Multiscale Modeling of Platelet Adhesion and Thrombus Growth

Blood flow analysis with computational fluid dynamics and 4D-flow MRI for vascular diseases

Both computational fluid dynamics (CFD) and time-resolved, three-dimensional, phase-contrast, magnetic resonance imaging (4D-flow MRI) enable visualization of time-varying blood flow structures and quantification of blood flow in vascular diseases. However, they are totally different. CFD is a method to calculate blood flow by solving the governing equations of fluid mechanics, so the obtained flow field is somewhat virtual. On the other hand, 4D-flow MRI measures blood flow in vivo, thus the flow is real. Recently, with the development and enhancement of computers, medical imaging techniques, and related software, blood flow analysis has become more accessible to clinicians and its usefulness in vascular diseases has been demonstrated. In this review, we have outlined the methods and characteristics of CFD and 4D-flow MRI, respectively. We have discussed the differences in the characteristics between both methods; reviewed the milestones achieved by blood flow analysis in various vascular diseases; and discussed the usefulness, challenges, and limitations of blood flow analysis. We have discussed the difficulties and limitations of current blood flow analysis. We have also discussed our views on future directions.

Recent Advances in Computational Modeling of Biomechanics and Biorheology of Red Blood Cells in Diabetes

Diabetes mellitus, a metabolic disease characterized by chronically elevated blood glucose levels, affects about 29 million Americans and more than 422 million adults all over the world. Particularly, type 2 diabetes mellitus (T2DM) accounts for 90-95% of the cases of vascular disease and its prevalence is increasing due to the rising obesity rates in modern societies. Although multiple factors associated with diabetes, such as reduced red blood cell (RBC) deformability, enhanced RBC aggregation and adhesion to the endothelium, as well as elevated blood viscosity are thought to contribute to the hemodynamic impairment and vascular occlusion, clinical or experimental studies cannot directly quantify the contributions of these factors to the abnormal hematology in T2DM. Recently, computational modeling has been employed to dissect the impacts of the aberrant biomechanics of diabetic RBCs and their adverse effects on microcirculation. In this review, we summarize the recent advances in the developments and applications of computational models in investigating the abnormal properties of diabetic blood from the cellular level to the vascular level. We expect that this review will motivate and steer the development of new models in this area and shift the attention of the community from conventional laboratory studies to combined experimental and computational investigations, aiming to provide new inspirations for the development of advanced tools to improve our understanding of the pathogenesis and pathology of T2DM.

Microfluidic chip grafted with integrin tension sensors for evaluating the effects of flowing shear stress and ROCK inhibitor on platelets

Integrins are key players in platelet adhesion and aggregation. Integrin molecular tensions, the forces transmitted by integrin molecules, are regulated by both mechanical and biochemical cues, and the outside-in and inside-out signaling has been extensively studied. While the mechanical properties of platelets at static status have been studied by atomic force microscopy, traction force microscopy and tension sensors, the biomechanical properties of flowing platelets remain elusive. Herein, we report microfluidic chips grafted with integrin tension sensors for microfluidic-force mapping in platelets. Specifically, the process of integrin αIIbβ3 mediating tension transmission and platelet adhesion under low flow rates has been obtained, and the process of platelet clustering at post-stenotic regions has been demonstrated. We found that flowing shear force can postpone the integrin-mediated tension transmission and platelet adhesion. We further evaluated the effect of Y-27632, a ROCK inhibitor that has been proven to reduce integrin-mediated platelet adhesion, at a series of concentrations and demonstrated that microfluidic chips with integrin tension sensors are sensitive to the concentration-dependent effects of Y-27632. Given their low cost and scalable throughput, these chips are ideal technical platforms for biological studies of platelets at flowing status and for platelet inhibitor or potential antiplatelet drug screening.

