A three-dimensional phase-field model for multiscale modeling of thrombus biomechanics in blood vessels

Hemodynamics affects factor XI/XII anticoagulation efficacy in patient-derived left atrial models

BACKGROUND AND OBJECTIVE

Atrial fibrillation (AF) is a common arrhythmia that disrupts blood circulation in the left atrium (LA), causing stasis in the left atrial appendage (LAA) and increasing thromboembolic risk. In patients at sufficiently high risk, anticoagulation is indicated. This benefit may be counterbalanced by an increased risk of bleeding. Novel anticoagulants under development, such as factor XI/XII inhibitors, may be associated with a lower bleeding risk. However, their efficacy in preventing thrombosis is not fully understood. We hypothesized that patient-specific flow patterns in the LA and LAA not only influence the risk of thrombosis but also the effectiveness of anticoagulation agents.

METHODS

To test our hypothesis, we simulated blood flow and the intrinsic coagulation pathway in patient-specific LA anatomies with and without factor XI/XII inhibition. We included a heterogeneous cohort of thirteen patients, some in sinus rhythm and others in AF, four of whom had an LAA thrombus or a history of transient ischemic attacks. We used computational fluid dynamics based on 4D CT imaging and a detailed 32-coagulation factor system to run 247 simulations. We analyzed baseline LA flow patterns and evaluated various factor XI/XII inhibition levels. Implementing a novel multi-fidelity coagulation modeling approach accelerated computations by two orders of magnitude, enabling many simulations to be performed.

RESULTS

The simulations provided spatiotemporally resolved maps of thrombin concentration throughout the LA, showing that it peaks inside the LAA. Coagulation metrics based on peak LAA thrombin dynamics suggested patients could be classified as having no, moderate or high thromboembolic risk. High-risk patients had slower flows and higher residence times in the LAA than those with moderate thromboembolic risk, and they required stronger factor XI/XII inhibition to prevent thrombin growth. These data suggest that the anticoagulation effect was also related to the LAA hemodynamics.

CONCLUSION

The methodology outlined in this study has the potential to enable personalized assessments of coagulation risk and to tailor anticoagulation therapy by analyzing flow dynamics in patient-derived LA models, representing a significant step towards advancing the application of digital twins in cardiovascular medicine.

Coagulo-Net: Enhancing the mathematical modeling of blood coagulation using physics-informed neural networks

Blood coagulation, which involves a group of complex biochemical reactions, is a crucial step in hemostasis to stop bleeding at the injury site of a blood vessel. Coagulation abnormalities, such as hypercoagulation and hypocoagulation, could either cause thrombosis or hemorrhage, resulting in severe clinical consequences. Mathematical models of blood coagulation have been widely used to improve the understanding of the pathophysiology of coagulation disorders, guide the design and testing of new anticoagulants or other therapeutic agents, and promote precision medicine. However, estimating the parameters in these coagulation models has been challenging as not all reaction rate constants and new parameters derived from model assumptions are measurable. Although various conventional methods have been employed for parameter estimation for coagulation models, the existing approaches have several shortcomings. Inspired by the physics-informed neural networks, we propose Coagulo-Net, which synergizes the strengths of deep neural networks with the mechanistic understanding of the blood coagulation processes to enhance the mathematical models of the blood coagulation cascade. We assess the performance of the Coagulo-Net using two existing coagulation models with different extents of complexity. Our simulation results illustrate that Coagulo-Net can efficiently infer the unknown model parameters and dynamics of species based on sparse measurement data and data contaminated with noise. In addition, we show that Coagulo-Net can process a mixture of synthetic and experimental data and refine the predictions of existing mathematical models of coagulation. These results demonstrate the promise of Coagulo-Net in enhancing current coagulation models and aiding the creation of novel models for physiological and pathological research. These results showcase the potential of Coagulo-Net to advance computational modeling in the study of blood coagulation, improving both research methodologies and the development of new therapies for treating patients with coagulation disorders.

