Biomechanical behaviour of cerebral aneurysm and its relation with the formation of intraluminal thrombus: a patient-specific modelling study

Cerebral aneurysm is an irreversible dilatation causing intracranial haemorrhage with severe complications. It is assumed that the biomechanical factor plays a significant role in the development of cerebral aneurysm. However, reports on the correlations between the formation of intraluminal thrombus and the flow pattern, wall shear stress (WSS) distribution of the cerebral aneurysm as well as wall compliance are still limited. In this research, patient-specific numerical simulation was carried out for three cerebral aneurysms based on magnetic resonance imaging (MRI) data-sets. The interaction between pulsatile blood and aneurysm wall was taken into account. The biomechanical behaviour of cerebral aneurysm and its relation with the formation of intraluminal thrombus was studied systematically. The results of the numerical simulation indicated that the region of low blood flow velocity and the region of swirling recirculation were nearly coincident with each other. Besides, there was a significant correlation between the slow swirling flow and the location of thrombus deposition. Excessively low WSS was also found to have strong association with the regions of thrombus formation. Moreover, the relationship between cerebral aneurysm compliance and thrombus deposition was discovered. The patient-specific modelling study based on fluid–structure interaction) may provide a basis for future investigation on the prediction of thrombus formation in cerebral aneurysm.     

Modeling the effect of blood vessel bifurcation ratio on occlusive thrombus formation

Vascular geometry is a major determinant of the hemodynamics that promote or prevent unnecessary vessel occlusion from thrombus formation. Bifurcations in the vascular geometry are repeating structures that introduce flow separation between parent and daughter vessels. We modelled the blood flow and shear rate in a bifurcation during thrombus formation and show that blood vessel bifurcation ratios determine the maximum shear rate on the surface of a growing thrombus. We built an analytical model that may aid in predicting microvascular bifurcation ratios that are prone to occlusive thrombus formation. We also observed that bifurcation ratios that adhere to Murray’s law of bifurcations may be protected from occlusive thrombus formation. These results may be useful in the rational design of diagnostic microfluidic devices and microfluidic blood oxygenators.     

Mathematical analysis of mural thrombogenesis. Concentration profiles of platelet-activating agents and effects of viscous shear flow.

The concentration profiles of adenosine diphosphate (ADP), thromboxane A2 (TxA2), thrombin, and von Willebrand factor (vWF) released extracellularly from the platelet granules or produced metabolically on the platelet membrane during thrombus growth, were estimated using finite element simulation of blood flow over model thrombi of various shapes and dimensions. The wall fluxes of these platelet-activating agents were estimated for each model thrombus at three different wall shear rates (100 s-1, 800 s-1, and 1,500 s-1), employing experimental data on thrombus growth rates and sizes. For that purpose, whole human blood was perfused in a parallel-plate flow chamber coated with type l fibrillar human collagen, and the kinetic data collected and analyzed by an EPl-fluorescence video microscopy system and a digital image processor. It was found that thrombin concentrations were large enough to cause irreversible platelet aggregation. Although heparin significantly accelerated thrombin inhibition by antithrombin lll, the remaining thrombin levels were still significantly above the minimum threshold required for irreversible platelet aggregation. While ADP concentrations were large enough to cause irreversible platelet aggregation at low shear rates and for small aggregate sizes, TxA2 concentrations were only sufficient to induce platelet shape change over the entire range of wall shear rates and thrombi dimensions studied. Our results also indicated that the local concentration of vWF multimers released from the platelet alpha-granules could be sufficient to modulate platelet aggregation at low and intermediate wall shear rates (less than 1,000 s-1). The sizes of standing vortices formed adjacent to a growing aggregate and the embolizing stresses and the torque, acting at the aggregate surface, were also estimated in this simulation. It was found that standing vortices developed on both sides of the thrombus even at low wall shear rates. Their sizes increased with thrombus size and wall shear rate, and were largely dependent upon thrombus geometry. The experimental observation that platelet aggregation occurred predominantly in the spaces between adjacent thrombi, confirmed the numerical prediction that those standing vortices are regions of reduced fluid velocities and high concentrations of platelet-activating substances, capable of trapping and stimulating platelets for aggregation. The average shear stress and normal stress, as well as the torque, acting to detach the thrombus, increased with increasing wall shear rate. Both stresses were found to be nearly independent of thrombus size and only weekly dependent upon thrombus geometry. Although both stresses had similar values at low wall shear rates, the average shear stress became the predominant embolizing stress at high wall shear rates.     

