A review of macroscopic thrombus modeling methods

A numerical study of the effect of thrombus breakdown on predicted thrombus formation and growth

Thrombosis is a complex biological process which involves many biochemical reactions and is influenced by blood flow. Various computational models have been developed to simulate natural thrombosis in diseases such as aortic dissection (AD), and device-induced thrombosis in blood-contacting biomedical devices. While most hemodynamics-based models consider the role of low shear stress in the initiation and growth of thrombus, they often ignore the effect of thrombus breakdown induced by elevated shear stress. In this study, a new shear stress-induced thrombus breakdown function is proposed and implemented in our previously published thrombosis model. The performance of the refined model is assessed by quantitative comparison with experimental data on thrombus formation in a backward-facing step geometry, and qualitative comparison with in vivo data obtained from an AD patient. Our results show that incorporating thrombus breakdown improves accuracy in predicted thrombus volume and captures the same pattern of thrombus evolution as measured experimentally and in vivo. In the backward-facing step geometry, thrombus breakdown impedes growth over the step and downstream, allowing a stable thrombus to be reached more quickly. Moreover, the predicted thrombus volume, height and length are in better agreement with the experimental measurements compared to the original model which does not consider thrombus breakdown. In the patient-specific AD, the refined model outperforms the original model in predicting the extent and location of thrombosis. In conclusion, the effect of thrombus breakdown is not negligible and should be included in computational models of thrombosis.

Investigating clot-flow interactions by integrating intravital imaging with in silico modeling for analysis of flow, transport, and hemodynamic forces

As a blood clot forms, grows, deforms, and embolizes following a vascular injury, local clot-flow interactions lead to a highly dynamic flow environment. The local flow influences transport of biochemical species relevant for clotting, and determines the forces on the clot that in turn lead to clot deformation and embolization. Despite this central role, quantitative characterization of this dynamic clot-flow interaction and flow environment in the clot neighborhood remains a major challenge. Here, we propose an approach that integrates dynamic intravital imaging with computer geometric modeling and computational flow and transport modeling to develop a unified in silico framework to quantify the dynamic clot-flow interactions. We outline the development of the methodology referred to as Intravital Integrated In Silico Modeling or IVISim, and then demonstrate the method on a sample set of simulations comprising clot formation following laser injury in two mouse cremaster arteriole injury model data: one wild-type mouse case, and one diYF knockout mouse case. Simulation predictions are verified against experimental observations of transport of caged fluorescent Albumin (cAlb) in both models. Through these simulations, we illustrate how the IVISim methodology can provide insights into hemostatic processes, the role of flow and clot-flow interactions, and enable further investigations comparing and contrasting different biological model scenarios and parameter variations.

Multi-Objective Optimisation of a Novel Bypass Graft with a Spiral Ridge

The low long-term patency of bypass grafts is a major concern for cardiovascular treatments. Unfavourable haemodynamic conditions in the proximity of distal anastomosis are closely related to thrombus creation and lumen lesions. Modern graft designs address this unfavourable haemodynamic environment with the introduction of a helical component in the flow field, either by means of out-of-plane helicity graft geometry or a spiral ridge. While the latter has been found to lack in performance when compared to the out-of-plane helicity designs, recent findings support the idea that the existing spiral ridge grafts can be further improved in performance through optimising relevant design parameters. In the current study, robust multi-objective optimisation techniques are implemented, covering a wide range of possible designs coupled with proven and well validated computational fluid dynamics (CFD) algorithms. It is shown that the final set of suggested design parameters could significantly improve haemodynamic performance and therefore could be used to enhance the design of spiral ridge bypass grafts.

Modelling of thrombus formation using smoothed particle hydrodynamics method

In this paper a novel model, based on the smoothed particle hydrodynamics (SPH) method, is proposed to simulate thrombus formation. This describes the main phases of the coagulative cascade through the balance of four biochemical species and three type of platelets. SPH particles can switch from fluid to solid phase when specific biochemical and physical conditions are satisfied. The interaction between blood and the forming blood clot is easily handled by an innovative monolithic FSI approach. Fluid-solid coupling is modelled by introducing elastic binds between solid particles, without requiring detention and management of the interface between the two media. The proposed model is able to realistically reproduce the thromboembolic process, as confirmed by the comparison of numerical results with experimental data available in the literature.

Models of Shear-Induced Platelet Activation and Numerical Implementation With Computational Fluid Dynamics Approaches

Shear-induced platelet activation is one of the critical outcomes when blood is exposed to elevated shear stress. Excessively activated platelets in the circulation can lead to thrombus formation and platelet consumption, resulting in serious adverse events such as thromboembolism and bleeding. While experimental observations reveal that it is related to the shear stress level and exposure time, the underlying mechanism of shear-induced platelet activation is not fully understood. Various models have been proposed to relate shear stress levels to platelet activation, yet most are modified from the empirically calibrated power-law model. Newly developed multiscale platelet models are tested as a promising approach to capture a single platelet's dynamic shape during activation, but it would be computationally expensive to employ it for a large-scale analysis. This paper summarizes the current numerical models used to study the shear-induced platelet activation and their computational applications in the risk assessment of a particular flow pattern and clot formation prediction.