Venous Thromboembolism: Review of Clinical Challenges, Biology, Assessment, Treatment, and Modeling

Venous thromboembolism (VTE) is a massive clinical challenge, annually affecting millions of patients globally. VTE is a particularly consequential pathology, as incidence is correlated with extremely common risk factors, and a large cohort of patients experience recurrent VTE after initial intervention. Altered hemodynamics, hypercoagulability, and damaged vascular tissue cause deep-vein thrombosis and pulmonary embolism, the two permutations of VTE. Venous valves have been identified as likely locations for initial blood clot formation, but the exact pathway by which thrombosis occurs in this environment is not entirely clear. Several risk factors are known to increase the likelihood of VTE, particularly those that increase inflammation and coagulability, increase venous resistance, and damage the endothelial lining. While these risk factors are useful as predictive tools, VTE diagnosis prior to presentation of outward symptoms is difficult, chiefly due to challenges in successfully imaging deep-vein thrombi. Clinically, VTE can be managed by anticoagulants or mechanical intervention. Recently, direct oral anticoagulants and catheter-directed thrombolysis have emerged as leading tools in resolution of venous thrombosis. While a satisfactory VTE model has yet to be developed, recent strides have been made in advancing in silico models of venous hemodynamics, hemorheology, fluid-structure interaction, and clot growth. These models are often guided by imaging-informed boundary conditions or inspired by benchtop animal models. These gaps in knowledge are critical targets to address necessary improvements in prediction and diagnosis, clinical management, and VTE experimental and computational models.

A computational investigation of occlusive arterial thrombosis

The generation of occlusive thrombi in stenotic arteries involves the rapid deposition of millions of circulating platelets under high shear flow. The process is mediated by the formation of molecular bonds of several distinct types between platelets; the bonds capture the moving platelets and stabilize the growing thrombi under flow. We investigated the mechanisms behind occlusive thrombosis in arteries with a two-phase continuum model. The model explicitly tracks the formation and rupture of the two types of interplatelet bonds, the rates of which are coupled with the local flow conditions. The motion of platelets in the thrombi results from competition between the viscoelastic forces generated by the interplatelet bonds and the fluid drag. Our simulation results indicate that stable occlusive thrombi form only under specific combinations for the ranges of model parameters such as rates of bond formation and rupture, platelet activation time, and number of bonds required for platelet attachment.

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.

Decoding thrombosis through code: a review of computational models

From the molecular level up to a blood vessel, thrombosis and hemostasis involves many interconnected biochemical and biophysical processes over a wide range of length and time scales. Computational modeling has gained eminence in offering insights into these processes beyond what can be obtained from in vitro or in vivo experiments, or clinical measurements. The multiscale and multiphysics nature of thrombosis has inspired a wide range of modeling approaches that aim to address how a thrombus forms and dismantles. Here, we review recent advances in computational modeling with a focus on platelet-based thrombosis. We attempt to summarize the diverse range of modeling efforts straddling the wide-spectrum of physical phenomena, length scales, and time scales; highlighting key advancements and insights from existing studies. Potential information gleaned from models is discussed, ranging from identification of thrombus-prone regions in patient-specific vasculature to modeling thrombus deformation and embolization in response to fluid forces. Furthermore, we highlight several limitations of current models, future directions in the field, and opportunities for clinical translation, to illustrate the state-of-the-art. There are a plethora of opportunity areas for which models can be expanded, ranging from topics of thromboinflammation to platelet production and clearance. Through successes demonstrated in existing studies described here, as well as continued advancements in computational methodologies and computer processing speeds and memory, in silico investigations in thrombosis are poised to bring about significant knowledge growth in the years to come.

Combined computational modeling and experimental study of the biomechanical mechanisms of platelet-driven contraction of fibrin clots

While blood clot formation has been relatively well studied, little is known about the mechanisms underlying the subsequent structural and mechanical clot remodeling called contraction or retraction. Impairment of the clot contraction process is associated with both life-threatening bleeding and thrombotic conditions, such as ischemic stroke, venous thromboembolism, and others. Recently, blood clot contraction was observed to be hindered in patients with COVID-19. A three-dimensional multiscale computational model is developed and used to quantify biomechanical mechanisms of the kinetics of clot contraction driven by platelet-fibrin pulling interactions. These results provide important biological insights into contraction of platelet filopodia, the mechanically active thin protrusions of the plasma membrane, described previously as performing mostly a sensory function. The biomechanical mechanisms and modeling approach described can potentially apply to studying other systems in which cells are embedded in a filamentous network and exert forces on the extracellular matrix modulated by the substrate stiffness.

