum every 0.25s. For comparison with Van Laar et al. [165, 167], the total frequency band is chosen torange from 0.04 to 1.5 Hz, the low frequency band (LF) from 0.04 to 0.15 Hz, and the highfrequency band (HF) from 0.4 to 1.5 Hz. The absolute spectral power is calculated in each ofthese bands, whereafter normalized powers (LFn and HFn) are computed by dividing LF andHF power by total power.


We simulate FHR variability for a full term fetus of 3.5 kg. Parameter settings are identicalto the settings described in our previous study [81, 82] (chapter 2 and 3), except for thebaroreceptor low pass �lter, which was omitted in this study. The e�ect of the three di�erentsources of variability on FHR variability is investigated by performing simulations withoutnoise, with 1/f noise, and with white noise. For each type of noise (1/f or white) ten randomnoise signals are created and used to perform simulations of 30 minutes for each sourceof variability. Hereafter, values for HFn, LFn and BW are computed, and the power spectraldensity plots are generated. Values and plots shown, are the average of the ten simulations.

The e�ect of uterine contractions on FHR and FHRV is investigated by simulating a set ofthree contractions varying in uterine pressure amplitude (70 ± 20 mmHg) and contraction

51

Chapter 4

duration (60 ± 20 s), resulting in umbilical cord compression, see also our previous study[82] (chapter 3). For the latter simulations, two noise signals (1/f and white) are created andsuperimposed on each of the three sources of variability.

Finally, the e�ect of variation of the vagal and sympathetic gains on FHRV is investigated byrepeating the simulations with superimposed white noise, while increasing or decreasing thevagal and sympathetic gains by 50%.

Simulations are performed in MATLAB R2013a (The MathWorks, Inc., USA). Di�erential equa-tions are evaluated by explicit time integration with a time step of 0.01 s. Scenarios areinitiated from a steady-state situation at which variation of mean arterial transmural bloodpressure ptm,a [mmHg] and arterial oxygen pressure pO2,a [mmHg] is less than 1·10–4 mmHg/s,respectively.

4.3 Results

Results for the simulation without a source of variability are shown in �gure 4.2. FHR baselineis about 135 bpm and blood pressure baseline is about 45 mmHg. Three uterine contractionscausing umbilical cord occlusion are shown, with varying severity (60 s and 70 mmHg, 80 sand 90 mmHg, 40 s and 50 mmHg). Since the oxygen transport from the placenta to thefetus is blocked, fetal oxygen levels decrease. This decrease activates cerebral autoregulation,which leads to a decrease of cerebral resistance and an increase of cerebral blood �ow tocompensate for the reduced oxygen supply. The decrease in oxygen pressure also activatesthe sympathetic nerve system, increasing peripheral vascular resistance to minimize oxygenconsumption in non-essential systems, resulting in a rise of blood pressure. The changes inoxygen and blood pressure lead to a net FHR deceleration via the chemo- and baroreceptor.As a result, the FHR tracing shows three decelerations with varying depth. As described inour previous study [82] (chapter 3), the initial FHR increase (i.e. ‘shoulder’) is the result of thebaroreceptor-mediated response, evoked by an initial decrease in blood pressure. As shownin �gure 4.2, omission of the baroreceptor low pass �lter in the current study does not leadto large changes in the FHR signals with respect to simulations performed with the modelfrom our previous study, where the low pass �lter was switched on (light gray).

Figure 4.3 shows the results for simulations with noise. Adding noise does not change baselinelevels for FHR and blood pressure. For ease of comparison, FHR and blood pressure tracingsfor simulations with di�erent sources of variability are shifted vertically with respect to eachother. With 1/f noise, the required BW of about 15 ± 1 bpm was obtained by setting the noisemodulation factor m in eq. 4.2 to 17.5%, 8.2% and 2% for variation of peripheral resistance,baroreceptor output and e�erent vagal signal, respectively, while maintaining the others atzero. All tracings show similar FHR variability, however blood pressure variability is most

52


020406080

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]

Figure 4.2: Overview of simulation results without a source of variability. From top to bot-tom: uterine pressure put ; fetal arterial oxygen pressure pO2,a; fetal mean arterial transmuralblood pressure ptm,a; and fetal heart rate FHR. The response in each of these signals dependson contraction duration and amplitude. Simulations with low pass �lter are shown in lightgray.

pronounced if noise is added to the peripheral vascular resistance. With white noise, m wasset to 28.5%, 17.5% and 4.8% for variation of peripheral vascular resistance, baroreceptoroutput and e�erent vagal signal, respectively. Compared to the case with 1/f noise, more highfrequencies are present. However, when noise is superimposed on the peripheral resistance,large unphysiological variations in blood pressure and blood �ow (not shown) are observed.In all simulations FHRV is reduced during decelerations, whether 1/f or white noise is used.

Figure 4.4 shows the average power spectra of the heart period signals, obtained duringten 30-minute simulations without uterine contractions. For simulations with 1/f noise, allspectra show a monotonically decreasing trend. If white noise is applied, the 1/f characterin the spectra is observed as well, however now the power spectra show several peaks. Ifwhite noise was added to the peripheral resistance, a peak was observed around 0.08 Hz andaround 0.5 Hz. These peaks were also seen if white noise was applied to the baroreceptoroutput. A broader frequency spectrum is obtained if white noise is added to the e�erent

53

Chapter 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13

20 bpm

30 mmHg

Rtisa

rb

ev

Rtisa

rb

ev

time [min]

ptm

,a[m

mH

g]

FH

R[b

pm

]

A: 1/f noise

ptm,a

B: white noise

Figure 4.3: Typical examples of FHR and blood pressure signals if A) 1/f noise or B) whitenoise is added to peripheral resistance Rtisa (upper signals), baroreceptor output rb (middlesignals), or the e�erent vagal signal ev (lower signals). To facilitate comparison betweenthe di�erent simulations, all signals are shifted on the y-axis (with 50 bpm and 20 mmHg,respectively). Hence for all simulations FHR baseline is around 135 bpm and ptm,a baseline isaround 45 mmHg. The bandwidth of FHR variation was aimed at 15 ± 1 bpm.

54


0 0.5 1 1.50

1000

2000

3000

4000

5000

6000

7000

8000

Rtisa

f [Hz]

PS

D [m

s2 /Hz]

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6000

7000

8000

f [Hz]

ev

0 0.5 1 1.50

1000

2000

3000

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5000

6000

7000

8000

f [Hz]

rb

Figure 4.4: Power spectral density (PSD) of simulated heart period signals with baroreceptorlow pass �lter switched o� (black) or on (gray) are shown. Dashed lines represent spectrawith 1/f noise as input and solid lines represent spectra with white noise as input. Noise issuperimposed on peripheral resistance Rtisa (left); baroreceptor output rb (middle); e�erentvagal signal ev (right). Each of the power spectra represents the average of ten simulationsof 30 minutes.

vagal signal. However, this spectrum only shows one peak near 0.14 Hz. To illustrate the e�ectof the baroreceptor low pass �lter, the average power spectra of ten 30-minute stimulationswith low pass �lter are shown in gray. The same noise signals were used as for the simulationswithout low pass �lter, and again m was chosen such to obtain an FHR BW of 15 ± 1 bpm(except for the simulation where white noise was superimposed on the peripheral resistance,since then the model would become unstable). In general, addition of the low pass �lterresults in narrower power spectra, irrespective of noise type (1/f or white). In the modelwith baroreceptor low pass �lter, the LF peak is shifted to the left. Furthermore, when whitenoise is superimposed on the peripheral vascular resistance or baroreceptor output, a lesspronounced peak around 0.5 Hz is observed in simulations with low pass �lter, which meansthat less high frequencies are present in the FHR tracings.

55

Chapter 4

0 0.5 1 1.50

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D [m

s2/H

z]

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Figure 4.5: Results of sensitivity analysis on the sympathetic and vagal gains. White noise issuperimposed on peripheral resistance Rtisa (left); baroreceptor output rb (middle); e�erentvagal signal ev (right). Power spectral densities (PSD) of simulations with the standard modelare indicated in gray. The upper row shows results of simulations where all sympatheticgains were increased (dashed black line) or decreased (solid black line) by 50%. The lowerrow shows results of simulations where the vagal gain was increased (dashed black line)or decreased (solid black line) by 50%. Each of the PSDs represents the average of tensimulations of 30 min.

In �gure 4.5 the results of the sensitivity analysis to the sympathetic and vagal gains areshown. For these simulations white noise is used. If all sympathetic gains on heart period,cardiac contractility, venous unstressed volume, and peripheral vascular resistance are in-creased by 50% (dashed black lines), a clear increase of the 0.1 Hz peak and a small increaseof the 0.5 Hz peak is observed with respect to powers obtained during standard simulations(gray lines). The power around 0.3 Hz decreases. Opposite e�ects are observed if the sym-pathetic gains are decreased by 50% (solid black lines). Variations in sympathetic gains hardlya�ect the power spectrum if the noise is applied to the e�erent vagal signal. If the vagalgain is increased by 50%, all spectra show an increase of the power in the entire spectrum,without a�ecting the shape of the power spectrum. A decrease of the vagal gain by 50%has the opposite e�ect.

56


Rtisa (17.5%) rb (8.2%) ev (2%) v. Laar1

model simulations

with 1/f noise

model simulations

with white noise

experimental

data: quiet

sleep

Rtisa (28.5%) rb (17.5%) ev (4.8%)

0

1

no

rma

lize

d p

ow

er

LFn

HFn

experimental

data: active

sleep

v. Laar2 v. Laar1 v. Laar2

Figure 4.6: Overview of normalized LF (0.04-0.15 Hz) and HF (0.4-1.5 Hz) powers. LFn and HFnare calculated from ten 30-minute simulations with 1/f noise or white noise superimposedon each of the sources of variability (peripheral resistance Rtisa, baroreceptor output rb ore�erent vagal signal ev). The percentages in the horizontal axis indicate the percentage ofmodulation m as de�ned in eq. 4.2, chosen such to obtain an FHR bandwidth of 15 ± 1 bpm.On the right side LFn and HFn values represent data obtained during quiet and active sleepas given in literature: Van Laar et al.1 [165] and Van Laar et al.2 [167]. In the latter studystandard deviations were not given.

Figure 4.6 shows normalized low frequency (LFn) and high frequency (HFn) values obtainedfrom model simulations and from literature. If 1/f noise is applied to the peripheral resistance,LFn is about 0.82, while HFn is 0.03. If this noise is applied to the baroreceptor output, LFnis similar (0.82), however HFn is slightly increased (0.05). If 1/f noise is added to the e�erentvagal signal, LFn decreases to a level of 0.66, while HFn remains similar to the case wherenoise is added to the baroreceptor output (0.05). The common e�ect of replacing 1/f noiseby white noise, is the reduction of LFn and the increase of HFn. If white noise is applied tothe peripheral resistance, LFn decreases to 0.58 and HFn increases to 0.15. If white noise isapplied to the baroreceptor output, these changes are more pronounced, with LFn=0.52 andHFn=0.25. If this noise is applied to the e�erent vagal signal, LFn reduces even more to alevel of 0.34, and HFn reaches a level of 0.23. As a reference, �gure 4.6 also shows values ofLFn and HFn obtained in fetuses with a gestational age of 36-37 weeks [165] and 34-41 weeks[167]. During quiet sleep, LFn values of 0.69 and 0.59, and HFn values of 0.14 and 0.26 werefound, respectively. During active sleep LFn increased to 0.8 and 0.77, while HFn decreasedto 0.07 and 0.1, respectively.

57

Chapter 4

4.4 Discussion

We extended a computer model for simulation of the CTG [81, 82] (chapter 2 and 3), withFHRV, an important clinical indicator of fetal distress. FHRV was added to the model byimplementing three possible sources of variability, characterized by 1/f or white noise. Thein�uence of each of these sources of variability on FHR and blood pressure was investigatedby use of visual inspection and spectral analysis.