Volumetric lattice Boltzmann method for wall stresses of image-based pulsatile flows

Image-based computational fluid dynamics (CFD) has become a new capability for determining wall stresses of pulsatile flows. However, a computational platform that directly connects image information to pulsatile wall stresses is lacking. Prevailing methods rely on manual crafting of a hodgepodge of multidisciplinary software packages, which is usually laborious and error-prone. We present a new computational platform, to compute wall stresses in image-based pulsatile flows using the volumetric lattice Boltzmann method (VLBM). The novelty includes: (1) a unique image processing to extract flow domain and local wall normality, (2) a seamless connection between image extraction and VLBM, (3) an en-route calculation of strain-rate tensor, and (4) GPU acceleration (not included here). We first generalize the streaming operation in the VLBM and then conduct application studies to demonstrate its reliability and applicability. A benchmark study is for laminar and turbulent pulsatile flows in an image-based pipe (Reynolds number: 10 to 5000). The computed pulsatile velocity and shear stress are in good agreements with Womersley's analytical solutions for laminar pulsatile flows and concurrent laboratory measurements for turbulent pulsatile flows. An application study is to quantify the pulsatile hemodynamics in image-based human vertebral and carotid arteries including velocity vector, pressure, and wall-shear stress. The computed velocity vector fields are in reasonably well agreement with MRA (magnetic resonance angiography) measured ones. This computational platform is good for image-based CFD with medical applications and pore-scale porous media flows in various natural and engineering systems.

An Accelerated Thrombosis Model for Computational Fluid Dynamics Simulations in Rotary Blood Pumps

Purpose

Thrombosis ranks among the major complications in blood-carrying medical devices and a better understanding to influence the design related contribution to thrombosis is desirable. Over the past years many computational models of thrombosis have been developed. However, numerically cheap models able to predict localized thrombus risk in complex geometries are still lacking. The aim of the study was to develop and test a computationally efficient model for thrombus risk prediction in rotary blood pumps.

Methods

We used a two-stage approach to calculate thrombus risk. The first stage involves the computation of velocity and pressure fields by computational fluid dynamic simulations. At the second stage, platelet activation by mechanical and chemical stimuli was determined through species transport with an Eulerian approach. The model was compared with existing clinical data on thrombus deposition within the HeartMate II. Furthermore, an operating point and model parameter sensitivity analysis was performed.

Results

Our model shows good correlation (R² > 0.93) with clinical data and identifies the bearing and outlet stator region of the HeartMate II as the location most prone to thrombus formation. The calculation of thrombus risk requires an additional 10–20 core hours of computation time.

Conclusion

The concentration of activated platelets can be used as a surrogate and computationally low-cost marker to determine potential risk regions of thrombus deposition in a blood pump. Relative comparisons of thrombus risk are possible even considering the intrinsic uncertainty in model parameters and operating conditions.

Supplementary Information

The online version contains supplementary material available at 10.1007/s13239-021-00606-y.

Preclinical modeling of mechanical thrombectomy

Mechanical thrombectomy to treat large vessel occlusions (LVO) causing a stroke is one of the most effective treatments in medicine, with a number needed to treat to improve clinical outcomes as low as 2.6. As the name implies, it is a mechanical solution to a blocked artery and modeling these mechanics preclinically for device design, regulatory clearance and high-fidelity physician training made clinical applications possible. In vitro simulation of LVO is extensively used to characterize device performance in representative vascular anatomies with physiologically accurate hemodynamics. Embolus analogues, validated against clots extracted from patients, provide a realistic simulated use experience. In vitro experimentation produces quantitative results such as particle analysis of distal emboli generated during the procedure, as well as pressure and flow throughout the experiment. Animal modeling, used mostly for regulatory review, allows estimation of device safety. Other than one recent development, nearly all animal modeling does not incorporate the desired target organ, the brain, but rather is performed in the extracranial circulation. Computational modeling of the procedure remains at the earliest stages but represents an enormous opportunity to rapidly characterize and iterate new thrombectomy concepts as well as optimize procedure workflow. No preclinical model is a perfect surrogate; however, models available can answer important questions during device development and have to date been successful in delivering efficacious and safe devices producing excellent clinical outcomes. This review reflects on the developments of preclinical modeling of mechanical thrombectomy with particular focus on clinical translation, as well as articulate existing gaps requiring additional research.