A Computational Investigation of Occlusive Arterial Thrombosis

The generation of occlusive thrombi in stenotic arteries involves the rapid deposition of millions of circulating platelets under high shear flow. The process is mediated by the formation of molecular bonds of several distinct types between platelets; the bonds capture the moving platelets and stabilize the growing thrombi under flow. We investigated the mechanisms behind occlusive thrombosis in arteries with a two-phase continuum model. The model explicitly tracks the formation and rupture of the two types of interplatelet bonds, the rates of which are coupled with the local flow conditions. The motion of platelets in the thrombi results from competition between the viscoelastic forces generated by the interplatelet bonds and the fluid drag. Our simulation results indicate that stable occlusive thrombi form only under specific combinations for the ranges of model parameters such as rates of bond formation and rupture, platelet activation time, and number of bonds required for platelet attachment.

A Multiscale Model for Shear-Mediated Platelet Adhesion Dynamics: Correlating In Silico with In Vitro Results

Platelet adhesion to blood vessel walls is a key initial event in thrombus formation in both vascular disease processes and prosthetic cardiovascular devices. We extended a deformable multiscale model (MSM) of flowing platelets, incorporating Dissipative Particle Dynamics (DPD) and Coarse-Grained Molecular Dynamics (CGMD) describing molecular-scale intraplatelet constituents and their interaction with surrounding flow, to predict platelet adhesion dynamics under physiological flow shear stresses. Binding of platelet glycoprotein receptor Ibα (GPIbα) to von Willebrand factor (vWF) on the blood vessel wall was modeled by a molecular-level hybrid force field and validated with in vitro microchannel experiments of flowing platelets at 30 dyne/cm2. High frame rate videos of flipping platelets were analyzed with a Semi-Unsupervised Learning System (SULS) machine learning-guided imaging approach to segment platelet geometries and quantify adhesion dynamics parameters. In silico flipping dynamics followed in vitro measurements at 15 and 45 dyne/cm2 with high fidelity, predicting GPIbα-vWF bonding and debonding processes, distribution of bonds strength, and providing a biomechanical insight into initiation of the complex platelet adhesion process. The adhesion model and simulation framework can be further integrated with our established MSMs of platelet activation and aggregation to simulate initial mural thrombus formation on blood vessel walls.

A mathematical model of fibrinogen-mediated erythrocyte-erythrocyte adhesion

Erythrocytes are deformable cells that undergo progressive biophysical and biochemical changes affecting the normal blood flow. Fibrinogen, one of the most abundant plasma proteins, is a primary determinant for changes in haemorheological properties, and a major independent risk factor for cardiovascular diseases. In this study, the adhesion between human erythrocytes is measured by atomic force microscopy (AFM) and its effect observed by micropipette aspiration technique, in the absence and presence of fibrinogen. These experimental data are then used in the development of a mathematical model to examine the biomedical relevant interaction between two erythrocytes. Our designed mathematical model is able to explore the erythrocyte-erythrocyte adhesion forces and changes in erythrocyte morphology. AFM erythrocyte-erythrocyte adhesion data show that the work and detachment force necessary to overcome the adhesion between two erythrocytes increase in the presence of fibrinogen. The changes in erythrocyte morphology, the strong cell-cell adhesion and the slow separation of the two cells are successfully followed in the mathematical simulation. Erythrocyte-erythrocyte adhesion forces and energies are quantified and matched with experimental data. The changes observed on erythrocyte-erythrocyte interactions may give important insights about the pathophysiological relevance of fibrinogen and erythrocyte aggregation in hindering microcirculatory blood flow.