Methods. In literature, several models for simulation of HRV in adults can be found. Inthe model of Van de Vooren et al. [157] �uctuations were introduced directly to the low-pass �ltered baroreceptor output. De Boer et al. [41] introduced �uctuations via randomdisturbances on heart period and pulse pressure. In a study of Ursino et al. [155] a moreelaborate circulation model was used that allowed introduction of low frequency variationson the peripheral resistance via an LF noise source (up to 0.12 Hz). High frequency variations(0.2 Hz) were introduced via a respiration model. In this study we followed Ursino in addinga source of variability to the peripheral vascular resistance. In addition we also appliedvariations on the baroreceptor output and the e�erent vagal signal, according to Van Roonet al. [170] and Wesseling et al. [178]. We did not introduce high frequency variations, relatedto respiration.

It is unclear what type of noise should be used in each of these sources. Ursino used a noisesignal with a linear power spectrum decrease between 0 and 0.12 Hz [155], De Boer usedGaussian distributed noise [41]. Following Wesseling [178] and Van Roon [170], in our study 1/fnoise was used. As argued by Wesseling, this seems plausible for the peripheral resistance,since this resistance replaces the many parallel resistances representing the microcirculatorycapillaries of all organs. In reality the resistance of each individual capillary will be in�uencedby autoregulation in order to satisfy local oxygen demands. Due to the large number of cap-illaries contributing to the microcirculation, most of the rapid resistance variations (i.e. highfrequencies) are averaged out, leaving the low frequency �uctuations [178]. The motivationfor the 1/f character describing �uctuations originating from higher brain centers or othera�erent systems is less clear.

Ideally, for small variations around the homeostatic state, the behavior of the system couldbe characterized by a transfer function. However, in clinical practice it is not possible tode�ne a transfer function, since the input variability is unknown. In the model we used whitenoise as input, for which the spectral output approximates the transfer function. Figure 4.4shows that even when white noise is used, power spectra of FHR tracings have a 1/f character.This implies that the use of 1/f noise as input for the model is not required to obtain 1/f powerdensity spectra.

58


In our previous model [81, 82] (chapter 2 and 3), we included a low pass �lter in the barore-ceptor, following Van der Hout-van der Jagt et al. [161]. With this �lter, FHR tracings andpower spectra show an unphysiological lack of HF components (�gure 4.4). Removal of the�lter yields power spectra that more closely resemble experimental data. Indeed, includinga low pass �lter in the baroreceptor seems unrealistic, as it is known that the baroreceptordoes not only respond to changes in mean arterial pressure, but also to the rate of pressurechange [88]. To include this rate sensitivity, Wesseling introduced a high emphasis �lter inthe baroreceptor [178]. In the model by Ursino, this e�ect was neglected [155]. We did notinclude this e�ect either. Finally, it is known that the set-point of the baroreceptor is not�xed and may shift during chronic hypertension or hypotension [88]. Since the time scale ofinterest in this study is about 30 minutes, we did not take this e�ect into account. As shownin �gure 4.2, omission of the baroreceptor low pass �lter only results in minor changes withrespect to the results of our previously described model [81, 82] (chapter 2 and 3).

Results. In general, visual inspection shows that addition of white noise to each of thethree sources of variability increases the high frequency FHR variations compared to additionof 1/f noise (�gure 4.3). However, no clear di�erences are seen between the use of thethree di�erent sources of variability. In literature it is shown that in a healthy fetus FHRVspectral power increases during contractions, indicating fetal reactivity to external pressurechanges [25, 129, 175]. However, visual inspection of the simulated FHR tracings shows that thebandwidth of FHRV is reduced during contractions. For the case where temporal variationsare added to the peripheral resistance, this can be explained by the fact that blood pressureincreases during cord occlusions. This results in a reduced sensitivity of the baroreceptor,since its working point shifts to a less steep part on the baroreceptor curve. If variations areadded to the baroreceptor output or e�erent vagal signal, this mechanism is less important.The decreased FHRV during decelerations can then at least partly be explained by the inverserelation between heart period and FHR, as similar absolute variations in heart period willresult in smaller absolute variations in FHR, if FHR decreases. The discrepancy betweenmodel results and literature �ndings may indicate that other mechanisms also play a role.

Since details in the FHR tracings are di�cult to interpret by visual inspection (�gure 4.3),spectral analysis is used to examine di�erences in simulation results. Power spectra obtainedafter applying 1/f noise to either the peripheral vascular resistance, baroreceptor output, orvagal e�erent signal, do show a 1/f character without any peaks (�gure 4.4). If white noiseis added to each of the sources of variability, a peak around 0.1 Hz is observed in each ofthe three power spectra. In adults, a peak around 0.1 Hz is observed as well, known asMayer waves. The mechanism causing the oscillations is still not exactly known [83, 101]. Inthe human fetus this peak around 0.1 Hz is also observed [54, 89]. Furthermore, our modelresults show another peak around 0.5 Hz when white noise is applied to the peripheralvascular resistance or baroreceptor output. Ferrazzi et al. [54] observed a HF peak around

59

Chapter 4

0.7-0.9 Hz. However, these peaks occurred during periods of fetal breathing and disappearedduring apnea [54]. Since we did not model fetal breathing movements, in future studies itwill be interesting to investigate the in�uence of these movements on model outcome.

Wesseling et al. [178] also applied noise to each source of variability, one at a time. Althoughthey used 1/f noise, the 1/f character in the power density spectra of the heart rate was onlyobserved if the noise was superimposed on the e�erent vagal signal. Their spectra showed a0.1 Hz peak, which in our model was only observed if white noise was used. Di�erences in themodel results might be explained by the fact that Wesseling simulated baroreceptor feedbackin an adult, while our model describes the fetal regulation. Furthermore, the Wesseling modeldoes not include the sympathetic feedback on the heart, nor the chemore�ex. Finally, incontrast to our model, Wesseling does model the dynamic baroreceptor response.

Spectral analysis provides information about the power of di�erent frequency componentspresent in the FHR tracings. In order to gain insight into the in�uence of the sympathetic andparasympathetic nervous system on FHRV in our model, a sensitivity analysis was performedfor the case where white noise was added to each of the sources of variability (�gure 4.5).When the sympathetic gains are increased or decreased by 50%, the power spectra show anincrease or decrease of the peak around 0.1 Hz, respectively. This is similar to the �ndingsof Ursino et al. [155]. Variations of the vagal gain in�uences both the lower and the higherfrequencies, independent of the source of �uctuation. In this case the power of the 0.1 Hzpeak in our model changed in the opposite direction as shown by Ursino. The power spectraas described by Ursino also show a peak around 0.2 Hz, which is related to an imposed cyclicvariation of the intrathoracic and abdominal pressure to model respiration. Our results showa peak around 0.5 Hz, which is not found by Ursino.

Our �ndings indicate that sympathetic feedback mainly a�ects the lower frequencies and thatvagal feedback a�ects both low and higher frequencies. This is in accordance with observa-tions from vagal and sympathetic blocking studies in adult dogs, in which high frequencieswere found to be mediated by the parasympathetic nervous system and low frequenciesby both sympathetic and parasympathetic nervous system [5, 6]. In the dog the parasym-pathetic nervous system seems to play a dominant role in the low frequency range [5]. Inaddition, in vagal blocking studies in adult mice, absolute LF and HF power were reduced by93% and 77%, respectively [93]. However, review studies show that in the adult no consen-sus has been reached about the relative contribution of the two branches of the autonomicnervous system to the di�erent frequency bands [46, 149].

For the fetus, this discussion is further complicated by the di�erent rate of maturation of thesympathetic and parasympathetic nervous system. In studies in fetal sheep it was observedthat the sympathetic control of cardiovascular functions becomes active earlier in fetal lifethan the parasympathetic control [13, 112]. In blocking studies in the fetal sheep, the low

60


frequency power is found to be largely associated with sympathetic activity, although theparasympathetic nervous system does also play a role [86]. Similar to the e�ects found inadult mice [93], vagal blocking studies in the preterm infant showed reduction of the absoluteLF and HF powers by 94% and 67%, respectively [10]. Clinical studies showed an increase ofLF and HF power with gestational age [37, 165, 167]. In the preterm fetus, this increase wassuggested to re�ect autonomic development, while in the term fetus, interpretation was moredi�cult due to the increasing e�ect of variations in behavioral state [167]. Our model mightbe used to further investigate the relation between spectral properties and sympathovagalbalance, and behavioral states.

To further compare our model results to experimental data, in �gure 4.6 we show normalizedpowers of the LF and HF frequency bands. The choices for the ranges of the frequency bandsis not universal [166]. According to our power spectra, shown in �gure 4.4, the low frequencyband would be chosen to range from about 0 to 0.3 Hz if white noise is used. However, to beable to compare our results with the clinical results of Van Laar et al. [165, 167], we followedtheir de�nition. Van Laar calculated normalized LF and HF powers, which emphasizes thebalance between the sympathetic and parasympathetic nervous system by minimizing thee�ect of changes in total power on both frequency bands [149]. In our model, addition of1/f noise yields lower HFn values than found by Van Laar et al. [165, 167], irrespective of thesource of variability (see also �gure 4.6). When white noise is superimposed on the peripheralvascular resistance or baroreceptor output, LFn and HFn values more closely resemble theclinical data of Van Laar found during quiet sleep. In case white noise is added to the e�erentvagal signal, LFn values become much lower than found in literature, while HFn values stillcorrespond to clinical values obtained during quiet sleep.

In the study of van Roon et al. [170] a combination of the three sources of variability wassuggested to approximate clinical data. According to our �ndings it is hard to give an estima-tion of the contributions of each of the three sources in the fetus. Addition of noise to theperipheral resistance or baroreceptor output, shows similar power spectra (�gure 4.4), whichmakes it di�cult to distinguish between the contribution of these two sources of variabilityto FHRV. Furthermore, it is unknown what type of noise will most closely resemble �uctua-tions in each source of variability. In this study we used 1/f and white noise, but physiologicalvariations might show di�erent noise patterns. Unfortunately, these input signals cannot bemeasured in the human fetus. Furthermore, the contribution of the di�erent sources and thetype of noise probably also depends on the physiological condition of a fetus. For example,variations on the peripheral resistance may be di�erent during movements than during rest.

Conclusion. FHRV was included in the model by introducing variations to either peripheralvascular resistance, baroreceptor output or e�erent vagal signal. The model is inconclusiveabout the type of noise to be used as input, since both simulations with 1/f noise and with

61

Chapter 4

white noise, yielded FHR power spectra with a physiological 1/f character. This shows thatthe �ltering characteristics of the model seem physiological. Since the characteristic peakobserved clinically at 0.1 Hz was only obtained when white noise was superimposed on eachof the di�erent sources of variability, it can be hypothesized that white noise is more likely toresemble physiological input. Choosing between peripheral resistance or baroreceptor outputas source of variability was found to be di�cult, since similar power spectra were found forthese sources. In line with clinical observations, sympathetic control was found to determinepredominantly LF power, whereas vagal control a�ected both LF and HF power. Since themodel did not show the clinically observed increase of FHRV during FHR decelerations inducedby uterine contractions, it is worthwhile to investigate whether other mechanisms are involvedin the origin of FHRV. Still, the capability of the model to generate realistic FHR signals wasimproved, which increases applicability of the model for research and educational purposes.

62

Chapter 5

Hypoxia-induced catecholamine feedback on fetalheart rate:

A mathematical model study

The contents of this chapter are under review for Medical Engineering & PhysicsJongen GJLM, van der Hout-van der Jagt MB, Oei SG, van de Vosse FN, and Bovendeerd PHM

Chapter 5

Abstract

During labor and delivery, the cardiotocogram (CTG), the combined continuous registrationof fetal heart rate (FHR) and uterine contractions, is used to monitor fetal well-being. Togain insight into FHR responses to mild uterine contractions, leading to short-term hypoxia,previously a mathematical CTG simulation model was developed where FHR response wasdescribed by neural feedback through the chemore�ex and barore�ex. The model was notdesigned to describe FHR responses to more severe contraction scenarios, leading to pro-longed hypoxic episodes. These secondary FHR responses are thought to involve di�erentmechanisms including humoral feedback, vagal inhibition and myocard hypoxia.

