A Model for the Formation and Lysis of Blood Clots

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

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

Clot embolization studies and computational framework for embolization in a canonical tube model

Despite recent advances in the development of computational methods of modeling thrombosis, relatively little effort has been made in developing methods of modeling blood clot embolization. Such a model would provide substantially greater understanding of the mechanics of embolization, as in-vitro and in-vivo characterization of embolization is difficult. Here, a method of computationally simulating embolization is developed. Experiments are performed of blood clots formed in a polycarbonate tube, where phosphate-buffered saline is run through the tube at increasing flow rates until the clot embolizes. The experiments revealed embolization can be initiated by leading edge and trailing edge detachment or by non-uniform detachment. Stress-relaxation experiments are also performed to establish values of constitutive parameters for subsequent simulations. The embolization in the tube is reproduced in silico using a multiphase volume-of-fluid approach, where the clot is modeled as viscoelastic. By varying the constitutive parameters at the wall, embolization can be reproduced in-silico at varying flow rates, and a range of constitutive parameters fitting the experiments is reported. Here, the leading edge embolization is simulated at flow rates consistent with the experiments demonstrating excellent agreement in this specific behavior.

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 simplified mesoscale 3D model for characterizing fibrinolysis under flow conditions

One of the routine clinical treatments to eliminate ischemic stroke thrombi is injecting a biochemical product into the patient's bloodstream, which breaks down the thrombi's fibrin fibers: intravenous or intravascular thrombolysis. However, this procedure is not without risk for the patient; the worst circumstances can cause a brain hemorrhage or embolism that can be fatal. Improvement in patient management drastically reduced these risks, and patients who benefited from thrombolysis soon after the onset of the stroke have a significantly better 3-month prognosis, but treatment success is highly variable. The causes of this variability remain unclear, and it is likely that some fundamental aspects still require thorough investigations. For that reason, we conducted in vitro flow-driven fibrinolysis experiments to study pure fibrin thrombi breakdown in controlled conditions and observed that the lysis front evolved non-linearly in time. To understand these results, we developed an analytical 1D lysis model in which the thrombus is considered a porous medium. The lytic cascade is reduced to a second-order reaction involving fibrin and a surrogate pro-fibrinolytic agent. The model was able to reproduce the observed lysis evolution under the assumptions of constant fluid velocity and lysis occurring only at the front. For adding complexity, such as clot heterogeneity or complex flow conditions, we propose a 3-dimensional mesoscopic numerical model of blood flow and fibrinolysis, which validates the analytical model's results. Such a numerical model could help us better understand the spatial evolution of the thrombi breakdown, extract the most relevant physiological parameters to lysis efficiency, and possibly explain the failure of the clinical treatment. These findings suggest that even though real-world fibrinolysis is a complex biological process, a simplified model can recover the main features of lysis evolution.

Modelling of thrombus formation using smoothed particle hydrodynamics method

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

Fibrinolysis: an illustrated review

In response to vessel injury (or other pathological conditions), the hemostatic process is activated, resulting in a fibrous, cellular-rich structure commonly referred to as a blood clot. Succeeding the clot's function in wound healing, it must be resolved. This illustrated review focuses on fibrinolysis-the degradation of blood clots or thrombi. Fibrin is the main mechanical and structural component of a blood clot, which encases the cellular components of the clot, including platelets and red blood cells. Fibrinolysis is the proteolytic degradation of the fibrin network that results in the release of the cellular components into the bloodstream. In the case of thrombosis, fibrinolysis is required for restoration of blood flow, which is accomplished clinically through exogenously delivered lytic factors in a process called external lysis. Fibrinolysis is regulated by plasminogen activators (tissue-type and urokinase-type) that convert plasminogen into plasmin to initiate fiber lysis and lytic inhibitors that impede this lysis (plasminogen activator inhibitors, alpha 2-antiplasmin, and thrombin activatable fibrinolysis inhibitor). Furthermore, the network structure has been shown to regulate lysis: thinner fibers and coarser clots lyse faster than thicker fibers and finer clots. Clot contraction, a result of platelets pulling on fibers, results in densely packed red blood cells (polyhedrocytes), reduced permeability to fibrinolytic factors, and increased fiber tension. Extensive research in the field has allowed for critical advancements leading to improved thrombolytic agents. In this review, we summarize the state of the field, highlight gaps in knowledge, and propose future research questions.

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.