In-vitro thromboelastographic characterization of reconstituted whole blood utilizing cryopreserved platelets

Conducting in-vitro thrombosis research presents numerous challenges, the primary of which is working with blood products, whether whole blood or fractionated whole blood, that have limited functional shelf-lives. As a result, being able to significantly prolong the clotting functionality of whole blood via fractionation and recombination promises greater accessibility via resource minimization in the realm of thrombosis research. Whole blood with CPDA1 from healthy volunteers was fractionated and stored as frozen platelet-free plasma (PFP, -20°C), refrigerated packed red blood cells (pRBCs, 4°C) and cryopreserved platelets (-80°C). Subsequent recombination of the above components into their native ratios were tested via thromboelastography (TEG) to capture clotting dynamics over a storage period of 13 weeks in comparison to refrigerated unfractionated WB+CPDA1. Reconstituted whole blood utilizing PFP, pRCBs and cryopreserved platelets were able to maintain clot strength (maximum amplitude) akin to day-0 whole blood even after 13 weeks of storage. Clots formed by reconstituted whole blood exhibited quicker clotting dynamics with nearly two-fold shorter R-times and nearly 1.3-fold increase in fibrin deposition rate as measured by TEG. Storage of fractionated whole blood components, in their respective ideal conditions, provides a means of prolonging the usable life of whole blood for in-vitro thrombosis research. Cryopreserved platelets, when recombined with frozen PFP and refrigerated pRBCs, are able to form clots that nearly mirror the overall clotting profile expected of freshly drawn WB.

Refining a numerical model for device-induced thrombosis and investigating the effects of non-Newtonian blood models

Thrombosis is one of the main causes of failure in device implantation. Computational thrombosis simulation is a convenient approach to evaluate the risk of thrombosis for a device. However, thrombosis is a complicated process involving multiple species and reactions. Application of a macroscopic, single-scale computational model for device-induced thrombosis is a cost-effective approach. The current study has refined an existing thrombosis model, which simulated thrombosis by tracing four species in blood: non-activated platelets, activated platelets, surface adherent platelets, and ADP. Platelets are activated mechanically by shear stress, and chemically by ADP. Platelet adhesion occurs on surfaces with low wall shear stress with platelet aggregation inhibited in regions of high shear stress. The study improves the existing thrombosis model by: 1) Modifying the chemical platelet activation function so that ADP activates platelets; 2) Modifying the function describing thrombus deposition and growth to distinguish between thrombus deposition on wall surfaces and thrombus growth on existing thrombus surfaces; 3) Modifying the thrombus breakdown function to allow for thrombus breakdown by shear stress; 4) Modeling blood flow as non-Newtonian. The results show that the inclusion of ADP and the use of a non-Newtonian model improve agreement with experimental data.

Fluid-structure coupled biotransport processes in aortic valve disease

Biological transport processes near the aortic valve play a crucial role in calcific aortic valve disease initiation and bioprosthetic aortic valve thrombosis. Hemodynamics coupled with the dynamics of the leaflets regulate these transport patterns. Herein, two-way coupled fluid-structure interaction (FSI) simulations of a 2D bicuspid aortic valve and a 3D mechanical heart valve were performed and coupled with various convective mass transport models that represent some of the transport processes in calcification and thrombosis. Namely, five different continuum transport models were developed to study biochemicals that originate from the blood and the leaflets, as well as residence-time and flow stagnation. Low-density lipoprotein (LDL) and platelet activation were studied for their role in calcification and thrombosis, respectively. Coherent structures were identified using vorticity and Lagrangian coherent structures (LCS) for the 2D and 3D models, respectively. A very close connection between vortex structures and biochemical concentration patterns was shown where different vortices controlled the concentration patterns depending on the transport mechanism. Additionally, the relationship between leaflet concentration and wall shear stress was revealed. Our work shows that blood flow physics and coherent structures regulate the flow-mediated biological processes that are involved in aortic valve calcification and thrombosis, and therefore could be used in the design process to optimize heart valve replacement durability.

Assessment of surface roughness and blood rheology on local coronary haemodynamics: a multi-scale computational fluid dynamics study

The surface roughness of the coronary artery is associated with the onset of atherosclerosis. The study applies, for the first time, the micro-scale variation of the artery surface to a 3D coronary model, investigating the impact on haemodynamic parameters which are indicators for atherosclerosis. The surface roughness of porcine coronary arteries have been detailed based on optical microscopy and implemented into a cylindrical section of coronary artery. Several approaches to rheology are compared to determine the benefits/limitations of both single and multiphase models for multi-scale geometry. Haemodynamic parameters averaged over the rough/smooth sections are similar; however, the rough surface experiences a much wider range, with maximum wall shear stress greater than 6 Pa compared to the approximately 3 Pa on the smooth segment. This suggests the smooth-walled assumption may neglect important near-wall haemodynamics. While rheological models lack sufficient definition to truly encompass the micro-scale effects occurring over the rough surface, single-phase models (Newtonian and non-Newtonian) provide numerically stable and comparable results to other coronary simulations. Multiphase models allow for phase interactions between plasma and red blood cells which is more suited to such multi-scale models. These models require additional physical laws to govern advection/aggregation of particulates in the near-wall region.