In this study, we extended the model to describe secondary FHR responses via a simplecatecholamine feedback submodel. Simulation results of repeated severe uterine blood �owreductions showed an initial decrease of inter-occlusion FHR, followed by a gradual increase.This trend was also observed in sheep experiments. Simulations of repeated severe umbilical�ow reductions resulted in FHR overshoots, which were less sharp as compared to experi-mental data. Model results might be improved by including feedback through vagal inhibitionand myocard hypoxia.

64

Catecholamine feedback

5.1 Introduction

Ideally, during labor and delivery fetal well-being is monitored via fetal oxygen status. Since incurrent clinical practice reliable continuous intrapartum oxygen measurements are not avail-able, fetal status is mainly estimated from the cardiotocogram (CTG). This is the combined,continuous registration of uterine contractions and fetal heart rate (FHR). Interpretation ofthe CTG is not straightforward, since FHR is not only a�ected by the fetal oxygen level, butalso by e.g. blood pressure variations. To obtain insight into the di�erent pathways thatlead to FHR variations during uterine contractions, in previous studies a mathematical modelwas developed to simulate the CTG [78, 81, 82] (chapter 2, 3 and 4). It was shown that FHRdecelerations during short-term hypoxia, resulting from single uterine contractions inducinguterine blood �ow reduction alone, or combined uterine and umbilical blood �ow reduction,can be modeled as function of the chemo- and barore�ex [81, 82] (chapter 2 and 3). How-ever, secondary FHR e�ects, including FHR baseline increase and FHR overshoots, occurringin response to prolonged episodes of hypoxia, could not be mimicked with the existing CTGsimulation model.

Clinically, an increase in FHR baseline has been hypothesized to be related to progressionof hypoxic insults [115, 152]. Furthermore, FHR overshoots following variable decelerationsdevelop during prolonged umbilical cord compression [138, 177]. In sheep experiments, itwas observed that a series of repeated severe uterine blood �ow reductions resulted inan initial decrease of inter-occlusion FHR, followed by a gradual increase [71, 130]. Besides,FHR overshoot patterns and inter-occlusion FHR increase were observed in sheep duringrepeated severe umbilical �ow reductions [39, 58, 94, 136, 179, 180]. FHR decelerations areinitiated by the baro- and chemoreceptor acting on the vagal and sympathetic nerve system.When the occlusion is continued, the vagal contribution to the deceleration is gradually takenover by myocard depression [136, 179, 180]. The rise of FHR baseline and the appearanceof FHR overshoots is presumably caused by beta-adrenergic stimulation that is no longercounteracted by the vagal nerve system at the end of the occlusion [115, 136, 179, 180]. Ithas been suggested that sympathetic activity is suppressed during the inter-occlusion periodand that catecholamines play an important role in the beta-adrenergic stimulation at the endof occlusions [94].

Aim of this study is to gain insight into the development of secondary FHR e�ects duringrepeated severe hypoxic events in the human fetus. Therefore, we extend our previous modelwith a description of the e�ect of catecholamines on FHR. We will focus on the responsesto 30 minutes of severe contractions and neglect potential e�ects of myocard hypoxia andvagal tone depression for the sake of simplicity. We demonstrate the capability of the modelto simulate scenarios of repeated abrupt, complete uterine or umbilical blood �ow reductionas performed by Jensen et al. [71], and by the group of Galinsky and Westgate [58, 179]. Finally,

65

Chapter 5

the e�ect of catecholamine feedback during scenarios with physiologic uterine contractions,which result in more gradual and less severe blood �ow reductions, is investigated. Theextended model is expected to be of increased value for educational purposes, such asscreen-based training of CTG evaluation and simulation-based (team-)training with manikins.


5.2.1 Physiological background

Catecholamines a�ect the cardiovascular system in a similar fashion as the sympathetic ner-vous system and thus increase heart rate and blood pressure [88, 109, 115]. In fetal sheep andrhesus monkeys, infusion of catecholamines was found to result in an increase of blood pres-sure [4, 28, 75]. FHR was initially decreased, presumably caused by the barore�ex, whereafterFHR increased above resting levels [4, 28, 75, 76]. A positive correlation between FHR baselineand umbilical artery catecholamine concentration was found in human fetuses after delivery[119]. However, in other studies, increase in catecholamine level was related to both brady-cardia and tachycardia [16, 91]. Presumably, bradycardia is an initial e�ect induced by thevagal re�ex, whereas tachycardia occurs as soon as the catecholamine concentration is highenough to overcome this FHR decelerating e�ect [16, 91]. Furthermore, signi�cant increasesof catecholamines were observed in human fetuses that showed late or moderate/severevariable FHR decelerations during labor [16, 91].

In this study, we focus on the catecholamines adrenaline and noradrenaline. Catecholamineconcentration depends on the balance between catecholamine production and elimination.In adults, catecholamines are removed from the circulation via neuronal and extra-neuronaluptake, where the latter pathway predominates [47]. In the fetus, elimination also takes placein the placenta [23, 47, 119]. Adrenal catecholamine secretion in the sheep fetus is primarilyevoked by reduction of arterial oxygen pressure, rather than by changes in arterial pCO2, pH,or lactic acid [31]. The response of the adrenal medulla to asphyxia is established via twopathways: directly, by the drop of oxygen levels, and indirectly, through nerve stimulation[31, 32]. In the fetal sheep, nervous stimulation of the adrenal medulla is already presentbefore birth, and the direct response wanes at the end of pregnancy [31, 32]. However, in otherspecies like the fetal cow [33], pony [34], and rat [141], innervation of the adrenal glands is stillimmature at birth and the direct hypoxic response on the adrenal medulla still dominates. Inthe human fetus, the exact mechanism of adrenal catecholamine secretion remains unknown.In sheep, the ratio of adrenaline and noradrenaline release depends on maturation and therelative contribution of adrenaline increases towards the end of pregnancy [32]. The relationbetween adrenal catecholamine secretion and arterial oxygen pressure has been investigatedin fetal lambs [30, 31]. However, to the best of our knowledge, no data is available on the

66


relation between hypoxia and spillover from nerve endings.

5.2.2 Mathematical model

Our CTG simulation model [78, 81, 82] (chapter 2, 3 and 4) describes a full term 3.5 kg humanfetus and includes feto-maternal hemodynamics, oxygenation, and fetal regulation, see �gure5.1. In the maternal cardiovascular model the uterine circulation is modeled explicitly, whilethe remainder of the peripheral circulation is lumped into the tissues. In the fetal model,the cerebral and umbilical circulation are modeled explicitly. The fetal regulation submodeldescribes the e�ect of changes in arterial oxygen pressure and blood pressure on the car-diovascular system. Via the chemo- and baroreceptor and e�erent vagal and sympatheticpathways, four cardiovascular e�ectors are a�ected: heart period T , cardiac contractilityEmax, venous unstressed volume Vven,0, and peripheral artery resistance Rtisa. Like in ourprevious study, the baroreceptor low pass �lter was omitted from the model [78] (chapter 4).We use this model as a basis to investigate the e�ect of catecholamine feedback on FHR.

5.2.2.1 Catecholamine submodel

In this study, fetal catecholamine feedback (focusing on adrenaline and noradrenaline) isadded to the model. For the sake of simplicity, we chose not to di�erentiate between theadrenaline and noradrenaline response, thus the catecholamine concentrations representcombined concentrations. The catecholamine submodel consists of the catecholamine dis-tribution model, describing catecholamine appearance, elimination and convection; and afeedback model, describing the e�ect of increased catecholamine levels in the blood on thefetal heart (�gure 5.1).

Catecholamine distributionThe structure of the catecholamine distribution model is similar to that of the oxygen dis-tribution model previously described [81]. Catecholamine appearance, representing adrenalcatecholamine secretion and catecholamine spillover from nerve endings, takes place in thefetal tissues. From the tissues, catecholamines are convectively transported to the systemicveins, from which they �ow into the heart and to the remainder of the body. Catecholamineelimination takes place in the placental villi as well as in the tissues.

The rate of change of catecholamine content in a compartment (catecholamine concentrationcCat [ng/ml] multiplied by the blood volume of the compartment V ) is determined by con-vective transport QC , catecholamine plasma appearance QA, and catecholamine extractionQE:

d(cCat ·V)dt

= QC + QA – QE (5.1)

67

Chapter 5

Figure 5.1: Schematic overview of the CTG simulation model. The maternal circulation con-sists of a heart, systemic veins, and arteries. The intervillous space (IVS) is modeled explicitly,while the remainder of the periphery is lumped into the tissues. In the fetus, the umbilicaland cerebral circulation are modeled explicitly. Oxygen �ows are indicated with thin dashedlines. Oxygen enters the maternal system via the veins and is consumed in the maternaltissues. In the placenta, oxygen di�uses from the IVS into the umbilical circulation. In thefetus oxygen metabolism takes place in the tissues and brain. Contractions are simulatedvia an increase in uterine pressure put , acting on the IVS and on the fetus, a�ecting uterineblood �ow. Cord compression increases the external pressure on the umbilical cord pum, af-fecting umbilical blood �ow. Both scenarios change fetal arterial oxygen pressure pO2,a andtransmural blood pressure ptm,a. A decreased oxygen pressure activates the chemoreceptor,which via the output signal rc stimulates the vagal and sympathetic centers. An increasedblood pressure activates the baroreceptor, which via the output signal rb increases the vagal,but inhibits the sympathetic center. Via the e�erent vagal output signal ev, stimulation ofthe vagal center increases heart period T . Increased sympathetic output es in�uences allfour cardiovascular e�ectors: T is decreased; cardiac contractility Emax is increased; venousunstressed volume Vven,0 is decreased; peripheral vascular resistance Rtisa is increased. Hu-moral feedback is indicated with thick dashed lines. This model extension consist of twoparts: catecholamine distribution and catecholamine feedback. Catecholamine appearanceQA takes place in the fetal tissues and elimination tales place in the tissues QEx,tis and pla-centa QEx,plac. An increased arterial catecholamine concentration cCata decreases T . Thechanged e�ectors all in�uence the fetal cardiovascular system. Adapted from [78].

68


Convective transport of catecholamines through the fetal cardiovascular system is describedby:

QC = ∑i

qiincCatiin –∑

jqj

outcCat (5.2)

The �rst term represents the sum of catecholamine in�ows in the current compartment.Here i runs across all segments with an in�ow qi

in in the current compartment, with cCatiinthe catecholamine concentration of the in�ow compartments. The second term representsthe sum of catecholamine out�ows. Now j runs across all segments with an out�ow fromthe current compartment, with cCat the catecholamine concentration of the current com-partment.

Catecholamine appearance QA is modeled as a delayed response to the arterial oxygen pres-sure pO2,a. The delay represents the limited ability of adrenal catecholamine secretion toinstantaneously respond to changes in pO2,a and the time required for the catecholaminesderived from nerve endings to reach the blood stream, and is modeled via a low pass �lterwith time constant τQA :

dQAdt

=1

τQA

(Q∗A – QA

)(5.3)

Here Q∗A is related to arterial oxygen pressure pO2,a via a sigmoid relation:

Q∗A =Amin + Amax · e

pO2,a–pO2,a,nκpO2

1 + epO2,a–pO2,a,n

κpO2

(5.4)

where Amin and Amax represent the minimum and maximum appearance rate, respectively,pO2,a,n represents the working point of the sigmoid relation, and κpO2 determines the slopein the working point.

Catecholamine extraction takes place in the fetal placenta and tissues and is assumed to beproportional to the catecholamine concentration of the compartment:

QE = E · cCat (5.5)

Here E is a constant.

