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Home , Aneurysm, Atherosclerosis

Physics of flow in and its relation to intra-luminal and

Jacopo Biasetti

Doctoral thesis no. 84, 2013 KTH School of Engineering Sciences Department of Solid Mechanics - vascuMECH KTH Royal Institute of Technology SE-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 tillst˚andav Kungliga Tekniska H¨ogskolan i Stockholm framl¨aggestill offentlig granskning f¨oravl¨aggandeav teknisk doktorsexamen torsdag den 22 augusti kl. 10.00 i sal F3, Kungliga Tekniska H¨ogskolan, Lindstedtsv¨agen26, Stockholm. Abstract

Vascular pathologies such as Abdominal Aortic (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 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 , 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 and the carotid . 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 s˚asombukaortaaneurysm och ˚aderf¨orkalkning ¨arkomplexa vaskul¨arasjukdomar som involverar biologiska, mekaniska och str¨omningsmekaniska faktorer. Denna avhandling f¨oljerett multidisciplin¨arttillv¨agag˚angss¨attoch presenterar en integrerad str¨omnings-kemisk teori g¨allandeILT-tillv¨axtoch analyserar den skjuvinducerade migrationen av r¨odablod- celler (RBCs) i stora art¨arermed avseende p˚ahypoxi och dess m¨ojligaroll i ˚aderf¨orkalkning. Konceptet innefattande virvelstrukturer anv¨ands,med vilken en teori g¨allandestr¨omnings- kemiskt driven ILT-tillv¨axtformuleras. Teorin f¨oresl˚aratt virvelstrukturer har en viktig roll i att transportera och aktivera blodpl¨attari den aneurysmatiska ansv¨allningen.Blodpl¨attar transporteras till den distala aneurysmregionen inuti virvelk¨arnoroch aktiveras via en kom- bination av en l˚anguppeh˚allstid och relativt h¨ogskjuvsp¨anningvid virvelgr¨ansen. Efter att virveln har brutits upp kan blodpl¨attarnaobehindrat f¨astasig vid den trombogeniska v¨aggytan. Virvelstrukturerna transporterar ¨aven trombin, ett potent prokoagulant enzym, f˚angati k¨arnan,genom det aneurysmatiska h˚alrummetoch p˚atvingard¨armeden ansamling i den distala delen av bukaortaaneurysmen. Denna struktur ¨overensst¨ammermed den kliniska observationen att den tjockaste delen av ILT ses oftast i den distala regionen av bukaor- taaneurysmen. Unders¨okningenav str¨omningsmekaniska aspekter i art¨arerledde till studien av skjuvsp¨anningsinduceradmigration av RBCs i stora k¨arls˚asomden abdominala aortan och halspuls˚adern.Markant RBC-migration kan observeras i regionen kring halspuls˚aderns sinus och i iliacaart¨arerna,regioner som ¨arben¨agnaatt utveckla aterogenes. Detta leder till hypotesen att tillg¨anglighetenp˚aoxyhemoglobin kan minska i regionen n¨arav¨aggenoch d¨armedbidra till v¨agghypoxi, en faktor som impliceras i ˚aderf¨orkalkning. Denna avhandling framl¨aggeren ny potentiell mekanisk f¨orILT-tillv¨axt,driven av stimuli fr˚anstr¨omnings- mekaniska och kemiska faktorer, som kan anv¨andasf¨oratt unders¨oka utveckling av ILT ¨over fysiologiskt relevanta tidsskalor och kan anv¨andas som en metod f¨oratt pr¨ova nya hypoteser; avhandlingen tillf¨orocks˚anya insikter g¨allande tillg¨anglighetenav oxyhemoglobin i regionen n¨arav¨aggenmed direkt influens p˚a˚aderf¨orkalkning. 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: conditions of the normal aorta compared to fusiform and saccular abdominal aortic with emphasis on a potential thrombus formation mechanism J. Biasetti, T. C. Gasser*, M. Auer, U. Hedin and F. Labruto Ann. 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 : a fluid dynamical approach to intra-luminal thrombus formation J. Biasetti*, F. Hussain and T. C. Gasser J. 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-luminal thrombus in abdominal aortic aneurysms J. Biasetti*, P. G. Spazzini, J. Swedenborg and T. C. Gasser Front Physiol., 3:266, 2012 (doi: 10.3389/fphys.2012.00266).