Uncertainty quantification of a thrombosis model considering the clotting assay PFA-100®

Mathematical models of thrombosis are currently used to study clinical scenarios of pathological thrombus formation. As these models become more complex to predict thrombus formation dynamics high computational cost must be alleviated and inherent uncertainties must be assessed. Evaluating model uncertainties allows to increase the confidence in model predictions and identify avenues of improvement for both thrombosis modeling and anti-platelet therapies. In this work, an uncertainty quantification analysis of a multi-constituent thrombosis model is performed considering a common assay for platelet function (PFA-100®). The analysis is facilitated thanks to time-evolving polynomial chaos expansions used as a parametric surrogate for the full thrombosis model considering two quantities of interest; namely, thrombus volume and occlusion percentage. The surrogate is thoroughly validated and provides a straightforward access to a global sensitivity analysis via computation of Sobol' coefficients. Six out of 15 parameters linked to thrombus consitution, vWF activity, and platelet adhesion dynamics were found to be most influential in the simulation variability considering only individual effects; while parameter interactions are highlighted when considering the total Sobol' indices. The influential parameters are related to thrombus constitution, vWF activity, and platelet to platelet adhesion dynamics. The surrogate model allowed to predict realistic PFA-100® closure times of 300,000 virtual cases that followed the trends observed in clinical data. The current methodology could be used including common anti-platelet therapies to identify scenarios that preserve the hematological balance.

Anomalous aggregation regimes of temperature-dependent Smoluchowski equations

Temperature-dependent Smoluchowski equations describe the ballistic agglomeration. In contrast to the standard Smoluchowski equations for the evolution of cluster densities, with constant rate coefficients, the temperature-dependent equations describe both-the evolution of the densities as well as cluster temperatures, which determine the agglomeration rates. To solve these equations, we develop a Monte Carlo technique based on the low-rank approximation for the aggregation kernel. Using this highly effective approach, we perform a comprehensive study of the kinetic phase diagram of the system and reveal a few surprising regimes, including permanent temperature growth and "density separation" regime, with a large gap in the size distribution for middle-size clusters. We perform scaling analysis and classify the aggregation kernels for the temperature-dependent equations. Furthermore, we conjecture the lack of gelation in such systems. The results of the scaling theory agree well with the simulation data.

A New Score for Determining Thrombus Burden in STEMI Patients: The MAPH Score

Aim

to investigate whether the MAPH score, which is a new score that combines blood viscosity biomarkers such as mean platelet volume (MPV), total protein and hematocrit, can be used to predict thrombus burden in ST-segment elevation myocardial infarction (STEMI) patients.

Methods

A total of 473 consecutive patients with STEMI were included in the study. Intracoronary tirofiban/abciximab infusion was applied to patients with thrombus load ≥3 and these patients (n = 71) were defined as the patient group with high thrombus load. MPV, age, hematocrit and total protein values of the patients were recorded. High shear rate (HSR) and low shear rate (LSR) were calculated from total protein and hematocrit values. Cut-off values were determined for high thrombus load by using Youden index, and score was determined as 0 or 1 according to cut-offs. The sum of the scores was calculated as the MAPH score.

Results

The mean age of the patients included in the study was 59.6 ± 12.6 (n = 354 male, 74.8%). There was no difference between the groups in terms of gender, HT and DM (P = .127, P = .402 and P = .576, respectively). In the group with high thrombus load; total protein, MPV and hematocrit values were higher (P < .001, P = .001 and P = .03, respectively). Comparison of receiver operating characteristic (ROC) curve analysis revealed that the MAPH score had better performance in predicting higher thrombus load than both other self-containing parameters and HSR and LSR.

Conclusion

The MAPH score may be a new score that can be used to determine thrombus burden in STEMI patients.

Thrombolysis: Observations and numerical models

This perspective paper considers thrombolysis in the context of ischemic strokes, intending to build eventually a numerical model capable of simulating the thrombolytic treatment and predicting patient outcomes. Numerical modeling is a scientific methodology based on an abstraction of a system but requires understanding their spatio-temporal interactions. However, although important, the current knowledge on thrombolysis is fragmented in contributions from which it is difficult to obtain a complete picture of the process, especially in a clinically relevant setup. This paper discusses, from a general point of view, how to develop a numerical model to describe the evolution of a patient clot under the action of a thrombolytic drug. We will present critical, yet fundamental, open questions that have emerged during this elaboration and discuss original experimental observations that challenge some of our current knowledge of thrombolysis.

An integrated fluid-chemical model toward modeling the thrombus formation in an idealized model of aortic dissection

Type B aortic dissection is a major aortic catastrophe that can be acutely complicated by rapid expansion, rupture, and malperfusion syndromes. The separation of the intima from aortic walls will form a second blood-filled lumen defined as "false lumen (FL)", where the thrombus is more likely to form due to the local stasis hemodynamic conditions. Complete thrombosis of FL is associated with a beneficial outcome while patency and partial thrombosis will lead to later complications. However, the thrombosis mechanism is still unclear and little is known about the impact of chemical species transported by blood flow on this process. The proteins involved in the coagulation cascade (CC) may play an important role in the process of thrombosis, especially in the activation and stabilization of platelets. Based on this hypothesis, a reduced-order fluid-chemical model was established to simulate CC in an aortic dissection phantom with two tears. A high level of fibrin is continuously observed at the top of the FL and some time-varying areas between two tears, indicating a high likelihood of thrombus formation there. This finding is consistent with the clinical observation. The time evolution of coagulation factors is greatly affected by local hemodynamics, especially in the high disturbance zone where the evolution has characteristics of periodic changes consistent with the flow field. The ability of the proposed model to reproduce the CC response provides a potential application to integrate with a model that can simulate platelet activities, forming a biochemical-based model which would help unveil the mechanisms of thrombosis in FL and the clinical decision of appropriate treatment.

