physics of blood ow in arteries and its relation to intra-luminal ... - …640492/... ·...

Physics of blood flow in arteries and itsrelation to intra-luminal thrombus and

atherosclerosis

Jacopo Biasetti

Doctoral thesis no. 84, 2013KTH School of Engineering Sciences

Department of Solid Mechanics - vascuMECHKTH Royal Institute of TechnologySE-100 44 Stockholm, Sweden

TRITA HFL-0546

ISSN 1104-6813

ISRN KTH/HFL/R-13/14-SE

ISBN 978-91-7501-836-2

Akademisk avhandling som med tillstand av Kungliga Tekniska Hogskolan i Stockholmframlagges till offentlig granskning for avlaggande av teknisk doktorsexamen torsdag den 22augusti kl. 10.00 i sal F3, Kungliga Tekniska Hogskolan, Lindstedtsvagen 26, Stockholm.

Abstract

Vascular pathologies such as Abdominal Aortic Aneurysm (AAA) and atherosclerosis are

complex vascular diseases involving biological, mechanical, and fluid-dynamical factors. This

thesis follows a multidisciplinary approach and presents an integrated fluid-chemical theory

of ILT growth and analyzes the shear-induced migration of red blood cells (RBCs) in large

arteries with respect to hypoxia and its possible role in atherosclerosis. The concept of

Vortical Structures (VSs) is employed, with which a theory of fluid-chemically-driven ILT

growth is formulated. The theory proposes that VSs play an important role in convecting and

activating platelets in the aneurysmatic bulge. In particular, platelets are convected toward

the distal aneurysm region inside vortex cores and are activated via a combination of high

residence times and relatively high shear stress at the vortex boundary. After vortex break-

up, platelets are free to adhere to the thrombogenic wall surface. VSs also convect thrombin,

a potent procoagulant enzyme, captured in their core, through the aneurysmatic lumen and

force its accumulation in the distal portion of the AAA. This framework is in line with the

clinical observation that the thickest ILT is usually seen in the distal AAA region. The

investigation of the fluid-dynamics in arteries led to the study of the shear-induced migration

of RBCs in large vessels such as the abdominal aorta and the carotid artery. Marked RBCs

migration is observed in the region of the carotid sinus and in the iliac arteries, regions prone

to atherogenesis. This leads to the hypothesis that oxyhemoglobin availability can decrease in

the near-wall region thus contributing to wall hypoxia, a factor implicated in atherosclerosis.

The thesis proposes a new potential mechanism of ILT growth, driven by fluid and chemical

stimuli, which can be used to study ILT progression over physiologically relevant timeframes

and be used as a framework to test new hypotheses; the thesis also provides new insights on

the oxyhemoglobin availability in the near-wall region with direct influence on atherosclerosis.

Sammanfattning

Patologier sasom bukaortaaneurysm och aderforkalkning ar komplexa vaskulara sjukdomar

som involverar biologiska, mekaniska och stromningsmekaniska faktorer. Denna avhandling

foljer ett multidisciplinart tillvagagangssatt och presenterar en integrerad stromnings-kemisk

teori gallande ILT-tillvaxt och analyserar den skjuvinducerade migrationen av roda blod-

celler (RBCs) i stora artarer med avseende pa hypoxi och dess mojliga roll i aderforkalkning.

Konceptet innefattande virvelstrukturer anvands, med vilken en teori gallande stromnings-

kemiskt driven ILT-tillvaxt formuleras. Teorin foreslar att virvelstrukturer har en viktig roll

i att transportera och aktivera blodplattar i den aneurysmatiska ansvallningen. Blodplattar

transporteras till den distala aneurysmregionen inuti virvelkarnor och aktiveras via en kom-

bination av en lang uppehallstid och relativt hog skjuvspanning vid virvelgransen. Efter

att virveln har brutits upp kan blodplattarna obehindrat fasta sig vid den trombogeniska

vaggytan. Virvelstrukturerna transporterar aven trombin, ett potent prokoagulant enzym,

fangat i karnan, genom det aneurysmatiska halrummet och patvingar darmed en ansamling i

den distala delen av bukaortaaneurysmen. Denna struktur overensstammer med den kliniska

observationen att den tjockaste delen av ILT ses oftast i den distala regionen av bukaor-

taaneurysmen. Undersokningen av stromningsmekaniska aspekter i artarer ledde till studien

av skjuvspanningsinducerad migration av RBCs i stora karl sasom den abdominala aortan

och halspulsadern. Markant RBC-migration kan observeras i regionen kring halspulsaderns

sinus och i iliacaartarerna, regioner som ar benagna att utveckla aterogenes. Detta leder

till hypotesen att tillgangligheten pa oxyhemoglobin kan minska i regionen nara vaggen och

darmed bidra till vagghypoxi, en faktor som impliceras i aderforkalkning. Denna avhandling

framlagger en ny potentiell mekanisk for ILT-tillvaxt, driven av stimuli fran stromnings-

mekaniska och kemiska faktorer, som kan anvandas for att undersoka utveckling av ILT over

fysiologiskt relevanta tidsskalor och kan anvandas som en metod for att prova nya hypoteser;

avhandlingen tillfor ocksa nya insikter gallande tillgangligheten av oxyhemoglobin i regionen

nara vaggen med direkt influens pa aderforkalkning.

Preface

The present work has been financially supported by the Young Faculty Grant No. 2006-

7568 provided by the Swedish Research Council, VINNOVA and the Swedish Foundation

for Strategic Research and by the Project Grant No. 2010-4446 from the Swedish Research

Council, which are gratefully acknowledged.

Stockholm, July 2013

To Barbara...

...Thank you

List of appended papers

Paper A: Hemodynamics conditions of the normal aorta compared to fusiform and saccularabdominal aortic aneurysms with emphasis on a potential thrombus formation mechanismJ. Biasetti, T. C. Gasser*, M. Auer, U. Hedin and F. LabrutoAnn. Biomed. Eng., 38:380-390, 2009 (doi:10.1007/s10439-009-9843-6).