Biomechanics in thrombus formation from direct cellular simulations

Numerically reproducing the process of thrombus formation is highly desired for understanding its mechanism but still remains challenging due to the polydisperse feature of blood components and their multiple biochemical or biomechanical behaviors involved. We numerically implemented a simplified version of the process from the perspective of biomechanics, using a mesoscale particle-based method, smoothed dissipative particle dynamics-immersed boundary method. This version covers the adhesion and aggregation of platelets (PLTs), the deformation and aggregation of red blood cells (RBCs), and the interaction between PLTs and RBCs, as well as the blockage of microvessels. Four critical factors that can affect thrombus formation were investigated: the velocity of blood flow, the adhesive ability of PLTs, the interaction strength between PLTs and RBCs, and the deformability of RBCs. Increasing the velocity of blood flow was found to be the most effective way to reduce the microvessel blockage, and reducing the adhesive ability of PLTs is also a direct and efficient way. However, decreasing the interaction strength between PLTs and RBCs sometimes does not alleviate thrombus formation, and similarly, increasing the deformability of RBCs does not have a significant improvement for the severely blocked microvessel. These results imply that maintaining high-rate blood flow plays a crucial role in the prevention and treatment of thrombosis, which is even more effective than antiplatelet or anticoagulant drugs. The drugs or treatments concentrating on reducing the PLT-RBC interaction or softening the RBCs may not have a significant effect on the thrombosis.

The Art and Science of Building a Computational Model to Understand Hemostasis

Computational models of various facets of hemostasis and thrombosis have increased substantially in the last decade. These models have the potential to make predictions that can uncover new mechanisms within the complex dynamics of thrombus formation. However, these predictions are only as good as the data and assumptions they are built upon, and therefore model building requires intimate coupling with experiments. The objective of this article is to guide the reader through how a computational model is built and how it can inform and be refined by experiments. This is accomplished by answering six questions facing the model builder: (1) Why make a model? (2) What kind of model should be built? (3) How is the model built? (4) Is the model a “good” model? (5) Do we believe the model? (6) Is the model useful? These questions are answered in the context of a model of thrombus formation that has been successfully applied to understanding the interplay between blood flow, platelet deposition, and coagulation and in identifying potential modifiers of thrombin generation in hemophilia A.

Integrating blood cell mechanics, platelet adhesive dynamics and coagulation cascade for modelling thrombus formation in normal and diabetic blood

Normal haemostasis is an important physiological mechanism that prevents excessive bleeding during trauma, whereas the pathological thrombosis especially in diabetics leads to increased incidence of heart attacks and strokes as well as peripheral vascular events. In this work, we propose a new multiscale framework that integrates seamlessly four key components of blood clotting, namely transport of coagulation factors, coagulation kinetics, blood cell mechanics and platelet adhesive dynamics, to model the development of thrombi under physiological and pathological conditions. We implement this framework to simulate platelet adhesion due to the exposure of tissue factor in a three-dimensional microchannel. Our results show that our model can simulate thrombin-mediated platelet activation in the flowing blood, resulting in platelet adhesion to the injury site of the channel wall. Furthermore, we simulate platelet adhesion in diabetic blood, and our results show that both the pathological alterations in the biomechanics of blood cells and changes in the amount of coagulation factors contribute to the excessive platelet adhesion and aggregation in diabetic blood. Taken together, this new framework can be used to probe synergistic mechanisms of thrombus formation under physiological and pathological conditions, and open new directions in modelling complex biological problems that involve several multiscale processes.

Computationally Driven Discovery in Coagulation

Bleeding frequency and severity within clinical categories of hemophilia A are highly variable and the origin of this variation is unknown. Solving this mystery in coagulation requires the generation and analysis of large data sets comprised of experimental outputs or patient samples, both of which are subject to limited availability. In this review, we describe how a computationally driven approach bypasses such limitations by generating large synthetic patient data sets. These data sets were created with a mechanistic mathematical model, by varying the model inputs, clotting factor, and inhibitor concentrations, within normal physiological ranges. Specific mathematical metrics were chosen from the model output, used as a surrogate measure for bleeding severity, and statistically analyzed for further exploration and hypothesis generation. We highlight results from our recent study that employed this computationally driven approach to identify FV (factor V) as a key modifier of thrombin generation in mild to moderate hemophilia A, which was confirmed with complementary experimental assays. The mathematical model was used further to propose a potential mechanism for these observations whereby thrombin generation is rescued in FVIII-deficient plasma due to reduced substrate competition between FV and FVIII for FXa (activated factor X).