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.

Review of pulmonary emboli and techniques for their mechanical removal to inform device design

Pulmonary emboli present a significant burden of disease, with limited treatment options for some patients. Mechanical devices for pulmonary emboli removal are becoming increasingly prevalent though more work remains to be done. This paper briefly discusses the mechanical properties of pulmonary emboli, the disease state they cause, and the existing embolectomy devices. The goal of this paper is to aid the design of minimally invasive mechanical pulmonary emboli removal devices, by providing a review of this topic as well as some key design specifications.

Modeling Thrombin Generation in Plasma under Diffusion and Flow

We investigate the capacity of published numerical models of thrombin generation to reproduce experimentally observed threshold behavior under conditions in which diffusion and/or flow are important. Computational fluid dynamics simulations incorporating species diffusion, fluid flow, and biochemical reactions are compared with published data for thrombin generation in vitro in 1) quiescent plasma exposed to patches of tissue factor and 2) plasma perfused through a capillary coated with tissue factor. Clot time is correctly predicted in individual cases, and some models qualitatively replicate thrombin generation thresholds across a series of tissue factor patch sizes or wall shear rates. Numerical results suggest that there is not a genuine patch size threshold in quiescent plasma-clotting always occurs given enough time-whereas the shear rate threshold observed under flow is a genuine physical limit imposed by flow-mediated washout of active coagulation factors. Despite the encouraging qualitative results obtained with some models, no single model robustly reproduces all experiments, demonstrating that greater understanding of the underlying reaction network, and particularly of surface reactions, is required. In this direction, additional simulations provide evidence that 1) a surface-localized enzyme, speculatively identified as meizothrombin, is significantly active toward the fluorescent thrombin substrate used in the experiments or, less likely, 2) thrombin is irreversibly inhibited at a faster-than-expected rate, possibly explained by a stimulatory effect of plasma heparin on antithrombin. These results highlight the power of simulation to provide novel mechanistic insights that augment experimental studies and build our understanding of complex biophysicochemical processes. Further validation work is critical to unleashing the full potential of coagulation models as tools for drug development and personalized medicine.

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.

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

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

Longer Length of Delayed-Contrast Filling of Clot on 4-Dimensional Computed Tomographic Angiography Predicts Cardiogenic Embolism

Background and Purpose- We hypothesized the length of delayed-contrast filling sign (DCFS) of intraarterial clot, indicating contrast medium penetration into the thrombus, was associated with stroke etiology. Methods- We retrospectively included patients with large vessel occlusion in anterior circulation who underwent computed tomographic perfusion within 24 hours poststroke onset. We defined DCFS as contrast medium diffusion through the thrombi after the arterial peak phase on 4-dimensional computed tomographic angiography derived from computed tomographic perfusion. We measured the length of DCFS and investigated its value for predicting the stroke etiology. Results- Three hundred twenty-one patients were analyzed, and their stroke etiologies included cardiogenic embolism (CE, n=167), large artery atherosclerosis (n=64), other etiology group (n=4), and undetermined etiology (n=86). CE patients had longer length of DCFS than non-CE patients (2.3 versus 0.5 mm; P<0.001). The optimal cutoff value of DCFS length for predicting CE was 1.5 mm. The sensitivity, specificity, positive predictive value, and negative predictive value of a length of DCFS >1.5 mm for predicting CE were 83.2%, 70.8%, 75.5%, and 79.6%. Conclusions- Longer length of DCFS was associated with CE in patients with large vessel occlusion in anterior circulation, which may provide stroke etiology information.

