gaussian modelling characteristics of peripheral arterial...

Research ArticleGaussian Modelling Characteristics of Peripheral Arterial PulseDifference between Measurements from the Three Trimesters ofHealthy Pregnancy

Kunyan Li 12 Song Zhang 1 Lin Yang 1 Hongqing Jiang 3 Dongmei Hao 1

Lei Zhang 1 and Dingchang Zheng 2

1College of Life Science and Bioengineering Beijing University of Technology Beijing 100124 China2Department of Medical Science and Public Health Faculty of Medical Science Anglia Ruskin UniversityChelmsford CM1 1SQ UK3Haidian Maternal amp Child Health Hospital Beijing 100026 China

Correspondence should be addressed to Lin Yang yanglinbjuteducn and Dingchang Zheng dingchangzhengangliaacuk

Received 25 June 2018 Accepted 4 September 2018 Published 11 October 2018

Guest Editor Yu Shang

Copyright copy 2018 Kunyan Li et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Arterial pulse wave analysis has been attempted to monitor the maternal physiological changes of circulatory system duringpregnancy is study aimed to quantify the difference of Gaussian modelling characteristics derived from radial pulses measuredfrom the three trimesters of healthy pregnant women Radial pulses were recorded from seventy pregnant women betweengestational week 11ndash13 week 20ndash22 and then week 37ndash39 ey were then normalized and decomposed into three independentGaussian waves for deriving four key modelling characteristic parameters including the peak time interval (T) and peakamplitude ratio (R) between the first and second Gaussian waves (T12 and R12) and their corresponding values between the firstand third Gaussian waves (T13 and R13) Post hoc multiple comparisons after analysis of variance was then applied to study thewithin-subject differences in Gaussian modelling characteristics between the three trimesters e key results were that T12 andT13 increased significantly (T12 128 plusmn 13 vs 132 plusmn 13 plt 005 T13 395 plusmn 43 vs 454 plusmn 51 plt 0001) and R13 decreasedsignificantly from the first to second trimester (060 plusmn 015 vs 053 plusmn 011 plt 0001) From the second to third trimester T12decreased significantly (132 plusmn 13 vs 128 plusmn 12 plt 001) and T13 and R13 decreased slightly but nonsignificantly Since larger T12and T13 and smaller R13 are associated with more compliant peripheral arteries our results indicated that peripheral arteriesbecome more compliant from the first to second trimester and then have a tendency of returning to baseline during normalpregnancy In conclusion this study has quantitatively demonstrated significant changes of Gaussian modelling characteristicsderived from radial pulses at the three trimesters of normal pregnant women suggesting that these modelling characteristics couldbe used as parameters in monitoring maternal physiological changes during normal pregnancy

1 Introduction

e maternal physiological changes of circulatory systemduring pregnancy are essential to support and protect thedevelopment of fetus [1 2] e cardiovascular system ofpregnant women adapts to the increased cardiac demandIncreased cardiac output has been observed at the early stageof pregnancy with increased stroke volume and heart rate(HR) As pregnancy progresses the increased stoke volumereaches a plateau state but HR continues to increase In

addition it has been reported that systemic vascular re-sistance decreases during normal pregnancy [3 4]

Arterial pulse wave analysis has been attempted to assessmaternal physiological changes since arterial pulses containsuseful physiological information about cardiovascular sys-tem [5ndash8] e commonly used indices include the carotid-radial pulse wave velocity (crPWV) augmentation index(AIx) or AIx at heart rate of 75min (AIx-75) derived fromcarotid arterial pulses [9ndash12] eir longitudinal changesduring normal pregnancy and their differences between

HindawiJournal of Healthcare EngineeringVolume 2018 Article ID 1308419 9 pageshttpsdoiorg10115520181308419

normotensive and hypertensive pregnant women have beenquantified [13ndash15] Although different arterial pulse waveanalysis techniques have been employed in these publishedstudies a similar conclusion has been drawn which was thatthe carotid arteries becomemore compliant at the early stageof pregnancy then return to baseline at the late stage ofpregnancy ere were also a few studies to investigate thematernal physiological changes during normal pregnancyusing peripheral arterial pulses Oyama-Kato et al andGomez et al used pulse wave velocity (PWV)measured frombrachial artery and concluded that peripheral arterialcompliance increased at the early stage of pregnancy andthen returned to baseline at late pregnancy [16 17] In orderto obtain the arterial pulse waveform characteristics thepublished studies mainly used derivatives methods emain disadvantage of using derivatives methods is that theywere quite sensitive to noise and its measurement reliabilitywas not good enough especially when there were no obvioustidal or dicrotic points on the arterial pulses [18]

In order to overcome these difficulties Gaussian mod-elling of arterial pulses has been proposed which can de-compose the arterial pulse waveform into differentindividual Gaussian waves [19] Liu et al reported that bothcarotid and radial arterial pressure pulse waveforms could beaccurately modelled using three Gaussian functions whichwere considered to be associated with forward wave the tideand dicrotic or backward waves [20] Several Gaussianmodelling characteristics including the peak amplitude thepeak time positions and half-width of Gaussian waves havebeen extracted from each Gaussian function to reflect thephysiological changes of peripheral circulatory systemRubins applied Gaussian modelling methods to simulta-neously measured finger and ear photoplethymography(PPG) pulses to evaluate the ageing effect on the Gaussianmodelling characteristics [18] e differences in Gaussianmodelling characteristics between healthy subjects and heartfailure patients and during exercise and recovery have alsobeen investigated to explore its potential clinical applications[21 22] However to the best of our knowledge there is nostudy to quantify the changes of Gaussian modellingcharacteristics during normal pregnancy

is study aimed to comprehensively quantify thechanges of Gaussian modelling characteristics derived fromradial pulses measured from the three trimesters of normalpregnancy

2 Materials and Methods

21 Subjects Seventy healthy pregnant women volunteerswith average age of 31 plusmn 4 years height of 162 plusmn 6 cm weightof 56 plusmn 4 kg and body mass index of 21 plusmn 2 kgm2 wererecruited at the Haidian Maternal and Child Health Hos-pital Beijing Pregnant women with multiple pregnanciesabnormal menstrual cycle chronic hypertension diabetesanemia and any other known diseases during pregnancywere excluded from this study

e institutional review board of Beijing University ofTechnology approved the study which was conducted incompliance with the Declaration of Helsinki After each

individual volunteer read the Participant Consent Formunderstood the purpose of this study and agreed to take partin a written informed consent was obtained Before theexperiments all the volunteers were abstained from alcoholcaffeine and any drugs