Methods to Determine the Lagrangian Shear Experienced by Platelets during Thrombus Growth

Platelets can become activated in response to changes in flow-induced shear; however, the underlying molecular mechanisms are not clearly understood. Here we present new techniques for experimentally measuring the flow-induced shear rate experienced by platelets prior to adhering to a thrombus. We examined the dynamics of blood flow around experimentally grown thrombus geometries using a novel combination of experimental (ex vivo) and numerical (in silico) methodologies. Using a microcapillary system, platelet aggregate formation was analysed at elevated shear rates in the presence of coagulation inhibitors, where thrombus formation is predominantly platelet-dependent. These approaches permit the resolution and quantification of thrombus parameters at the scale of individual platelets (2 μm) in order to quantify real time thrombus development. Using our new techniques we can correlate the shear rate experienced by platelets with the extent of platelet adhesion and aggregation. The techniques presented offer the unique capacity to determine the flow properties for a temporally evolving thrombus field in real time.     

Oscillating Couette flow for in vitro cell loading

Synovial joints are loaded by weight bearing, stretching, and fluid-driven shear. To simulate in vitro fluid-driven shear, we developed an "oscillating Couette flow mechanical shear loader". Oscillating Couette flow mimics relative motion of articular surfaces; hence, characterizing flow-induced shear by the loader enhances understanding of mechanotransduction in the joint tissue. Here, the analytical and computational models for an oscillating Couette flow were used to predict time-varying shear distribution on a plate surface, applying numerical simulation to evaluate the effects of finite plate dimension in a 2D flow. Shear stress on the plate was significantly different from that in simpler models (unbounded plates and viscous low-frequency flow). High-stress spots appeared near the leading and trailing edges of a moving plate, and a relatively uniform shear region was restricted to the interior area. Stress prediction in an example experimental geometry is presented, where the frequency and finite width effects are feasibly accounted.     

An integrated fluid–structure interaction and thrombosis model for type B aortic dissection

False lumen thrombosis (FLT) in type B aortic dissection has been associated with the progression of dissection and treatment outcome. Existing computational models mostly assume rigid wall behavior which ignores the effect of flap motion on flow and thrombus formation within the FL. In this study, we have combined a fully coupled fluid–structure interaction (FSI) approach with a shear-driven thrombosis model described by a series of convection–diffusion reaction equations. The integrated FSI-thrombosis model has been applied to an idealized dissection geometry to investigate the interaction between vessel wall motion and growing thrombus. Our simulation results show that wall compliance and flap motion can influence the progression of FLT. The main difference between the rigid and FSI models is the continuous development of vortices near the tears caused by drastic flap motion up to 4.45 mm. Flap-induced high shear stress and shear rates around tears help to transport activated platelets further to the neighboring region, thus speeding up thrombus formation during the accelerated phase in the FSI models. Reducing flap mobility by increasing the Young’s modulus of the flap slows down the thrombus growth. Compared to the rigid model, the predicted thrombus volume is 25% larger using the FSI-thrombosis model with a relatively mobile flap. Furthermore, our FSI-thrombosis model can capture the gradual effect of thrombus growth on the flow field, leading to flow obstruction in the FL, increased blood viscosity and reduced flap motion. This model is a step closer toward simulating realistic thrombus growth in aortic dissection, by taking into account the effect of intimal flap and vessel wall motion.