Paper B: Blood flow and coherent vortices in the normal and aneurysmatic aortas: a fluiddynamical approach to intra-luminal thrombus formationJ. Biasetti*, F. Hussain and T. C. GasserJ. R. Soc. Interface, 8:1449-1461, 2011 (doi:10.1098/rsif.2011.0041).

Paper C: An integrated fluid-chemical model toward modeling the formation of intra-luminalthrombus in abdominal aortic aneurysmsJ. Biasetti*, P. G. Spazzini, J. Swedenborg and T. C. GasserFront Physiol., 3:266, 2012 (doi: 10.3389/fphys.2012.00266).

Paper D: Shear-induced migration of red blood cells in the abdominal aorta and the carotidbifurcation: considerations on oxygen transportJ. Biasetti*, P. G. Spazzini and T. C. GasserTo be submitted

In addition to the appended papers, the work has resulted in the following publications andpresentations1:

Biomechanical determinants of Abdominal Aortic Aneurysms - fusiform versuspseudo(saccular) formationsJ. Biasetti, M. Auer, T.C. Gasser, U. Hedin and J. SwedenborgWCCM8 and ECCOMAS, Venice, Italy, June 30 - July 5, 2008 (O)

Hemodynamic simulations towards a biomechanical model of thrombus formationin Abdominal Aortic AneurysmJ. Biasetti, T.C. Gasser, M. Auer, U. Hedin and F. LabrutoEndovascular Surgery - Bringing Basic Science into Clinical Practice, Stockholm, Sweden,March 19-21, 2009 (O)

Hemodynamic simulations in Abdominal Aortic Aneurysms - Insights into throm-bus formationJ. Biasetti, T.C. Gasser, M. Auer, U. Hedin and F. Labruto10th US National Congress on Computational Mechanics, Columbus, Ohio, US, July 16-19,2009 (O)

Structural and hemodynamical analysis of Aortic Aneurysms from ComputerizedTomography Angiography dataT. C. Gasser, M. Auer and J. Biasetti

1O = Oral presentation, P = Poster presentation

Proceedings of the World Congress 2009 - Medical Physics and Biomedical Engineering, Mu-nich, Germany, September 7-12, 2009 (O)

Coherent structure and blood flow dynamics in the normal and aneurysmaticaortaJ. Biasetti, F. Hussain and T.C. GasserECCOMAS CFD 2010 - Fifth European Conference on Computational Fluid Dynamics, Lis-bon, Portugal, June 14-17, 2010 (O)

A blood flow based model for platelet activation in Abdominal Aortic AneurysmsJ. Biasetti and T.C. GasserWCB 2010 - 6th World Congress on Biomechanics, Singapore, Singapore, August 1-6, 2010(O)

A fluido-chemical model of Thrombus formationJ. Biasetti and T.C. GasserCMBE 2011 - 2nd International Conference on Mathematical and Computational BiomedicalEngineering, Washington D.C., USA, March 30 - April 1, 2011 (O)

The Intra-Luminal Thrombus in Abdominal Aortic Aneurysms: a fluido-chemicalapproach to explain its developmentJ. Biasetti and T.C. Gasser6th International Symposium on Biomechanics in Vascular Biology and Cardiovascular Dis-ease, Rotterdam, The Netherland, April 14-15, 2011 (P)

An integrated fluid-chemical model towards modeling the formation of Intra-Luminal Thrombus in Abdominal Aortic AneurysmsJ. Biasetti, F. Hussain, P.G. Spazzini and T.C. GasserWCCM 2012 - 10th Word Congress on Computational Mechanics, Sao Paulo, Brazil, July8-13, 2012 (O)

Growth of the small AAA: hemodynamic sideJ. BiasettiFAD Annual Scientific Meeting (Invited Talk), Madrid, Spain, May 3, 2012 (O)

A fluido-chemical model to predict the growth of Intra-Luminal Thrombus inAbdominal Aortic AneurysmsJ. Biasetti and T.C. GasserECCOMAS 2012 - 6th European Congress on Computational Methods in Applied Sciencesand Engineering, Vienna, Austria, September 10-14, 2012 (O)

The Intra-Luminal Thrombus in Abdominal Aortic Aneurysms: a fluid-chemicalapproach to model its developmentJ. Biasetti, P.G. Spazzini, J. Swedenborg, F. Hussain and T.C. GasserIMAD 2012 - 3rd International Meeting on Aortic Diseases, Liege, Belgium, October 4-6,2012 (P)

Contents

Introduction 11

Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

AAA Pathophysiology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

AAA natural history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Intra-luminal thrombus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Atherosclerosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Computational Fluid Dynamics (CFD) of AAAs . . . . . . . . . . . . . . . . . . . 14

Blood constitutive properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Blood modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Governing equations, initial and boundary conditions . . . . . . . . . . . . . . 15

General flow characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Shear-induced migration of RBCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Coagulation cascade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Experimental investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Methods 21

Patient-specific geometry reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 21

Computational Fluid Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Coagulation cascade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Shear-induced migration of RBCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Post-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Results 23

Importance of shear-thinning in AAA blood flow . . . . . . . . . . . . . . . . . . . 23

Theory of fluid-driven ILT growth . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Integrated fluid-chemical framework for ILT growth . . . . . . . . . . . . . . . . . 23

RBCs migration and its effect on oxygen transport . . . . . . . . . . . . . . . . . . 26

Discussion and Conclusions 29

9

Physics of blood flow in arteries and its relation to intra-luminal thrombus andatherosclerosis

Summary of appended papers 31

10

Introduction

Background

The circulatory system is responsible for the delivery of oxygen and nutrients to all cells,

the removal of carbon dioxide and waste products, the maintenance of optimum pH, and the

mobility of the proteins and cells of the immune system. The arterial system is the higher-

pressure portion of the circulatory system and carries oxygenated blood away from the heart.

The aorta is the largest artery in the human body and consists of three segments, the ascend-

ing aorta, also called aortic arch, the descending thoracic and the abdominal aorta, the latter

being one focus of the present work.