22Radial PulseMeasurement Radial pulses were measuredfrom each pregnant woman at three different stages ofnormal pregnancy the early pregnancy (the first trimesterbetween week 11ndash13) middle pregnancy (the second tri-mester between week 20ndash22) and late pregnancy (the thirdtrimester between week 37ndash39) is is referred to theguidelines of American Congress of Obstetricians andGynecologists [23] All pregnant women were required toattend the three visits for radial pulse measurements at theabove three gestational weeks

e arterial pulsemeasurements were performed in a quietclinical measurement room at the HaidianMaternal and ChildHealthHospital Beijing China During each of the three visitsall the pregnant women were firstly asked to sit on a chairquietly for five minutes to achieve stable cardiovascular statusbefore formal arterial pulse recording Resting systolic anddiastolic blood pressures (SBP and DBP) and HR were thenmeasured using a validated electronic sphygmomanometer(HEM-7124 fromOmronCrop)With the pregnant woman ina supine position a pressure sensor (MB-3) was placed on theleft wrist above the radial artery where was marked to recordanalyzable radial pulses for three minutes using a PowerLabdata collection system (ADInstrumrnts Pty Ltd PowerLab835 Bella Vista NSW 2153 Australia) at a sampling rate of1000Hz for three times Univariate ANOVA analyses showedthat there were no significant differences between the threerepeated measurements (all pgt 005) demonstrating the re-liability of this experiment erefore their average valuesfrom the three repeated measurements were calculated asreference values for each subject which were used for furtherstatistical analysis erefore there were three radial pulserecordings from each of the seventy pregnant women

23 Gaussian Modelling of Radial Pulse All the recordedradial pulses were firstly processed to remove baseline driftey were then normalized in both amplitude and widthand then decomposed into three positive Gaussian functionsfi(n) i 1 2 3 as proposed by Liu et al [20] e firstGaussian function f1(n) denotes the main wave or theforward wave the second Gaussian function f2(n) denotesthe tidal wave and the third Gaussian function f3(n) de-notes the dicrotic wave or the backward wave EachGaussian function was defined as

fi(n) Hi times eminus2 nminusNi( )

2W2i( 1113857

i 1 2 3 n 1 2 100

(1)

where Hi means the peak amplitudeNi means the peak timeposition and Wi means the half-width of each Gaussianwave as shown in Figure 1 e acquired curve as show inblack the yellow curve shows the Gaussian fitted radialwaveform ere is no significant difference between theacquired curve and fitted curve (pgt 005)

2 Journal of Healthcare Engineering

24 Determination of Gaussian Modelling Characteristics ofRadial Arterial Pulse Nine basic Gaussian modellingcharacteristics including the peak amplitude (H1 H2 H3)peak time position (N1 N2 N3) and half-width (W1 W2W3) were derived from the three Gaussian curves as shownin Figure 1 Four extended modelling characteristics werealso determined including the peak time interval (T12 T13)and amplitude ratio (R12 R13) between rst and secondGaussian waves and between the rst and third Gaussianwaves which were calculated as

T12 N2 minusN1

T13 N3 minusN1

R12 H2

H1

R13 H3

H1

(2)

25 Data and Statistical Analysis emeans plusmn SDs of bloodpressure (BP) HR and all the derived Gaussian modellingcharacteristics (H1H2H3N1N2N3W1W2W3 T12 T13R12 R13) were calculated across all the pregnant womenseparately for the three trimesters Analysis of variance andpost hoc multiple comparisons were then performed usingSPSS (Version 200 SPSS Inc Chicago IL USA) to in-vestigate the eect of the three trimesters on all the Gaussianmodelling characteristics and to compare whether therewere signicant within-subject dierences between the threetrimesters during pregnancy A plt 005 was used as thesignicant criterion

3 Results and Discussion

31 Changes of Heart Rate and Blood Pressures at reeTrimesters As shown in Table 1 HR increased signi-cantly and BPs (SBP and DBP) decreased signicantlyduring normal pregnancy (all plt 001 with the comparisons

ndash51 11 12 13 14 15 16 17

times104

0

5

10

times10ndash3 Radial pulse

(a)

0 N1 N2 N3

W3

W2

W1

N2ndashN1 N3ndashN1Normalized sampling points

Nor

mal

ized

ampl

itude

1000

H3

H1

H2

1

Normalized radial waveformFirst Guassian waveSecond Guassian wave

Third Guassian waveFitted raidal waveform

(b)

Figure 1 Demonstration of Gaussian modelling characteristics derived from orginal radial pulse waveform (a) A segment of the originalarterial pulse waveform measured by the pressure sensor (b) Gaussian modelling of a radial pulse waveform e radial pulse waveform wasdecomposed into three positive Gaussian waves as shown in red blue and green e yellow curve shows the Gaussian tted radial waveform

Journal of Healthcare Engineering 3

between the first and second trimesters and between the firstand third trimesters)

32 Gaussian Wave Peak Height and Half-Width betweenthe 3ree Trimesters Figure 2 gives one example of theGaussian modelling of a normalized radial pulse waveformat the three trimesters of a pregnant woman It illustratesthat the peak time positions of all the three Gaussian wavesmoved toward right from the first to the second trimesterand then moved backward at the third trimester e peakamplitude of third Gaussian wave decreased continuouslyat the second and third trimesters in comparison with thefirst trimester