     

alpha4 beta1-Integrin regulates directionally persistent cell migration in response to shear flow stimulation

alpha(4)beta(1)-Integrin plays a pivotal role in cell migration in vivo. This integrin has been shown to regulate the front-back polarity of migrating cells via localized inhibition of alpha(4)-integrin/paxillin binding by phosphorylation at the alpha(4)-integrin cytoplasmic tail. Here, we demonstrate that alpha(4)beta(1)-integrin regulates directionally persistent cell migration via a more complex mechanism in which alpha(4)-integrin phosphorylation and paxillin binding act via both cooperative and independent pathways. We show that, in response to shear flow, alpha(4)beta(1)-integrin binding to the CS-1 region of fibronectin was necessary and sufficient to promote directionally persistent cell migration when this integrin was ectopically expressed in CHO cells. Under shear flow, the alpha(4)beta(1)-integrin-expressing cells formed a fan shape with broad lamellipodia at the front and retracted trailing edges at the back. This "fanning" activity was enhanced by disrupting paxillin binding alone and inhibited by disrupting phosphorylation alone or together with disrupting paxillin binding. Notably, the phosphorylation-disrupting mutation and the double mutation resulted in the formation of long trailing tails, suggesting that alpha(4)-integrin phosphorylation is required for trailing edge retraction/detachment independent of paxillin binding. Furthermore, the stable polarity and directional persistence of shear flow-stimulated cells were perturbed by the double mutation but not the single mutations alone, indicating that paxillin binding and alpha(4)-integrin phosphorylation can facilitate directionally persistent cell migration in an independent and compensatory manner. These findings provide a new insight into the mechanism by which integrins regulate directionally persistent cell migration.     

Potential fluid mechanic pathways of platelet activation

Platelet activation is a precursor for blood clotting, which plays leading roles in many vascular complications and causes of death. Platelets can be activated by chemical or mechanical stimuli. Mechanically, platelet activation has been shown to be a function of elevated shear stress and exposure time. These contributions can be combined by considering the cumulative stress or strain on a platelet as it is transported. Here, we develop a framework for computing a hemodynamic-based activation potential that is derived from a Lagrangian integral of strain rate magnitude. We demonstrate that such a measure is generally maximized along, and near to, distinguished material surfaces in the flow. The connections between activation potential and these structures are illustrated through stenotic flow computations. We uncover two distinct structures that may explain observed thrombus formation at the apex and downstream of stenoses. More broadly, these findings suggest fundamental relationships may exist between potential fluid mechanic pathways for mechanical platelet activation and the mechanisms governing their transport.     

Tortuosity triggers platelet activation and thrombus formation in microvessels

Tortuous blood vessels are often seen in humans in association with thrombosis, atherosclerosis, hypertension, and aging. Vessel tortuosity can cause high fluid shear stress, likely promoting thrombosis. However, the underlying physical mechanisms and microscale processes are poorly understood. Accordingly, the objectives of this study were to develop and use a new computational approach to determine the effects of venule tortuosity and fluid velocity on thrombus initiation. The transport, collision, shear-induced activation, and receptor-ligand adhesion of individual platelets in thrombus formation were simulated using discrete element method. The shear-induced activation model assumed that a platelet became activated if it experienced a shear stress above a relative critical shear stress or if it contacted an activated platelet. Venules of various levels of tortuosity were simulated for a mean flow velocity of 0.10?cm s(-1), and a tortuous arteriole was simulated for a mean velocity of 0.47?cm s(-1). Our results showed that thrombus was initiated at inner walls in curved regions due to platelet activation in agreement with experimental studies. Increased venule tortuosity modified fluid flow to hasten thrombus initiation. Compared to the same sized venule, flow in the arteriole generated a higher amount of mural thrombi and platelet activation rate. The results suggest that the extent of tortuosity is an important factor in thrombus initiation in microvessels.     

Developing pulsatile flow in a deployed coronary stent

A major consequence of stent implantation is restenosis that occurs due to neointimal formation. This patho-physiologic process of tissue growth may not be completely eliminated. Recent evidence suggests that there are several factors such as geometry and size of vessel, and stent design that alter hemodynamic parameters, including local wall shear stress distributions, all of which influence the restenosis process. The present three-dimensional analysis of developing pulsatile flow in a deployed coronary stent quantifies hemodynamic parameters and illustrates the changes in local wall shear stress distributions and their impact on restenosis. The present model evaluates the effect of entrance flow, where the stent is placed at the entrance region of a branched coronary artery. Stent geometry showed a complex three-dimensional variation of wall shear stress distributions within the stented region. Higher order of magnitude of wall shear stress of 530 dyn/cm2 is observed on the surface of cross-link intersections at the entrance of the stent. A low positive wall shear stress of 10 dyn/cm2 and a negative wall shear stress of -10 dyn/cm2 are seen at the immediate upstream and downstream regions of strut intersections, respectively. Modified oscillatory shear index is calculated which showed persistent recirculation at the downstream region of each strut intersection. The portions of the vessel where there is low and negative wall shear stress may represent locations of thrombus formation and platelet accumulation. The present results indicate that the immediate downstream regions of strut intersections are areas highly susceptible to restenosis, whereas a high shear stress at the strut intersection may cause platelet activation and free emboli formation.     