Paper D: Shear-induced migration of red blood cells in the and the carotid bifurcation: considerations on transport J. Biasetti*, P. G. Spazzini and T. C. Gasser To be submitted

In addition to the appended papers, the work has resulted in the following publications and presentations1:

Biomechanical determinants of Abdominal Aortic Aneurysms - fusiform versus pseudo(saccular) formations J. Biasetti, M. Auer, T.C. Gasser, U. Hedin and J. Swedenborg WCCM8 and ECCOMAS, Venice, Italy, June 30 - July 5, 2008 (O)

Hemodynamic simulations towards a biomechanical model of thrombus formation in Abdominal J. Biasetti, T.C. Gasser, M. Auer, U. Hedin and F. Labruto Endovascular - Bringing Basic Science into Clinical Practice, Stockholm, Sweden, March 19-21, 2009 (O)

Hemodynamic simulations in Abdominal Aortic Aneurysms - Insights into throm- bus formation J. Biasetti, T.C. Gasser, M. Auer, U. Hedin and F. Labruto 10th US National Congress on Computational Mechanics, Columbus, Ohio, US, July 16-19, 2009 (O)

Structural and hemodynamical analysis of Aortic Aneurysms from Computerized Tomography data T. 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 aneurysmatic aorta J. Biasetti, F. Hussain and T.C. Gasser ECCOMAS CFD 2010 - Fifth European Conference on Computational Fluid Dynamics, Lis- bon, Portugal, June 14-17, 2010 (O)

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

A fluido-chemical model of Thrombus formation J. Biasetti and T.C. Gasser CMBE 2011 - 2nd International Conference on Mathematical and Computational Biomedical Engineering, Washington D.C., USA, March 30 - April 1, 2011 (O)

The Intra-Luminal Thrombus in Abdominal Aortic Aneurysms: a fluido-chemical approach to explain its development J. Biasetti and T.C. Gasser 6th 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 Aneurysms J. Biasetti, F. Hussain, P.G. Spazzini and T.C. Gasser WCCM 2012 - 10th Word Congress on Computational Mechanics, S˜aoPaulo, Brazil, July 8-13, 2012 (O)

Growth of the small AAA: hemodynamic side J. Biasetti FAD Annual Scientific Meeting (Invited Talk), Madrid, Spain, May 3, 2012 (O)

A fluido-chemical model to predict the growth of Intra-Luminal Thrombus in Abdominal Aortic Aneurysms J. Biasetti and T.C. Gasser ECCOMAS 2012 - 6th European Congress on Computational Methods in Applied Sciences and Engineering, Vienna, Austria, September 10-14, 2012 (O)

The Intra-Luminal Thrombus in Abdominal Aortic Aneurysms: a fluid-chemical approach to model its development J. Biasetti, P.G. Spazzini, J. Swedenborg, F. Hussain and T.C. Gasser IMAD 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 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 and atherosclerosis Summary of appended papers 31

10 Introduction

Background

The is responsible for the delivery of oxygen and 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 . The arterial system is the higher- pressure portion of the circulatory system and carries oxygenated blood away from the . 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 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 -graft is inserted through the and placed at the site of the AAA down to the iliac arteries.

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

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

Atherosclerosis is the most common 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 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 , 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 and smooth muscles in the arterial wall. AAAs are the end result of irreversible proteolytic degradation of elastin and in the artery wall (21). Genetics and risk factors like , , 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 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 (LDL) and other -bearing materials in the arterial wall. Atheroscle- rosis normally begins as a on the endothelial surface and develops into a focally thickened intima via accumulation of cells, , connective tissue, , and pultaceous debris (45). A characteristic feature of atherosclerosis is its focal nature (86). Risk factors are numerous and the primary are: elevated serum , elevated serum levels of triglyc- erides, mellitus, smoking, genetic predisposition, stress, , 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 Physics of blood flow in arteries and its relation to intra-luminal thrombus and atherosclerosis 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)

∂u  ρ + u · ∇u = −∇p + ∇ · τ + ρf b, (2) ∂t where u is the velocity vector, ρ the density (assumed constant), p the pressure, τ = 2µD the deviatoric viscous stress tensor and f b 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 Physics of blood flow in arteries and its relation to intra-luminal thrombus and atherosclerosis 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 τ n = 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 (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 Physics of blood flow in arteries and its relation to intra-luminal thrombus and atherosclerosis

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 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 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 involved in the CC. For example the model presented in (51) provides a set of ODEs describing the reactions constituting the (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 Physics of blood flow in arteries and its relation to intra-luminal thrombus and atherosclerosis

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

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

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

24 Figure 3: Schematic of the suggested mechanism of intra-luminal thrombus (ILT) formation in abdominal aortic aneurysms (AAAs). (a) A platelet travels at the boundary of a vortex (i.e. in the region of high 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 ILT formation in an AAA. Phase 1: vortices are formed in the geometrically complex neck region and they capture non-activated platelets (grey dots). Phase 2: vortices reinforce and become mixed up while travelling downstream. Residence times are in the order of seconds and high shear at the periphery of the vortices activates platelets (black dots). Phase 3: the vortex breaks up in the distal part of the AAA and releases activated platelets, which in turn can aggregate and/or attach to the wall.

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

Figure 4: Thrombin (IIa) distribution once the periodic state is reached in the two investigated cases in Paper C. Considering a large, Case (A), and a small, Case (B), subendothelial exposure both concentration patterns are strongly shifted toward the distal AAA region. A larger area of high thrombin 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 , 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 RBCs migration on the external wall of the carotid sinus (inner curvature wall) and on the internal curvature wall of the common carotid artery. . 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 Physics of blood flow in arteries and its relation to intra-luminal thrombus and atherosclerosis

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

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

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

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