Figure 3 shows the changes of the nine basic Gaussianmodelling characteristics at the three trimesters It can beobserved from the first Gaussian wave that its peak timeposition and half-width had a similar changing trend eysignificantly increased from the first to second trimester (N1130 plusmn 21 vs 142 plusmn 18 W1 142 plusmn 22 vs 163 plusmn 19 bothplt 0001) and then decreased slightly but nonsignificantlytowards baseline at the third trimester e peak amplitudehad a similar changing trend at the peak time position andhalf-width but there was no significant difference betweenany two trimesters (all pgt 005)

e three basic modelling characteristics from the sec-ond Gaussian wave changed in a similar pattern as thosefrom the first Gaussian wave e peak time position sig-nificantly increased from the first to second trimester (N2258 plusmn 28 vs 275 plusmn 24 plt 001) then decreased slightly butnonsignificantly towards baseline at the third trimester ehalf-width increased significantly from the first to secondtrimester (W2 266 plusmn 25 vs 281 plusmn 26 plt 001) then de-creased significantly to return to baseline from the second tothird trimester (W2 281 plusmn 26 vs 267 plusmn 32 plt 001)

Regarding the modelling characteristics from the thirdGaussian wave there were significant differences betweenthe first and second and between first and third trimestersfor the three characteristics (all plt 0001) but not betweensecond and third trimesters In detail the peak amplitudeand the half-width of the third Gaussian wave decreasedsignificantly and the peak time position increased signifi-cantly (H3 387 plusmn 78 vs 331 plusmn 58 W3 532 plusmn 46 vs 476 plusmn49N3 525 plusmn 55 vs 596 plusmn 59 all plt 0001) from the first tosecond trimester

33GaussianWavePeakTime Interval at the3reeTrimestersFigure 4 shows the Gaussian peak time interval derived fromthe three Gaussian waves of the radial pulses measured at thethree trimesters of healthy pregnant women e peak timeinterval (T12) between the first and second Gaussian wavesincreased significantly from the first to second trimester(128 plusmn 13 vs 132 plusmn 13 plt 005) and then decreasedsignificantly from the second to third trimester (132 plusmn 13 vs128 plusmn 12 plt 001) e peak time interval between the firstand third Gaussian waves (T13) also increased significantly(395 plusmn 43 vs 454 plusmn 51 plt 0001) and then decreasedslightly at the third trimester to return to the baseline

34 Gaussian Wave Amplitude Ratio at the 3ree TrimestersFigure 5 shows the Gaussian amplitude ratio derived fromthe three Gaussian waves of the radial pulses measured at thethree trimesters of healthy pregnant women e significantfinding is that the amplitude ratio (R13) between the first andthird Gaussian waves decreased significantly from the first tosecond trimester (060 plusmn 015 vs 053 plusmn 011 plt 0001) andthen kept a stable level until the third trimester

4 Discussion

In this study Gaussian modelling characteristics derivedfrom normalized radial pulses have been quantified andcompared between the three trimesters during normalpregnancy To the best of our knowledge this is the firststudy to comprehensively investigate the peripheral arterialpulse waveform changes during normal pregnancy usingGaussian modelling approach

e first observation of this study with regard to thematernal HR and BPs changes during pregnancy agreed withpublished studies [24 25] HR increased significantly andBPs decreased significantly from the first to second trimesterof normal healthy pregnancy However it is noted that it isinappropriate to use the automatic BP monitor to measureBPs in pregnant women for clinical diagnosis

e key results of this study were about the arterial pulsewaveform changes during normal pregnancy It is knownthat the arterial pulse waveform is a composite of the for-ward wave and reflects waves from periphery and that theforward wave or the first Gaussian wave is associated withthe ventricular contraction [26] During pregnancy an in-crease in oxygen and nutrients demand requires increasedcardiac function of pregnant women including cardiacoutput HR and stroke volume [1 27 28] is has beenevidenced in the study with increased peak time position andthe half-width of the first Gaussian wave from the first tosecond trimester during normal pregnancy

e second and third Gaussian waves are associated withthe reflection from the periphery mainly at branch pointswhich can be used to quantify the properties of the pe-ripheral arteries [29] Some published studies have reportedthat the vascular resistance of peripheral arteries decreasesduring normal pregnancy [30 31] e previous study re-ported how arterial pulse waveform characteristics changedwith lower peripheral resistance where a narrow and highmain wave unnoticeable tidal wave highlighted dicroticwave and decreased PWV were observed [32] e de-creased PWV causes the tidal or dicrotic waves to movebackward further resulting in increased N2 and N3 [22] Inthis study N2 and N3 increased at early pregnancy and then

Table 1 Means plusmn SDs of heart rate and blood pressures measuredat the three trimesters of normal pregnancy

Trimesters HR (beatsmin) SBP (mmHg) DBP (mmHg)First 85 plusmn 12 115 plusmn 10 73 plusmn 9Second 93 plusmn 11lowastlowast 111 plusmn 8lowastlowast 70 plusmn 7lowastlowastird 94 plusmn 13lowastlowast 109 plusmn 11lowastlowast 69 plusmn 9lowastlowastlowastlowastplt 001 in comparison with the first trimester


Normalized sampling points

00 20 40 60 80 100

02040608

1

Nor

mal

ized

ampl

itude

e first trimester

Normalized radial pulse waveform

Second Gaussian waveFirst Gaussian wave

ird Gaussian wave

(a)


Nor

mal

ized

ampl

itude

e second trimester

Normalized radial pulse waveformFirst Gaussian waveSecond Gaussian waveird Gaussian wave

00 20 40 60 80 100

02040608

1

(b)


Nor

mal

ized

ampl

itude

e third trimester


00

02040608

1

20 40 60 80 100

(c)

Figure 2 Illustration of Gaussian modelling of normalized radial pulse waveform at the rst (a) second (b) and third (c) trimesters ofa pregnant woman e three Gaussian waves are shown in red blue and green e arrows show the changes of Gaussian peak timeposition and peak amplitude

Peak

ampl

itude

50

60

70

80

90

First gaussian wave

1 2 3Trimesters

(a)

Peak

ampl

itude

50

60

70

80

90

Second gaussian wave

1 2 3Trimesters

(b)

20

30

40

50

60

Peak

ampl

itude

ird gaussian wave

1 2 3

lowastlowast

lowastlowast

Trimesters

(c)

Peak

pos

ition

0

10

20

30

1 2 3

lowastlowast

lowastlowast

Trimesters

First gaussian wave

(d)

Peak

pos

ition

10

20

30

40

1 2 3

lowastlowast

lowastlowast

Trimesters


(e)