An Introductory Overview of Image-Based Computational Modeling in Personalized Cardiovascular Medicine

Cardiovascular diseases account for the number one cause of deaths in the world. Part of the reason for such grim statistics is our limited understanding of the underlying mechanisms causing these devastating pathologies, which is made difficult by the invasiveness of the procedures associated with their diagnosis (e.g., inserting catheters into the coronal artery to measure blood flow to the heart). Likewise, it is also difficult to design and test assistive devices without implanting them in vivo. However, with the recent advancements made in biomedical scanning technologies and computer simulations, image-based modeling (IBM) has arisen as the next logical step in the evolution of non-invasive patient-specific cardiovascular medicine. Yet, due to its novelty, it is still relatively unknown outside of the niche field. Therefore, the goal of this manuscript is to review the current state-of-the-art and the limitations of the methods used in this area of research, as well as their applications to personalized cardiovascular investigations and treatments. Specifically, the modeling of three different physics – electrophysiology, biomechanics and hemodynamics – used in the cardiovascular IBM is discussed in the context of the physiology that each one of them describes and the mechanisms of the underlying cardiac diseases that they can provide insight into. Only the “bare-bones” of the modeling approaches are discussed in order to make this introductory material more accessible to an outside observer. Additionally, the imaging methods, the aspects of the unique cardiac anatomy derived from them, and their relation to the modeling algorithms are reviewed. Finally, conclusions are drawn about the future evolution of these methods and their potential toward revolutionizing the non-invasive diagnosis, virtual design of treatments/assistive devices, and increasing our understanding of these lethal cardiovascular diseases.

Simulation of thrombosis in a stenotic microchannel: The effects of vWF-enhanced shear activation of platelets

This study was undertaken to develop a numerical/computational simulation of von Willebrand Factor (vWF) - mediated platelet shear activation and deposition in an idealized stenosis. Blood is treated as a multi-constituent mixture comprised of a linear fluid component and a porous solid component (thrombus). Chemical and biological species involved in coagulation are modeled using a system of coupled convection-reaction-diffusion (CRD) equations. This study considers the cumulative effect of shear stress (history) on platelet activation. The vWF activity is modeled as an enhancement function for the shear stress accumulation and is related to the experimentally-observed unfolding rate of vWF. A series of simulations were performed in an idealized stenosis in which the predicted platelets deposition agreed well with previous experimental observations spatially and temporally, including the reduction of platelet deposition with decreasing expansion angle. Further simulation indicated a direct relationship between vWF-mediated platelet deposition and degree of stenosis. Based on the success with these benchmark simulations, it is hoped that the model presented here may provide additional insight into vWF-mediated thrombosis and prove useful for the development of more hemo-compatible blood-wetted devices in the future.

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.

In vivo measurement of blood clot mechanics from computational fluid dynamics based on intravital microscopy images

Ischemia which leads to heart attacks and strokes is one of the major causes of death in the world. Whether an occlusion occurs or not depends on the ability of a growing thrombus to resist flow forces exerted on its structure. This manuscript provides the first known in vivo measurement of how much stress a clot can withstand, before yielding to the surrounding blood flow. Namely, Lattice-Boltzmann Method flow simulations are performed based on 3D clot geometries, which are estimated from intravital microscopy images of laser-induced injuries in cremaster microvasculature of live mice. In addition to reporting the blood clot yield stresses, we also show that the thrombus "core" does not experience significant deformation, while its "shell" does. This indicates that the shell is more prone to embolization. Therefore, drugs should be designed to target the shell selectively, while leaving the core intact to minimize excessive bleeding. Finally, we laid down a foundation for a nondimensionalization procedure which unraveled a relationship between clot mechanics and biology. Hence, the proposed framework could ultimately lead to a unified theory of thrombogenesis, capable of explaining all clotting events. Thus, the findings presented herein will be beneficial to the understanding and treatment of heart attacks, strokes and hemophilia.

Fibrin polymerization simulation using a reactive dissipative particle dynamics method

The study on the polymerization of fibrinogen molecules into fibrin monomers and eventually a stable, mechanically robust fibrin clot is a persistent and enduring topic in the field of thrombosis and hemostasis. Despite many research advances in fibrin polymerization, the change in the structure of fibrin clots and its influence on the formation of a fibrous protein network are still poorly understood. In this paper, we develop a new computational method to simulate fibrin clot polymerization using dissipative particle dynamics simulations. With an effective combination of reactive molecular dynamics formularies and many body dissipative particle dynamics principles, we constructed the reactive dissipative particle dynamics (RDPD) model to predict the complex network formation of fibrin clots and branching of the fibrin network. The 340 kDa fibrinogen molecule is converted into a spring-bead coarse-grain system with 11 beads using a topology representing network algorithm, and using RDPD, we simulated polymerization and formation of the fibrin clot. The final polymerized structure of the fibrin clot qualitatively agrees with experimental results from the literature, and to the best of our knowledge this is the first molecular-based study that simulates polymerization and structure of fibrin clots.