Determining possible thrombus sites in an extracorporeal device,using computational fluid dynamics-derived relative residence time

The prediction of conditions that may result in thrombus formation is a useful application of computational fluid dynamics. A number of techniques exist, based on the consideration of wall shear stress and regions of low blood flow; however, no clear guideline exists for the best practice of their use. In this paper, the sensitivity of each parameter and the specific mechanical forces are explained, before the optimal indicator of thrombosis risk is outlined. An extracorporeal access device cavity provides a suitable geometry to test the methodology. The recommended method for thrombus prediction considers areas with a calculated residence time (RT) and shear strain rate (SSR) thresholds, here set to RT>1 and SSR < 10 s^? 1. Evidence of thrombosis was found for physiological waveforms with an absence of reverse flow, which is expected to ‘wash out’ the cavity. The predicted thrombosis sites compare well with evidence collected from explanted devices.     

Computational simulation of hemodynamic-driven growth and remodeling of embryonic atrioventricular valves

Embryonic heart valves develop under continuous and demanding hemodynamic loading. The particular contributions of fluid pressure and shear tractions in valve morphogenesis are difficult to decouple experimentally. To better understand how fluid loads could direct valve formation, we developed a computational model of avian embryonic atrioventricular (AV) valve (cushion) growth and remodeling using experimentally derived parameters for the blood flow and the cushion stiffness. Through an iterative scheme, we first solved the fluid loads on the axisymmetric AV canal and cushion model geometry. We then applied the fluid loads to the cushion and integrated the evolution equations to determine the growth and remodeling. After a set time of growth, we updated the fluid domain to reflect the change in cushion geometry and resolved for the fluid forces. The rate of growth and remodeling was assumed to be a function of the difference between the current stress and an isotropic homeostatic stress state. The magnitude of the homeostatic stress modulated the rate of volume addition during the evolution. We found that the pressure distribution on the AV cushion was sufficient to generate leaflet-like elongation in the direction of flow, through inducing tissue resorption on the inflow side of cushion and expansion on the outflow side. Conversely, shear tractions minimally altered tissue volume, but regulated the remodeling of tissue near the cushion surface, particular at the leading edge. Significant shear and circumferential residual stresses developed as the cushion evolved. This model offers insight into how natural and perturbed mechanical environments may direct AV valvulogenesis and provides an initial framework on which to incorporate more mechano-biological details.     

Flow and thrombosis at orifices simulating mechanical heart valve leakage regions

BACKGROUND: While it is established that mechanical heart valves (MHVs) damage blood elements during leakage and forward flow, the role in thrombus formation of platelet activation by high shear flow geometries remains unclear. In this study, continuously recalcified blood was used to measure the effects of blood flow through orifices, which model MHVs, on the generation of procoagulant thrombin and the resulting formation of thrombus. The contribution of platelets to this process was also assessed. METHOD OF APPROACH: 200, 400, 800, and 1200 microm orifices simulated the hinge region of bileaflet MHVs, and 200, 400, and 800 microm wide slits modeled the centerline where the two leaflets meet when the MHV is closed. To assess activation of coagulation during blood recirculation, samples were withdrawn over 0-47 min and the plasmas assayed for thrombin-antithrombin-llI (TAT) levels. Model geometries were also inspected visually. RESULTS: The 200 and 400 microm round orifices induced significant TAT generation and thrombosis over the study interval. In contrast, thrombin generation by the slit orifices, and by the 800 and 1200 microm round orifices, was negligible. In additional experiments with nonrecalcified or platelet-depleted blood, TAT levels were markedly reduced versus the studies with fully anticoagulated whole blood (p < 0.05). CONCLUSIONS: Using the present method, a significant increase in TAT concentration was found for 200 and 400 microm orifices, but not 800 and 1200 microm orifices, indicating that these flow geometries exhibit a critical threshold for activation of coagulation and resulting formation of thrombus. Markedly lower TAT levels were produced in studies with platelet-depleted blood, documenting a key role for platelets in the thrombotic process.     