40

50

60

70

Peak

pos

ition

1 2 3

lowastlowast

lowastlowast

Trimesters

ird gaussian wave

(f )

Figure 3 Continued


returned towards baseline is agreed with Oyama et alrsquosstudy where it has been reported that the peripheral re-sistance was reduced firstly and then enhanced duringnormal pregnancy [16] It merits further evaluation of thesignificance of these three constituent waves and themechanisms that act on them is could provide evidencethat these differences are justified during pregnancy

It has been explained in the previous studies that thepeak time intervals T12 and T13 between different Gaussian

waves are associated with the compliance of peripheralarteries [19] It has also been reported that the amplituderatios R12 and R13 are related to the AI and reflection index(RI) of peripheral arterial pulses which are two arterial pulsewaveform indices commonly used to quantify peripheralarterial stiffness [18 19 33 34] In general the larger the T12and T13 are or the lower the R13 are more compliant theperipheral arteries is [19] e stiffness of carotid arteries ofpregnant women has been studied during normal pregnancy

15

10

Hal

f-wid

th

15

20

25

2 3

lowastlowast

lowastlowast

Trimesters

First gaussian wave

(g)

15

20

25

30

35

Hal

f-wid

th1 2 3

lowastlowast lowastlowast

Trimesters


(h)

40

45

50

55

60

Hal

f-wid

th

1 2 3

lowastlowast

lowastlowast

Trimesters

ird gaussian wave

(i)

Figure 3 Gaussian modelling characteristics of the radial pulse measured at the three trimesters of healthy pregnant womeneir means plusmnSDs are given (andashc) show peak amplitude changes of the first second and third Gaussian waves (H1 H2 H3) at the three trimesters (dndashf)show changes of peak time position of the first second and third Gaussian waves (N1N2N3) at the three trimesters (gndashi) shows changes ofhalf-width of the first second and third Gaussian waves (W1 W2 W3) at the three trimesters lowastlowast represents plt 001

0

1 2 3

5

Peak

tim

e int

erva

l

10

15

20

25

Between 1st and 2ndguassian wave

Trimesters

lowast lowastlowast

(a)

Peak

tim

e int

erva

l

Trimesters

Between 1st and 3rdguassian wave

30

1 2 3

35

40

45

50

55lowastlowast

lowastlowast

(b)

Figure 4 Peak time interval derived from the three Gaussian waves of the radial pulses measured at the three trimesters of healthy pregnantwomen eir means plusmn SDs are given (a) Changes of peak time interval between first and second Gaussian waves at the three trimesters (b)Changes of peak time interval between first and third Gaussian waves at the three trimesters lowast represents plt 005 and lowastlowast represents plt 001


using other measurement techniques including PWV wherethey concluded that arterial compliance of carotid arteriesincreased significantly from the first to the second trimesterand then decreased toward baseline at the third trimester[16 35] Similar findings have been observed in this studywith increased peak time intervals T12 and T13 and de-creased amplitude ratios R12 and R13 from the first to thesecond trimester of normal pregnancy indicating thatmaternal peripheral arterial compliance increases from theearly to middle stage of pregnancy

It is also noted that from the second to third trimesterthe Gaussian modelling characteristics of peripheral arte-rial pulses had a tendency of returning towards baselinevalues although these changes were not significant for themajority of Gaussian modelling characteristics in thisstudy Our results were different from those significantchanges of cfPWV and AIx derived from aortic reportedbetween the second the third trimesters [13 16 36 37]ese studies demonstrated that indexes derived fromcentral arteries significantly change between the secondand third trimesters Khalil et al and Fujime et al reportedthat central aortic AIx-75 decreased firstly and reacheda nadir at the middle phase of pregnancy then significantlyincreased at the late stage of pregnancy [13 36] indicatingthat the aortic elasticity becomes better and then worseduring normal pregnancy Similar changing pattern in bothcarotid PWV and brachial-ankle PWV was also observedduring normal pregnancy by Yuan et al and Oyama-Katoet al [16 37] is could be partially explained by thedifferent indices used from different techniques or thedifferent measurement sites along the arterial trees or thedifferent comparisons between different gestational weekserefore a comprehensive investigation to understand

the different changes of these indirect measurementsof arterial stiffness at late stage of pregnancy should beconducted in future studies

ere were some limitations to this study First eventhough the same trained operator have been used during thewhole experiments the contact pressure still is difficult tocontrol Pulse contour could be affected Moreover the wavepropagation could be related to heart rate and bloodpressure However it is worth further investigating how thechanges in heart rate and blood pressure influence theGaussian modelling parameters

5 Conclusions

In conclusion this study has quantitatively demonstratedsignificant changes of Gaussian modelling characteristicsderived from radial pulses at the three trimesters of normalpregnant women is indicates that peripheral arteriesbecome more compliant from the first to second trimesterand then have a tendency of returning to baseline duringnormal pregnancy and suggests that these modellingcharacteristics could be used as parameters in monitoringmaternal physiological changes during normal pregnancy

Data Availability

All data used to support the finding of this study are availablefrom the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

05

1 2Trimesters

3

07

09Am

plitu

de ra

tio

11

13

15


(a)

Trimesters

Am

plitu

de ra

tio

00

02

04

06

08

10

1 2 3


lowastlowast

lowastlowast

(b)

Figure 5 Gaussian amplitude ratio derived from the three Gaussian waves of the radial pulses measured at the three trimesters eirmeans plusmn SDs are given (a) Changes of amplitude ratio between first and second Gaussian waves at the three trimesters (b) Changes ofamplitude ratio between first and third Gaussian wave at the three trimesters lowastlowast represents plt 001


Acknowledgments

is study was supported by the International Program forGraduate Students of Beijing University of Technology eresearch was supported by Intelligent Physiological Mea-surement and Clinical Translation Beijing InternationalBase of Scientific and Technological Cooperation

References

[1] S Datta B S Kodali and S Segal ldquoMaternal physiologicalchanges during pregnancy labor and the postpartum periodrdquoin Obstetric Anesthesia Handbook pp 1ndash14 5th edition 2010

[2] R Bedson and A Riccoboni ldquoPhysiology of pregnancyclinical anaesthetic implicationsrdquo Continuing Education inAnaesthesia Critical Care and Pain vol 14 no 2 pp 69ndash722014