Model development and comparison of low hemorrhage-risk endoluminal patch thrombolytic treatment for ischemic stroke

Clot dissolution drugs delivered into the systemic circulation can dissolve intracranial blood clots in 90 min with 20-50% hemorrhage rate. Immobilizing <5% of the intravenous dosage on an endoluminal patch can reduce the dissolution time to <20 min with negligible hemorrhage risk. The thrombus dissolution behavior in endoluminal patch thrombolytic treatment is modeled and compared with experimental results from a companion study. Analyses showed that the thrombus dissolution time decreases with increasing dosage, but the dissolution time reaches a dosage-independent minimum when uPA dosage on the patch is >800 IU. Model analyses showed that dissolution time in the plateau regime is controlled by diffusion. Further results showed that dissolution time could be reduced in this regime by reducing thrombus thickness. This suggests that a stented endoluminal thrombolytic >800 IU patch that compresses the thrombus to thin the clot thickness can help reduce dissolution time. This ultra-low transition dosage (i.e., 800 IU), compared to 0.6-2.4 million IU in conventional thrombolysis suggests that hemorrhage risk in endoluminal patch thrombolytic treatment is low. The low hemorrhagic-risk endoluminal patch can be considered for use in patients who are ineligible for conventional thrombolytic treatment because of high hemorrhagic treatment risk.

Thrombosis in Cerebral Aneurysms and the Computational Modeling Thereof: A Review

Thrombosis is a condition closely related to cerebral aneurysms and controlled thrombosis is the main purpose of endovascular embolization treatment. The mechanisms governing thrombus initiation and evolution in cerebral aneurysms have not been fully elucidated and this presents challenges for interventional planning. Significant effort has been directed towards developing computational methods aimed at streamlining the interventional planning process for unruptured cerebral aneurysm treatment. Included in these methods are computational models of thrombus development following endovascular device placement. The main challenge with developing computational models for thrombosis in disease cases is that there exists a wide body of literature that addresses various aspects of the clotting process, but it may not be obvious what information is of direct consequence for what modeling purpose (e.g., for understanding the effect of endovascular therapies). The aim of this review is to present the information so it will be of benefit to the community attempting to model cerebral aneurysm thrombosis for interventional planning purposes, in a simplified yet appropriate manner. The paper begins by explaining current understanding of physiological coagulation and highlights the documented distinctions between the physiological process and cerebral aneurysm thrombosis. Clinical observations of thrombosis following endovascular device placement are then presented. This is followed by a section detailing the demands placed on computational models developed for interventional planning. Finally, existing computational models of thrombosis are presented. This last section begins with description and discussion of physiological computational clotting models, as they are of immense value in understanding how to construct a general computational model of clotting. This is then followed by a review of computational models of clotting in cerebral aneurysms, specifically. Even though some progress has been made towards computational predictions of thrombosis following device placement in cerebral aneurysms, many gaps still remain. Answering the key questions will require the combined efforts of the clinical, experimental and computational communities.

Modeling of the effects of IL-17 and TNF-α on endothelial cells and thrombus growth

Rheumatoid and psoriatic arthritis are chronic inflammatory diseases, with massive increase of cardiovascular events (CVE), and contribution of the cytokines TNF-α and IL-17. Chronic inflammation inside the joint membrane or synovium results from the activation of fibroblasts/synoviocytes, and leads to the release of cytokines from monocytes (Tumor Necrosis Factor or TNF) and from T lymphocytes (Interleukin-17 or IL-17). At the systemic level, the very same cytokines affect endothelial cells and vessel wall. We have previously shown [1,2] that IL-17 and TNF-α, specifically when combined, increase procoagulation, decrease anticoagulation and increase platelet aggregation, leading to thrombosis. These results are the basis for the models of interactions between IL-17 and TNF, and genes expressed by activated endothelial cells. This work is devoted to mathematical modeling and numerical simulations of blood coagulation and clot growth under the influence of IL-17 and TNF-α. We show that they can provoke thrombosis, leading to the complete or partial occlusion of blood vessels. The regimes of blood coagulation and conditions of occlusion are investigated in numerical simulations and in approximate analytical models. The results of mathematical modeling allow us to predict thrombosis development for an individual patient.

Modelling of thrombin generation under flow in realistic left anterior descending geometries

Currently there are no available methods for prediction of thrombotic complications in Coronary Artery disease. Additionally, blood coagulation tests are mainly performed in a steady system while coagulation in vivo occurs under flow conditions. In this work, a phenomenological model for coagulation up-to thrombin generation is proposed; the model is mainly based on the results of thrombin generation assays and therefore it can account for the variation of the coagulability that is observed in different individuals. The model is applied on 3 cases of left anterior descending arteries (LAD) with 50% maximum stenosis placed at a different location and have been statistically assessed as of different complication risk. The simulations showed that parameters of thrombin generation assays obtain different values when they refer to thrombin generation under realistic coronary flow conditions. The flow conditions prevailing locally because of the geometric differences among the arterial trees can lead to different initiation times and thrombin production rates and it also alters the spatial distribution of the coagulation products. Similarly, small changes of the coagulation characteristics of blood under identical flow conditions can allow or prevent the initiation of coagulation. The results indicate that combined consideration of geometry and coagulation characteristics of blood can lead to entirely different conclusions compared to independent assessment of each factor.