Thrombotic risk stratification using computational modeling in patients with coronary artery aneurysms following Kawasaki disease

Kawasaki disease (KD) is the leading cause of acquired heart disease in children and can result in life-threatening coronary artery aneurysms in up to 25 % of patients. These aneurysms put patients at risk of thrombus formation, myocardial infarction, and sudden death. Clinicians must therefore decide which patients should be treated with anticoagulant medication, and/or surgical or percutaneous intervention. Current recommendations regarding initiation of anticoagulant therapy are based on anatomy alone with historical data suggesting that patients with aneurysms \(\ge \) 8 mm are at greatest risk of thrombosis. Given the multitude of variables that influence thrombus formation, we postulated that hemodynamic data derived from patient-specific simulations would more accurately predict risk of thrombosis than maximum diameter alone. Patient-specific blood flow simulations were performed on five KD patients with aneurysms and one KD patient with normal coronary arteries. Key hemodynamic and geometric parameters, including wall shear stress, particle residence time, and shape indices, were extracted from the models and simulations and compared with clinical outcomes. Preliminary fluid structure interaction simulations with radial expansion were performed, revealing modest differences in wall shear stress compared to the rigid wall case. Simulations provide compelling evidence that hemodynamic parameters may be a more accurate predictor of thrombotic risk than aneurysm diameter alone and motivate the need for follow-up studies with a larger cohort. These results suggest that a clinical index incorporating hemodynamic information be used in the future to select patients for anticoagulant therapy.     

Slowness of blood flow and resultant thrombus formation in cerebral aneurysms

It is not yet fully understood what causes cerebral aneurysms to rupture. Although no definitive conclusion has been reached, it is considered that there are haemodynamic, biochemical and physiological factors contributing to rupture. Numerical techniques seem promising for investigation of this multi-physical phenomenon. In fact, recent intensive numerical studies with computational fluid dynamics have revealed detailed haemodynamic features of the flow in cerebral aneurysms such as velocity, pressure and wall shear stress distributions. It is, therefore, expected that biochemical and physiological aspects of aneurysmal rupture will also be actively investigated using numerical approaches. Considering this background, the authors have been working on modelling of thrombus formation in cerebral aneurysms caused by stagnant blood flow, because many studies have suggested that slow blood flow and resulting low wall shear stress are connected with rupture. Firstly, in this review paper, slowness of the intra-aneurysmal flow is reviewed with an energy balance theory, and secondly, thrombus formation in cerebral bifurcation aneurysms is discussed from the viewpoint of numerical modelling. A computational result obtained by application of the authors’ platelet aggregation–adhesion model is also provided.     

Pattern formation of vascular smooth muscle cells subject to nonuniform fluid shear stress: mediation by gradient of cell density

Smooth muscle cells (SMCs) are organized in various patterns in blood vessels. Whereas straight blood vessels mainly contain circumferentially aligned SMCs, curved blood vessels are composed of axially aligned SMCs in regions with vortex blood flow. The vortex flow-dependent feature of SMC alignment suggests a role for nonuniform fluid shear stress in regulating the pattern formation of SMCs. Here, we demonstrate that, in experimental models with vascular polymer implants designed for the observation of neointima formation and SMC migration under defined fluid shear stress, nonuniform shear stress possibly plays a role in regulating the direction of SMC migration and alignment in the neointima of the vascular implant. It was found that fluid shear stress inhibited cell growth, and the presence of nonuniform shear stress influenced the distribution of total cell density and induced the formation of cell density gradients, which in turn directed SMC migration and alignment. In contrast, uniform fluid shear stress in a control model influenced neither the distribution of total cell density nor the direction of SMC migration and alignment. In both the uniform and nonuniform shear models, the gradient of total cell density was consistent with the alignment of SMCs. These observations suggest that nonuniform shear stress may regulate the pattern formation of SMCs, possibly via mediating the gradient of cell density in the neointima of vascular polymer implants.     