[3] P P Soma P C Nelson H Tolppanen and A MebazaaldquoPhysiological changes in pregnancyrdquo Cardiovascular Journalof Africa vol 27 no 2 pp 89ndash94 2016

[4] A Carlin and Z Alfirevic ldquoPhysiological changes of preg-nancy and monitoringrdquo Best Practice and Research ClinicalObstetrics and Gynaecology vol 22 no 5 pp 801ndash823 2008

[5] L M Macedo D D Luminoso M M SavvidouH C McEniery and H K Nicolaides ldquoMaternal wave re-flections and arterial stiffness in normal pregnancy as assessedby applanation tonometryrdquo Hypertension vol 51 no 4pp 1047ndash1051 2008

[6] M Spasojevic S Smith and J Morris ldquoPeripheral arterialpulse wave analysis in women with pre-eclampsia and ges-tational hypertensionrdquo An International Journal of ObstetricsGynaecology vol 112 no 11 pp 1475ndash1478 2005

[7] A Mahendru T R Everett G A Hackett C M McEnieryI B Wilkinson and C Lees ldquoEarly pregnancy changes inmaternal haemodynamics using pulse wave analysis oralcommunication abstractsrdquo Ultrasound in Obstetrics andGynecology vol 38 no 1 p 18 2011

[8] M B Franz M Burgmann A Neubauer et al ldquoAugmen-tation index and pulse wave velocity in normotensive and pre-eclamptic pregnanciesrdquo Acta Obstetricia et GynecologicaScandinavica vol 92 no 8 pp 960ndash966 2013

[9] D M Carty U Neisius L K Rooney A F Dominiczak andC Delles ldquoPulse wave analysis for the prediction of pre-eclampsiardquo Journal of Human Hypertension vol 28 no 2p 98 2013

[10] B Avni G Frenkel L Shahar A Golik D Sherman andV Dishy ldquoAortic stiffness in normal and hypertensivepregnancyrdquo Blood Pressure vol 19 no 1 pp 11ndash15 2009

[11] K Irene S Kostas P Ioannis et al ldquoe use of pulse wavevelocity in predicting pre-eclampsia in high-risk womenrdquoHypertension Research vol 37 no 8 pp 733ndash740 2014

[12] M Rnnback K Lampinen P H Groop and R Kaaja ldquoPulsewave reflection in currently and previously preeclampticwomenrdquo Hypertension in Pregnancy vol 24 no 2 pp 171ndash180 2005

[13] A Khalil E Jauniaux D Cooper and K Harrington ldquoPulsewave analysis in normal pregnancy a prospective longitudinalstudy (pulse wave in pregnancy)rdquo PLoS ONE vol 4 no 7Article ID e6134 2009

[14] J Torrado I Farro F Farro et al ldquoCarotid-radial pulse wavevelocity as an alternative tool for the evaluation of endothelialfunction during pregnancy potential role in identifyinghypertensive disorders of pregnancyrdquo in Proceedings of

Conference on the IEEE Engineering in Medicine and BiologySociety San Diego CA USA August 2012

[15] D C Ghossein A Khalil C Lees et al ldquoLongitudinal study ofvascular structure and function during normal pregnancyrdquoUltrasound in Obstetrics and Gynaecology vol 49 no 1pp 46ndash53 2017

[16] M Oyama-Kato M Ohmichi K Takahashi et al ldquoChange inpulse wave velocity throughout normal pregnancy and itsvalue in predicting pregnancy-induced hypertension a lon-gitudinal studyrdquo America Journal of Obstetrics and Gyne-cology vol 195 no 2 pp 464ndash469 2006

[17] Y H Gomez Z Hudda N Mahdi et al ldquoPulse pressureamplification and arterial stiffness in low-risk uncomplicatedpregnanciesrdquo Angiology vol 67 no 4 pp 375ndash383 2016

[18] U Rubins ldquoFinger and ear photoplethysmogram waveformanalysis by fitting with Gaussiansrdquo Medical and BiologicalEngineering and Computing vol 46 no 12 pp 1271ndash12762008

[19] R Couceiro P Carvalho R P Paiva et al ldquoAssessment ofcardiovascular function from Multi-Gaussian fitting of a fin-ger photoplethysmogramrdquo Physiological Measurementvol 36 no 9 pp 1801ndash1825 2015

[20] C Liu T Zhuang L Zhao et al ldquoModelling arterial pressurewaveforms using Gaussian functions and two-stage particleswarm optimizerrdquo BioMed Research Internetional vol 2014Article ID 923260 10 pages 2014

[21] C Liu D Zheng L Zhao and C Liu ldquoGaussian fitting forcarotid and radial artery pressure waveforms comparisonbetween normal subjects and heart failure patientsrdquo Bio-Medical Materials and Engineering vol 24 no 1 pp 271ndash277 2014

[22] A Wang L Yang W Wen S Zhang G Gu and D ZhengldquoGaussian modelling characteristics changes derived fromfinger photoplethysmographic pulses during exercise andrecoveryrdquo Microvascular Research vol 116 pp 20ndash25 2018

[23] K Tunon S H Eik P Grottum D V Von and J A KahnldquoGestational age in pregnancies conceived after in vitro fer-tilization a comparison between age assessed from oocyteretrieval crown-rump length and biparietal diameterrdquo Ul-trasound in Obstetrics and Gynecology vol 15 no 1 pp 41ndash462000

[24] A Mahendru T Everett C M McEniery I Wilkinson andC Lees ldquoMaternal cardiovascular function longitudinalchanges prior to and in pregnancyrdquo Archives of Disease inChildood-Fetal and Neonatal Edition vol 97 no 1pp A30ndashA31 2012

[25] T Ghi M Kuleva A Youssef et al ldquoMaternal cardiacfunction in complicated twin pregnancy a longitudinalstudyrdquoUltrasound in Obstetrics and Gynecology vol 38 no 5pp 581ndash585 2011

[26] C Liu D Zheng A Murray and C Liu ldquoModelling carotidand radial artery pulse pressure waveforms by curve fittingwith Gaussian functionsrdquo Biomedical Signal Processing andControl vol 8 no 5 pp 449ndash454 2013