Computational modeling of hypercoagulability in COVID-19

Coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has infected more than 100 million people worldwide and claimed millions of lives. While the leading cause of mortality in COVID-19 patients is the hypoxic respiratory failure from acute respiratory distress syndrome, there is accumulating evidence that shows excessive coagulation also increases the fatalities in COVID-19. Thus, there is a pressing demand to understand the association between COVID-19-induced hypercoagulability and the extent of formation of undesired blood clots. Mathematical modeling of coagulation has been used as an important tool to identify novel reaction mechanisms and to identify targets for new drugs. Here, we employ the coagulation factor data of COVID-19 patients reported from published studies as inputs for two mathematical models of coagulation to identify how the concentrations of coagulation factors change in these patients. Our simulation results show that while the levels of many of the abnormal coagulation factors measured in COVID-19 patients promote the generation of thrombin and fibrin, two key components of blood clots, the increased level of fibrinogen and then the reduced level of antithrombin are the factors most responsible for boosting the level of fibrin and thrombin, respectively. Altogether, our study demonstrates the potential of mathematical modeling to identify coagulation factors responsible for the increased clot formation in COVID-19 patients where clinical data is scarce.

Effects of cardiac function alterations on the risk of postoperative thrombotic complications in patients receiving endovascular aortic repair

Introduction: Chronic heart disease (CHD) is a common comorbidity of patients receiving endovascular aneurysm repair (EVAR) for abdominal aortic aneurysms (AAA). The explicit relationship between ventricular systolic function and EVAR complication of thrombotic events is unknown. Methods: In this study, we proposed a three-dimensional numerical model coupled with the lumped-elements heart model, which is capable of simulating thrombus formation in diverse systolic functions. The relation of cardiac functions and the predicted risk of thrombus formation in the aorta and/or endograft of 4 patients who underwent EVAR was investigated. Relative risks for thrombus formation were identified using machine-learning algorithms. Results: The computational results demonstrate that thrombus tended to form on the interior side of the aorta arch and iliac branches, and cardiac function can affect blood flow field and affect thrombus formation, which is consistent with the four patients' post-operative imaging follow-up. We also found that RRT, OSI, TAWSS in thrombosis area are lower than whole average. In addition, we found that the thrombus formation has negative correlations with the maximum ventricular contractile force (r = -.281 ± .101) and positive correlations with the minimum ventricular contractile force (r = .238 ± .074), whereas the effect of heart rate (r = -.015 ± .121) on thrombus formation is not significant. Conclusion: In conclusion, changes in ventricular systolic function may alter the risk of thrombotic events after EVAR repair, which could provide insight into the selection of adjuvant therapy strategies for AAA patients with CHD.

Nanodroplet-Coated Microbubbles Used in Sonothrombolysis with Two-Step Cavitation Strategy

Thrombosis is a major cause of morbidity and mortality and sonothrombolysis is a promising method for its treatment. However, the slow diffusion of the thrombolytic agents into the thrombus results in slow recanalization. Here, nanodroplet-coated microbubbles (NCMBs) are designed and fabricated and a two-step cavitation strategy is used to accelerate the thrombolysis. The first cavitation of the NCMBs, cavitation and collapse of the microbubbles induced by low frequency ultrasound, drives the nanodroplets on the shell into the thrombus, while the second cavitation, the phase-change and volume expansion of drug-loaded nanodroplets triggered by high frequency ultrasound, loosens the thrombus by the sono-porosity effect. This two-step cavitation of the NCMBs is verified using a fibrin agarose model, where a rapid diffusion of the thrombolytic agents is observed. Furthermore, the NCMBs reach much higher thrombolysis efficiency in both in vitro and proof-of-concept experiments performed with living mice. The nanodroplet-coated microbubbles are a promising diffusion medicines carrier for efficient drug delivery.

von Willebrand factor unfolding mediates platelet deposition in a model of high-shear thrombosis

Thrombosis under high-shear conditions is mediated by the mechanosensitive blood glycoprotein von Willebrand factor (vWF). vWF unfolds in response to strong flow gradients and facilitates rapid recruitment of platelets in flowing blood. While the thrombogenic effect of vWF is well recognized, its conformational response in complex flows has largely been omitted from numerical models of thrombosis. We recently presented a continuum model for the unfolding of vWF, where we represented vWF transport and its flow-induced conformational change using convection-diffusion-reaction equations. Here, we incorporate the vWF component into our multi-constituent model of thrombosis, where the local concentration of stretched vWF amplifies the deposition rate of free-flowing platelets and reduces the shear cleaning of deposited platelets. We validate the model using three benchmarks: in vitro model of atherothrombosis, a stagnation point flow, and the PFA-100, a clinical blood test commonly used for screening for von Willebrand disease (vWD). The simulations reproduced the key aspects of vWF-mediated thrombosis observed in these experiments, such as the thrombus location, thrombus growth dynamics, and the effect of blocking platelet-vWF interactions. The PFA-100 simulations closely matched the reported occlusion times for normal blood and several hemostatic deficiencies, namely, thrombocytopenia, vWD type 1, and vWD type 3. Overall, this multi-constituent model of thrombosis enables macro-scale 3D simulations of thrombus formation in complex geometries over a wide range of shear rates and accounts for qualitative and quantitative hemostatic deficiencies in patient blood.