An abdominal aortic aneurysm (AAA) is a focal dilatation of the abdominal aorta, see Figure

1, frequently observed in the aging population (30) and affecting 6% to 9% of the people in

the industrialized world aged 65 and older. AAAs can remain asymptomatic for most of their

development and, if left untreated, they enlarge and may eventually rupture with a mortality

rate of up to 90% (90). An AAA ruptures if the mechanical stress exceeds the local wall

strength (92); consequently, peak wall stress (PWS) (29) and peak wall rupture risk (PWRR)

(36) have been found to be more reliable parameters than diameter, presently the most com-

monly used determinant of rupture risk in clinical diagnosis, in assessing AAA rupture risk.

Despite this improvement, no definite method to assess the risk of rupture is currently avail-

able and the ability to predict aneurysms that are at risk is required to optimize medical

and economic outcomes. The natural history of AAAs is frequently (38) characterized by

the development of an intra-luminal thrombus (ILT), a tissue found in nearly all AAAs large

enough to indicate risk of rupture (38). ILTs may vary in thickness from a few micrometers

to several centimeters and have complex natural histories and structures. At the present day

their mechanical and biological effects in AAAs pathophysiology are not fully understood.

Two different types of surgical treatment are available to treat AAAs: open repair and en-

dovascular aneurysm repair (EVAR). Open repair involves an incision of the abdomen to

directly visualize the AAA. Once the abdomen is opened, the AAA is repaired by the use

of a graft. EVAR is a minimally-invasive procedure where a small incision in each groin is

performed to visualize the femoral arteries in each leg. Then a stent-graft is inserted through

the femoral artery and placed at the site of the AAA down to the iliac arteries.

11


Figure 1: Localization of the abdominal aorta in the human body and comparison between a normal and ananeurysmatic aorta. Image from A.D.A.M. Images (http://www.adamimages.com/Home).

Atherosclerosis is the most common vascular disease and involves accumulation of fatty ma-

terial in the arterial wall with consequent thickening. It is a chronic disease that can remain

asymptomatic for decades (78). Atherosclerotic lesions tend to be focal (86), involving pre-

dominantly regions of disrupted flow (45). This characteristic has led to hypothesise that

factors related to geometry and flow patterns are involved in its genesis and development,

see for example (43). The most common medical therapy consists in the administration of

beta-blockers while in the most serious cases surgical intervention is required. A series of tech-

niques are nowadays available to treat atherosclerotic lesions, for example endarterectomy,

bypass surgery, balloon angioplasty, stenting, and laser ablation.

AAA Pathophysiology

AAA natural history

AAA pathogenesis is still debated but the initial dilatation is thought to be caused partly by

degeneration of the medial elastin and smooth muscles in the arterial wall. AAAs are the end

result of irreversible proteolytic degradation of elastin and collagen in the artery wall (21).

Genetics and risk factors like smoking, hypertension, chronic obstructive pulmonary disease

(COPD), inflammation and atherosclerosis play key roles in AAA genesis and progression

(21). The AAA wall, in a later stage, has up to 90% less elastin (77), mostly fragmented

(54), and few smooth muscle cells (17, 62). Media and adventitia see a turnover of fibrillar

collagen and increased collagen cross-linking which reinforces and increases wall stiffness; the

12

media also experiences loss of elastin. Metalloproteinases (MMPs) are upregulated in AAAs

leading to an enhanced degradation of the aneurysmatic wall compared with normal aorta.

At a later stage the collagen synthesis is unable to withstand the increased mechanical wall

stress (21), leading to rupture. For a more comprehensive review the reader is referred to, for

example, (21).

Intra-luminal thrombus

A thin or thick ILT is a tissue found in nearly all AAAs large enough to indicate risk of

rupture (38). While the thin ILT is not explored very well, the thick ILT (31) has solid-

like properties (35) and is composed of a fibrin mesh, traversed by a continuous network of

interconnected canaliculi (88), incorporated with blood cells, e.g., erythrocytes (also called

red blood cells or RBCs) and neutrophils, aggregated thrombocytes (also called platelets or

PLTs), blood proteins, and cellular debris. The ILT is thought to play an important role in

the pathology and natural history of AAAs with a series of effects on the underlying aortic

wall. Specifically it causes localized hypoxia, possibly leading to increased neovascularization,

inflammation, and local wall weakening (93). In addition, the changes to matrix-degrading

protease expression (55), to structural and cellular composition (54) lead to a thinner wall

compared to the aneurysm wall exposed to flowing blood (88). The ILT has a significant

structural impact on the biomechanics of AAAs and influences both the magnitude and the

distribution of wall stress (47, 72, 95) and needs to be considered through a biomechanical

rupture risk assessment (36). Despite ILT’s role in AAA’s pathophysiology its formation

mechanism and progression are remain still unclear. For a more complete review of the

biochemomechanics of ILT see (97).

Atherosclerosis

Atherosclerosis is the most common vascular disease and involves the accumulation of low-

density lipoprotein (LDL) and other lipid-bearing materials in the arterial wall. Atheroscle-

rosis normally begins as a fatty streak on the endothelial surface and develops into a focally

thickened intima via accumulation of cells, lipids, connective tissue, calcium, and pultaceous

debris (45). A characteristic feature of atherosclerosis is its focal nature (86). Risk factors are

numerous and the primary are: elevated serum cholesterol, elevated serum levels of triglyc-

erides, diabetes mellitus, smoking, genetic predisposition, stress, sedentary lifestyle, obesity

and hypertension (45). Atherosclerotic plaques can be classified into into two broad cat-

egories: stable and unstable (also called vulnerable) (79). Ruptures of unstable plaques

expose thrombogenic material, such as collagen to the circulation and eventually induce

thrombus formation in the lumen. The intraluminal thrombi formed can occlude arteries

outright or they can move into the circulation and eventually occlude smaller downstream

13


branches. Chronically expanding atherosclerotic lesions can cause complete closure of the

lumen. Atherosclerosis initiation is not fully understood, and several hypotheses have been

put forward, see for example (9, 32, 60, 67, 78, 84). The location of atherosclerotic plaques

seems to prefer regions of complex geometry, e.g. the outer walls (inner curvature wall) of a

bifurcation, usually in the abdominal aorta, iliacs, coronaries, femorals, popliteals, carotids

and cerebrals arteries (45). Many biomechanical factors are thought to be implicated in the

pathogenesis of atherosclerosis, for example low and oscillatory wall shear stress (37, 64) is

thought to induce an atherogenic phenotipe in endothelial cells. Mass transport from and to

the wall also plays a role; (89) proposed four mass transport mechanisms that may be impor-

tant in atherosclerosis: blood phase controlled hypoxia, leaky endothelial junctions, transient

intercellular junction remodeling, and convective clearance of the subendothelial intima and

media.