Conditions of microvessel occlusion for blood coagulation in flow

Vessel occlusion is a perturbation of blood flow inside a blood vessel because of the fibrin clot formation. As a result, blood circulation in the vessel can be slowed down or even stopped. This can provoke the risk of cardiovascular events. In order to explore this phenomenon, we used a previously developed mathematical model of blood clotting to describe the concentrations of blood factors with a reaction-diffusion system of equations. The Navier-Stokes equations were used to model blood flow, and we treated the clot as a porous medium. We identify the conditions of partial or complete occlusion in a small vessel depending on various physical and physiological parameters. In particular, we were interested in the conditions on blood flow and diameter of the wounded area. The existence of a critical flow velocity separating the regimes of partial and complete occlusion was demonstrated through the mathematical investigation of a simplified model of thrombin wave propagation in Poiseuille flow. We observed different regimes of vessel occlusion depending on the model parameters both for the numerical simulations and in the theoretical study. Then, we compared the rate of clot growth in flow obtained in the simulations with experimental data. Both of them showed the existence of different regimes of clot growth depending on the velocity of blood flow.

Computational Study of Thrombus Formation and Clotting Factor Effects under Venous Flow Conditions

A comprehensive understanding of thrombus formation as a physicochemical process that has evolved to protect the integrity of the human vasculature is critical to our ability to predict and control pathological states caused by a malfunctioning blood coagulation system. Despite numerous investigations, the spatial and temporal details of thrombus growth as a multicomponent process are not fully understood. Here, we used computational modeling to investigate the temporal changes in the spatial distributions of the key enzymatic (i.e., thrombin) and structural (i.e., platelets and fibrin) components within a growing thrombus. Moreover, we investigated the interplay between clot structure and its mechanical properties, such as hydraulic resistance to flow. Our model relied on the coupling of computational fluid dynamics and biochemical kinetics, and was validated using flow-chamber data from a previous experimental study. The model allowed us to identify the distinct patterns characterizing the spatial distributions of thrombin, platelets, and fibrin accumulating within a thrombus. Our modeling results suggested that under the simulated conditions, thrombin kinetics was determined predominantly by prothrombinase. Furthermore, our simulations showed that thrombus resistance imparted by fibrin was ∼30-fold higher than that imparted by platelets. Yet, thrombus-mediated bloodflow occlusion was driven primarily by the platelet deposition process, because the height of the platelet accumulation domain was approximately twice that of the fibrin accumulation domain. Fibrinogen supplementation in normal blood resulted in a nonlinear increase in thrombus resistance, and for a supplemented fibrinogen level of 48%, the thrombus resistance increased by ∼2.7-fold. Finally, our model predicted that restoring the normal levels of clotting factors II, IX, and X while simultaneously restoring fibrinogen (to 88% of its normal level) in diluted blood can restore fibrin generation to ∼78% of its normal level and hence improve clot formation under dilution.

Multi-Constituent Simulation of Thrombus Deposition

In this paper, we present a spatio-temporal mathematical model for simulating the formation and growth of a thrombus. Blood is treated as a multi-constituent mixture comprised of a linear fluid phase and a thrombus (solid) phase. The transport and reactions of 10 chemical and biological species are incorporated using a system of coupled convection-reaction-diffusion (CRD) equations to represent three processes in thrombus formation: initiation, propagation and stabilization. Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: in vivo thrombus growth in an injured blood vessel and in vitro thrombus deposition in micro-channels (1.5 mm × 1.6 mm × 0.1 mm) with small crevices (125 μm × 75 μm and 125 μm × 137 μm). For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally. Based on the success with these two benchmark problems, which have very different flow conditions and biological environments, we believe that the current model will provide useful insight into the genesis of thrombosis in blood-wetted devices, and provide a tool for the design of less thrombogenic devices.

Physicochemical properties and anticoagulant activity of polyphenols derived from Lachnum singerianum

In this study, polyphenols (LSP) were obtained from the fermentation broth of Lachnum singerianum. Two fractions were isolated by Sephadex LH-20 chromatographic column, and the primary fraction (LSP-1) was collected. The comprehensive physicochemical properties of phenolic acids and polyhydroxy phenolic compounds of LSP-1 were determined by UV-visible spectroscopy, Fourier transform infrared spectroscopy, and gas chromatography–mass spectrometry. Results of anticoagulant activity assay in vitro showed that LSP-1 could lengthen prothrombin time, activated partial thromboplastin time, and thrombin time of mouse plasma. In addition, anticoagulant activity results in vivo showed that high dose of LSP-1 could significantly prolong bleeding time, coagulation time, prothrombin time, activated partial thromboplastin time, and thrombin time of hypercoagulable mice induced by adrenaline, reduce the content of fibrinogen and enhance antithrombin III activity. All results indicated that the LSP-1 could serve well as an anticoagulant, and might be used as a potential natural drug candidate for thrombosis.