A fibrin enhanced thrombosis model for medical devices operating at low shear regimes or large surface areas

Over the past decade, much of the development of computational models of device-related thrombosis has focused on platelet activity. While those models have been successful in predicting thrombus formation in medical devices operating at high shear rates (> 5000 s⁻¹), they cannot be directly applied to low-shear devices, such as blood oxygenators and catheters, where emerging information suggest that fibrin formation is the predominant mechanism of clotting and platelet activity plays a secondary role. In the current work, we augment an existing platelet-based model of thrombosis with a partial model of the coagulation cascade that includes contact activation of factor XII and fibrin production. To calibrate the model, we simulate a backward-facing-step flow channel that has been extensively characterized in-vitro. Next, we perform blood perfusion experiments through a microfluidic chamber mimicking a hollow fiber membrane oxygenator and validate the model against these observations. The simulation results closely match the time evolution of the thrombus height and length in the backward-facing-step experiment. Application of the model to the microfluidic hollow fiber bundle chamber capture both gross features such as the increasing clotting trend towards the outlet of the chamber, as well as finer local features such as the structure of fibrin around individual hollow fibers. Our results are in line with recent findings that suggest fibrin production, through contact activation of factor XII, drives the thrombus formation in medical devices operating at low shear rates with large surface area to volume ratios.

Patients treated with blood-contacting medical devices suffer from clotting complications. Over the past decades, a great effort has been made to develop computational tools to predict and prevent clot formation in these devices. However, most models have focused on platelet activity and neglected other important parts of the problem such as the coagulation cascade reactions that lead to fibrin formation. In the current work, we incorporate this missing element into a well-established and validated model for platelet activity. We then use this novel approach to predict thrombus formation in two experimental configurations. Our results confirm that to accurately predict the clotting process in devices where surface area to volume ratios are large and flow velocity and shear stresses remain low, coagulation reactions and subsequent fibrin formation must be considered. This new model could have great implications for the design and optimization of medical devices such as blood oxygenators. In the long term, the model could evolve into a functional tool to inform anticoagulation therapies for these patients.

Computational Biomechanical Modeling of Fibrin Networks and Platelet-Fiber Network Interactions

Fibrin deformation and interaction of fibrin with other blood components play critical roles in hemostasis and thrombosis. In this review, computational and mathematical biomechanical models of fibrin network deformation and contraction at different spatio-temporal scales as well as challenges in developing and calibrating multiscale models are discussed. There are long standing challenges. For instance, applicability of models to identify and test potential mechanisms of the biomechanical processes mediating interactions between platelets and fiber networks in blood clot stretching and contraction needs to be examined carefully. How the structural and mechanical properties of major blood clot components influences biomechanical responses of the entire clot subjected to external forces, such as blood flow or vessel wall deformations needs to be investigated thoroughly.

Multiphysics and multiscale modeling of microthrombosis in COVID-19

Emerging clinical evidence suggests that thrombosis in the microvasculature of patients with Coronavirus disease 2019 (COVID-19) plays an essential role in dictating the disease progression. Because of the infectious nature of SARS-CoV-2, patients’ fresh blood samples are limited to access for in vitro experimental investigations. Herein, we employ a novel multiscale and multiphysics computational framework to perform predictive modeling of the pathological thrombus formation in the microvasculature using data from patients with COVID-19. This framework seamlessly integrates the key components in the process of blood clotting, including hemodynamics, transport of coagulation factors and coagulation kinetics, blood cell mechanics and adhesive dynamics, and thus allows us to quantify the contributions of many prothrombotic factors reported in the literature, such as stasis, the derangement in blood coagulation factor levels and activities, inflammatory responses of endothelial cells and leukocytes to the microthrombus formation in COVID-19. Our simulation results show that among the coagulation factors considered, antithrombin and factor V play more prominent roles in promoting thrombosis. Our simulations also suggest that recruitment of WBCs to the endothelial cells exacerbates thrombogenesis and contributes to the blockage of the blood flow. Additionally, we show that the recent identification of flowing blood cell clusters could be a result of detachment of WBCs from thrombogenic sites, which may serve as a nidus for new clot formation. These findings point to potential targets that should be further evaluated, and prioritized in the anti-thrombotic treatment of patients with COVID-19. Altogether, our computational framework provides a powerful tool for quantitative understanding of the mechanism of pathological thrombus formation and offers insights into new therapeutic approaches for treating COVID-19 associated thrombosis.