[27] T G Hennessy D Macdonald M S Hennessy et al ldquoSerialchanges in cardiac output during normal pregnancya Doppler ultrasound studyrdquo European Journal of Obstetricsand Gynecology vol 70 no 2 pp 117ndash122 1996

[28] A Vanoppen R Stigter and H Bruinse ldquoCardiac output innormal pregnancy a critical reviewrdquo Obstetetrics and Gy-necology vol 87 no 2 pp 310ndash318 1996

[29] R Couceiro P Carvalho R P Paiva et al ldquoMulti-Gaussianfitting for the assessment of left ventricular ejection timefrom the Photoplethysmogramrdquo in Proceedings of Conference


on the IEEE Engineering in Medicine and Biology Society SanDiego CA USA August 2012

[30] B Schiessl C J Strasburger M Spannagl and F KainerldquoDecreasing peripheral resistance during pregnancy moni-tored at the cubital arteryrdquo European Journal of ClinicalInvestigation vol 33 no 4 pp 346ndash351 2003

[31] J R Sowers M B Zemel M FWalsh et al ldquoEffects of normalpregnancy on cellular cation metabolism and peripheralvascular resistancerdquo American Journal of Hypertension vol 3no 1 pp 16ndash22 1990

[32] B Kingwell K Berry J Cameron G Jennings and A DartldquoArterial compliance increases after moderate-intensity cy-clingrdquo American Jornal Physiology vol 273 no 5pp h2186ndashh2191 1997

[33] L S Lim L H Ling C M Cheung et al ldquoRelationship ofsystemic endothelial function and peripheral arterial stiffnesswith diabetic retinopathyrdquo British Journal of Ophthalmologyvol 99 no 6 pp 837ndash841 2015

[34] S Wallbergjonsson K Caidahl N Klintland G Nyberg andS Rantapaadahlqvist ldquoIncreased arterial stiffness and in-dication of endothelial dysfunction in longstanding rheu-matoid arthritisrdquo Scandinavian Journal of Rheumatologyvol 37 no 1 pp 1ndash5 2008

[35] S Rang L B Pablo J Vleugels G Montfrans K Wesselingand H Wolf ldquoChanges in aortic stiffness during normalpregnancy determined from pulse wave velocityrdquo AmericanJournal of Obstetetrics and Gynecology vol 185 no 6 p S2272001

[36] M Fujime T Tomimatsu Y Okaue et al ldquoCentral aorticblood pressure and augmentation index during normalpregnancyrdquo Hypertens Res vol 35 no 6 pp 633ndash638 2012

[37] L J Yuan D Xue Y Y Duan T S Cao and N ZhouldquoMaternal carotid remodeling and increased carotid arterialstiffness in normal late-gestational pregnancy as assessed byradio-frequency ultrasound techniquerdquo BMC Pregnancy andChildbirth vol 13 no 1 p 122 2013


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normotensive and hypertensive pregnant women have beenquantified [13ndash15] Although different arterial pulse waveanalysis techniques have been employed in these publishedstudies a similar conclusion has been drawn which was thatthe carotid arteries becomemore compliant at the early stageof pregnancy then return to baseline at the late stage ofpregnancy ere were also a few studies to investigate thematernal physiological changes during normal pregnancyusing peripheral arterial pulses Oyama-Kato et al andGomez et al used pulse wave velocity (PWV)measured frombrachial artery and concluded that peripheral arterialcompliance increased at the early stage of pregnancy andthen returned to baseline at late pregnancy [16 17] In orderto obtain the arterial pulse waveform characteristics thepublished studies mainly used derivatives methods emain disadvantage of using derivatives methods is that theywere quite sensitive to noise and its measurement reliabilitywas not good enough especially when there were no obvioustidal or dicrotic points on the arterial pulses [18]

In order to overcome these difficulties Gaussian mod-elling of arterial pulses has been proposed which can de-compose the arterial pulse waveform into differentindividual Gaussian waves [19] Liu et al reported that bothcarotid and radial arterial pressure pulse waveforms could beaccurately modelled using three Gaussian functions whichwere considered to be associated with forward wave the tideand dicrotic or backward waves [20] Several Gaussianmodelling characteristics including the peak amplitude thepeak time positions and half-width of Gaussian waves havebeen extracted from each Gaussian function to reflect thephysiological changes of peripheral circulatory systemRubins applied Gaussian modelling methods to simulta-neously measured finger and ear photoplethymography(PPG) pulses to evaluate the ageing effect on the Gaussianmodelling characteristics [18] e differences in Gaussianmodelling characteristics between healthy subjects and heartfailure patients and during exercise and recovery have alsobeen investigated to explore its potential clinical applications[21 22] However to the best of our knowledge there is nostudy to quantify the changes of Gaussian modellingcharacteristics during normal pregnancy

is study aimed to comprehensively quantify thechanges of Gaussian modelling characteristics derived fromradial pulses measured from the three trimesters of normalpregnancy

2 Materials and Methods

21 Subjects Seventy healthy pregnant women volunteerswith average age of 31 plusmn 4 years height of 162 plusmn 6 cm weightof 56 plusmn 4 kg and body mass index of 21 plusmn 2 kgm2 wererecruited at the Haidian Maternal and Child Health Hos-pital Beijing Pregnant women with multiple pregnanciesabnormal menstrual cycle chronic hypertension diabetesanemia and any other known diseases during pregnancywere excluded from this study

e institutional review board of Beijing University ofTechnology approved the study which was conducted incompliance with the Declaration of Helsinki After each

individual volunteer read the Participant Consent Formunderstood the purpose of this study and agreed to take partin a written informed consent was obtained Before theexperiments all the volunteers were abstained from alcoholcaffeine and any drugs