A computational model based on fibrin accumulation for the prediction of stasis thrombosis following flow-diverting treatment in cerebral aneurysms

Flow diverters, the specially designed low porosity stents, have been used to redirect blood flow from entering aneurysm, which induces flow stasis in aneurysm and promote thrombosis for repairing aneurysm. However, it is not clear how thrombus develops following flow-diversion treatment. Our objective was to develop a computation model for the prediction of stasis-induced thrombosis following flow-diversion treatment in cerebral aneurysms. We proposed a hypothesis to initiate coagulation following flow-diversion treatment. An experimental model was used by ligating rat's right common carotid artery (RCCA) to create flow-stasis environment. Thrombus formed in RCCA as a result of flow stasis. The fibrin distributions in different sections along the axial length of RCCA were measured. The fibrin distribution predicted by our computational model displayed a trend of increase from the proximal neck to the distal tip, consistent with the experimental results on rats. The model was applied on a saccular aneurysm treated with flow diverter to investigate thrombus development following flow diversion. Thrombus was predicted to form inside the sac, and the aneurysm was occluded with only a small remnant neck remained. Our model can serve as a tool to evaluate flow-diversion treatment outcome and optimize the design of flow diverters.

Study of blood flow in several benchmark micro-channels using a two-fluid approach

It is known that in a vessel whose characteristic dimension (e.g., its diameter) is in the range of 20 to 500 microns, blood behaves as a non-Newtonian fluid, exhibiting complex phenomena, such as shear-thinning, stress relaxation, and also multi-component behaviors, such as the Fahraeus effect, plasma-skimming, etc. For describing these non-Newtonian and multi-component characteristics of blood, using the framework of mixture theory, a two-fluid model is applied, where the plasma is treated as a Newtonian fluid and the red blood cells (RBCs) are treated as shear-thinning fluid. A computational fluid dynamic (CFD) simulation incorporating the constitutive model was implemented using OpenFOAM® in which benchmark problems including a sudden expansion and various driven slots and crevices were studied numerically. The numerical results exhibited good agreement with the experimental observations with respect to both the velocity field and the volume fraction distribution of RBCs.

Mathematical Modeling of Intravascular Blood Coagulation under Wall Shear Stress

Increased shear stress such as observed at local stenosis may cause drastic changes in the permeability of the vessel wall to procoagulants and thus initiate intravascular blood coagulation. In this paper we suggest a mathematical model to investigate how shear stress-induced permeability influences the thrombogenic potential of atherosclerotic plaques. Numerical analysis of the model reveals the existence of two hydrodynamic thresholds for activation of blood coagulation in the system and unveils typical scenarios of thrombus formation. The dependence of blood coagulation development on the intensity of blood flow, as well as on geometrical parameters of atherosclerotic plaque is described. Relevant parametric diagrams are drawn. The results suggest a previously unrecognized role of relatively small plaques (resulting in less than 50% of the lumen area reduction) in atherothrombosis and have important implications for the existing stenting guidelines.

A Computational Model of Biochemomechanical Effects of Intraluminal Thrombus on the Enlargement of Abdominal Aortic Aneurysms

Abdominal aortic aneurysms (AAAs) typically develop an intraluminal thrombus (ILT), yet most computational models of AAAs have focused on either the mechanics of the wall or the hemodynamics within the lesion, both in the absence of ILT. In the few cases wherein ILT has been modeled directly, as, for example, in static models that focus on the state of stress in the aortic wall and the associated rupture risk, thrombus has been modeled as an inert, homogeneous, load-bearing material. Given the biochemomechanical complexity of an ILT, there is a pressing need to consider its diverse effects on the evolving aneurysmal wall. Herein, we present the first growth and remodeling model that addresses together the biomechanics, mechanobiology, and biochemistry of thrombus-laden AAAs. Whereas it has been shown that aneurysmal enlargement in the absence of ILT depends primarily on the stiffness and turnover of fibrillar collagen, we show that the presence of a thrombus within lesions having otherwise the same initial wall composition and properties can lead to either arrest or rupture depending on the biochemical effects (e.g., release of proteases) and biomechanical properties (e.g., stiffness of fibrin) of the ILT. These computational results suggest that ILT should be accounted for when predicting the potential enlargement or rupture risk of AAAs and highlight specific needs for further experimental and computational research.