Emerging clinical evidence suggests that thrombosis in the microvasculature of patients with Coronavirus disease 2019 (COVID-19) plays an essential role in dictating the disease progression. We employ a novel multiphysics and multiscale computational framework to investigate the underlying mechanism of the pathological formation of microthrombi and circulating cell clusters in COVID-19. We quantify the contributions of many prothrombotic factors reported in the literature, such as stasis, the derangement in blood coagulation factor levels and activities, inflammatory responses of endothelial cells and leukocytes to the microthrombus formation in COVID-19, through which we identify the potential targets that should be further evaluated, and prioritized in the anti-thrombotic treatment of patients with COVID-19.

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.

A Narrow Straight Microchannel Array for Analysis of Transiting Speed of Floating Cancer Cells

Investigating floating cells along a narrow microchannel (e.g., a blood vessel) for their transiting speeds and the corresponding roles of cell physical properties can deepen our understanding of circulating tumor cells (CTCs) metastasis via blood vessels. Many existing studies focus on the cell transiting process in blood vessel-like microchannels; further analytical studies are desired to summarize behaviors of the floating cell movement under different conditions. In this work, we perform a theoretical analysis to establish a relation between the transiting speed and key cell physical properties. We also conduct computational fluid dynamics simulation and microfluidic experiments to verify the theoretical model. This work reveals key cell physical properties and the channel configurations determining the transiting speed. The reported model can be applied to other works with various dimensions of microchannels as a more general way to evaluate the cancer cell metastasis ability with microfluidics.

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.

Mathematical and Computational Modeling of Device-Induced Thrombosis

Given the extensive and routine use of cardiovascular devices, a major limiting factor to their success is the thrombotic rate that occurs. This both poses direct risk to the patient and requires counterbalancing with anticoagulation and other treatment strategies, contributing additional risks. Developing a better understanding of the mechanisms of device-induced thrombosis to aid in device design and medical management of patients is critical to advance the ubiquitous use and durability. Thus, mathematical and computational modelling of device-induced thrombosis has received significant attention recently, but challenges remain. Additional areas that need to be explored include microscopic/macroscopic approaches, reconciling physical and numerical timescales, immune/inflammatory responses, experimental validation, and incorporating pathologies and blood conditions. Addressing these areas will provide engineers and clinicians the tools to provide safe and effective cardiovascular devices.

Thrombosis and Hemodynamics: external and intrathrombus gradients

Distinct from dilute, isotropic, and homogeneous reaction systems typically used in laboratory kinetic assays, blood is concentrated, two-phase, flowing, and highly anisotropic when clotting on a surface. This review focuses on spatial gradients that are generated and can dictate thrombus structure and function. Novel experimental and computational tools have recently emerged to explore reaction-transport coupling during clotting. Multiscale simulations help bridge tissue length scales (the coronary arteries) to millimeter scales of a growing clot to the microscopic scale of single-cell signaling and adhesion. Microfluidic devices help create and control pathological velocity profiles, albeit at a low Reynolds number. Since rate processes and force loading are often coupled, this review highlights prevailing convective-diffusive transport physics that modulate cellular and molecular processes during thrombus formation.