Computational Fluid Dynamics (CFD) of AAAs

Blood constitutive properties

Blood is a suspension of cells in a fluid called plasma. It delivers oxygen and nutrients to the

cells and remove waste products. Blood cells occupy around 50% in volume of whole blood

while plasma consists of water (92% by volume), proteins, glucose, mineral ions, hormones,

carbon dioxide. Blood cells are composed of erythrocytes (RBCs), leukocytes (also called

white blood cells or WBCs) and thrombocytes (PLTs). RBCs are the most abundant cells in

blood and contain the hemoglobin protein which binds to oxygen and allows for its transport

throughout the body. WBCs are part of the immune system and their main task is to defend

the body against pathogens and foreign substances. PLTs are involved in the coagulation

process and among other roles they regulate the conversion of fibrinogen into fibrin and they

are a component of the ensuing clot.

Plasma behaves as a Newtonian fluid but whole blood shows a remarkable non-Newtonian

behavior consisting of shear-thinning, thixotropy and viscoelasticity (66, 69). RBC-RBC

interactions and RBC-protein interactions are the primary cause of the non-Newtonian be-

havior: the aggregation and disaggregation of RBCs and their deformation dictate the value

of viscosity (18, 19).

Blood modeling

As already delineated, blood shows marked non-Newtonian effects and proper constitutive

equations able to capture these effects are required. Despite the majority of work in the biome-

chanical literature is still based on the Newtonian approximation, see for example (16, 76, 81),

it has been shown that the shear-thinning behavior of blood, i.e. the instantaneous decrease

in viscosity for increasing shear rate, has a profound influence on the flow field (11). The

14

non-Newtonian effects are important both at the local and the global level: size and strength

of vortical structures and recirculating regions and phenomena like PLTs’ dynamics, PLTs ac-

tivation and aggregation, transition to turbulence and dissipation are all affected, to a degree

not completely characterized, by them. Focusing on the shear-thinning behavior, different

models have been proposed to capture its characteristics, for example the Carreau-Yasuda

and the Power-Law models (13). The Quemada model (74) enhances the mentioned models

by formulating blood viscosity as dependent from shear rate and hematocrit (volume fraction

of RBCs). According to the specific simulation objectives also models taking into account

thixotropy, viscoelasticity and anisotropy might be required. A considerable amount of work

in literature claims the presence of turbulence in AAAs’ flow, see for example (58), using

as indicator the turbulent kinetic energy (TKE). This quantity cannot completely identify a

turbulent flow; the energy cascade is the ultimate identifier of genuine turbulence in a flow.

Up to now, to the best of authors’ knowledge, no indication of the presence of the energy

cascade in AAAs’ blood flow has been presented. It is noteworthy to observe that taking

into account the shear-thinning behavior of blood (11) predicted the almost complete absence

of streamwise vortices. Such vortices are known to be an essential part of the turbulence

regeneration cycle (14, 40, 46, 48, 49, 83). Moreover, considering also the higher dissipation

in the low shear rate region due to higher viscosity, it appears legitimate to postulate that

turbulence is absent in AAAs, or present in a very limited fashion. The present thesis followed

this assumption.

Governing equations, initial and boundary conditions

Blood flow is governed by the continuity equation (conservation of mass) for an incompressible

medium

∇ · u = 0, (1)

and the Navier-Stokes equations (conservation of momentum)

ρ

(∂u

∂t+ u · ∇u

)= −∇p+∇ · τ + ρfb, (2)

where u is the velocity vector, ρ the density (assumed constant), p the pressure, τ = 2µD the

deviatoric viscous stress tensor and fb represents the body forces per unit mass accounting

for gravitational effects (3). The incompressibility condition is employed being blood very

well approximated as a perfectly incompressible material. In order to completely specify the

problem, initial and boundary conditions are needed. Initial conditions normally consist in

zero velocity in the whole computational domain and pressure equal to a reference pressure.

Boundary conditions are applied to the inlet surface, the outlet surfaces and the luminal wall

surface. At the inlet surface three different types of boundary condition are usually applied, a

plug-flow profile (constant velocity over the whole inlet section), a specified velocity profile or

15


a mass flow rate. In the case of applied mass flow rate the inlet velocity profile is calculated as

part of the solution. At the outlets pressure waves are typically applied, in some cases with the

addition of the no-viscous stress condition τn = 0. At the luminal wall the no-slip condition,

uw = 0, is applied. Notice that in the case of rigid wall and incompressible fluid the imposition

of a pressure wave at the outlet is not strictly necessary since given the mass flow rate, the

pressure gradient, which appears in the Navier-Stokes equations, is calculated. This means

that a constant pressure may also be applied. However, in order to get a meaningful pressure

distribution (amplitude and phase) and a correct flow splitting a physiological pressure wave(s)

need to be used. For a detailed explanation of different boundary conditions see (91). If there

is the additional requirement of the presence of major proximal branches such as the celiac,

superior mesenteric and renal arteries, additional boundary conditions are required, see for

example (58).

General flow characteristics of AAA’s blood flow

Restricting the focus, for now, on fusiform AAAs, the most frequent occurence, several fluid

dynamical features are common characteristics despite the great variety of AAA shapes, sizes

and intra- and inter-patient variability of the boundary conditions. The first common feature

is the formation of vortices (also called vortical structures or VSs) during systole and early

diastole. During this phase unstable near-wall shear layers, also called vortex sheets, in the

proximal AAA region undergo a Kelvin-Helmholtz (KH) instability (3) causing a roll up,

generating spanwise vortical structures, such as hairpin or ring vortices, the latter if the AAA

presents enough axialsymmetry. The presence of vortices in AAAs has been clearly shown

numerically in (11) and experimentally in (24, 25, 80, 85).