The key events of thrombus formation: platelet adhesion and aggregation

Thrombus formation is a complex, dynamic and multistep process, involving biochemical reactions, mechanical stimulation, hemodynamics, and so on. In this study, we concentrate on its two crucial steps: (i) platelets adhered to a vessel wall, or simply platelet adhesion, and (ii) platelets clumping and arrested to the adherent platelets, named platelet aggregation. We report the first direct simulation of three modes of platelet adhesion, detachment, rolling adhesion and firm adhesion, as well as the formation, disintegration, arrestment and consolidation of platelet plugs. The results show that the bond dissociation in the detachment mode is mainly attributed to a high probability of rupturing bonds, such that any existing bond can be quickly ruptured and all bonds would be completely broken. In the rolling adhesion, however, it is mainly attributed to the strong traction from the shear flow or erythrocytes, causing that the bonds are ruptured at the trailing edge of the platelet. The erythrocytes play an important role in platelet activities, such as the formation, disintegration, arrestment and consolidation of platelet plugs. They exert an aggregate force on platelets, a repulsion at a near distance but an attraction at a far distance to the platelets. This aggregate force can promote platelets to form a plug and/or bring along a part of a platelet plug causing its disintegration. It also greatly influences the arrestment and consolidation of platelet plugs, together with the adhesive force from the thrombus.

Recent advances in computational modeling of fibrin clot formation: A review

The field of thrombosis and hemostasis is crucial for understanding and developing new therapies for pathologies such as deep vein thrombosis, diabetes related strokes, pulmonary embolisms, and hemorrhaging related diseases. In the last two decades, an exponential growth in studies related to fibrin clot formation using computational tools has been observed. Despite this growth, the complete mechanism behind thrombus formation and hemostasis has been long and rife with obstacles; however, significant progress has been made in the present century. The computational models and methods used in this context are diversified into different spatiotemporal scales, yet there is no single model which can predict both physiological and mechanical properties of fibrin clots. In this review, we list the major strategies employed by researchers in modeling fibrin clot formation using recent and existing computational techniques. This review organizes the computational strategies into continuum level, system level, discrete particle (DPD), and multi-scale methods. We also discuss strengths and weaknesses of various methods and future directions in which computational modeling of fibrin clots can advance.

Automated reduction of blood coagulation models

Mathematical modeling of thrombosis typically involves modeling the coagulation cascade. Models of coagulation generally involve the reaction kinetics for dozens of proteins. The resulting system of equations is difficult to parameterize, and its numerical solution is challenging when coupled to blood flow or other physics important to clotting. Prior research suggests that essential aspects of coagulation may be reproduced by simpler models. This evidence motivates a systematic approach to model reduction. We herein introduce an automated framework to generate reduced-order models of blood coagulation. The framework consists of nested optimizations, where an outer optimization selects the optimal species for the reduced-order model and an inner optimization selects the optimal reaction rates for the new coagulation network. The framework was tested on an established 34-species coagulation model to rigorously consider what level of model fidelity is necessary to capture essential coagulation dynamics. The results indicate that a nine-species reduced-order model is sufficient to reproduce the thrombin dynamics of the benchmark 34-species model for a range of tissue factor concentrations, including those not included in the optimization process. Further model reduction begins to compromise the ability to capture the thrombin generation process. The framework proposed herein enables automated development of reduced-order models of coagulation that maintain essential dynamics used to model thrombosis.

Mathematical modelling indicates that lower activity of the haemostatic system in neonates is primarily due to lower prothrombin concentration

Haemostasis is governed by a highly complex system of interacting proteins. Due to the central role of thrombin, thrombin generation and specifically the thrombin generation curve (TGC) is commonly used as an indicator of haemostatic activity. Functional characteristics of the haemostatic system in neonates and children are significantly different compared with adults; at the same time plasma levels of haemostatic proteins vary considerably with age. However, relating one to the other has been difficult, both due to significant inter-individual differences for individuals of similar age and the complexity of the biochemical reactions underlying haemostasis. Mathematical modelling has been very successful at representing the biochemistry of blood clotting. In this study we address the challenge of large inter-individual variability by parameterising the Hockin-Mann model with data from individual patients, across different age groups from neonates to adults. Calculating TGCs for each patient of a specific age group provides us with insight into the variability of haemostatic activity across that age group. From our model we observe that two commonly used metrics for haemostatic activity are significantly lower in neonates than in older patients. Because both metrics are strongly determined by prothrombin and prothrombin levels are considerably lower in neonates we conclude that decreased haemostatic activity in neonates is due to lower prothrombin availability.