Catecholamine feedbackCatecholamines are assumed to only in�uence the fetal heart rate through the model e�ectorheart period T , see �gure 5.1. The actual e�ector response is a combination of the vagallyand sympathetically induced heart period variations, zTv and zTs , respectively [81] (chapter2), and the catecholamine induced e�ector variation zTCat :

T = Tref · (1 + zTv – zTs – zTCat ) (5.6)

69

Chapter 5

The minus signs indicate the inhibitory e�ect of the sympathetic and catecholamine feedbackon T . The e�ect of catecholamines on heart period is modeled proportionally to the arterialcatecholamine concentration cCata:

zTCat = kCat,T · cCata (5.7)

where kCat,T is a constant.

5.2.3 Parameter estimation

Where possible, human data was used for parameter estimation, complemented with sheepdata if human data was not available. Parameters were scaled to a full term 3.5 kg fetus.

In sheep experiments, steady-state catecholamine plasma appearance rate was found be-tween 85 and 160 ng/min/kg for noradrenaline [23, 113, 142, 143], and between 5 and 26ng/min/kg for adrenaline [113, 142, 143, 145]. In our model, catecholamine appearance rep-resents the combination of catecholamine spillover from nerve endings and catecholaminesecretion by the adrenal medulla. We chose a steady-state catecholamine appearance rateAmin of 500 ng/min for a 3.5 kg fetus, representing the sum of noradrenaline and adrenalineappearance rate, which is equivalent to 143 ng/min/kg. Tuning of catecholamine appearanceparameters Amax, pO2,a,n, and κpO2 was based on a study of Jensen et al. [72] where arelation was given between the uterine artery occlusion time (repeated every 3 min) and cat-echolamine concentration after 33 min of occlusions, and on a study of Galinksy et al. [58]in which catecholamine concentrations were measured at several time points during 2 minumbilical cord occlusions, repeated every 5 min. The time constant τQA was set to a valueof 5 min such that both a gradual inter-occlusion FHR increase, observed during repeateduterine artery occlusions [71], and FHR overshoots, observed during repeated umbilical cordocclusions [58, 179], could be simulated.

According to Paulick et al. [119], who found a constant placental extraction ratio for a largerange of umbilical catecholamine concentrations, we set the placental as well as the tissueextraction ratios to a constant value. For the placental extraction, we assumed that themeasured concentrations are described by the steady-state solution of eq. 5.1:

qum · (cCata – cCatvilli) = Eplac · cCatvilli, with cCatvilli = (1 – α) · cCata (5.8)

Here qum represents the umbilical blood �ow, cCata and cCatvilli the arterial and villouscatecholamine concentration, respectively, Eplac the placental extraction constant as de�nedin eq. 5.5, and α the placental fractional catecholamine extraction. Substitution results inthe following relation:

Eplac =(

α

1 – α

)·qum (5.9)

70


From human studies in which venous and arterial catecholamine measurements were per-formed in the umbilical cord after birth [48, 91, 119], an extraction ratio of 0.5 to 0.75 could becalculated. With α equal to 0.65 in our study and qum being about 400 ml/min, this resultsin a value of about 750 ml/min for Eplac.

The steady-state noradrenaline and adrenaline concentrations in the systemic arteries rangefrom 0.53 to 1.0 ng/ml [23, 113, 142, 143] and from 0.04 to 0.19 ng/ml [113, 142, 143, 145],respectively. We chose a combined catecholamine concentration of 1 ng/ml. The tissueextraction constant Etis was set to a value of 180 ml/min in order to obtain the desiredarterial catecholamine concentration of 1 ng/ml and a total extraction rate of 500 ng/min insteady state.

The value for kCat,T was set to 1.7 ·10–2 (ml blood/ng Cat) to obtain a maximum FHR of 255bpm during repeated 2:5 min umbilical cord occlusions [58, 179]. In these sheep experimentsa maximum FHR of about 300 bpm was observed [58, 179]. A value of 255 bpm was chosenfor the human fetus, according to the scaling factor between the steady-state FHR level,which is about 160 bpm in the fetal sheep [133] and 135 bpm in our human model. Parametervalues can be found in table 5.1.

Table 5.1: Catecholamine distribution and feedback parameters.

Parameter Value Unit Parameter Value UnitAmin 500 ng/min τz 5 minAmax 6.5·104 ng/min Eplac 750 ml blood/minpO2,a,n 10 mmHg Etis 180 ml blood/minκpO2 -1 mmHg kCat,T 1.7·10–2 (ml blood/ng Cat)


The model was implemented in MATLAB R2013a (The MathWorks, Inc., USA). Di�erentialequations were evaluated by forward Euler time integration with a time step of 0.02 s. Sce-narios described below, were initiated from a steady-state situation at which variation ofptm,a and pO2,a was less than 1 ·10–4 mmHg/s, respectively.

5.2.4.1 Sheep experiments

Sheep experiments in which uterine blood �ow was repeatedly decreased by use of a ballooncatheter in the maternal descending aorta [71, 72], were simulated by linearly increasinguterine artery resistance by a factor 100 in 5 s, keeping it at its maximum level for a certaintime period, and linearly decreasing the resistance to steady-state levels at the end of theocclusion (see also [81], chapter 2). Uterine artery occlusions were performed with a durationof 60 s or 90 s, and repeated every 180 s, to simulate the 1:3 and 1.5:3 min repeated occlusions

71

Chapter 5

as performed in the sheep experiments.

Experiments of repeated umbilical cord occlusion in fetal sheep, induced by in�ating anoccluder cu� placed around the umbilical cord [58, 179], were simulated by linearly increasingthe external pressure on the umbilical cord pum to a maximum level of 90 mmHg in 5 s,keeping it constant for a prede�ned time period, and linearly decreasing it at the end of theocclusion (see also [82], chapter 3). Umbilical cord occlusions were performed with a durationof 1 min and 2 min, and repeated every 5 min, to simulate the 1:5 and a 2:5 min repeatedocclusions in the experiments.

For comparison with experimental data, catecholamine concentration samples from themodel were calculated as the mean over the repetition interval (3 min during uterine arteryocclusions and 5 min during umbilical cord occlusions) preceding the measurement time.

We observed that the trend in FHR increase strongly depends on the time constant τQA .Therefore, the e�ect of τQA on FHR was investigated by varying its value by 50%.

5.2.4.2 Contraction scenarios

The sheep experiments were repeated while replacing the occluder scenarios by more phys-iological uterine contractions, leading to a more gradual uterine vein and/or umbilical cordresistance increase (see our previous papers for a brief description [81, 82], chapter 2 and3). The uterine pressure changes are modeled as a sine-squared function [81, 82]. Thesecontractions have an amplitude of 70 mmHg and a contraction duration and interval similarto the occlusion times in the sheep experiments.

5.3 Results

Simulation results for the scenario of 1.5:3 min uterine artery occlusions are shown in �gure5.2. As targeted, in steady state FHR is about 135 bpm, blood pressure 45 mmHg and oxygenpressure 18.5 mmHg. We �rst consider the case without catecholamine feedback (light gray).During uterine artery occlusions, the oxygen transport from mother to child is decreased,resulting in reduced fetal oxygen pressures. As a result, fetal cerebral autoregulation isactivated, thus increasing cerebral blood �ow in order to compensate for the reduced oxygensupply. The drop in oxygen pressure also stimulates the chemoreceptor, which, via activationof the sympathetic nervous system, increases peripheral vascular resistance to raise arterialblood pressure. As a result, blood and oxygen supply are increased to the vital organs anddecreased to non-essential organs, known as brain-sparing or blood �ow redistribution. Viathe sympathetic and vagal pathways, reduced oxygen pressure and increased blood pressureboth a�ect fetal heart rate, resulting in a net FHR deceleration.

72


0 5 10 15 20 25 300

5

10

15

20

pO

2,a

[mm

Hg

]

0 5 10 15 20 25 3040

60

80

ptm

,a[m

mH

g]

0 5 10 15 20 25 300

20

40

60

cC

at a

[ng

/ml]

0 5 10 15 20 25 3050

100

150

time [min]

FH

R [

bp

m]

Figure 5.2: Simulation results of repeated uterine artery occlusion. Uterine artery blood �owwas completely blocked for 1:3 min (dark gray) and 1.5:3 min (black). For the more severescenario of 1.5:3 occlusions, simulation results without catecholamine feedback are shownas well (light gray). Occlusion periods are indicated by the squares. From top to bottomsignals represent arterial oxygen pressure pO2,a, mean arterial transmural blood pressureptm,a, arterial catecholamine concentration cCata, and FHR.

Simulation results of 1.5:3 min uterine artery occlusions with catecholamine feedback areshown in black. Oxygen levels show almost the same pattern as during the simulation withoutcatecholamine feedback. However, blood pressure levels are slightly increased. This can beexplained by the increase of FHR (bottom panel) in response to the increase of catecholaminelevels. Within 30 min, arterial catecholamine concentration rises from a steady-state level of1.0 ng/ml to a level of 20.9 ng/ml (averaged over 3 min). The increased arterial catecholamineconcentration leads to higher FHR values with subsequent contractions. The minimum FHRvalues increase as well, but at a slower rate than the FHR maxima. As a consequence, thedepth of the FHR decelerations is increased.

During 1:3 min uterine artery occlusions (dark gray), as expected, variations in oxygen andblood pressure are reduced, since the uterine artery occlusions are less severe. Furthermore,oxygen and blood pressure levels have more time to restore during the longer inter-occlusionperiods. The 3-minute-averaged arterial catecholamine concentration increases only slightly,

73

Chapter 5

up to a level of 3.4 ng/ml after 30 min. Since catecholamine appearance is reduced, thee�ect on FHR during the resting period is diminished, and FHR maxima do no longer increasewith subsequent occlusions.

Simulation results of umbilical cord occlusions are shown in �gure 5.3. Simulation results of2:5 min occlusions without catecholamine feedback are indicated in light gray. Similar to thescenario of uterine artery occlusion, oxygen transport to the fetus is reduced, resulting inlow oxygen pressures and raised blood pressure. Since the oxygen bu�er in the IVS is nolonger available, oxygen pressures drop deeper compared to the scenario of uterine arteryocclusion, even if occlusion periods are of the same duration. (Also see our previous studies[81, 82], chapter 2 and 3.) Via the baro- and chemoreceptor, increased blood pressure anddecreased oxygen pressure result in FHR decelerations.

0 5 10 15 20 25 300

5

10

15

20

pO

2,a

[mm

Hg

]

0 5 10 15 20 25 3040

60

80

ptm

,a[m

mH

g]

0 5 10 15 20 25 300

20

40

60

cC

at a

[ng

/ml]

0 5 10 15 20 25 3050

100

150

200

250

time [min]

FH

R [

bp

m]

Figure 5.3: Simulation results of repeated umbilical cord occlusion. Umbilical blood �ow wasblocked for 1:5 min (dark gray) and 2:5 min (black). For the the more severe scenario of 2:5occlusions, simulation results without catecholamine feedback are shown as well (light gray).Occlusion periods are indicated by the squares. From top to bottom signals represent arterialoxygen pressure pO2,a, mean arterial transmural blood pressure ptm,a, arterial catecholamineconcentration cCata, and FHR. (Note the di�erence in the axis of the FHR plot compared to�gure 5.2.)

74


If catecholamine feedback is included in the model (black), the oxygen pressure graduallyreaches a higher level during the inter-occlusion periods than during simulations withoutcatecholamines, which is caused by the increased FHR, enhancing umbilical blood �ow be-tween occlusions (not shown). Furthermore, blood pressure is increased. Again this can beexplained by the increased FHR levels, caused by the increased catecholamine concentra-tion, which now reaches a level of 40.9 ng/ml after 30 min (averaged over 5 min). During theinter-occlusion periods, FHR shows an increasing trend, reaching maximum levels of about255 bpm, whereafter FHR decreases again towards steady-state levels. However, the inter-occlusion intervals are too short for the FHR to actually reach the FHR level preceding theexperiment.

During 1:5 min occlusions (dark gray), the reductions in oxygen pressure and increases inblood pressure are less severe compared to 2:5 min occlusions. The 5-minuted-averagedcatecholamine concentration increases to a level of 9.4 ng/ml after 30 min. FHR decreasesduring occlusions and only exceeds the initial steady-state FHR level by maximum 16 bpmduring the inter-occlusion periods.