Another common feature, which is also associated with the formation of vortices, is the

presence of a jet which penetrates the AAA bulge (10, 24) with consequent formation of

a shear layer. This shear layer, being unstable, undergoes a KH instability leading to the

formation of secondary vortices (80). This shear layer might be locally turbulent, but direct

evidence of the presence of turbulence is missing and its biological relevance is unknown.

Flow separation is also always observed (11, 80) as a result of the aneurysmal expansion and

consequent VSs formation.

The average flow velocity in the aneurysmatic bulge is lower compared to normal aortas due

to the conservation of mass (10). Wall shear stresses can be several times lower compared to

normal aortas’ values (11). On the other hand, though, the vortices shed during late systole

have been shown to impinge on the distal wall (12, 25, 80) resulting in transient peaks of wall

shear stress.

Saccular aneurysms are less frequent and their fluid dynamics is also less investigated. In

(11) a saccular AAA was investigated and the formation of a vortex in the proximal region

16

was observed, which moved downstream and tore into two worm-like streamwise vortices that

eventually entered the distal portion of the aorta. Noteworthy, low shear rates were observed

in the aneurysmatic bulge, which was free of VSs throughout the entire cardiac cycle.

Shear-induced migration of RBCs

A wide body of experimental evidence shows that flowing suspensions exhibit particle migra-

tion (2, 5, 22, 33, 44, 52, 53, 57) with a general trend showing migration from regions of higher

shear rate to regions of lower shear rate. RBCs also show this behavior and their migration

to the center of micro and small vessels (µm to mm size) and the consequent segregation of

platelets near the wall has been subject of intense study in the past years, both numerically

(7, 65, 82, 96) and experimentally (1, 20, 73). RBCs distribution influences blood viscosity,

and therefore the velocity profile, and also a series of biological activities such as oxygen

distribution in the lumen and the scavenging of nitric oxide (NO) by hemoglobin in the RBCs

(61). Local arterial wall hypoxia has been proposed as a contributing factor to atherosclerosis

and intimal hyperplasia (89) and altered NO transport in the artery has been postulated to

induce atherogenesis (61). Based on considerations on the Sherwood and Damkholer num-

bers, it is thought (89) that oxygen supply to the arterial wall is more likely to be fluid-phase

limited, therefore underlining the importance of mass transport from the lumen to the wall.

It has been shown in (68) that the effect of disregarding the presence of hemoglobin, and

therefore its possible lowering in concentration due to RBCs migration, is a drastic decrease

in oxygen transport to the wall. Therefore, given the importance of RBCs concentration in

the aforementioned series of biological activities, the evaluation of RBCs distribution as a

results of shear-induced migration is of primary importance. In (7) a mesoscopic approach

employing the immersed boundary method was used to simulate the motion of red blood

cells, modeled as deformable capsules, flowing through two-dimensional channels of size 20-

300 µm. The work shows migration of RBCs perpendicular to the wall and formation of a

cell-free layer. An extension to the three-dimensional case of the same mesoscopic approach

is presented in (27). Also in (100) the immersed boundary method was employed to model

RBCs migration in two dimensional channels of 6-12 µm and cell migration from the vessel

wall was also observed. In (28) the dissipative particle dynamics method was applied to blood

flow in microtubes ranging from 10 µm to 40 µm and cell migration away from the wall to the

tube center was reported. Another approach is represented by continuum models, which are

able to simulate larger domains for longer time scales. An example of this approach can be

found in (65), where blood flow in vessels with diameter ranging from 40 µm to 100 µm was

investigated using the shear-induced migration model proposed in (71). Particle migration

away from the wall was also observed in this case.

17


Coagulation cascade

The hemostatic system maintains the integrity of the circulatory system in case of vascular

damage. It maintains blood in a fluid state and responds to vessel injury by the rapid forma-

tion of a clot. Clot formation is the end result of a process initiated by the injury of a vessel

wall and subsequent exposure of the subendothelium to blood flow. This triggers two inter-

connected processes: PLTs aggregation and the coagulation cascade (CC). The CC consists

of a series of enzymatic reactions, in which a series of proenzymes (zymogens) is turned into

their active enzyme form. The series of reactions leads to the formation of thrombin, which

in turn converts fibrinogen into fibrin (34, 63). Evidences that blood dynamics can influence

the clotting process were already pointed out in (15) where it was shown, for a steady flow

case, that the recirculation zone formed inside the aneurysm creates favorable conditions for

thrombus formation. Hemostasis and thrombosis research has been mostly performed through

experiment, but in the last decade a body of computational work started to provide useful

insights into this complex problem.

Coagulation pathway models have been developed allowing the simulation of the interaction

between the different enzymes involved in the CC. For example the model presented in (51)

provides a set of ODEs describing the reactions constituting the tissue factor (TF) pathway

to thrombin. An extension to this model was provided in (42) where the stoichiometric and

dynamic inhibitory processes were also taken into account. By coupling a coagulation model

to a very simplified fluid-dynamical model the role of binding site densities was considered in

(56). Several works tried to incorporate the effect of blood flow but with severe approxima-

tions, like assuming Poiseuille flow, see for example (41). In order to model the CC under fluid

flow the need to couple a model of the CC to the full Navier-Stokes equations is clear. One

example comes from (99) where a multiscale approach incorporates the Navier-Stokes equa-

tions to model the growth of a thrombus in flowing blood in a two-dimensional rectangular

domain. Another example comes from (12) where the CC was coupled with the Navier-Stokes

equations and solved in an idealized AAA with physiological boundary conditions.