22Radial PulseMeasurement Radial pulses were measuredfrom each pregnant woman at three different stages ofnormal pregnancy the early pregnancy (the first trimesterbetween week 11ndash13) middle pregnancy (the second tri-mester between week 20ndash22) and late pregnancy (the thirdtrimester between week 37ndash39) is is referred to theguidelines of American Congress of Obstetricians andGynecologists [23] All pregnant women were required toattend the three visits for radial pulse measurements at theabove three gestational weeks

e arterial pulsemeasurements were performed in a quietclinical measurement room at the HaidianMaternal and ChildHealthHospital Beijing China During each of the three visitsall the pregnant women were firstly asked to sit on a chairquietly for five minutes to achieve stable cardiovascular statusbefore formal arterial pulse recording Resting systolic anddiastolic blood pressures (SBP and DBP) and HR were thenmeasured using a validated electronic sphygmomanometer(HEM-7124 fromOmronCrop)With the pregnant woman ina supine position a pressure sensor (MB-3) was placed on theleft wrist above the radial artery where was marked to recordanalyzable radial pulses for three minutes using a PowerLabdata collection system (ADInstrumrnts Pty Ltd PowerLab835 Bella Vista NSW 2153 Australia) at a sampling rate of1000Hz for three times Univariate ANOVA analyses showedthat there were no significant differences between the threerepeated measurements (all pgt 005) demonstrating the re-liability of this experiment erefore their average valuesfrom the three repeated measurements were calculated asreference values for each subject which were used for furtherstatistical analysis erefore there were three radial pulserecordings from each of the seventy pregnant women

23 Gaussian Modelling of Radial Pulse All the recordedradial pulses were firstly processed to remove baseline driftey were then normalized in both amplitude and widthand then decomposed into three positive Gaussian functionsfi(n) i 1 2 3 as proposed by Liu et al [20] e firstGaussian function f1(n) denotes the main wave or theforward wave the second Gaussian function f2(n) denotesthe tidal wave and the third Gaussian function f3(n) de-notes the dicrotic wave or the backward wave EachGaussian function was defined as

fi(n) Hi times eminus2 nminusNi( )

2W2i( 1113857

i 1 2 3 n 1 2 100

(1)

where Hi means the peak amplitudeNi means the peak timeposition and Wi means the half-width of each Gaussianwave as shown in Figure 1 e acquired curve as show inblack the yellow curve shows the Gaussian fitted radialwaveform ere is no significant difference between theacquired curve and fitted curve (pgt 005)



T12 N2 minusN1

T13 N3 minusN1

R12 H2

H1

R13 H3

H1

(2)




ndash51 11 12 13 14 15 16 17

times104

0

5

10


(a)

0 N1 N2 N3

W3

W2

W1


Nor

mal

ized

ampl

itude

1000

H3

H1

H2

1



(b)










4 Discussion









00 20 40 60 80 100

02040608

1

Nor

mal

ized

ampl

itude

e first trimester



ird Gaussian wave

(a)


Nor

mal

ized

ampl

itude

e second trimester


00 20 40 60 80 100

02040608

1

(b)


Nor

mal

ized

ampl

itude

e third trimester


00

02040608

1

20 40 60 80 100

(c)


Peak

ampl

itude

50

60

70

80

90

First gaussian wave

1 2 3Trimesters

(a)

Peak

ampl

itude

50

60

70

80

90


1 2 3Trimesters

(b)

20

30

40

50

60

Peak

ampl

itude

ird gaussian wave

1 2 3

lowastlowast

lowastlowast

Trimesters

(c)

Peak

pos

ition

0

10

20

30

1 2 3

lowastlowast

lowastlowast

Trimesters

First gaussian wave

(d)

Peak

pos

ition

10

20

30

40

1 2 3

lowastlowast

lowastlowast

Trimesters


(e)

40

50

60

70

Peak

pos

ition

1 2 3

lowastlowast

lowastlowast

Trimesters

ird gaussian wave

(f )

Figure 3 Continued





15

10

Hal

f-wid

th

15

20

25

2 3

lowastlowast

lowastlowast

Trimesters

First gaussian wave

(g)

15

20

25

30

35

Hal

f-wid

th1 2 3


Trimesters


(h)

40

45

50

55

60

Hal

f-wid

th

1 2 3

lowastlowast

lowastlowast

Trimesters

ird gaussian wave

(i)


0

1 2 3

5

Peak

tim

e int

erva

l

10

15

20

25


Trimesters

lowast lowastlowast

(a)

Peak

tim

e int

erva

l

Trimesters


30

1 2 3

35

40

45

50

55lowastlowast

lowastlowast

(b)







5 Conclusions


Data Availability




05

1 2Trimesters

3

07

09Am

plitu

de ra

tio

11

13

15


(a)

Trimesters

Am

plitu

de ra

tio

00

02

04

06

08

10

1 2 3


lowastlowast

lowastlowast

(b)



Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



T12 N2 minusN1

T13 N3 minusN1

R12 H2

H1

R13 H3

H1

(2)




ndash51 11 12 13 14 15 16 17

times104

0

5

10


(a)

0 N1 N2 N3

W3

W2

W1


Nor

mal

ized

ampl

itude

1000

H3

H1

H2

1



(b)










4 Discussion









00 20 40 60 80 100

02040608

1

Nor

mal

ized

ampl

itude

e first trimester



ird Gaussian wave

(a)


Nor

mal

ized

ampl

itude

e second trimester


00 20 40 60 80 100

02040608

1

(b)


Nor

mal

ized

ampl

itude

e third trimester


00

02040608

1

20 40 60 80 100

(c)


Peak

ampl

itude

50

60

70

80

90

First gaussian wave

1 2 3Trimesters

(a)

Peak

ampl

itude

50

60

70

80

90


1 2 3Trimesters

(b)

20

30

40

50

60

Peak

ampl

itude

ird gaussian wave

1 2 3

lowastlowast

lowastlowast

Trimesters

(c)

Peak

pos

ition

0

10

20

30

1 2 3

lowastlowast

lowastlowast

Trimesters

First gaussian wave

(d)

Peak

pos

ition

10

20

30

40

1 2 3

lowastlowast

lowastlowast

Trimesters


(e)

40

50

60

70

Peak

pos

ition

1 2 3

lowastlowast

lowastlowast

Trimesters

ird gaussian wave

(f )

Figure 3 Continued





15

10

Hal

f-wid

th

15

20

25

2 3

lowastlowast

lowastlowast

Trimesters

First gaussian wave

(g)

15

20

25

30

35

Hal

f-wid

th1 2 3


Trimesters


(h)