In �gure 5.4 the e�ect of variations in the low pass �lter time constant τQA is shown. If τQA isdecreased (dashed black lines), the FHR tracing of 1.5:3 min uterine artery occlusions shows a

0 5 10 15 20 25 3050

100

150

FH

R [bpm

]

0 5 10 15 20 25 3050

175

300

FH

R [bpm

]

time [min]

Figure 5.4: The e�ect of τQA on FHR. The upper panel shows FHR variations during simu-lations of 1.5:3 min uterine artery occlusions, the lower panel shows FHR tracings obtainedduring 2:5 min umbilical cord occlusions. The value of τQA is varied with respect to its stan-dard value of 5 s (gray line) and set to a value of 2.5 s (dashed black line) and 7.5 s (solidblack line). (Note the di�erence in the axis of both plots.)

75

Chapter 5

0 5 10 15 20 25 300

20

cC

at a

[ng/m

l]

0 5 10 15 20 25 3050

100

150

200

FH

R [bpm

]

0 5 10 15 20 25 300

20406080

100120

pu

t[m

mH

g]

time [min]

0 5 10 15 20 25 300

20

cC

at a

[ng/m

l]

0 5 10 15 20 25 3050

100

150

200

FH

R [bpm

]

0 5 10 15 20 25 300

20406080

100120

pu

t[m

mH

g]

time [min]

Figure 5.5: Contraction scenarios. The upper three panels represent arterial catecholamineconcentration cCata, FHR and uterine pressure put tracings during repeated uterine contrac-tions causing uterine vein occlusion alone. Contractions with an amplitude of 70 mmHg anda duration of 1.5 min are repeated every 3 min. The lower three panels show the resultsduring repeated uterine contractions causing both uterine vein and umbilical cord occlusion.Contractions with an amplitude of 70 mmHg and a duration of 2 min are repeated every 5min. (Note the di�erence in the axis of the cCata plot with respect to �gure 5.2 and 5.3.)

76


more abrupt increase of the maximum FHR levels, with respect to the standard settings (graylines). The maximum inter-occlusion level is reached within four repeated occlusions. If τQA

is increased (solid black line), inter-occlusion FHR values show a more gradual increase. Forthe 2:5 min umbilical cord occlusions, a reduction of τQA leads to more spiky FHR overshootsand a faster FHR reduction at the end of the inter-occlusion period (dashed black lines), whilean increase of τQA results in a less spiky pattern and a gradual increase of inter-occlusionFHR levels (solid black lines).

Figure 5.5 shows the results of the contraction scenarios. During repeated uterine contrac-tions with a duration of 1.5 min and a contraction interval of 3 min, which result in uterine�ow reduction alone (upper panels), no clear increase in catecholamine concentration is ob-served. As a consequence, no secondary FHR e�ects are present. During the inter-occlusionperiod, FHR reaches baseline levels again. The lower panels show the results of contractionsa�ecting both uterine and umbilical blood �ow. Contractions have a duration of 2 min andare repeated every 5 min. The arterial catecholamine concentration increases up to a levelof 10.5 ng/ml. As a result, the inter-occlusion FHR increases with a maximum of 19 bpm.The small initial increases of FHR preceding the decelerations are caused by blood pressurereductions, as explained previously.

5.4 Discussion

Aim of this study was to gain insight into the role of catecholamines in the development ofsecondary FHR e�ects, such as increase of FHR baseline and appearance of FHR overshoots,during repeated severe hypoxic events. To this end we extended our CTG simulation model[78, 81, 82] (chapter 2, 3 and 4) with a catecholamine feedback submodel. Because of the lackof clinical data on hypoxia and catecholamine concentrations in the human fetus, we had touse data from animal experiments for parameter estimation. Therefore, while to the best ofour knowledge this is the �rst mathematical model describing the e�ect of catecholamineson FHR, we must be reticent in interpreting these data for the human fetus. Nevertheless, thesimulations in this paper can be regarded as proof of principle and can be used to investigatetrends in catecholamine concentrations and cardiovascular responses.

Model setup. In view of the limited experimental data available, catecholamine appearancewas modeled as function of oxygen pressure, to describe the combined e�ect of nervousspillover and adrenal secretion.

We also did not distinguish between adrenaline and noradrenaline, neither in the cate-cholamine distribution submodel, nor in the catecholamine feedback submodel. Experimentaldata in the sheep fetus show mixed cardiovascular responses [28, 75, 76]. Although all studiesshow an increase in blood pressure if adrenaline or noradrenaline is infused, in some studies

77

Chapter 5

an initial decrease of FHR is observed by infusing adrenaline [75], while others observe thise�ect by infusing noradrenaline [28]. In all studies the initial FHR decrease is followed byan FHR increase. Due to the limited and ambiguous experimental data, it is very di�cult tomodel the individual e�ect of both catecholamines on the fetal cardiovascular system.

Finally, we only included the e�ect of catecholamines on FHR and neglected the e�ect onthe other sympathetic e�ectors: cardiac contractility, peripheral vascular resistance andvenous unstressed volume. This choice was motivated by the availability of informationon catecholamine feedback on FHR [71, 179], and the lack thereof on peripheral vascularresistance, venous unstressed volume, or cardiac contractility.

Choice of experimental studies. Since most studies are performed in sheep, we focus onsheep experiments to estimate model parameter values. Ideally, sheep studies should pro-vide a well de�ned description of occlusion severity, and measurements of oxygen pressure,FHR and catecholamine concentrations at several time points. Unfortunately, such experi-ments are not available. In the studies of Jensen et al. [71, 72], catecholamine concentrationswere only measured at the beginning and end of the occlusion experiments. In the studiesof Galinsky and Westgate [58, 179], oxygen pressure was measured in between occlusionsand not during the occlusions. In the study of Lewis et al. [95], the timing and severity ofcord occlusion was based on the drop in oxygen pressure, and thus occlusion parameterswere not exactly known. There are several sheep studies available that describe the e�ectof repeated uterine artery occlusions on FHR and catecholamine concentration [71, 72, 130].However, these studies show di�erent FHR responses during 1:3 min occlusions. We choseto use the studies of Jensen et al. [71, 72] for model tuning. The e�ects of repeated umbilicalcord occlusions have also been investigated in several sheep studies [39, 58, 94, 136, 179, 180].We used the studies of Galinsky [58] and Westgate [179] to estimate parameter values. Whenwe subsequently tested the model by simulating the experiments performed by Saito [136](15 times 40:120 s followed by 45 times 60:120 s umbilical cord occlusions), we found thatthe catecholamine concentration was similar to the sheep data, but that oxygen saturationremained higher in the model (data not shown). Inter-occlusion FHR baseline increased, al-though the increase was smaller than observed in sheep data. It is unclear whether thediscrepancies between model and experimental results are caused by fundamental short-comings of the model or by large inter-subject variations in sheep [58, 71, 72].

Results. Simulation results of 1:3 min uterine artery occlusions show FHR decelerationsduring the occlusion periods, which is in accordance with sheep data of Jensen et al. [71](�gure 5.2). In between occlusions, FHR returns towards the steady-state level, precedingthe occlusion experiment. This is also observed in the study of Jensen, however, in thesheep, FHR inter-occlusion baseline remains lower as compared to our simulation results[71]. Simulation results of 1.5:3 min uterine artery occlusions show a similar FHR deceleration

78


during the �rst occlusion as compared to the sheep experiments [71]. Furthermore, an initialdecrease of inter-occlusion FHR is observed, followed by a gradual increase. However, boththe initial decrease and the subsequent increase are not as large as observed in the sheepexperiments. In addition, the drop of oxygen saturation (data not shown) in the model issmaller compared to the sheep studies. Since catecholamines are not yet expected to playa signi�cant role after the �rst occlusion, the cause of these di�erences must be soughtin the original model without catecholamine feedback, possibly in the oxygen submodel.Furthermore, one should keep in mind that in this study a human model of hemodynamics,oxygenation and regulation is used to simulate sheep catecholamine responses.

During 1:5 min umbilical cord occlusions, simulated FHR tracings did not show an overshootpattern (�gure 5.3), which is in accordance with sheep experiments [179]. During 2:5 minumbilical cord occlusions, FHR overshoots are obtained in the simulation results, which arealso observed in experimental tracings [58, 179]. Target maximum FHR levels are reached(here 255 bpm based on scaling). These values still seem to be quite high for the human fetus.However, such severe experiments have never been performed on human fetuses. The shapeof the overshoots is less sharp compared to the sheep experiments. This can be improvedby decreasing the low pass �lter time constant τQA (�gure 5.4). However, decreasing τQA

would result in a more abrupt rise of FHR baseline during repeated uterine artery occlusions(�gure 5.4), which is not in accordance with experiments of repeated uterine artery occlusionin sheep [71]. As a compromise, we set τQA to a value of 5 min.

The model also predicts the initial increase of blood pressure during the repeated uterineartery [71] or umbilical cord [58, 179] occlusions, but fails to predict the secondary decreaseduring the occlusion period. Furthermore, inter-occlusion blood pressure does not show aclear increase.

Comparison of catecholamine concentrations between model and experiments is not straight-forward. During simulations of umbilical cord occlusions, catecholamine concentrationsshowed large �uctuations (see �gure 5.3), suggesting that knowledge on the exact timingand duration of the experimental sampling procedure is crucial. However, this detailed in-formation is not available in the experimental data. In order to compare simulation resultswith experimental data, simulated arterial catecholamine concentrations were averaged overa whole occlusion-repetition period (3 min in case of uterine artery occlusions and 5 minfor umbilical cord occlusions). With the chosen parameters settings for catecholamine ap-pearance and elimination, after 30 min of simulation, arterial catecholamine concentrationscorresponded well with experimental data, for both repeated uterine artery occlusions (1:3min: 3.4 ng/ml model vs. 2.8 ng/ml after 33 min by Jensen et al. [72], and 1.5:3 min: 20.9ng/ml model vs. 20.5 ng/ml after 33 min by Jensen [72]) and umbilical cord occlusions (2:5min: 40.9 ng/ml vs. 43.1 ng/ml after 12 min and 33.1 ng/ml after 42 min by Galinsky et al. [58]).

79

Chapter 5

Catecholamine concentrations were not measured during 1:5 min umbilical cord occlusions[58], therefore we cannot evaluate model predictions for this scenario.

In the sheep experiments, occluders are used to block uterine or umbilical blood �ow, leadingto a direct and complete �ow reduction in contrast to the gradual �ow reduction in responseto increasing uterine pressure during actual uterine contractions. Therefore, we also sim-ulated the e�ect of uterine contraction patterns. To enable comparison with the occluderexperiments, we adopted the same timing of the contractions. When the contraction sce-narios (�gure 5.5) are compared to the simulated sheep experiments (�gure 5.2 and 5.3),a smaller increase in arterial catecholamine concentration is observed, resulting in smallersecondary FHR responses. During the 1.5:3 min uterine contractions, causing uterine �ow re-duction alone, FHR does not show inter-occlusion tachycardia. Apparently, the catecholaminethreshold to induce additional changes in FHR was not reached. During 2:5 min uterine con-tractions, causing combined uterine and umbilical �ow reduction, inter-occlusion tachycardiais observed, however no overshoots are present in the FHR tracing. The FHR values of 255bpm, that were reached in the simulations of the sheep experiments, were not reached inthese scenarios, indicating that the e�ect of complete uterine artery or cord occlusions ismuch stronger than the occluding e�ect of physiological uterine contractions with similarduration.