Experimental investigations

Experimental investigations of AAA flows are feasible in-vivo using MRI techniques, see for

example (87), but more details on the relevant flow features can be obtained using in-vitro

experiments. In (80) a Particle Image Velocimetry (PIV) apparatus was used to perform

measurements in an idealized rigid symmetric AAA model made out of glass using water

as working fluid. The authors found flow separation from the proximal wall and observed

the formation of a vortex ring traveling downstream. This reflected in a WSS as low as

26% of the value in a normal abdominal aorta and in peaks of WSS in the distal region

where the ring vortex impinges to the wall. In (24) PIV experiments using idealized rigid

18

(glass) and compliant (molded polyurethane) asymmetric models of AAA were conducted

using an aqueous glycerin solution. The authors found that the motion of the compliant wall

contributed to the progression of the vortices downstream during the deceleration phase until

vortex impingement at the distal wall. Impingement was not observed in the rigid model

case. This reinforces the theory put forward in (11) by showing that vortices formed in the

proximal region are actually impinging the distal wall in real AAA geometries. In (85) the

flow of a water-glycerin solution was studied using PIV in a patient-specific rigid abdominal

aortic aneurysm including the aortic bifurcation. The authors observed the formation of a

horse-shoe vortex in the proximal aneurysm region, and low shear stresses in the recirculation

region were also reported. In (25) the flow of aqueous glycerin solution was investigated using

PIV in a idealized compliant asymmetric AAA with and without aortic bifurcation. Also

in this case the development of a ring vortex in the proximal AAA region which propagates

downstream until impinging in the distal AAA region was observed.

19


20

Methods

A brief summary of the methods employed in the appended papers is given below. For the

complete description see the Methods sections of Papers A-D.

Patient-specific geometry reconstruction

Patient-specific geometries were reconstructed from computer tomography-angiography (CT-

A) scans using the diagnostic software A4clinics (VASCOPS GmbH, Graz, Austria) (6).

A4clinics employs active contour (deformable models) which move under the action of ex-

ternal forces according to the image intensity and first and second spatial image gradients.

This approach supports an artifacts-insensitive (98) and automatic segmentation of the lumen,

a fundamental requirement in order to allow operator-independent geometries.

Computational Fluid Dynamics

Fluid dynamical computations were performed using either a Finite Volume (FV) approach

or a Finite Element (FE) approach. Once reconstructed, the geometries were meshed using

prismatic (3D) or quadrilateral (2D/2D-axi) elements in the near-wall region in order to

properly capture the sharp gradients inside the boundary layer, while the remaining volume

was discretized predominantly by tetrahedral (3D) or triangular (2D/2D-axi) elements.

To model blood flow in the normal and aneurysmatic abdominal aortas the continuity and

Navier-Stokes equations (3) were solved with ANSYS CFX (ANSYS Inc.) (4) using a FV

approach (Papers A-B) and with a FE approach using COMSOL Multiphysics (23) (Paper

C). A rigid wall model was assumed, and a cardiac cycle length of 1.0 s was set. The no-slip

boundary condition was applied at the luminal wall while a volumetric/mass flow rate was

applied at the inlet and a pressure wave was applied at the outlets. Blood was modeled

as a Newtonian fluid with constant density (Paper B), as a non-Newtonian shear-thinning

fluid (Papers A-B-C) with constant density with its constitutive properties modeled using

the Carreau-Yasuda model (13), and as a non-Newtonian shear-thinning fluid (Paper D) with

constant density with its constitutive properties modeled using the Quemada viscosity model

(74).

21


Coagulation cascade

The CC in flowing blood (Paper C) was modeled with a set of convection-diffusion-reaction

equations (CDR) defining the evolution in space and time of the chemical species involved in

the coagulation process until thrombin formation. The arising equations were solved with a

FE approach in COMSOL Multiphysics.

Shear-induced migration of RBCs

RBCs migration (Paper D) was modeled with a modified version of Phillips’ model (71) for

shear-induced particle migration in concentrated suspensions. The modified version corre-

sponds to the extension of Phillips’ model (71) in the case of solid and fluid phases with

different densities developed in (75). The set of equations was solved with a FE approach

using COMSOL Multiphysics. In addition to the BCs already outlined, appropriate BCs for

the solid phase were employed: a constant inlet and outlet, the latter for stability reasons,

volume fractions of the solid phase were employed and a zero-flux condition for the solid phase

at the luminal wall was also set.

Post-processing

Output data were imported in Tecplot (Tecplot Inc.) for post-processing and a routine

to educe and visualize the λ2-isosurfaces was used. Additional data manipulations were

performed in Matlab (The MathWorks, Inc.).

22

Results

The key findings of the four attached papers are summarized below. For full details refer to

the Results sections of Papers A-D.

Importance of shear-thinning in AAA blood flow

The importance of considering the shear-thinning behavior of blood in AAA flows has been

shown in Paper B. The Newtonian approximation usually applied in literature overpredicted

the presence of VSs in the core flow, see Figure 2. Of particular relevance, the Newtonian

model showed a larger presence of streamwise structures, a basic requirement for sustained

turbulence. The Newtonian model seems, therefore, to be inadequate in representing the

correct fluid dynamics of blood flow, in particular for diseased states like AAAs, where the

increase in viscosity in the core flow at large vessel diameters (i.e. at low shear rates) cannot

be captured.

Theory of fluid-driven ILT growth

A theory of fluid-driven ILT growth has been formulated in Paper A and in a more complete

form in Paper B. The theory proposes that VSs play an active role in convecting and activating

platelets in the aneurysmatic bulge. In particular, platelets are convected toward the distal

aneurysm region inside vortex cores and are activated via a combination of high residence

times and relatively high shear stress at the vortex boundary. After vortex break-up platelets

are free to adhere to the thrombogenic wall surface, likely in regions of low wall shear stress,

see Figure 3.

Integrated fluid-chemical framework for ILT growth

In Paper C the theory proposed in Paper B has been enriched with the addition of the CC, a

key ingredient in ILT formation. Simulations showed that VSs convect thrombin, captured in

their core, through the aneurysmatic lumen and force its accumulation in the distal portion

23


Figure 2: Wall shear stress (WSS) and vortical structures (VSs) interaction in the fusiform abdominal aorticaneurysm (AAA) of Paper B at early systole (0.15 s), peak systole (0.2 s) and early diastole (0.4s). Simulations were based on (a) Newtonian and (b) Carreau-Yasuda blood models. The luminalsurface is colour-coded with the WSS and VSs (educed with the λ2-method using λ2tr = −20.0s−2) are superimposed, in grey in the right images.