Microstructure aware modeling of biochemical transport in arterial blood clots

Flow-mediated transport of biochemical species is central to thrombotic phenomena. Comprehensive three-dimensional modeling of flow-mediated transport around realistic macroscale thrombi poses challenges owing to their arbitrary heterogeneous microstructure. Here, we develop a microstructure aware model for species transport within and around a macroscale thrombus by devising a custom preconditioned fictitious domain formulation for thrombus-hemodynamics interactions, and coupling it with a fictitious domain advection-diffusion formulation for transport. Microstructural heterogeneities are accounted through a hybrid discrete particle-continuum approach for the thrombus interior. We present systematic numerical investigations on unsteady arterial flow within and around a three-dimensional macroscale thrombus; demonstrate the formation of coherent flow structures around the thrombus which organize advective transport; illustrate the role of the permeation processes at the thrombus boundary and subsequent intra-thrombus transport; and characterize species transport from bulk flow to the thrombus boundary and vice versa.

A 1D-3D Hybrid Model of Patient-Specific Coronary Hemodynamics

PURPOSE

Coronary flow is affected by evolving events such as atherosclerotic plaque formation, rupture, and thrombosis, resulting in myocardial ischemia and infarction. Highly resolved 3D hemodynamic data at the stenosis is essential to model shear-sensitive thrombotic events in coronary artery disease.

METHODS

We developed a hybrid 1D-3D simulation framework to compute patient-specific coronary hemodynamics efficiently. A 1D model of the coronary flow is coupled to an image-based 3D model of the region of interest. This framework affords the advantages of reduced-order modeling, decreasing the global computational cost, without sacrificing the accuracy of the quantities of interest.

RESULTS

We validated our 1D-3D model against full 3D coronary simulations in healthy and diseased conditions. Our results showed good agreement between the 3D and the 1D-3D models while reducing the computational cost by 40-fold compared to the 3D simulation. The 1D-3D model predicted left/right coronary flow distribution within 3% and provided an accurate estimation of fractional flow reserve and wall shear stress distribution at the stenosis comparable to the 3D simulation.

CONCLUSION

Savings in computational cost may be significant in situations with changing geometry, such as growing thrombosis. Also, this approach would allow quantifying the time-dependent effect of thrombotic growth and occlusion on the global coronary circulation.

Computational modeling of blood component transport related to coronary artery thrombosis in Kawasaki disease

Coronary artery thrombosis is the major risk associated with Kawasaki disease (KD). Long-term management of KD patients with persistent aneurysms requires a thrombotic risk assessment and clinical decisions regarding the administration of anticoagulation therapy. Computational fluid dynamics has demonstrated that abnormal KD coronary artery hemodynamics can be associated with thrombosis. However, the underlying mechanisms of clot formation are not yet fully understood. Here we present a new model incorporating data from patient-specific simulated velocity fields to track platelet activation and accumulation. We use a system of Reaction-Advection-Diffusion equations solved with a stabilized finite element method to describe the evolution of non-activated platelets and activated platelet concentrations [AP], local concentrations of adenosine diphosphate (ADP) and poly-phosphate (PolyP). The activation of platelets is modeled as a function of shear-rate exposure and local concentration of agonists. We compared the distribution of activated platelets in a healthy coronary case and six cases with coronary artery aneurysms caused by KD, including three with confirmed thrombosis. Results show spatial correlation between regions of higher concentration of activated platelets and the reported location of the clot, suggesting predictive capabilities of this model towards identifying regions at high risk for thrombosis. Also, the concentration levels of ADP and PolyP in cases with confirmed thrombosis are higher than the reported critical values associated with platelet aggregation (ADP) and activation of the intrinsic coagulation pathway (PolyP). These findings suggest the potential initiation of a coagulation pathway even in the absence of an extrinsic factor. Finally, computational simulations show that in regions of flow stagnation, biochemical activation, as a result of local agonist concentration, is dominant. Identifying the leading factors to a pro-coagulant environment in each case—mechanical or biochemical—could help define improved strategies for thrombosis prevention tailored for each patient.

Computational studies aiming to model thrombosis often rely on an arterial wall injury. Collagen and other extracellular matrix components are exposed to the bloodstream, which facilitates platelet adhesion to the wall and subsequent clot formation. However, these models are not adequate to explain thrombosis in other settings where even in the absence of a focal lesion, clots may still form under certain flow conditions. Coronary artery aneurysm thrombosis following KD is an example of the need to understand the mechanisms of thrombus initiation in the absence of an extrinsic factor. This study provides a new framework to investigate thrombus initiation in KD from a patient-specific perspective, which integrates fluid mechanics and biochemistry and which could help quantify the pro-coagulant environment induced by the aneurysm and become a predictive tool. The work presented here has broad relevance to other clinical situations where flow stagnation and transport are driving factors in thrombus formation.