Recommendations. In our model, secondary FHR responses are evoked by catecholamines.Although we can mimic experimental FHR data, inter-oclussion blood pressure increase couldnot be simulated. It is suggested that other mechanisms such as vagal inhibition and myocardhypoxia, may also play a role [136, 179, 180]. Likely, fetal blood pressure is also in�uencedby other vasoconstrictor agents e.g. arginine vasopressin, angiotensin II, and neuropeptideY [60, 115]. Vagal inhibition was recently included in a model by Wang et al. [173]. They alsoadded feedback of carbon dioxide on the chemoreceptor. With their model, FHR overshootscould be obtained after three hours of 1:2.5 min umbilical cord occlusions. However, it remainsunclear if their model can also predict FHR responses during the �rst 30 min of severe uterineartery or umbilical cord occlusions. It would be interesting to combine the mechanisms asimplemented by Wang, with the catecholamine feedback proposed in this study. Duringlonger simulations of severe hypoxia, other e�ects such as catecholamine depletion andmyocard hypoxia might also play a role. Although experimental data concerning myocardhypoxia is scarce, it would be very interesting to include these e�ects in the model.

The current model was based on a mixture of experimental observations in human and sheep,making comparison between model data and experimental data a di�cult task. In view ofthe many questions on catecholamine feedback, adapting the model for sheep physiologymight be an option, since for fetal sheep much more data is available. With this model, thein�uence of catecholamines on FHR responses can then be investigated in the sheep fetus.

80


Still, even when a coherent model for the sheep fetus is obtained, translation to the humanfetus is not straightforward.

Conclusion. A catecholamine feedback model was developed and included in the CTG simu-lation model to simulate secondary FHR responses that occur during repeated severe hypoxicepisodes. Simulation results of repeated severe uterine blood �ow reductions showed an ini-tial decrease of inter-occlusion FHR, followed by a gradual increase, which is in qualitativeagreement with sheep data. Simulations of repeated severe umbilical �ow reductions resultedin FHR overshoots, which were less sharp as compared to experimental data. We concludethat catecholamines might at least partly play a role in the origin of secondary heart rateresponses, but we can not exclude that other mechanisms, such as myocard hypoxia andvagal inhibition, are also involved.

81

Chapter 5

82

Chapter 6

General discussion

Chapter 6

6.1 Introduction

Although improvements have been made between 2004 [51] and 2010 [52], currently in Eu-rope still babies die during the perinatal period. Steps have to be taken to reduce perinatalmortality. Therefore, in 2012, the perinatal IMPULS program, a collaboration between Máx-ima Medical Center, Eindhoven University of Technology, and Philips, was initiated. In thisprogram about 20 PhDs with a medical or technical background, work together in order toimprove perinatal care and to contribute to medical research and education. The researchwithin the perinatal IMPULS program focuses on development of patient studies, design ofnew measurement techniques, and development of signal processing tools. Another impor-tant aspect within the IMPULS program is the development of mathematical models, to beused to improve understanding of fetal and neonatal physiology and to contribute to clinicalresearch, education, and decision making.

In the research described in this thesis, a mathematical model is used to improve under-standing of the CTG. Despite its high intra- and inter-observer variability [27, 110, 125], theCTG is commonly used to evaluate fetal well-being during labor and delivery. Interpreta-tion of the CTG signals is very complex, which hampers evaluation of fetal well-being andrecognition of fetal distress. Timely intervention during emergency scenarios will reduce fetalmorbidity and mortality. In this thesis, the CTG simulation model of Van der Hout-van derJagt [161–163] was used as a starting point. It was adapted and extended to gain more insightinto the mechanisms underlying the FHR variations and to improve applicability of the modelfor research and education.

6.2 Main achievements

First, the new CTG simulation model was described (chapter 2 and 3). With respect to theprevious model, the physical description of the e�ect of uterine pressure on uterine andumbilical blood vessels was enhanced. Furthermore, the complexity of the cardiac functionand central regulation submodels was drastically reduced.

In chapter 2, the e�ects of uterine contractions, inducing uterine vein occlusion, on thefetal cardiovascular system were investigated. During a contraction, the uterine vein is com-pressed, which results in a reduced uterine blood �ow. As a consequence, less oxygen will besupplied to the fetus. This results in a chemoreceptor-mediated increase of peripheral resis-tance, reducing peripheral blood �ow. Concurrently, cerebral blood �ow is increased via cere-bral autoregulation. This mechanism is called redistribution or brain-sparing. The increasedblood pressure and decreased oxygen pressure lead to a net baro- and chemoreceptor-mediated FHR reduction. Due to the oxygen bu�er function of the IVS, which delays theoxygen drop in the fetus, these simulations result in so-called ‘late decelerations’. The pre-

84

General discussion

dicted FHR decelerations are considered more realistic than those obtained with the previousmodel, since they only show a drop of 3 bpm during a standard contraction. Usually, regularcontractions do not cause signi�cant FHR decelerations in an uncompromised fetus.

The e�ect of combined uterine vein and umbilical cord occlusions resulting from contractionswas investigated in chapter 3. The direct e�ect of cord occlusion is a blood volume shift fromthe fetus to the fetal placenta, and a reduction of fetal blood pressure. As a consequence,an initial baroreceptor-mediated FHR increase is observed in the FHR tracings, referred toas a ‘shoulder’. This shoulder is followed by an FHR deceleration, initiated by the reductionin oxygen pressure and the subsequent increase in blood pressure. Since cord occlusionimmediately reduces oxygen levels in the fetus, FHR decelerations are less delayed comparedto the scenario of uterine vein occlusion alone. Simulations of contractions with varyingcontraction amplitude or duration, reveal the wide variation in deceleration shapes causedby umbilical cord occlusions, which therefore are referred to as ’variable decelerations’.

In chapter 4, fetal heart rate variability (FHRV) was added to the model. Whereas FHRV waspreviously added in the post-processing step [161–163], now a more fundamental approachwas used. In this chapter the e�ect of three possible sources of variability was investigated:peripheral autoregulation, in�uence of higher brain centers on the processing of the barore-ceptor output in the nucleus tractus solitarius of the medulla oblongata, and in�uence ofa�erent systems on the vagal nerve center. To each of the sources of variability either 1/for white noise was applied. By use of spectral analysis of the FHR tracings, power densityspectra were obtained, showing a physiological 1/f character, independent of the noise typeused. This reveals the physiological �ltering characteristic of the model. However, the clin-ically observed peak around 0.1 Hz [54, 89] was only obtained when white noise was used.Realistic FHRV could be obtained by using di�erent sources of variability, although the exactcontribution of each of these sources in the human fetus remains unknown. The main issuein this research is that the output (FHRV), which can be measured in clinic, is in�uencedby both the input (source of variability and type of noise) and the system itself (fetal body).With the model it is possible to systematically distinguish between the noise source and type,and the characteristics of the fetal regulation system. Thereby, the model might assist inthe assessment of the physiological causes of FHRV. Although the clinically observed FHRVincrease during contractions [25, 129, 175] was not observed in model simulations, additionof FHRV improved the realism of the simulated FHR tracings, which enhances application ofthe model for research and education.

In chapter 5, the model was used as a basis to investigate the contribution of catecholaminefeedback to the generation of secondary FHR responses during repeated episodes of severehypoxia. A simple model describing the combined e�ect of adrenal catecholamine secre-tion and catecholamine nerve spillover as function of oxygen pressure, and catecholamine

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elimination in the placenta and tissues, was developed. Catecholamine feedback on FHRwas modeled as a linear relation between arterial catecholamine concentration and changein heart period. The e�ect of adrenaline and noradrenaline was combined in the model.Tuning of the model was based on sheep experiments in which the uterine artery [71, 72]or umbilical cord [58, 179] was repeatedly occluded. Parameter estimation and scaling wasdi�cult due to the limited available human data and the known large interspecies di�er-ences. Therefore, model simulations can be regarded as proof of principle, but one must bereticent in interpreting the results for the human fetus. Simulation results of repeated se-vere uterine blood �ow reductions showed an initial decrease of inter-occlusion FHR, followedby a gradual increase. This trend was also observed in sheep experiments. Simulations ofrepeated severe umbilical blood �ow reductions showed FHR overshoots, following the FHRdecelerations. However, these overshoots were less sharp compared to experimental �nd-ings in sheep. The model shows that catecholamines at least partly play a role in developinginter-occlusion tachycardia and FHR overshoots during severe hypoxic episodes. However,likely other mechanisms, such as vagal inhibition or myocard hypoxia, are also involved.

6.3 Application of the CTG simulation model

The current CTG simulation model can be used to gain understanding of the underlyingmechanisms and serve as a tool for hypothesis testing and formation. As an example, thepreviously developed CTG simulation model of Van der Hout-van der Jagt et al. [161–163] wasused to investigate the e�ect of maternal hyperoxygenation on fetal oxygenation and FHRdecelerations during labor [22]. Results of that study showed a reduction of decelerationdepth and duration when 100% oxygen was administered to the mother. These e�ects werealso observed in small, non-randomized human studies [8, 85]. As a result, this e�ect iscurrently tested in a larger patient population in a randomized clinical trial.

It has been shown that team-training of obstetric emergency scenarios is associated withimproved team performance and medical technical skills [42, 56, 104], and with neonataloutcome [44, 45]. During these training sessions, simulation manikins can be used to prac-tice various delivery scenarios [42, 56, 104]. The fetal and maternal state are projected onmonitors. During training sessions, the instructor has to observe medical interventions andactions from the trainees and has to adapt the fetal CTG accordingly. This is not only verytime consuming, but also requires detailed physiological knowledge by the instructor. Thissystem can be improved by using the CTG simulation model as an intelligent addition to thesimulation manikins, in order to have them automatically and consistently respond to theclinical interventions during training sessions.

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Another relatively new �eld in medical education is computer-based serious gaming. Seriousgames can be used to simulate scenarios which are di�cult to practice in real life and to trainclinical skills at relatively low costs [40]. Our model for CTG simulation can be implementedin such a game in order to gain understanding of the e�ect of di�erent interventions onfetal well-being and to gain insight into the clinical consequences of such actions. Simula-tion training, either manikin-based or computer-based, is especially useful to practice skillsnecessary in emergency situations that do not occur on a regular basis in the clinic.

Ultimately, the CTG simulation model could be used as a clinical decision support system.Two successful examples were discussed in chapter 1. However, there are several reasonswhy it is less straightforward for the current model to be used for clinical decision support.First, the previously discussed model examples focus on a limited part of the human system.In contrast, the CTG-simulation model describes the complete feto-maternal system, includ-ing circulation, oxygenation, and regulation. The mathematical relations describing most ofthese submodels are less well known. Besides, in our model, feedback mechanisms areincluded, which complicates the analysis of the input-output relations. Second, the givenmodel examples require input data, which to a large extent consists of geometric data, forwhich measurement tools, such as CT, ultrasound or MRI, are available. These measurementtechniques allow patient-speci�c parameter estimation. Since from the human fetus mostparameters cannot be measured, especially for the regulation and catecholamine feedbacksubmodels, parameters have to be estimated and scaled from human adult or animal data,as discussed in chapter 3 and 5. A sensitivity analysis can help in assessing which parameterscan be set to generic values, and which parameters have to be set to patient-speci�c values.The model can be used to guide the design of experiments in order to obtain measurementvalues of parameters that dominate model response, and thus have to be determined veryaccurately. Third, ideally, patient measurements are performed to establish the input for themathematical model, prior to clinical interventions. Hereafter the model is used to simulatedi�erent scenarios and treatment options. Simulation results can then be used to assist inthe treatment selection. However, the time frame during labor and delivery, when most mea-surements should be performed, is relatively short. Finally, the limited data available frommeasurements in the human fetus and mother impair validation of the model. Therefore,use of the CTG simulation model as a clinical decision support system is not straightfor-ward. Whereas patient-speci�c modeling will be di�cult, pathology-speci�c modeling, whichgives insight into the di�erent processes involved in various pathologies, might be an option.However, still for these pathology-speci�c models, parameter estimation will be a challenge.

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6.4 Future perspectives

As discussed previously, one of the main concerns for development of the CTG simulationmodel is the availability of experimental data. Further development of the model will requireadditional parameter estimation and model evaluation. Since a lot of research is performedin fetal sheep, a sheep model might be developed, as a �rst step, combining hemodynamics,oxygenation, neuronal regulation, and humoral feedback for one single species. With themathematical sheep model, the di�erent processes in the fetal lamb can be investigatedand understanding of the regulation of FHR can be improved. Hereafter, it might be morefeasible to translate the model to a human fetus. Nevertheless, one has to keep in mind thedi�erences between the sheep and human fetus. For example, in the fetal sheep brain sizeis smaller, while umbilical blood �ow is larger [133]. Besides, many interspecies di�erencesare observed concerning catecholamine feedback, as discussed in chapter 5.