24

Figure 3: Schematic of the suggested mechanism of intra-luminal thrombus (ILT) formation in abdominalaortic aneurysms (AAAs). (a) A platelet travels at the boundary of a vortex (i.e. in the region ofhigh shear stress) prior to being released and attaching itself to the wall at sites of low shear stress.Light grey, low shear stress region; dark grey, high shear stress region. (b) Different phases of ILTformation in an AAA. Phase 1: vortices are formed in the geometrically complex neck region andthey capture non-activated platelets (grey dots). Phase 2: vortices reinforce and become mixedup while travelling downstream. Residence times are in the order of seconds and high shear atthe periphery of the vortices activates platelets (black dots). Phase 3: the vortex breaks up in thedistal part of the AAA and releases activated platelets, which in turn can aggregate and/or attachto the wall.

25


Figure 4: Thrombin (IIa) distribution once the periodic state is reached in the two investigated cases inPaper C. Considering a large, Case (A), and a small, Case (B), subendothelial exposure bothconcentration patterns are strongly shifted toward the distal AAA region. A larger area of highthrombin concentration is found in Case (A) due to the larger subendothelial damage.

of the AAA, see Figure 4. This finding is in line with the clinical observation that the thickest

ILT is usually seen in the distal AAA region.

RBCs shear-induced migration and its effect on oxygen trans-

port

In Paper D, shear-induced RBCs migration has been shown to take place also in large vessels

such as the carotid artery and the abdominal aorta. Simulations show a migration of RBCs

from the near wall region with a lowering of wall hematocrit (volume fraction of RBCs) on

the posterior side (inner curvature wall) of the normal aorta and in the iliac arteries. A

marked migration is observed on the outer wall (inner curvature wall) of the carotid sinus,

the inner curvature wall of the common carotid artery, see Figure 5, and in the carotid

26

Figure 5: Wall hematocrit in the normal carotid bifurcation at t = 0.10 s. Note the region of high RBCsmigration on the external wall of the carotid sinus (inner curvature wall) and on the internalcurvature wall of the common carotid artery.

stenosis. No significant migration is observed in the AAA. The spatial and temporal patterns

of wall hematocrit are correlated with the near-wall shear layer and with the secondary flow

induced by the vessel curvature. The results are in line with data in literature showing a

decrease in oxygen partial pressure on the inner curvature wall of the carotid sinus and, more

in general, on inner curvature walls. The lowering of wall hematocrit is postulated to induce

a decrease in oxygen availability at the luminal surface through a diminished concentration

of oxyhemoglobin, hence contributing, with the lowered oxygen partial pressure, to local

hypoxia.

27


28

Discussion and Conclusions

Hemodynamics is thought to play a key role in the complex pathophysiology of AAA and

atherosclerosis, complicated vascular diseases involving biological, mechanical, and fluid-

dynamical factors. In the past years it became clear that to effectively approach the study

of these pathologies the integration of their different aspects was crucial. Therefore, an in-

tegrated mechanochemical view may help understand AAA development, the role played by

the ILT in AAA pathophysiology and also investigate the development of atherosclerosis.

The research work contained in this thesis focused primarily on the fluid-chemical aspects of

AAAs, with a brief extension to carotid bifurcations.

In this thesis the powerful concept of VSs was applied to the study of blood flow in the ab-

dominal aorta, providing a framework for a theory of fluid-chemically-driven ILT growth. It

has been shown that VSs can promote favorable conditions for PLTs activation, convection,

and deposition at the distal AAA wall. The observed pattern of VSs motion correlates with

the finding that ILT is thickest in the distal portion of the AAA, see Paper B. This view has

found indirect support by the particle-hemodynamics analysis of (8) and the predicted VSs

dynamics has been observed in-vitro in (24, 25, 80).

The shear-thinning behavior of blood has been shown to produce appreciable differences in

the flow field. Perhaps the most important effect of shear-thinning, compared to a Newto-

nian approximation, was to render blood more viscous, in the regions of low shear rate, and

therefore more dissipative. Streamwise vortices were not observed when the non-Newtonian

model was used.

The ILT can be loosely seen as the end product of an abnormal coagulation process, for this

reason the CC in AAAs has been investigated. It has been shown that VSs capture chemicals

in their core and convey them until VSs’ burst in the distal AAA region. Thrombin accumu-

lates distally, correlating with the location of maximum ILT thickness.

Due to its link with hypoxia and therefore to the development of atherosclerosis, investiga-

tions on the possible presence of shear-induced migration of RBCs in the abdominal aorta

and the carotid artery was also pursued. It has been found that a marked RBCs migration

was present in the region of the carotid sinus and in the iliac arteries of the normal abdominal

aorta case. Oxyhemoglobin availability can decrease in the near-wall region hence contribut-

ing to wall hypoxia, a factor implicated in atherosclerosis.

29


The relevance of the integrated approach presented in the thesis stands in the fact that a

model able to predict the development of the ILT over physiologically relevant timeframes

can be integrated in a AAA’s growth and remodeling (G&R) model to help predict which

lesions are at risk of rupture. This information can improve clinical planning and the conse-

quent medical and economical outcomes.

Future modeling efforts should tackle the development of an ILT-growth model and focus

on the experimental validation of the proposed fluid-chemical ILT growth framework. In-

vestigations should also focus on the oxygen mass transfer both from a computational and

experimental point of view in order to establish the effect on the arterial wall of RBCs mi-

gration.

In conclusion, the results of this thesis provide a framework and a set of hypotheses which can

be tested and falsified in order to advance in the understanding of AAA and atherosclerosis

pathophysiology.

30

Summary of appended papers

Paper A: Hemodynamics of the normal aorta compared to fusiform and saccular abdominal

aortic aneurysms with emphasis on a potential thrombus formation mechanism.

Abdominal Aortic Aneurysms (AAAs), i.e., focal enlargements of the aorta in the ab-

domen are frequently observed in the elderly population and their rupture is highly mortal.

