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

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.

Longitudinal investigation of aortic dissection in mice with computational fluid dynamics

Predicting late adverse events in aortic dissections is challenging. One commonly observed risk factor is partial thrombosis of the false lumen. In this study we investigated false lumen thrombus progression over 7 days in four mice with angiotensin II-induced aortic dissection. We performed computational fluid dynamic simulations with subject-specific boundary conditions from velocity and pressure measurements. We investigated endothelial cell activation potential, mean velocity, thrombus formation potential, and other hemodynamic factors. Our findings support the hypothesis that flow stagnation is the predominant hemodynamic factor driving a large thrombus ratio in false lumina, particularly those with a single fenestration.

Predictors of Myocardial Ischemia in Patients with Kawasaki Disease: Insights from Patient-Specific Simulations of Coronary Hemodynamics

Current treatments for patients with coronary aneurysms caused by Kawasaki disease (KD) are based primarily on aneurysm size. This ignores hemodynamic factors influencing myocardial ischemic risk. We performed patient-specific computational hemodynamics simulations for 15 KD patients, with parameters tuned to patients' arterial pressure and cardiac function. Ischemic risk was evaluated in 153 coronary arteries from simulated fractional flow reserve (FFR), wall shear stress, and residence time. FFR correlated weakly with aneurysm [Formula: see text]-scores (correlation coefficient, [Formula: see text]) but correlated better with the ratio of maximum-to-minimum aneurysmal lumen diameter ([Formula: see text]). FFR dropped more rapidly distal to aneurysms, and this correlated more with the lumen diameter ratio ([Formula: see text]) than [Formula: see text]-score ([Formula: see text]). Wall shear stress correlated better with the diameter ratio ([Formula: see text]), while residence time correlated more with [Formula: see text]-score ([Formula: see text]). Overall, the maximum-to-minimum diameter ratio predicted ischemic risk better than [Formula: see text]-score. Although FFR immediately distal to aneurysms was nonsignificant, its rapid rate of decrease suggests elevated risk.

Efficient multi-fidelity computation of blood coagulation under flow

Clot formation is a crucial process that prevents bleeding, but can lead to severe disorders when imbalanced. This process is regulated by the coagulation cascade, a biochemical network that controls the enzyme thrombin, which converts soluble fibrinogen into the fibrin fibers that constitute clots. Coagulation cascade models are typically complex and involve dozens of partial differential equations (PDEs) representing various chemical species' transport, reaction kinetics, and diffusion. Solving these PDE systems computationally is challenging, due to their large size and multi-scale nature. We propose a multi-fidelity strategy to increase the efficiency of coagulation cascade simulations. Leveraging the slower dynamics of molecular diffusion, we transform the governing PDEs into ordinary differential equations (ODEs) representing the evolution of species concentrations versus blood residence time. We then Taylor-expand the ODE solution around the zero-diffusivity limit to obtain spatiotemporal maps of species concentrations in terms of the statistical moments of residence time, [Formula: see text], and provide the governing PDEs for [Formula: see text]. This strategy replaces a high-fidelity system of N PDEs representing the coagulation cascade of N chemical species by N ODEs and p PDEs governing the residence time statistical moments. The multi-fidelity order (p) allows balancing accuracy and computational cost providing a speedup of over N/p compared to high-fidelity models. Moreover, this cost becomes independent of the number of chemical species in the large computational meshes typical of the arterial and cardiac chamber simulations. Using a coagulation network with N = 9 and an idealized aneurysm geometry with a pulsatile flow as a benchmark, we demonstrate favorable accuracy for low-order models of p = 1 and p = 2. The thrombin concentration in these models departs from the high-fidelity solution by under 20% (p = 1) and 2% (p = 2) after 20 cardiac cycles. These multi-fidelity models could enable new coagulation analyses in complex flow scenarios and extensive reaction networks. Furthermore, it could be generalized to advance our understanding of other reacting systems affected by flow.