Strongly Coupled Morphological Features of Aortic Aneurysms Drive Intraluminal Thrombus

Over 75% of abdominal aortic aneurysms harbor an intraluminal thrombus, and increasing evidence suggests that biologically active thrombus contributes to the natural history of these potentially lethal lesions. Thrombus formation depends on the local hemodynamics, which in turn depends on morphological features of the aneurysm and near vasculature. We previously presented a hemodynamically motivated “thrombus formation potential” that predicts where and when thrombus might form. Herein, we combine detailed studies of the three-dimensional hemodynamics with methods of sparse grid collocation and interpolation via kriging to examine roles of five key morphological features of aneurysms on thrombus formation: lesion diameter, axial position, length, curvature, and renal artery position. Computational simulations suggest that maximum diameter is a key determinant of thrombogenicity, but other morphological features modulate this dependence. More distally located lesions tend to have a higher thrombus formation potential and shorter lesions tend to have a higher potential than longer lesions, given the same aneurysmal dilatation. Finally, movement of vortical structures through the infrarenal aorta and lesion can significantly affect thrombogenicity. Formation of intraluminal thrombus within an evolving abdominal aortic aneurysm thus depends on coupled morphological features, not all intuitive, and computational simulations can be useful for predicting thrombogenesis.

Effect of Local Coil Density on Blood Flow Stagnation in Densely Coiled Cerebral Aneurysms: A Computational Study Using a Cartesian Grid Method

Aneurysm recurrence is the most critical concern following coil embolization of a cerebral aneurysm. Adequate packing density (PD) and coil uniformity are believed necessary to achieve sufficient flow stagnation, which decreases the risk of aneurysm recurrence. The effect of coil distribution on the extent of flow stagnation, however, especially in cases of dense packing (high PD), has received less attention. Thus, the cause of aneurysm recurrence despite dense packing is still an open question. The primary aim of this study is to evaluate the effect of local coil density on the extent of blood flow stagnation in densely coiled aneurysms. For this purpose, we developed a robust computational framework to determine blood flow using a Cartesian grid method, by which the complex fluid pathways in coiled aneurysms could be flexibly treated using an implicit function. This tool allowed us to conduct blood flow analyses in two patient-specific geometries with 50 coil distribution patterns in each aneurysm at clinically adequate PD. The results demonstrated that dense packing in the aneurysm may not necessarily block completely the inflow into the aneurysm and local flow that formed in the neck region, whose strength was inversely related to this local PD. This finding suggests that local coil density in the neck region still plays an important role in disturbing the remaining local flow, which possibly prevents thrombus formation in a whole aneurysm sac, increasing the risk of aneurysm regrowth and subsequent recurrence.

A FSI computational framework for vascular physiopathology: A novel flow-tissue multiscale strategy

A novel fluid-structure computational framework for vascular applications is herein presented. It is developed by combining the double multi-scale nature of vascular physiopathology in terms of both tissue properties and blood flow. Addressing arterial tissues, they are modelled via a nonlinear multiscale constitutive rationale, based only on parameters having a clear histological and biochemical meaning. Moreover, blood flow is described by coupling a three-dimensional fluid domain (undergoing physiological inflow conditions) with a zero-dimensional model, which allows to reproduce the influence of the downstream vasculature, furnishing a realistic description of the outflow proximal pressure. The fluid-structure interaction is managed through an explicit time-marching approach, able to accurately describe tissue nonlinearities within each computational step for the fluid problem. A case study associated to a patient-specific aortic abdominal aneurysmatic geometry is numerically investigated, highlighting advantages gained from the proposed multiscale strategy, as well as showing soundness and effectiveness of the established framework for assessing useful clinical quantities and risk indexes.

Molecular dynamics simulations indicate that deoxyhemoglobin, oxyhemoglobin, carboxyhemoglobin, and glycated hemoglobin under compression and shear exhibit an anisotropic mechanical behavior

We developed a new mechanical model for determining the compression and shear mechanical behavior of four different hemoglobin structures. Previous studies on hemoglobin structures have focused primarily on overall mechanical behavior; however, this study investigates the mechanical behavior of hemoglobin, a major constituent of red blood cells, using steered molecular dynamics (SMD) simulations to obtain anisotropic mechanical behavior under compression and shear loading conditions. Four different configurations of hemoglobin molecules were considered: deoxyhemoglobin (deoxyHb), oxyhemoglobin (HbO₂), carboxyhemoglobin (HbCO), and glycated hemoglobin (HbA_1C). The SMD simulations were performed on the hemoglobin variants to estimate their unidirectional stiffness and shear stiffness. Although hemoglobin is structurally denoted as a globular protein due to its spherical shape and secondary structure, our simulation results show a significant variation in the mechanical strength in different directions (anisotropy) and also a strength variation among the four different hemoglobin configurations studied. The glycated hemoglobin molecule possesses an overall higher compressive mechanical stiffness and shear stiffness when compared to deoxyhemoglobin, oxyhemoglobin, and carboxyhemoglobin molecules. Further results from the models indicate that the hemoglobin structures studied possess a soft outer shell and a stiff core based on stiffness.