An experimental study of shear-dependent human platelet adhesion and underlying protein-binding mechanisms in a cylindrical Couette system

Undesirable thrombotic reactions count among the most frequent and serious complications for patients who rely on the use of medical devices. To improve the design of medical devices, it is essential to develop a more precise understanding of platelet reactions. Clinical studies and experiments have shown a strong dependence of platelet deposition behavior on the flow. However, today the influence of hemodynamic parameters such as the shear rate on thrombotic reactions is not well understood. For the study of the shear-dependent mechanisms leading to the activation, adhesion and aggregation of platelets, a Couette flow system was used to investigate thrombocyte behavior with regard to well-defined flow conditions at shear-rate values between γ˙=400 $\dot \gamma = {\rm{400}}$ and 1400 1/s. Results were calculated for physiological temperature. It could be shown that the platelet adhesion density increased with increasing shear rates up to γ˙=800 1/s $\dot \gamma = {\rm{800 1/s}}$ and the adhesion pattern was homogeneous. At γ˙=800 1/s, $\dot \gamma = {\rm{800 1/s}},$ a sudden drop in platelet adhesion density occurred and platelets adhered in filaments. Fluorescence microscopy results of von Willebrand factor (vWF) confirm that a shear rate of γ˙=800 1/s $\dot \gamma = {\rm{800 1/s}}$ represents the threshold where a switch of the platelet-binding mechanism from fibrinogen-mediated to vWF-mediated platelet adhesion takes place.

The Effect of Hematocrit on Platelet Adhesion: Experiments and Simulations

The volume fraction of red blood cells (RBCs) in a capillary affects the degree to which platelets are promoted to marginate to near a vessel wall and form blood clots. In this work we investigate the relationship between RBC hematocrit and platelet adhesion activity. We perform experiments flowing blood samples through a microfluidic channel coated with type 1 collagen and observe the rate at which platelets adhere to the wall. We compare these results with three-dimensional boundary integral simulations of a suspension of RBCs and platelets in a periodic channel where platelets can adhere to the wall. In both cases, we find that the rate of platelet adhesion varies greatly with the RBC hematocrit. We observe that the relative decrease in platelet activity as hematocrit falls shows a similar profile for simulation and experiment.

Platelets and hemostasis: a new perspective on an old subject

Publisher's Note: This article has a companion Counterpoint by Kapur and Semple. Publisher's Note: Join in the discussion of these articles at Blood Advances Community Conversations.

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.

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.

Characterization of Nanoparticle Dispersion in Red Blood Cell Suspension by the Lattice Boltzmann-Immersed Boundary Method

Nanodrug-carrier delivery in the blood stream is strongly influenced by nanoparticle (NP) dispersion. This paper presents a numerical study on NP transport and dispersion in red blood cell (RBC) suspensions under shear and channel flow conditions, utilizing an immersed boundary fluid-structure interaction model with a lattice Boltzmann fluid solver, an elastic cell membrane model and a particle motion model driven by both hydrodynamic loading and Brownian dynamics. The model can capture the multiphase features of the blood flow. Simulations were performed to obtain an empirical formula to predict NP dispersion rate for a range of shear rates and cell concentrations. NP dispersion rate predictions from the formula were then compared to observations from previous experimental and numerical studies. The proposed formula is shown to accurately predict the NP dispersion rate. The simulation results also confirm previous findings that the NP dispersion rate is strongly influenced by local disturbances in the flow due to RBC motion and deformation. The proposed formula provides an efficient method for estimating the NP dispersion rate in modeling NP transport in large-scale vascular networks without explicit RBC and NP models.

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.