There are di�erent possibilities to extend the fetal model in order to make it more usefulfor eduction and research. For example, the hemodynamic model of the fetus might beenhanced by including shunts and preferential blood �ows. In the fetus, several shunts arepresent in the circulatory system [109, 115]. The ductus venosus partly shunts the oxygen-richblood that enters the fetal system via the umbilical vein, directly into the inferior vena cava.The oxygenated blood thereby short-cutts the liver circulation, and �ows directly towards theheart. Here, the oxygen-rich blood preferentially �ows, through the foramen ovale, which isanother shunt that allows blood to �ow from the right atrium into the left atrium, in orderto supply the coronary and cerebral circulation with relatively well-oxygenated blood. Bloodfrom the right ventricle is partly directed to the pulmonary circulation, but mostly enters theascending aorta via another shunt, the ductus arteriosus. Explicitly modeling these shuntswill improve estimation of the di�erence between cerebral and peripheral oxygenation andenhance evaluation of the risks of asphyxia.

During severe hypoxic episodes, myocard hypoxia, which plays a role when the oxygen trans-port to the heart is insu�cient, will also e�ect FHR and might result in late decelerations[63, 103, 115]. Besides, it is suggested that vagal inhibition is involved in the origin of FHRovershoots during severe repeated umbilical cord occlusions [136, 173, 179]. In future studies,it will be interesting to include both of these mechanisms in the fetal model.

In clinical practice, fetal blood sampling is performed, in order to gain more insight into thefetal condition in case of a suboptimal CTG. From this blood sample, amongst others, the pHcan be obtained. A decreased pH indicates a distressed fetus, and intervention is performedif the pH drops below 7.20 [159]. Addition of a pH submodel would improve clinical relevanceof the model. It will also enable implementation of the Bohr e�ect, which leads to a shift ofthe fetal oxygen dissociation curve, resulting from variations in pH. Several candidate modelshave been described in literature [24, 36, 173]. After birth, neonatal well-being is assessed via

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General discussion

the one and �ve minute Apgar scores. This score is based on the breathing e�ort, heart rate,re�exes, muscle tone, and skin color of the newborn. Although it will be a challenging taskto estimate the Apgar score from the model, an indication of the Apgar score will furtherincrease the clinical relevance of the model.

Also the maternal model can be extended. Except for changes in uterine blood �ow follow-ing uterine contractions, the maternal cardiovascular system is currently not subjected tocardiovascular changes during labor. Clinical studies have shown variations in heart rate andcardiac output during the di�erent stages of labor as well as during periods of rest and con-tractions [127, 144]. Especially during active pushing, high heart rate levels were reached [144].However, when accounting for cardiovascular changes during labor, a maternal cardiovascularregulation model should be included as well. The maternal model might further be enhancedby including a breathing model. Since labor and delivery require much e�ort of the mother,presumably breathing patterns will change during labor, a�ecting maternal oxygenation andsubsequently fetal oxygen delivery.

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104

Samenvatting

105

Samenvatting

Simulatie van het cardiotocogram tijdens de bevalling: meer inzicht inde foetale fysiologie met behulp van een model

Tijdens de bevalling is het van belang om de toestand van het ongeboren kind te bewakenom tijdig in te kunnen grijpen in geval van nood. Bij voorkeur zou meting van de foetalezuurstofhuishouding onderdeel uit moeten maken van de bewaking. Echter, betrouwbarezuurstofmetingen kunnen alleen tijdens de bevalling, na het breken van de vliezen, verrichtworden. Bovendien kunnen deze metingen niet continu, maar op slechts een beperkt aan-tal momenten in de tijd uitgevoerd worden. In de kliniek wordt daarom gebruik gemaaktvan cardiotocogra�e om het foetale welzijn in te schatten. Het cardiotocogram (CTG) be-treft de gelijktijdige registratie van het foetale hartritme (FHR) en de baarmoedercontracties(weeën). De relatie tussen baarmoedercontracties en de uiteindelijke veranderingen van hetFHR wordt gevormd door een complexe keten van fysiologische gebeurtenissen. Zo zullenveranderingen in bloed- en zuurstofdruk, via de baro- en chemore�ex, invloed hebben ophet FHR. Waarschijnlijk speelt ook de terugkoppeling via hormonen een rol. Door de com-plexiteit van dit systeem is het afschatten van de foetale toestand aan de hand van het CTGeen moeilijke taak.

Om meer inzicht te verkrijgen in de complexe keten waarlangs baarmoedercontracties leidentot veranderingen de bloed- en zuurstofdruk en uiteindelijk tot veranderingen in het FHR,kan een wiskundig computermodel gebruikt worden. In voorgaande studies is zo‘n com-putermodel ontwikkeld. Het model beschrijft de hemodynamica van moeder en kind, dezuurstofhuishouding, de foetale regulatie en de generatie van baarmoedercontracties. Hetmodel kan gebruikt worden om verschillende scenario‘s te simuleren die kunnen optredentijdens een baarmoedercontractie, zoals compressie van het hoofdje van het kind, reductievan de bloedstroom naar de baarmoeder, of compressie van de navelstreng. Deze sce-nario‘s leiden tot het ontstaan van respectievelijk vroege, late en variabele deceleraties inhet FHR-signaal.

In dit proefschrift is eerst de complexiteit van het bestaande computermodel gereduceerdvoor die submodellen waar parameterschatting gecompliceerd was (door een gebrek aan ex-perimentele data) of waar volstaan kon worden met minder gedetailleerde modeluitkomsten.Bovendien is de fysische beschrijving van andere submodellen verbeterd. Omdat de foetalehartritme variabiliteit (FHRV) een belangrijke indicator is voor foetale stress, is in een vol-gende stap de FHRV toegevoegd aan het model. Als laatste is de bijdrage van terugkoppelingvia hormonen, die van belang wordt tijdens herhaaldelijke ernstige perioden van hypoxie,onderzocht met het model.

Met het verbeterde model uit de eerste stap is de cascade van gebeurtenissen tussen baar-moedercontracties en FHR veranderingen onderzocht. Baarmoedercontracties kunnen leidentot een afname van de bloedstroom in de baarmoeder en/of de navelstreng en beïnvloeden

106

zo de foetale bloed- en zuurstofdruk, wat leidt tot stimulatie van de baro- en chemoreceptor.Uiteindelijk zullen via het sympatische en parasympathische zenuwstelsel veranderingen inhet FHR teweeg gebracht worden. Baarmoedercontracties die zowel leiden tot bloedstroom-reducties in de baarmoeder als in de navelstreng, leiden tot een snellere en ernstigere afnamein het FHR dan contracties die alleen invloed hebben op de bloedstroom naar de baarmoeder.Dit verschil kan verklaard worden door de zuurstofbu�erfunctie van de intervilleuze ruimtein de baarmoeder. Indien alleen de bloedstroom naar de baarmoeder verminderd wordt, isdeze zuurstofbu�er namelijk nog beschikbaar voor de foetus, wat leidt tot een vertraagdeen langzamere afname van de foetale zuurstofdruk. Als gevolg hiervan zal de chemoreceptorpas later gestimuleerd worden en de FHR reductie ook vertraagd en minder sterk zijn. In-dien ook de navelstreng afgekneld wordt, is de zuurstofbu�er in de intervilleuze ruimte nietbeschikbaar voor de foetus. Tijdens beide scenario’s vindt er herverdeling van de foetalebloedstroom plaats van de perifere naar de cerebrale circulatie. Op deze manier wordt hetzuurstoftransport naar de hersenen zo veel mogelijk op peil gehouden. De initiële toenamevan het FHR tijdens navelstrengcompressies wordt veroorzaakt door de verplaatsing vanbloed vanuit de foetus naar de foetale placenta. Deze resulteert in een afname van debloeddruk en leidt via de baroreceptor tot een toename van het FHR. De verplaatsing vanhet foetale bloed wordt veroorzaakt door een vertraging tussen het sluiten van de navel-strengvene en de navelstrengarterieën. Het model is geëvalueerd aan de hand van data uitschapenexperimenten: er worden vergelijkbare trends in bloeddruk, zuurstofdruk en FHRverkregen. Dit laat zien dat het model in staat is om realistische deceleraties te beschrijven.

Aangezien de exacte bron voor FHRV niet bekend is, hebben we drie mogelijke bronnenvoor FHRV onderzocht met het model: autoregulatie van de perifere bloedvaten, de invloedvan hogere breincentra op de verwerking van de baroreceptor-output in de nucleus tractussolitarius van de medulla oblongata, en de invloed van a�erente systemen, zoals het hart,de longen en spieren, op het vagale centrum. Tijdens de simulaties is er 1/f-ruis of witte ruisgeplaatst op respectievelijk de perifere vaatweerstand, de baroreceptor-output, en de vagalee�erente output van het zenuwstelsel. We hebben de FHR-signalen geëvalueerd op basisvan visuele inspectie en met behulp van spectraalanalyse. Alle vermogensspectra lieten eenfysiologisch 1/f-karakter zien, ongeacht de ruisbron en het ruistype dat gebruikt werd. Deklinisch waargenomen piek rondom 0.1 Hz was alleen zichtbaar in het spectrum indien witteruis gebruikt werd. Daarom kan verondersteld worden dat de fysiologische input waarschijn-lijk door witte ruis beschreven kan worden. De sympathische tak van het zenuwstelsel heeftoverwegend invloed op het vermogen van lage frequenties, terwijl de vagale tak het vermogenvan zowel lage als de hoge frequenties beïnvloedt. Dit is in overeenstemming met klinischedata. Door de toevoeging van FHRV aan het model is het model beter in staat om realistischeFHR signalen te simuleren. Dit is belangrijk indien het model gebruikt wordt voor educatievedoeleinden.

107

Samenvatting

Tijdens ernstige episodes van hypoxie, veroorzaakt door ernstige contracties, worden vaaksecundaire FHR responsen gezien, zoals toename van het FHR basisniveau en korte FHRverhogingen (‘overshoots’). Waarschijnlijk worden deze FHR responsen veroorzaakt door ver-schillende mechanismen, waaronder terugkoppeling via stresshormonen en afname van devagale tonus. Om deze secundaire FHR responsen te simuleren, hebben we het model uitge-breid met een eenvoudig submodel dat de feedback via catecholamines beschrijft. Resultatenvan simulaties waarin de bloedstroom naar de baarmoeder verminderd wordt laten een trendzien die vergelijkbaar is met de trend die waargenomen is tijdens experimenten in schapen:een initiële afname van het FHR tussen de occlusies in, gevolgd door een geleidelijke toe-name. Simulaties van herhaalde ernstige navelstrengcompressies laten FHR overshoots zien,volgend op FHR deceleraties. Echter, deze overshoots hebben een minder scherp verloop danovershoots waargenomen in schapenexperimenten. Het model laat zien dat catecholamineseen rol spelen in het ontstaan van secundaire FHR responsen, maar dat andere mechanismen,zoals vagale inhibitie en myocard hypoxie, niet uitgesloten kunnen worden.

Het verbeterde en uitgebreide CTG-simulatiemodel is geschikter dan het oude model voorhet vormen en toetsen van hypothesen en voor gebruik voor educatieve doeleinden. Hetnieuwe model draagt bij aan het begrip van de cascade van gebeurtenissen tussen de baar-moedercontracties en veranderingen in het FHR.

108

Dankwoord

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Dankwoord

Promoveren doe je niet alleen. Buiten de samenwerking op wetenschappelijk gebied, is desteun van familie, vrienden en collega’s ook belangrijk om je een weg te banen door alle upsen downs die een promotietraject kent. Graag wil ik dan ook een aantal mensen bedankenvoor hun bijdrage aan de totstandkoming van dit proefschrift.