Computational investigation of platelet thrombus mechanics and stability in stenotic channels

The stability of a platelet thrombus under flow is believed to depend strongly on the local hemodynamics and on the thrombus' porosity, permeability, and elasticity. A two-phase continuum model is used to investigate the biomechanics of thrombus stability in stenotic channels. It treats the thrombus as a porous, viscoelastic material moving differently than the background fluid. The dynamic clot-flow interaction is modeled through a frictional drag term. The model explicitly tracks the formation and breaking of interplatelet molecular bonds, which directly determine the viscoelastic property of the thrombus and govern its ability to resist fluid drag. We characterize the stability/fragility of thrombi for various flow speeds, porosities, bond concentrations, and bond types.

Influence of shear rate and surface chemistry on thrombus formation in micro-crevice

Thromboembolic complications remain a central issue in management of patients on mechanical circulatory support. Despite the best practices employed in design and manufacturing of modern ventricular assist devices, complexity and modular nature of these systems often introduces internal steps and crevices in the flow path which can serve as nidus for thrombus formation. Thrombotic potential is influenced by multiple factors including the characteristics of the flow and surface chemistry of the biomaterial. This study explored these elements in the setting of blood flow over a micro-crevice using a multi-constituent numerical model of thrombosis. The simulations reproduced the platelet deposition patterns observed experimentally and elucidated the role of flow, shear rate, and surface chemistry in shaping the deposition. The results offer insights for design and operation of blood-contacting devices.

Non-invasive Inference of Thrombus Material Properties with Physics-Informed Neural Networks

We employ physics-informed neural networks (PINNs) to infer properties of biological materials using synthetic data. In particular, we successfully apply PINNs on inferring permeability and viscoelastic modulus from thrombus deformation data, which can be described by the fourth-order Cahn-Hilliard and Navier-Stokes Equations. In PINNs, the partial differential equations are encoded into a loss function, where partial derivatives can be obtained through automatic differentiation (AD). In addition to tackling the challenge of calculating the fourth-order derivative in the Cahn-Hilliard equation with AD, we introduce an auxiliary network along with the main neural network to approximate the second-derivative of the energy potential term. Our model can simultaneously predict unknown material parameters and velocity, pressure, and deformation gradient fields by merely training with partial information among all data, i.e., phase field and pressure measurements, while remaining highly flexible in sampling within the spatio-temporal domain for data acquisition. We validate our model by numerical solutions from the spectral/hp element method (SEM) and demonstrate its robustness by training it with noisy measurements. Our results show that PINNs can infer the material properties from noisy synthetic data, and thus they have great potential for inferring these properties from experimental multi-modality and multi-fidelity data.

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.

Computational investigation of blood flow and flow-mediated transport in arterial thrombus neighborhood

A pathologically formed blood clot or thrombus is central to major cardiovascular diseases like heart attack and stroke. Detailed quantitative evaluation of flow and flow-mediated transport processes in the thrombus neighborhood within large artery hemodynamics is crucial for understanding disease progression and assessing treatment efficacy. This, however, remains a challenging task owing to the complexity of pulsatile viscous flow interactions with arbitrary shape and heterogeneous microstructure of realistic thrombi. Here, we address this challenge by conducting a systematic parametric simulation-based study on characterizing unsteady hemodynamics and flow-mediated transport in the neighborhood of an arterial thrombus. We use a hybrid particle-continuum-based finite element approach to handle arbitrary thrombus shape and microstructural variations. Results from a cohort of 50 different unsteady flow scenarios are presented, including unsteady vortical structures, pressure gradient across the thrombus boundary, finite time Lyapunov exponents, and dynamic coherent structures that organize advective transport. We clearly illustrate the combined influence of three key parameters-thrombus shape, microstructure, and extent of wall disease-in terms of: (a) determining hemodynamic features in the thrombus neighborhood and (b) governing the balance between advection, permeation, and diffusion to regulate transport processes in the thrombus neighborhood.