Growth kinetics of platelet thrombi

A model for the kinetics of a platelet thrombus growth is presented, which takes into account the principal hydrodynamic and cellular adhesion features of thrombus development. These consist of the rate at which platelets encounter the growing thrombus, their residence time near the surface of the thrombus, the rate of escape over the potential barrier between the free platelets and the surface of the thrombus, and the influence of ADP or related agents on the height of this potential barrier. The latter is explained in terms of the changes in the shape and surface potential of platelets, which are induced by exposure to ADP or related agents.In qualitative agreement with available experimental data, the model predicts an approximately exponential growth of the thrombus volume, a maximum in the growth rate with respect to the blood flow rate, and a plateau value which is reached by the thrombus volume with time. It is shown that at low flow rates the rate of provision of platelets by the blood stream is the determining factor, while at high flow rates the kinetics of adhesion to the surface of the thrombus are predominant. Under all circumstances, when the blood conduit becomes more than about half occluded, the resulting decrease in the blood flow rate decreases, in turn, the growth rate of the thrombus.     

Simulation of blood flow in a small-diameter vascular graft model with a swirl (spiral) flow guider

Small-diameter vascular grafts are in large demand for coronary and peripheral bypass procedures, but present products still fail in long-term clinical application. In the present communication, a new type of small-diameter graft with a swirl flow guider was proposed to improve graft patency rate. Flow pattern in the graft was simulated numerically and compared with that in a conventional graft. The numerical results revealed that the swirl flow guider could indeed make the blood flow rotate in the new graft. The swirling flow distal to the flow guider significantly altered the flow pattern in the new graft and the ve- locity profiles were re-distributed. Due to the swirling flow, the blood velocity near the vessel wall and wall shear rate were greatly enhanced. We believe that the increased blood velocity near the wall and the wall shear rate can impede the occurrence of acute thrombus formation and intimal hyperplasia, hence can improve the graft patency rate for long-term clinical use.     

Proliferation, differentiation, and tube formation by endothelial progenitor cells in response to shear stress.

Endothelial progenitor cells (EPCs), circulating in peripheral blood, migrate toward target tissue, differentiate, and contribute to the formation of new vessels. In this study, we report that shear stress generated by blood flow or tissue fluid flow can accelerate the proliferation, differentiation, and capillary-like tube formation of EPCs. When EPCs cultured from human peripheral blood were subjected to laminar shear stress, the cells elongated and oriented their long axes in the direction of flow. The cell density of the EPCs exposed to shear stress was higher, and a larger percentage of these cells were in the G2-M phase of the cell cycle, compared with EPCs cultured under static conditions. Shear stress markedly increased the EPC expression of two vascular endothelial growth factor receptors, kinase insert domain-containing receptor and fms-like tyrosine kinase-1, and an intercellular adhesion molecule, vascular endothelial-cadherin, at both the protein and mRNA levels. Assays for tube formation in the collagen gels showed that the shear-stressed EPCs formed tubelike structures and developed an extensive tubular network significantly faster than the static controls. These findings suggest that EPCs are sensitive to shear stress and that their vasculogenic activities may be modulated by shear stress.     

Modeling pulsatile flow in aortic aneurysms: effect of non-Newtonian properties of blood

Pulsatile flow in an axisymmetric rigid-walled model of an abdominal aorta aneurysm was analyzed numerically for various aneurysm dilations using physiologically realistic resting waveform at time-averaged Reynolds number of 300 and peak Reynolds number of 1607. Discretization of the governing equations was achieved using a finite element scheme based on the Galerkin method of weighted residuals. Comparisons with previously published work on the basis of special cases were performed and found to be in excellent agreement. Our findings indicate that the velocity fields are significantly affected by non-Newtonian properties in pathologically altered configurations. Non-Newtonian fluid shear stress is found to be greater than Newtonian fluid shear stress during peak systole. Further, the maximum shear stress is found to occur near the distal end of AAA during peak systole. The impact of non-Newtonian blood flow characteristics on pressure compared to Newtonian model is found insignificant under resting conditions. Viscous and inertial forces associated with blood flow are responsible for the changes in the wall that result in thrombus deposition and dilation while rupture of AAA is more likely determined by much larger mechanical stresses imposed by pulsatile pressure on the wall of AAA.