Allereerst mijn dagelijks begeleider en copromotor Peter Bovendeerd. Peter, bedankt voor alje steun, hulp en feedback de afgelopen vier jaar. Ik had me geen betere copromotor kunnenwensen. Je maakte altijd tijd als ik vastliep en advies nodig had. Ik waardeer je geduld en hetmeedenken, vooral als ik, vanwege mijn kritische en precieze instelling, nogmaals terugkwamop bepaalde keuzes die we gemaakt hadden. Naast de inhoudelijke besprekingen was er ookaltijd ruimte voor informele gesprekken. We hebben vaak goed kunnen lachen. Ik kijk hiermet heel veel plezier op terug.

Dan mijn tweede begeleider en adviseur van de promotiecommissie Beatrijs van der Hout.Beatrijs, aan het begin van mijn promotie, toen jij ook nog met je promotieonderzoek bezigwas, hebben we veel samengewerkt. Het was erg �jn om iemand te hebben die ik vanallesen nog wat kon vragen over het model. Ook later, toen je als postdoc in MMC ging werken,bleven we veel contact houden. Door jouw achtergrond in zowel de biomedische technologieals in de verloskunde wist je het technische en medische aspect van het onderzoek goed inhet oog te houden. Bedankt voor de leuke gesprekken, die overigens lang niet allemaal overhet onderzoek gingen. Net als jij, zal ook ík de BG’s, de oneindige catecholamineconcentratiesen de chocolademelkmomentjes in MMC nooit vergeten!

Frans van de Vosse, mijn eerste promotor. Frans, bedankt voor je tijd en waardevolle feedbacktijdens onze twee-maandelijkse overlegmomenten. Ondanks dat de verloskunde op sommigepunten toch wel heel iets anders is dan cardiovasculaire biomechanica, zijn er wat het modelbetreft toch zeker ook een hoop raakvlakken. Bedankt voor al jouw meedenken en voor dewaardevolle adviezen.

Mijn tweede promotor, Guid Oei. Guid, bedankt voor al je klinische input. Het is mooi omte zien hoe jij voor ieder probleem weer een oplossing probeert te zoeken en bovendienbij iedere vraag weer een leuk onderzoeksproject weet te verzinnen. Bedankt ook voor jegastvrijheid tijdens de FUN-meetings, die eens per maand bij jou thuis worden gehouden.Het zeer gevarieerde programma met de vele workshops, en natuurlijk het lekkere eten, zalik niet vergeten!

Verder wil ik prof. dr. ir. Bergmans, prof. dr. Vandenbussche en prof. dr. Hilbers bedankenvoor het beoordelen van mijn proefschrift en voor hun deelname in de promotiecommissie.Prof. dr. Ursino, thank you very much for being part of the committee and for reviewingmy dissertation. Prof. dr. ir. Brunsveld, bedankt voor het overnemen van de voorzittersroltijdens de ceremonie.

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Zoals bij elke promovendus bekend is, kent ieder promotieonderzoek zijn dalen, maar zekerook zijn pieken, zoals de acceptatie van een artikel of een succesvolle presentatie op eencongres. Ik heb het erg �jn gevonden om al deze momenten te kunnen delen met mijn col-lega’s. Ik wil dan ook mijn kamergenootjes van 4.09 bedanken! Andrès, Arianna, Franscesco,Gitta, Inge, Johanna, Joke, Jeroen, Lorenza, Lúcia, Marc, Marieke, Marleen, Renee, Saskia, Tilaïen Tomasso, bedankt voor alle gezelligheid, zowel op kantoor maar ook tijdens onze veleetentjes met ‘hok’ 4.09!

Dan wil ik de CVBM-groep bedanken, niet alleen voor de inspirerende meetings, maar ookvoor de gezelligheid tijdens de verschillende etentjes en natuurlijk het jaarlijkse dagje uit.Mijn dank gaat ook uit naar de verschillende Bachelor en Master studenten aan de TU/edie ik begeleid heb en die elk hun steentje hebben bijgedragen aan dit onderzoek. Ik wilalle IMPULS-collega’s bedanken voor de vele inhoudelijke meetings. En dan uiteraard nogde FUN-groep, bedankt dat ik deel mocht uitmaken van deze multidisciplinaire groep. Doorjullie verschillende achtergronden konden er altijd levendige discussies gevoerd worden overallerlei uiteenlopende onderwerpen. Ondanks dat ik maar een keer per week in MMC was,heb ik me er altijd welkom gevoeld. En niet te vergeten, bedankt voor de gezelligheid tijdensde onvergetelijke buitenlandse congressen in Orlando, Parijs, Saint-Vincent en Lyon.

Beste BMT-vrienden, we zijn in 2006 samen begonnen aan de opleiding BMT. Inmiddels heeftiedereen zijn eigen draai gevonden en zijn we allemaal op onze pootjes terecht gekomen. Eengroot aantal van jullie is ook gaan promoveren. Het is heel �jn dat we elkaar zo nu en daneen steuntje in de rug kunnen geven. Anneloes, Bart, Ellen Klein, Ellen Nijssen, Jeire, Joke, Raf,Stefan en Stijn, bedankt! In het speciaal wil ik Anne en Esther bedanken. Super tof dat julliemijn paranimfen willen zijn! Bedankt voor al jullie steun, bij jullie kon ik echt altijd terecht. Ikhoop dat we nog heel lang zulke goede vriendinnen mogen blijven.

Lieve (schoon)familie, ondanks dat promoveren voor jullie ook allemaal nieuw is en jullie jewaarschijnlijk wel vaker hebben afgevraagd wat ik nu precies aan het doen ben en waarvoordan eigenlijk, voelde ik me altijd door jullie gesteund. Hortense, lief zusje, het is echt heel�jn om iemand zo dichtbij te hebben die precies weet wat promoveren is en waar je altijdbij terecht kunt. Ondanks dat de onderwerpen van onze studies compleet verschillend zijn,begrijpen wij elkaar wat promoveren betreft volkomen. Bedankt voor je luisterend oor, en jepeptalks. Heel veel succes bij het afronden van jouw promotieonderzoek, dat gaat je zekerlukken! Papa en mama, bedankt voor jullie onvoorwaardelijke steun, jullie geduld en advies.Promoveren was voor jullie ook nog onbekend terrein, totdat beide dochters besloten om nahun studie een promotietraject in te gaan. Zo langzaamaan kregen jullie steeds meer meevan wat promoveren inhoudt en ondertussen weten jullie er alles van. Bedankt dat ik altijdbij jullie terecht kan, altijd kan bellen en mag langskomen!

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Dankwoord

En als laatste en belangrijkste natuurlijk, lieve Rob, bedankt voor al je steun de afgelopenvier jaar. Met name ook in de afrondende fase waarin de laatste hoofdstukken van mijnproefschrift geschreven moesten worden, maar we ondertussen ook al aan het verhuizenwaren naar onze nieuwe woning om vanuit daar allebei met een nieuwe, uitdagende baan testarten. Ik kijk er naar uit om samen nog vele gezellige, leuke en mooie momenten te gaanmeemaken, maar vooral ook om te gaan genieten van alles wat we tot nu toe samen hebbenopgebouwd!

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About the author

About the author

Curriculum Vitae

Germaine Jongen was born on the 5th of September1988 in Maastricht, the Netherlands. She attendedsecondary education at the Sint-Maartenscollege inMaastricht, where she obtained her atheneum (pre-university) diploma in 2006. Hereafter, she startedstudying Biomedical Engineering at Eindhoven Uni-versity of Technology. She obtained her Bachelor’sdegree (cum laude) in 2009. In the same year, shestarted her Master’s program Medical Engineering,also at Eindhoven University of Technology. Dur-ing her Master’s she did a four-month internship atSINTEF, department of Medical Technology in Trond-heim, Norway, where she worked on the displacementand strain estimation in abdominal aortic aneurysms,using 2D ultrasound. For her Master’s project sheperformed research at the Biomedical Engineeringdepartment at Maastricht University and investigated the mechanical characterization andimaging of healthy aortas and abdominal aortic aneurysms with 2D ultrasound. She obtainedher Master’s degree in Medical Engineering (cum laude) in 2011. In 2012 she started her PhD-project, which focused on the improvement and extension of a mathematical CTG simulationmodel, to be used for research and education. This research project was performed withinthe IMPULS perinatology framework, a collaboration between Máxima Medical Center, Eind-hoven University of Technology and Philips. As of May 2016, she works as a medical physicistin training at Radboudumc in Nijmegen.

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Publications

Jongen GJLM, van der Hout-van der Jagt MB, Oei SG, van de Vosse FN, Bovendeerd PHM.Hypoxia-induced catecholamine feedback on fetal heart rate: A mathematical model study,under review for Med Eng Phys.

Jongen GJLM, van der Hout-van der Jagt MB, Oei SG, van de Vosse FN, Bovendeerd PHM.Simulation of fetal heart rate variability with a mathematical model, under review for Med EngPhys.

Jongen GJLM, van der Hout-van der Jagt MB, van de Vosse FN, Oei SG, Bovendeerd PHM.A mathematical model to simulate the cardiotocogram during labor. Part B: Parameter es-timation and simulation of variable decelerations, J Biomech, 2016, http://dx.doi.org/10.1016/j.jbiomech.2016.01.046.

Jongen GJLM, van der Hout-van der Jagt MB, van de Vosse FN, Oei SG, Bovendeerd PHM. Amathematical model to simulate the cardiotocogram during labor. Part A: Model setup andsimulation of late decelerations, J Biomech, 2016, http://dx.doi.org/10.1016/j.jbiomech.2016.01.036.

van der Hout-van der Jagt MB, Jongen GJLM, Bovendeerd PHM, Oei SG. Insight into variablefetal heart rate decelerations from a mathematical model, Early Hum Dev, 89:361-369, 2013.

Non peer-reviewed publications

Jongen GJLM, van der Hout-van der Jagt MB, van de Vosse FN, Bovendeerd PHM, Oei SG. Derol van mathematische modellen in de kliniek: Een CTG-simulatiemodel als voorbeeld, MTIntegraal, 2016, www.mtintegraal.nl.

Jongen GJLM, van der Hout-van der Jagt MB, van de Vosse FN, Bovendeerd PHM, Oei SG. Watdoet een medisch ingenieur in het ziekenhuis?, Medisch Journaal, 44:108-112, 2015.

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About the author

Conference abstracts

Jongen GJLM, van der Hout-van der Jagt MB, van de Vosse FN, Oei SG, Bovendeerd PHM. Anew model for simulation of fetal heart rate variations during labor, oral presentation, 2nd JanBeneken Conference, Nijmegen (NL), April 23-24, 2015.

Jongen GJLM, van der Hout-van der Jagt MB, van de Vosse FN, Bovendeerd PHM, Oei SG.Computer simulation of the cardiotocogram: the e�ect of catecholamines, oral presentation,FNPS, Saint Vincent (IT), August 31 - September 3, 2014.

Jongen GJLM, van der Hout-van der Jagt MB, van de Vosse FN, Bovendeerd PHM, Oei SG.Modeling the contribution of humoral feedback to fetal heart rate responses during labor,oral presentation, SESAM 2013, Paris (FR), June 13-15, 2013.

Jongen GJLM, van der Hout-van der Jagt MB, Bullens L, Fransen AF, Oei SG. Simulation of thecirculation: Hands-on simulation & model development, workshop, SESAM 2013, Paris (FR),June 13-15, 2013.

Jongen GJLM, van der Hout-van der Jagt MB, van de Vosse FN, Bovendeerd PHM, Oei SG.Modeling the contribution of humoral feedback to fetal heart rate responses during labor,oral presentation, 1st Jan Beneken Conference, Eindhoven (NL), April 25-26, 2013.

van der Hout-van der Jagt MB, Jongen GJLM, Bullens L, Fransen AF, Oei SG. Physiologic modelsin simulation: An OB case study, workshop, IMSH 2013, Orlando (FL, USA), January 27-30, 2013.

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simulation of the cardiotocogram during labor : towards ... · simulation of the cardiotocogram...

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