Multi-scale biological and physical modelling of the tumour micro-environment

Paced by advances in high performance computing, and algorithms for multi-physics and multi-scale simulation, a number of groups have recently established numerical models of flowing blood systems, where cell-scale interactions are explicitly resolved. To be biologically representative, these models account for some or all of: (1) fluid dynamics of the carrier flow, (2) structural dynamics of the cells and vessel walls, (3) interaction and transport biochemistry, and, (4) methods for scaling to physiologically representative numbers of cells. In this article, our interest is the modelling of the tumour micro-environment. We review the broader area of cell-scale resolving blood flow modelling, while focusing on the particular interactions of tumour cells and white blood cells, known to play an important role in metastasis.

A Multiple Time Stepping Algorithm for Efficient Multiscale Modeling of Platelets Flowing in Blood Plasma

We developed a multiple time-stepping (MTS) algorithm for multiscale modeling of the dynamics of platelets flowing in viscous blood plasma. This MTS algorithm improves considerably the computational efficiency without significant loss of accuracy. This study of the dynamic properties of flowing platelets employs a combination of the dissipative particle dynamics (DPD) and the coarse-grained molecular dynamics (CGMD) methods to describe the dynamic microstructures of deformable platelets in response to extracellular flow-induced stresses. The disparate spatial scales between the two methods are handled by a hybrid force field interface. However, the disparity in temporal scales between the DPD and CGMD that requires time stepping at microseconds and nanoseconds respectively, represents a computational challenge that may become prohibitive. Classical MTS algorithms manage to improve computing efficiency by multi-stepping within DPD or CGMD for up to one order of magnitude of scale differential. In order to handle 3-4 orders of magnitude disparity in the temporal scales between DPD and CGMD, we introduce a new MTS scheme hybridizing DPD and CGMD by utilizing four different time stepping sizes. We advance the fluid system at the largest time step, the fluid-platelet interface at a middle timestep size, and the nonbonded and bonded potentials of the platelet structural system at two smallest timestep sizes. Additionally, we introduce parameters to study the relationship of accuracy versus computational complexities. The numerical experiments demonstrated 3000x reduction in computing time over standard MTS methods for solving the multiscale model. This MTS algorithm establishes a computationally feasible approach for solving a particle-based system at multiple scales for performing efficient multiscale simulations.

Examining platelet adhesion via Stokes flow simulations and microfluidic experiments

While critically important, the platelet function at the high shear rates typical of the microcirculation is relatively poorly understood. Using a large scale Stokes flow simulation, Zhao et al. recently showed that RBC-induced velocity fluctuations cause platelets to marginate into the RBC free near-wall region [Zhao et al., Physics of Fluids, 2012, 24, 011902]. We extend their work by investigating the dynamics of platelets in shear after margination. An overall platelet adhesion model is proposed in terms of a continuous time Markov process and the transition rates are established with numerical simulations involving platelet-wall adhesion. Hydrodynamic drag and Brownian forces are calculated with the boundary element method, while the RBC collisions are incorporated through an autoregressive process. Hookean springs with first order bond kinetics are used to model receptor-ligand bonds formed between the platelet and the wall. The simulations are compared with in vitro microfluidic experiments involving platelet adhesion to Von Willebrand Factor (VWF) coated surfaces.

Fluid Mechanics of Blood Clot Formation

Intravascular blood clots form in an environment in which hydrodynamic forces dominate and in which fluid-mediated transport is the primary means of moving material. The clotting system has evolved to exploit fluid dynamic mechanisms and to overcome fluid dynamic challenges to ensure that clots that preserve vascular integrity can form over the wide range of flow conditions found in the circulation. Fluid-mediated interactions between the many large deformable red blood cells and the few small rigid platelets lead to high platelet concentrations near vessel walls where platelets contribute to clotting. Receptor-ligand pairs with diverse kinetic and mechanical characteristics work synergistically to arrest rapidly flowing cells on an injured vessel. Variations in hydrodynamic stresses switch on and off the function of key clotting polymers. Protein transport to, from, and within a developing clot determines whether and how fast it grows. We review ongoing experimental and modeling research to understand these and related phenomena.