Modelling of platelet-fibrin clot formation in flow with a DPD-PDE method

The paper is devoted to mathematical modelling of clot growth in blood flow. Great complexity of the hemostatic system dictates the need of usage of the mathematical models to understand its functioning in the normal and especially in pathological situations. In this work we investigate the interaction of blood flow, platelet aggregation and plasma coagulation. We develop a hybrid DPD-PDE model where dissipative particle dynamics (DPD) is used to model plasma flow and platelets, while the regulatory network of plasma coagulation is described by a system of partial differential equations. Modelling results confirm the potency of the scenario of clot growth where at the first stage of clot formation platelets form an aggregate due to weak inter-platelet connections and then due to their activation. This enables the formation of the fibrin net in the centre of the platelet aggregate where the flow velocity is significantly reduced. The fibrin net reinforces the clot and allows its further growth. When the clot becomes sufficiently large, it stops growing due to the narrowed vessel and the increase of flow shear rate at the surface of the clot. Its outer part is detached by the flow revealing the inner part covered by fibrin. This fibrin cap does not allow new platelets to attach at the high shear rate, and the clot stops growing. Dependence of the final clot size on wall shear rate and on other parameters is studied.

A continuum model for platelet plug formation, growth and deformation

A numerical framework for modelling platelet plug dynamics is presented in this work. It consists of an extension of a biochemical and plug growth model with a solid mechanics model for the plug coupled with a fluid-structure interaction model for the blood flow-plug system. The platelet plug is treated as a neo-Hookean elastic solid, of which the implementation is based on an updated Lagrangian approach. The framework is applied to different haemodynamic configurations coupled with different shear moduli of the plug. Results about plug growth, shape and size, as well as the stress distribution, are shown. Based on the simulations performed, we conclude that the deformability of the platelet plug is essential for its growth.

Kinetic model facilitates analysis of fibrin generation and its modulation by clotting factors: implications for hemostasis-enhancing therapies

Current mechanistic knowledge of protein interactions driving blood coagulation has come largely from experiments with simple synthetic systems, which only partially represent the molecular composition of human blood plasma. Here, we investigate the ability of the suggested molecular mechanisms to account for fibrin generation and degradation kinetics in diverse, physiologically relevant in vitro systems. We represented the protein interaction network responsible for thrombin generation, fibrin formation, and fibrinolysis as a computational kinetic model and benchmarked it against published and newly generated data reflecting diverse experimental conditions. We then applied the model to investigate the ability of fibrinogen and a recently proposed prothrombin complex concentrate composition, PCC-AT (a combination of the clotting factors II, IX, X, and antithrombin), to restore normal thrombin and fibrin generation in diluted plasma. The kinetic model captured essential features of empirically detected effects of prothrombin, fibrinogen, and thrombin-activatable fibrinolysis inhibitor titrations on fibrin formation and degradation kinetics. Moreover, the model qualitatively predicted the impact of tissue factor and tPA/tenecteplase level variations on the fibrin output. In the majority of considered cases, PCC-AT combined with fibrinogen accurately approximated both normal thrombin and fibrin generation in diluted plasma, which could not be accomplished by fibrinogen or PCC-AT acting alone. We conclude that a common network of protein interactions can account for key kinetic features characterizing fibrin accumulation and degradation in human blood plasma under diverse experimental conditions. Combined PCC-AT/fibrinogen supplementation is a promising strategy to reverse the deleterious effects of dilution-induced coagulopathy associated with traumatic bleeding.

Early reperfusion rates with IV tPA are determined by CTA clot characteristics

BACKGROUND AND PURPOSE

An ability to predict early reperfusion with IV tPA in patients with acute ischemic stroke and intracranial clots can help clinicians decide if additional intra-arterial therapy is needed or not. We explored the association between novel clot characteristics on baseline CTA and early reperfusion with IV tPA in patients with acute ischemic stroke by using classification and regression tree analysis.

MATERIALS AND METHODS

Data are from patients with acute ischemic stroke and proximal anterior circulation occlusions from the Calgary CTA data base (2003-2012) and the Keimyung Stroke Registry (2005-2009). Patients receiving IV tPA followed by intra-arterial therapy were included. Clot location, length, residual flow within the clot, ratio of contrast Hounsfield units pre- and postclot, and the M1 segment origin to the proximal clot interface distance were assessed on baseline CTA. Early reperfusion (TICI 2a and above) with IV tPA was assessed on the first angiogram.

RESULTS

Two hundred twenty-eight patients (50.4% men; median age, 69 years; median baseline NIHSS score, 17) fulfilled the inclusion criteria. Median symptom onset to IV tPA time was 120 minutes (interquartile range = 70 minutes); median IV tPA to first angiography time was 70.5 minutes (interquartile range = 62 minutes). Patients with residual flow within the clot were 5 times more likely to reperfuse than those without it. Patients with residual flow and a shorter clot length (≤15 mm) were most likely to reperfuse (70.6%). Patients with clots in the M1 MCA without residual flow reperfused more if clots were distal and had a clot interface ratio in Hounsfield units of <2 (36.8%). Patients with proximal M1 clots without residual flow reperfused 8% of the time. Carotid-T/-L occlusions rarely reperfused (1.7%). Interrater reliability for these clot characteristics was good.

CONCLUSIONS

Our study shows that clot characteristics on CTA help physicians estimate a range of early reperfusion rates with IV tPA.