Virtual endovascular treatment of intracranial aneurysms: models and uncertainty

Virtual endovascular treatment models (VETMs) have been developed with the view to aid interventional neuroradiologists and neurosurgeons to pre-operatively analyze the comparative efficacy and safety of endovascular treatments for intracranial aneurysms. Based on the current state of VETMs in aneurysm rupture risk stratification and in patient-specific prediction of treatment outcomes, we argue there is a need to go beyond personalized biomechanical flow modeling assuming deterministic parameters and error-free measurements. The mechanobiological effects associated with blood clot formation are important factors in therapeutic decision making and models of post-treatment intra-aneurysmal biology and biochemistry should be linked to the purely hemodynamic models to improve the predictive power of current VETMs. The influence of model and parameter uncertainties associated to each component of a VETM is, where feasible, quantified via a random-effects meta-analysis of the literature. This allows estimating the pooled effect size of these uncertainties on aneurysmal wall shear stress. From such meta-analyses, two main sources of uncertainty emerge where research efforts have so far been limited: (1) vascular wall distensibility, and (2) intra/intersubject systemic flow variations. In the future, we suggest that current deterministic computational simulations need to be extended with strategies for uncertainty mitigation, uncertainty exploration, and sensitivity reduction techniques. WIREs Syst Biol Med 2017, 9:e1385. doi: 10.1002/wsbm.1385 For further resources related to this article, please visit the WIREs website.

Impact of Using Conventional Inlet/Outlet Boundary Conditions on Haemodynamic Metrics in a Subject-Specific Rabbit Aorta

Computational fluid dynamics is a tool capable of accurately measuring metrics currently used to predict the behaviour of cardiovascular diseases. This study quantifies the impact various commonly used inlet and outlet boundary conditions have on various shear rate–based haemodynamic metrics currently used for predicting the localisation of cardiovascular diseases. Simulations are conducted on an accurately represented rabbit aorta configuration and comparison has been made against available in vivo data. The boundary conditions studied include two different inlet profiles, three outlet boundary conditions, and steady-state versus pulsatile flow cases. Large variations were found in the results, particularly when using different outlet boundary conditions, and the discrepancies were evaluated both quantitatively and qualitatively. The results clearly highlight the importance of the type of boundary condition used when simulating complex cardiovascular models. By restricting the attention to the flow within the aorta and the intercostal branches, the results suggest that prescribing transient simulation and fully developed flow at the inlet are not required. Furthermore, assuming the widely accepted low wall shear stress theory of Caro, it was found that Murray’s law–based outlet boundary condition returns the most physiologically accurate results when compared to in vivo data.

Device thrombosis and pre-clinical blood flow models for assessing antithrombogenic efficacy of drug-device combinations

Thrombosis associated with blood-contacting devices is a complex process involving several component interactions that have eluded precise definition. Extensive investigations of individual biological modules such as protein adsorption, coagulation cascade activation and platelet activation/adhesion/aggregation have provided an initial foundation for developing biomaterials for blood-contacting devices, but a material that is intrinsically non-thrombogenic is yet to be developed. The well-recognized association between fluid dynamics parameters such as shear stress, vortices, stagnation and thrombotic processes such as platelet aggregation and coagulation aggravate thrombosis on most device geometries that elicit these flow disturbances. Thus, antithrombotic drugs that were developed to treat thrombosis associated with vascular diseases such as atherosclerosis have also been adapted to mitigate the risk of device thrombosis. However, balancing the risk of bleeding with the antithrombotic efficacy of these drugs continues to be a challenge, and surface modification of devices with these drug molecules to mitigate device thrombosis locally has been explored. Pre-clinical blood flow models to test the effectiveness of these drug-device combinations have also evolved and several in-vitro, ex-vivo, and in-vivo test configurations are available with their attendant merits and limitations. Despite considerable efforts toward iterative design and testing of blood contacting devices and antithrombogenic surface modifications, device thrombosis remains an unsolved problem.