In vitro quantification of time dependent thrombus size using magnetic resonance imaging and computational simulations of thrombus surface shear stresses

Thrombosis and thromboembolization remain large obstacles in the design of cardiovascular devices. In this study, the temporal behavior of thrombus size within a backward-facing step (BFS) model is investigated, as this geometry can mimic the flow separation which has been found to contribute to thrombosis in cardiac devices. Magnetic resonance imaging (MRI) is used to quantify thrombus size and collect topographic data of thrombi formed by circulating bovine blood through a BFS model for times ranging between 10 and 90 min at a constant upstream Reynolds number of 490. Thrombus height, length, exposed surface area, and volume are measured, and asymptotic behavior is observed for each as the blood circulation time is increased. Velocity patterns near, and wall shear stress (WSS) distributions on, the exposed thrombus surfaces are calculated using computational fluid dynamics (CFD). Both the mean and maximum WSS on the exposed thrombus surfaces are much more dependent on thrombus topography than thrombus size, and the best predictors for asymptotic thrombus length and volume are the reattachment length and volume of reversed flow, respectively, from the region of separated flow downstream of the BFS.

Hemodynamics in the microcirculation and in microfluidics

Hemodynamics in microcirculation is important for hemorheology and several types of circulatory disease. Although hemodynamics research has a long history, the field continues to expand due to recent advancements in numerical and experimental techniques at the micro-and nano-scales. In this paper, we review recent computational and experimental studies of blood flow in microcirculation and microfluidics. We first focus on the computational studies of red blood cell (RBC) dynamics, from the single cellular level to mesoscopic multiple cellular flows, followed by a review of recent computational adhesion models for white blood cells, platelets, and malaria-infected RBCs, in which the cell adhesion to the vascular wall is essential for cellular function. Recent developments in optical microscopy have enabled the observation of flowing blood cells in microfluidics. Experimental particle image velocimetry and particle tracking velocimetry techniques are described in this article. Advancements in micro total analysis system technologies have facilitated flowing cell separation with microfluidic devices, which can be used for biomedical applications, such as a diagnostic tool for breast cancer or large intestinal tumors. In this paper, cell-separation techniques are reviewed for microfluidic devices, emphasizing recent advances and the potential of this fast-evolving research field in the near future.

Blood compatible materials: state of the art

Devices that function in contact with blood are ubiquitous in clinical medicine and biotechnology. These devices include vascular grafts, coronary stents, heart valves, catheters, hemodialysers, heart-lung bypass systems and many others. Blood contact generally leads to thrombosis (among other adverse outcomes), and no material has yet been developed which remains thrombus-free indefinitely and in all situations: extracorporeally, in the venous circulation and in the arterial circulation. In this article knowledge on blood-material interactions and "thromboresistant" materials is reviewed. Current approaches to the development of thromboresistant materials are discussed including surface passivation; incorporation and/or release of anticoagulants, antiplatelet agents and thrombolytic agents; and mimicry of the vascular endothelium.

A systems approach to hemostasis: 2. Computational analysis of molecular transport in the thrombus microenvironment

Hemostatic thrombi formed after a penetrating injury have a heterogeneous architecture in which a core of highly activated, densely packed platelets is covered by a shell of less-activated, loosely packed platelets. In the first manuscript in this series, we show that regional differences in intrathrombus protein transport rates emerge early in the hemostatic response and are preserved as the thrombus develops. Here, we use a theoretical approach to investigate this process and its impact on agonist distribution. The results suggest that hindered diffusion, rather than convection, is the dominant mechanism responsible for molecular movement within the thrombus. The analysis also suggests that the thrombus core, as compared with the shell, provides an environment for retaining soluble agonists such as thrombin, affecting the extent of platelet activation by establishing agonist-specific concentration gradients radiating from the site of injury. This analysis accounts for the observed weaker activation and relative instability of platelets in the shell and predicts that a failure to form a tightly packed thrombus core will limit thrombin accumulation, a prediction tested by analysis of data from mice with a defect in clot retraction.

Tuneable resolution as a systems biology approach for multi-scale, multi-compartment computational models

The use of multi-scale mathematical and computational models to study complex biological processes is becoming increasingly productive. Multi-scale models span a range of spatial and/or temporal scales and can encompass multi-compartment (e.g., multi-organ) models. Modeling advances are enabling virtual experiments to explore and answer questions that are problematic to address in the wet-lab. Wet-lab experimental technologies now allow scientists to observe, measure, record, and analyze experiments focusing on different system aspects at a variety of biological scales. We need the technical ability to mirror that same flexibility in virtual experiments using multi-scale models. Here we present a new approach, tuneable resolution, which can begin providing that flexibility. Tuneable resolution involves fine- or coarse-graining existing multi-scale models at the user's discretion, allowing adjustment of the level of resolution specific to a question, an experiment, or a scale of interest. Tuneable resolution expands options for revising and validating mechanistic multi-scale models, can extend the longevity of multi-scale models, and may increase computational efficiency. The tuneable resolution approach can be applied to many model types, including differential equation, agent-based, and hybrid models. We demonstrate our tuneable resolution ideas with examples relevant to infectious disease modeling, illustrating key principles at work. WIREs Syst Biol Med 2014, 6:225–245. doi:10.1002/wsbm.1270