Recent advances in computational methodology for simulation of mechanical circulatory assist devices

Ventricular assist devices (VADs) provide mechanical circulatory support to offload the work of one or both ventricles during heart failure. They are used in the clinical setting as destination therapy, as bridge to transplant, or more recently as bridge to recovery to allow for myocardial remodeling. Recent developments in computational simulation allow for detailed assessment of VAD hemodynamics for device design and optimization for both children and adults. Here, we provide a focused review of the recent literature on finite element methods and optimization for VAD simulations. As VAD designs typically fall into two categories, pulsatile and continuous flow devices, we separately address computational challenges of both types of designs, and the interaction with the circulatory system with three representative case studies. In particular, we focus on recent advancements in finite element methodology that have increased the fidelity of VAD simulations. We outline key challenges, which extend to the incorporation of biological response such as thrombosis and hemolysis, as well as shape optimization methods and challenges in computational methodology.

A numerical study of blood flow using mixture theory

In this paper, we consider the two dimensional flow of blood in a rectangular microfluidic channel. We use Mixture Theory to treat this problem as a two-component system: One component is the red blood cells (RBCs) modeled as a generalized Reiner-Rivlin type fluid, which considers the effects of volume fraction (hematocrit) and influence of shear rate upon viscosity. The other component, plasma, is assumed to behave as a linear viscous fluid. A CFD solver based on OpenFOAM® was developed and employed to simulate a specific problem, namely blood flow in a two dimensional micro-channel, is studied. Finally to better understand this two-component flow system and the effects of the different parameters, the equations are made dimensionless and a parametric study is performed.

A simplified mathematical model for thrombin generation

A new phenomenological mathematical model based directly on laboratory data for thrombin generation and having a patient-specific character is described. A set of the solved equations for cell-based models of blood coagulation that can reproduce the temporal evolution of thrombin generation is proposed; such equations are appropriate for use in computational fluid dynamic (CFD) simulations. The initial values for the reaction rates are either taken from already existing model or experimental data, or they can obtained from simple reasoning under certain assumptions; it is shown that coefficients can be adjusted in order to fit a range of different thrombin generation curves as derived from thrombin generation assays. The behaviour of the model for different platelet concentration seems to be in good agreement with reported experimental data. It is shown that the reduced set of equations used represents to a good approximation a low-order model of the detailed mechanism and thus it can represent a cost-effective and-case specific mathematical model of coagulation reactions up to thrombin generation.

Biochemomechanics of intraluminal thrombus in abdominal aortic aneurysms

Most computational models of abdominal aortic aneurysms address either the hemodynamics within the lesion or the mechanics of the wall. More recently, however, some models have appropriately begun to account for the evolving mechanics of the wall in response to the changing hemodynamic loads. Collectively, this large body of work has provided tremendous insight into this life-threatening condition and has provided important guidance for current research. Nevertheless, there has yet to be a comprehensive model that addresses the mechanobiology, biochemistry, and biomechanics of thrombus-laden abdominal aortic aneurysms. That is, there is a pressing need to include effects of the hemodynamics on both the development of the nearly ubiquitous intraluminal thrombus and the evolving mechanics of the wall, which depends in part on biochemical effects of the adjacent thrombus. Indeed, there is increasing evidence that intraluminal thrombus in abdominal aortic aneurysms is biologically active and should not be treated as homogeneous inert material. In this review paper, we bring together diverse findings from the literature to encourage next generation models that account for the biochemomechanics of growth and remodeling in patient-specific, thrombus-laden abdominal aortic aneurysms.

Simulation of platelets suspension flowing through a stenosis model using a dissipative particle dynamics approach

Stresses on blood cellular constituents induced by blood flow can be represented by a continuum approach down to the μm level; however, the molecular mechanisms of thrombosis and platelet activation and aggregation are on the order of nm. The coupling of the disparate length and time scales between molecular and macroscopic transport phenomena represents a major computational challenge. In order to bridge the gap between macroscopic flow scales and the cellular scales with the goal of depicting and predicting flow induced thrombogenicity, multi-scale approaches based on particle methods are better suited. We present a top-scale model to describe bulk flow of platelet suspensions: we employ dissipative particle dynamics to model viscous flow dynamics and present a novel and general no-slip boundary condition that allows the description of three-dimensional viscous flows through complex geometries. Dissipative phenomena associated with boundary layers and recirculation zones are observed and favorably compared to benchmark viscous flow solutions (Poiseuille and Couette flows). Platelets in suspension, modeled as coarse-grained finite-sized ensembles of bound particles constituting an enclosed deformable membrane with flat ellipsoid shape, show self-orbiting motions in shear flows consistent with Jeffery's orbits, and are transported with the flow, flipping and colliding with the walls and interacting with other platelets.