Development of a platelet adhesion transport equation for a computational thrombosis model

Thrombosis is a significant issue for cardiovascular device development and use. While thrombosis models are available, very few are device-related and none have been thoroughly validated experimentally. Here, we introduce a surface adherent platelet transport equation into a continuum model to account for the biomaterial interface/blood interaction. Using a rotating disc system and polyurethane-urea material, we characterize steady and pulsatile flow fields using laser Doppler velocimetry. In vitro measurements of platelet adhesion are used in combination with the LDV data to provide further experimental validation. The rotating disc system is computationally studied using the device-induced thrombosis model with the surface platelet adherent transport equation. The results indicate that the flow field is in excellent agreement to the experimental LDV data and that the platelet adhesion simulations are in good agreement with the in vitro platelet data. These results provide good evidence that this transport equation can be used to express the relationship between blood and a biomaterial if the correct platelet adhesion characteristics are known for the biomaterial. Further validation is necessary with other materials.

Virtual flow-diverter treatment planning: The effect of device placement on bifurcation aneurysm haemodynamics

Bifurcation aneurysms account for a large fraction of cerebral aneurysms and often present morphologies that render traditional endovascular treatments, such as coiling, challenging and problematic. Flow-diverter stents offer a potentially elegant treatment option for such aneurysms, but clinical use of these devices remains controversial. Specifically, the deployment of a flow-diverter device in a bifurcation entails jailing one or more potentially vital vessels with a low-porosity mesh designed to restrict the flow. When multiple device placement configurations exist, the most appropriate clinical decision becomes increasingly opaque. In this study, three bifurcation aneurysm geometries were virtually treated by flow-diverter device. Each aneurysm was selected to offer two possible device deployment positions. Flow-diverters similar to commercially available designs were deployed with a fast-deployment algorithm before transient and steady state computational fluid dynamics simulations were performed. Reductions in aneurysm inflow, mean wall shear stress and maximum wall shear stress, all factors often linked with aneurysm treatment outcome, were compared for different device configurations in each aneurysm. In each of the three aneurysms modelled, a particular preferential device placement was shown to offer superior performance with the greatest reduction in the flow metrics considered. In all the three aneurysm geometries, substantial variations in inflow reduction (up to 25.3%), mean wall shear stress reduction (up to 14.6%) and maximum wall shear stress reduction (up to 12.1%) were seen, which were all attributed to device placement alone. Optimal device placement was found to be non-trivial and highly aneurysm specific; in only one-third of the simulated geometries, the best overall performance was achieved by deploying a device in the daughter vessel with the highest flow rate. Good correspondence was seen between transient results and steady state computations that offered a significant reduction in simulation run time. If accurate steady state computations are combined with the fast-deployment algorithm used, the modest run time and corresponding hardware make a virtual treatment pipeline in the clinical setting a meaningful possibility.

Development of a computational model for macroscopic predictions of device-induced thrombosis

While cardiovascular device-induced thrombosis is associated with negative patient outcomes, the convoluted nature of the processes resulting in a thrombus makes the full thrombotic network too computationally expensive to simulate in the complex geometries and flow fields associated with devices. A macroscopic, continuum computational model is developed based on a simplified network, which includes terms for platelet activation (chemical and mechanical) and thrombus deposition and growth in regions of low wall shear stress (WSS). Laminar simulations are performed in a two-dimensional asymmetric sudden expansion geometry and compared with in vitro thrombus size data collected using whole bovine blood. Additionally, the predictive power of the model is tested in a flow cell containing a series of symmetric sudden expansions and contractions. Thrombi form in the low WSS area downstream of the asymmetric expansion and grow into the nearby recirculation region, and thrombus height and length largely remain within 95 % confidence intervals calculated from the in vitro data for 30 min of blood flow. After 30 min, predicted thrombus height and length are 0.94 and 4.32 (normalized by the 2.5 mm step height). Importantly, the model also correctly predicts locations of thrombus deposition observed in the in vitro flow cell of expansions and contractions. As the simulation results, which rely on a greatly reduced model of the thrombotic network, are still able to capture the macroscopic behavior of the full network, the model shows promise for timely predictions of device-induced thrombosis toward optimizing and expediting the device development process.

Cooperation within von Willebrand factors enhances adsorption mechanism

von Willebrand factor (VWF) is a naturally collapsed protein that participates in primary haemostasis and coagulation events. The clotting process is triggered by the adsorption and conformational changes of the plasma VWFs localized to the collagen fibres found near the site of injury. We develop coarse-grained models to simulate the adsorption dynamics of VWF flowing near the adhesive collagen fibres at different shear rates and investigate the effect of factors such as interaction and cooperativity of VWFs on the success of adsorption events. The adsorption probability of a flowing VWF confined to the receptor field is enhanced when it encounters an adhered VWF in proximity to the collagen receptors. This enhancement is observed within a wide range of shear rates and is mostly controlled by the attractive van der Waals interactions rather than the hydrodynamic interactions among VWF monomers. The cooperativity between the VWFs acts as an effective mechanism for enhancing VWF adsorption to the collagen fibres. Additionally, this implies that the adsorption of such molecules is nonlinearly dependent on the density of flowing VWFs. These findings are important for studies of primary haemostasis as well as general adsorption dynamics processes in polymer physics.