Personalized coronary and myocardial blood flow models incorporating CT perfusion imaging and synthetic vascular trees

Computational simulations of coronary artery blood flow, using anatomical models based on clinical imaging, are an emerging non-invasive tool for personalized treatment planning. However, current simulations contend with two related challenges - incomplete anatomies in image-based models due to the exclusion of arteries smaller than the imaging resolution, and the lack of personalized flow distributions informed by patient-specific imaging. We introduce a data-enabled, personalized and multi-scale flow simulation framework spanning large coronary arteries to myocardial microvasculature. It includes image-based coronary models combined with synthetic vasculature for arteries below the imaging resolution, myocardial blood flow simulated using Darcy models, and systemic circulation represented as lumped-parameter networks. Personalized flow distributions and model parameters are informed by clinical CT myocardial perfusion imaging and cardiac function using surrogate-based optimization. We reveal substantial differences in flow distributions and clinical diagnosis metrics between the proposed personalized framework and empirical methods based on anatomy; these errors cannot be predicted a priori. This suggests virtual treatment planning tools would benefit from increased personalization informed by emerging imaging methods.

Efficient multi-fidelity computation of blood coagulation under flow

Clot formation is a crucial process that prevents bleeding, but can lead to severe disorders when imbalanced. This process is regulated by the coagulation cascade, a biochemical network that controls the enzyme thrombin, which converts soluble fibrinogen into the fibrin fibers that constitute clots. Coagulation cascade models are typically complex and involve dozens of partial differential equations (PDEs) representing various chemical species' transport, reaction kinetics, and diffusion. Solving these PDE systems computationally is challenging, due to their large size and multi-scale nature. We propose a multi-fidelity strategy to increase the efficiency of coagulation cascade simulations. Leveraging the slower dynamics of molecular diffusion, we transform the governing PDEs into ordinary differential equations (ODEs) representing the evolution of species concentrations versus blood residence time. We then Taylor-expand the ODE solution around the zero-diffusivity limit to obtain spatiotemporal maps of species concentrations in terms of the statistical moments of residence time, , and provide the governing PDEs for . This strategy replaces a high-fidelity system of N PDEs representing the coagulation cascade of N chemical species by N ODEs and p PDEs governing the residence time statistical moments. The multi-fidelity order( p ) allows balancing accuracy and computational cost, providing a speedup of over N/p compared to high-fidelity models. Using a simplified coagulation network and an idealized aneurysm geometry with a pulsatile flow as a benchmark, we demonstrate favorable accuracy for low-order models of p = 1 and p = 2. These models depart from the high-fidelity solution by under 16% ( p = 1) and 5% ( p = 2) after 20 cardiac cycles. The favorable accuracy and low computational cost of multi-fidelity models could enable unprecedented coagulation analyses in complex flow scenarios and extensive reaction networks. Furthermore, it can be generalized to advance our understanding of other systems biology networks affected by blood flow.

Tissue-growth-based synthetic tree generation and perfusion simulation

Biological tissues receive oxygen and nutrients from blood vessels by developing an indispensable supply and demand relationship with the blood vessels. We implemented a synthetic tree generation algorithm by considering the interactions between the tissues and blood vessels. We first segment major arteries using medical image data and synthetic trees are generated originating from these segmented arteries. They grow into extensive networks of small vessels to fill the supplied tissues and satisfy the metabolic demand of them. Further, the algorithm is optimized to be executed in parallel without affecting the generated tree volumes. The generated vascular trees are used to simulate blood perfusion in the tissues by performing multiscale blood flow simulations. One-dimensional blood flow equations were used to solve for blood flow and pressure in the generated vascular trees and Darcy flow equations were solved for blood perfusion in the tissues using a porous model assumption. Both equations are coupled at terminal segments explicitly. The proposed methods were applied to idealized models with different tree resolutions and metabolic demands for validation. The methods demonstrated that realistic synthetic trees were generated with significantly less computational expense compared to that of a constrained constructive optimization method. The methods were then applied to cerebrovascular arteries supplying a human brain and coronary arteries supplying the left and right ventricles to demonstrate the capabilities of the proposed methods. The proposed methods can be utilized to quantify tissue perfusion and predict areas prone to ischemia in patient-specific geometries.

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.

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.

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.