How to cite this article:WIREs Syst Biol Med 2014, 6:289–309. doi:10.1002/wsbm.1270

Simulation of platelet, thrombus and erythrocyte hydrodynamic interactions in a 3D arteriole with in vivo comparison

Cylindrical blood vessels, ellipsoid platelets and biconcave-shaped deformable erythrocytes (RBCs) are important participants in hemostasis and thrombosis. However, due to the challenge of combining these components in simulation tools, few simulation studies have included all of them in realistic three-dimensional models. In the present study, we apply a recently developed simulation model to incorporate these components and analyze the flow in a thrombotic tubular arteriole, particularly the detailed hydrodynamic interactions between the thrombus shape, RBCs and platelets. It was found that at certain azimuth positions, the velocity drops in the proximity of both the upstream and downstream edge of the thrombus, which is accompanied by a rapid velocity increase in the narrowed region. The RBCs alter the flow profiles significantly from the typical low Reynolds (Re) number flow, and also enhance the deposition of free flowing platelets onto the thrombus. By evaluating the platelet-thrombus interaction and platelet-RBC interaction together, several mechanisms of platelet deposition augmentation are identified. With in vivo data comparison, our model illustrates the potential of future thrombosis studies that incorporate detailed receptor-ligand adhesion modules.

Platelet size and density affect shear-induced thrombus formation in tortuous arterioles

Thrombosis accounts for 80% of deaths in patients with diabetes mellitus. Diabetic patients demonstrate tortuous microvessels and larger than normal platelets. Large platelets are associated with increased platelet activation and thrombosis, but the physical effects of large platelets in the microscale processes of thrombus formation are not clear. Therefore, the objective of this study was to determine the physical effects of mean platelet volume (MPV), mean platelet density (MPD) and vessel tortuosity on platelet activation and thrombus formation in tortuous arterioles. A computational model of the transport, shear-induced activation, collision, adhesion and aggregation of individual platelets was used to simulate platelet interactions and thrombus formation in tortuous arterioles. Our results showed that an increase in MPV resulted in a larger number of activated platelets, though MPD and level of tortuosity made little difference on platelet activation. Platelets with normal MPD yielded the lowest amount of mural thrombus. With platelets of normal MPD, the amount of mural thrombus decreased with increasing level of tortuosity but did not have a simple monotonic relationship with MPV. The physical mechanisms associated with MPV, MPD and arteriole tortuosity play important roles in platelet activation and thrombus formation.

Simulation of intrathrombus fluid and solute transport using in vivo clot structures with single platelet resolution

The mouse laser injury thrombosis model provides up to 0.22 μm-resolved voxel information about the pore architecture of the dense inner core and loose outer shell regions of an in vivo arterial thrombus. Computational studies were conducted on this 3D structure to quantify transport within and around the clot: Lattice Boltzmann method defined vessel hemodynamics, while passive Lagrangian Scalar Tracking with Brownian motion contribution simulated diffusive-convective transport of various inert solutes (released from lumen or the injured wall). For an input average lumen blood velocity of 0.478 cm/s (measured by Doppler velocimetry), a 0.2 mm/s mean flow rate was obtained within the thrombus structure, most of which occurred in the 100-fold more permeable outer shell region (calculated permeability of the inner core was 10(-11) cm(2)). Average wall shear stresses were 80-100 dyne/cm(2) (peak values >200 dyne/cm(2)) on the outer rough surface of the thrombus. Within the thrombus, small molecule tracers (0.1 kDa) experienced ~70,000 collisions/s and penetrated/exited it in about 1 s, whereas proteins (~50 kDa) had ~9000 collisions/s and required about 10 s (tortuosity ~2-2.5). These simulations help define physical processes during thrombosis and constraints for drug delivery to the thrombus.