A comprehensive study on different modelling approaches to predict platelet deposition rates in a perfusion chamber

Thrombus formation is a multiscale phenomenon triggered by platelet deposition over a protrombotic surface (eg. a ruptured atherosclerotic plaque). Despite the medical urgency for computational tools that aid in the early diagnosis of thrombotic events, the integration of computational models of thrombus formation at different scales requires a comprehensive understanding of the role and limitation of each modelling approach. We propose three different modelling approaches to predict platelet deposition. Specifically, we consider measurements of platelet deposition under blood flow conditions in a perfusion chamber for different time periods (3, 5, 10, 20 and 30 minutes) at shear rates of 212 s⁻¹, 1390 s⁻¹ and 1690 s⁻¹. Our modelling approaches are: i) a model based on the mass-transfer boundary layer theory; ii) a machine-learning approach; and iii) a phenomenological model. The results indicate that the three approaches on average have median errors of 21%, 20.7% and 14.2%, respectively. Our study demonstrates the feasibility of using an empirical data set as a proxy for a real-patient scenario in which practitioners have accumulated data on a given number of patients and want to obtain a diagnosis for a new patient about whom they only have the current observation of a certain number of variables.

Effect of anticoagulant treatment in deep vein thrombosis: A patient-specific computational fluid dynamics study

A methodology that might help physicians to establish a diagnostic and treatment tailored for each specific patient with a pathological thrombus is presented. A realistic model for the geometry of a popliteal vein with a thrombus just above the knee was reconstructed from in vivo computed tomography images acquired from one specific patient and then it was used to perform computational fluid dynamics (CFD) simulations. The wall shear stress (WSS) response to the administration of anticoagulant drugs and the influence of viscosity on the shape of the velocity distribution were investigated. Both a Newtonian and a non-Newtonian viscosity model were implemented for different blood flow rates in the range 3-7 cm(3)/s. The effect of anticoagulants on the blood was simulated by setting three different levels of viscosity in the Newtonian model (μ/μ∞=0.60, 0.80 and 1 with μ∞=3.45×10(-3) Pas). A reduction of μ by a given amount always led to a more modest reduction, typically by a factor of two, of the resulting WSS levels. Moreover, for a given flow rate the calculation with the non-Newtonian viscosity model yielded WSS levels between 20% and 40% larger than those obtained in the corresponding Newtonian fluid simulation. It was also found that blood moves slowly in the region between the thrombus and the vein wall, a fact that will favor the growth of the thrombotic mass. Both the mean WSS levels and the degree of sluggishness of the blood flow can be described by functions of the Reynolds number.

Spatial aspects of blood coagulation: two decades of research on the self-sustained traveling wave of thrombin

In a number of experimental studies, it has been demonstrated that the forefront of blood coagulation can propagate in the manner of a signal relay. These data strongly support the concept that the formation of a blood clot is governed by a self-sustained traveling wave of thrombin. The present review critically appraises the experimental data obtained in recent decades concerning the self-sustained spatial propagation of thrombin. Open questions regarding the experimental detection of the self-sustained propagation of thrombin are discussed.

A haemodynamic predictor of intraluminal thrombus formation in abdominal aortic aneurysms

Intraluminal thrombus (ILT) is present in over 75% of all abdominal aortic aneurysms (AAAs) and probably contributes to the complex biomechanics and pathobiology of these lesions. A reliable predictor of thrombus formation in enlarging lesions could thereby aid clinicians in treatment planning. The primary goal of this work was to identify a new phenomenological metric having clinical utility that is motivated by the hypothesis that two basic haemodynamic features must coincide spatially and temporally to promote the formation of a thrombus on an intact endothelium—platelets must be activated within a shear flow and then be presented to a susceptible endothelium. Towards this end, we propose a new thrombus formation potential (TFP) that combines information on the flow-induced shear history experienced by blood-borne particles that come in close proximity to the endothelium with information on both the time-averaged wall shear stress (WSS) and the oscillatory shear index (OSI) that locally affect the endothelial mechanobiology. To illustrate the possible utility of this new metric, we show computational results for 10 carotid arteries from five patients where regions of low WSS and high OSI tend not to be presented with activated platelets (i.e. they have a low TFP), consistent with the thrombo-resistance of the healthy carotid despite its complex haemodynamics. Conversely, we show results for three patients that high TFP co-localizes with regions of observed thin thrombus in AAAs, which contrasts with findings of low TFP for the abdominal aorta of three healthy subjects. We submit that these promising results suggest the need for further consideration of the TFP, or a similar combined metric, as a potentially useful clinical predictor of the possible formation of ILT in AAAs.