40

45

50

55

60

Hal

f-wid

th

1 2 3

lowastlowast

lowastlowast

Trimesters

ird gaussian wave

(i)


0

1 2 3

5

Peak

tim

e int

erva

l

10

15

20

25


Trimesters

lowast lowastlowast

(a)

Peak

tim

e int

erva

l

Trimesters


30

1 2 3

35

40

45

50

55lowastlowast

lowastlowast

(b)







5 Conclusions


Data Availability




05

1 2Trimesters

3

07

09Am

plitu

de ra

tio

11

13

15


(a)

Trimesters

Am

plitu

de ra

tio

00

02

04

06

08

10

1 2 3


lowastlowast

lowastlowast

(b)



Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









4 Discussion









00 20 40 60 80 100

02040608

1

Nor

mal

ized

ampl

itude

e first trimester



ird Gaussian wave

(a)


Nor

mal

ized

ampl

itude

e second trimester


00 20 40 60 80 100

02040608

1

(b)


Nor

mal

ized

ampl

itude

e third trimester


00

02040608

1

20 40 60 80 100

(c)


Peak

ampl

itude

50

60

70

80

90

First gaussian wave

1 2 3Trimesters

(a)

Peak

ampl

itude

50

60

70

80

90


1 2 3Trimesters

(b)

20

30

40

50

60

Peak

ampl

itude

ird gaussian wave

1 2 3

lowastlowast

lowastlowast

Trimesters

(c)

Peak

pos

ition

0

10

20

30

1 2 3

lowastlowast

lowastlowast

Trimesters

First gaussian wave

(d)

Peak

pos

ition

10

20

30

40

1 2 3

lowastlowast

lowastlowast

Trimesters


(e)

40

50

60

70

Peak

pos

ition

1 2 3

lowastlowast

lowastlowast

Trimesters

ird gaussian wave

(f )

Figure 3 Continued





15

10

Hal

f-wid

th

15

20

25

2 3

lowastlowast

lowastlowast

Trimesters

First gaussian wave

(g)

15

20

25

30

35

Hal

f-wid

th1 2 3


Trimesters


(h)

40

45

50

55

60

Hal

f-wid

th

1 2 3

lowastlowast

lowastlowast

Trimesters

ird gaussian wave

(i)


0

1 2 3

5

Peak

tim

e int

erva

l

10

15

20

25


Trimesters

lowast lowastlowast

(a)

Peak

tim

e int

erva

l

Trimesters


30

1 2 3

35

40

45

50

55lowastlowast

lowastlowast

(b)







5 Conclusions


Data Availability




05

1 2Trimesters

3

07

09Am

plitu

de ra

tio

11

13

15


(a)

Trimesters

Am

plitu

de ra

tio

00

02

04

06

08

10

1 2 3


lowastlowast

lowastlowast

(b)



Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



00 20 40 60 80 100

02040608

1

Nor

mal

ized

ampl

itude

e first trimester



ird Gaussian wave

(a)


Nor

mal

ized

ampl

itude

e second trimester


00 20 40 60 80 100

02040608

1

(b)


Nor

mal

ized

ampl

itude

e third trimester


00

02040608

1

20 40 60 80 100

(c)


Peak

ampl

itude

50

60

70

80

90

First gaussian wave

1 2 3Trimesters

(a)

Peak

ampl

itude

50

60

70

80

90


1 2 3Trimesters

(b)

20

30

40

50

60

Peak

ampl

itude

ird gaussian wave

1 2 3

lowastlowast

lowastlowast

Trimesters

(c)

Peak

pos

ition

0

10

20

30

1 2 3

lowastlowast

lowastlowast

Trimesters

First gaussian wave

(d)

Peak

pos

ition

10

20

30

40

1 2 3

lowastlowast

lowastlowast

Trimesters


(e)

40

50

60

70

Peak

pos

ition

1 2 3

lowastlowast

lowastlowast

Trimesters

ird gaussian wave

(f )

Figure 3 Continued





15

10

Hal

f-wid

th

15

20

25

2 3

lowastlowast

lowastlowast

Trimesters

First gaussian wave

(g)

15

20

25

30

35

Hal

f-wid

th1 2 3


Trimesters


(h)

40

45

50

55

60

Hal

f-wid

th

1 2 3

lowastlowast

lowastlowast

Trimesters

ird gaussian wave

(i)


0

1 2 3

5

Peak

tim

e int

erva

l

10

15

20

25


Trimesters

lowast lowastlowast

(a)

Peak

tim

e int

erva

l

Trimesters


30

1 2 3

35

40

45

50

55lowastlowast

lowastlowast

(b)







5 Conclusions


Data Availability




05

1 2Trimesters

3

07

09Am

plitu

de ra

tio

11

13

15


(a)

Trimesters

Am

plitu

de ra

tio

00

02

04

06

08

10

1 2 3


lowastlowast

lowastlowast

(b)



Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





15

10

Hal

f-wid

th

15

20

25

2 3

lowastlowast

lowastlowast

Trimesters

First gaussian wave

(g)

15

20

25

30

35

Hal

f-wid

th1 2 3


Trimesters


(h)

40

45

50

55

60

Hal

f-wid

th

1 2 3

lowastlowast

lowastlowast

Trimesters

ird gaussian wave

(i)


0

1 2 3

5

Peak

tim

e int

erva

l

10

15

20

25


Trimesters

lowast lowastlowast

(a)

Peak

tim

e int

erva

l

Trimesters


30

1 2 3

35

40

45

50

55lowastlowast

lowastlowast

(b)







5 Conclusions


Data Availability




05

1 2Trimesters

3

07

09Am

plitu

de ra

tio

11

13

15


(a)

Trimesters

Am

plitu

de ra

tio

00

02

04

06

08

10

1 2 3


lowastlowast

lowastlowast

(b)



Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






5 Conclusions


Data Availability




05

1 2Trimesters

3

07

09Am

plitu

de ra

tio

11

13

15


(a)

Trimesters

Am

plitu

de ra

tio

00

02

04

06

08

10

1 2 3


lowastlowast

lowastlowast

(b)



Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia














RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


gaussian modelling characteristics of peripheral arterial...

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