An intra-luminal thrombus is found in nearly all aneurysms of clinically relevant size and

multiply affects the underlying wall. However, from a biomechanical perspective thrombus

development and its relation to aneurysm rupture is still not clearly understood. In order to

explore the impact of blood flow on thrombus development, normal aortas (n = 4), fusiform

AAAs (n = 3), and saccular AAAs (n = 2) were compared on the basis of unsteady Com-

putational Fluid Dynamics simulations. To this end patient-specific luminal geometries were

segmented from Computerized Tomography Angiography data and five full heart cycles using

physiologically realistic boundary conditions were analyzed. Simulations were carried out with

computational grids of about half a million finite volume elements and the Carreau-Yasuda

model captured the non-Newtonian behavior of blood. In contrast to the normal aorta the

flow in aneurysm was highly disturbed and, particularly right after the neck, flow separation

involving regions of high streaming velocities and high shear stresses were observed. Natu-

rally, at the expanded sites of the aneurysm average flow velocity and wall shear stress were

much lower compared to normal aortas. These findings suggest platelets activation right after

the neck, i.e., within zones of pronounced recirculation, and platelet adhesion, i.e., thrombus

formation, downstream. This mechanism is supported by recirculation zones promoting the

advection of activated platelets to the wall.

Paper B: Blood flow and coherent vortices in the normal and aneurysmatic aortas: a fluid

dynamical approach to intra-luminal thrombus formation.

Abdominal aortic aneurysms (AAAs) are frequently characterized by the development of

an Intra-Luminal Thrombus (ILT), which is known to have multiple biochemical and biome-

chanical implications. Development of the ILT is not well understood, and shear stress-

triggered activation of platelets could be the first step in its evolution. Vortical structures

31


(VSs) in the flow affect platelet dynamics, which motivated the present study of a possible

correlation between VS and ILT formation in AAAs. VSs educed by the λ2-method using

computational fluid dynamics simulations of the backward-facing step problem, normal aorta,

fusiform AAA and saccular AAA were investigated. Patient-specific luminal geometries were

reconstructed from computed tomography scans, and Newtonian and Carreau-Yasuda models

were used to capture salient rheological features of blood flow. Particularly in complex flow

domains, results depended on the constitutive model. VSs developed all along the normal

aorta, showing that a clear correlation between VSs and high wall shear stress (WSS) existed,

and that VSs started to break up during late systole. In contrast, in the fusiform AAA, large

VSs developed at sites of tortuous geometry and high WSS, occupying the entire lumen, and

lasting over the entire cardiac cycle. Downward motion of VSs in the AAA was in the range

of a few centimetres per cardiac cycle, and with a VS burst at that location, the release (from

VSs) of shear-stress-activated platelets and their deposition to the wall was within the lower

part of the diseased artery, i.e. where the thickest ILT layer is typically observed. In the

saccular AAA, only one VS was found near the healthy portion of the aorta, while in the

aneurysmatic bulge, no VSs occurred. We present a fluid-dynamics motivated mechanism for

platelet activation, convection and deposition in AAAs that has the potential of improving

our current understanding of the pathophysiology of fluid-driven ILT growth.

Paper C: An integrated fluido-chemical model towards modeling the formation of intra-

luminal thrombus in abdominal aortic aneurysms.

Abdominal Aortic Aneurysms (AAAs) are frequently characterized by the presence of an

Intra-Luminal Thrombus (ILT) known to influence their evolution biochemically and biome-

chanically. The ILT progression mechanism is still unclear and little is known regarding

the impact of the chemical species transported by blood flow on this mechanism. Chemical

agonists and antagonists of platelets activation, aggregation, and adhesion and the proteins

involved in the coagulation cascade (CC) may play an important role in ILT development.

Starting from this assumption, the evolution of chemical species involved in the CC, their

relation to coherent vortical structures (VSs) and their possible effect on ILT evolution have

been studied. To this end a fluid-chemical model that simulates the CC through a series

of convection-diffusion-reaction (CDR) equations has been developed. The model involves

plasma-phase and surface-bound enzymes and zymogens, and includes both plasma-phase

and membrane-phase reactions. Blood is modeled as a non-Newtonian incompressible fluid.

VSs convect thrombin in the domain and lead to the high concentration observed in the distal

portion of the AAA. This finding is in line with the clinical observations showing that the

thickest ILT is usually seen in the distal AAA region.The proposed model, due to its ability

to couple the fluid and chemical domains, provides an integrated mechanochemical picture

32

that potentially could help unveil mechanisms of ILT formation and development.

Paper D: Shear-induced migration of red blood cells in the abdominal aorta and the carotid

artery: consideration on oxygen transport.

Shear-induced migration of red blood cells (RBCs) is a well known phenomenon charac-

terizing blood flow in the small vessels (µm to mm size) of the cardiovascular system. In

large vessels, like the abdominal aorta and the carotid artery (mm to cm size), the extent

of this migration has not been fully elucidated. RBCs migration exerts its influence primar-

ily on platelet concentration, oxygen transport and oxygen availability at the luminal sur-

face; this being of primary importance in, for example, intra-luminal thrombus (ILT) growth,

atherosclerosis, nitric oxide (NO) distribution and intima hyperplasia. Phillips’ shear-induced

particle migration model coupled to the Quemada viscosity model was employed to simulate

the macroscopic behavior of RBCs in four patient-specific geometries: a normal abdominal

aorta, an abdominal aortic aneurysm (AAA) and in two carotid bifurcations. Simulations

show a migration of RBCs from the near wall region with a lowering of wall hematocrit (vol-

ume fraction of RBCs) on the posterior side of the normal aorta and in the iliac arteries. A

marked migration is observed on the outer wall of the carotid sinus, the inner curvature wall

of the common carotid artery and in the carotid stenosis. No significant migration is observed

in the AAA. The spatial and temporal patterns of wall hematocrit are correlated with the

near-wall shear layer and with the secondary flow induced by the vessel curvature. The results

are in line with data in literature showing a decrease in oxygen partial pressure on the inner

curvature wall of the carotid sinus and, more in general, on the inner curvature wall. The

lowering of wall hematocrit is postulated to induce a decrease in oxygen availability at the

luminal surface through a diminished concentration of oxyhemoglobin, hence contributing,

with the lowered oxygen partial pressure, to local hypoxia.

33


34

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