Multiscale models of thrombogenesis (original) (raw)
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A multiscale model of thrombus development
Journal of The Royal Society Interface, 2008
A two-dimensional multiscale model is introduced for studying formation of a thrombus (clot) in a blood vessel. It involves components for modelling viscous, incompressible blood plasma; non-activated and activated platelets; blood cells; activating chemicals; fibrinogen; and vessel walls and their interactions. The macroscale dynamics of the blood flow is described by the continuum Navier–Stokes equations. The microscale interactions between the activated platelets, the platelets and fibrinogen and the platelets and vessel wall are described through an extended stochastic discrete cellular Potts model. The model is tested for robustness with respect to fluctuations of basic parameters. Simulation results demonstrate the development of an inhomogeneous internal structure of the thrombus, which is confirmed by the preliminary experimental data. We also make predictions about different stages in thrombus development, which can be tested experimentally and suggest specific experiments....
Biophysical Journal, 2010
A combination of the extended multiscale model, new image processing algorithms, and biological experiments is used for studying the role of Factor VII (FVII) in venous thrombus formation. A detailed submodel of the tissue factor pathway of blood coagulation is introduced within the framework of the multiscale model to provide a detailed description of coagulation cascade. Surface reactions of the extrinsic coagulation pathway on membranes of platelets are studied under different flow conditions. It is shown that low levels of FVII in blood result in a significant delay in thrombin production, demonstrating that FVII plays an active role in promoting thrombus development at an early stage.
Computational Approaches to Studying Thrombus Development
Arteriosclerosis, Thrombosis, and Vascular Biology, 2011
In addition to the descriptive biological models, many computational models have been developed for hemostasis/thrombosis that provide quantitative characterization of thrombus development. Simulations using computational models which have been developed for coagulation reactions, platelet activation and fibrinogen assembly were shown to be in close agreement with experimental data. Models of processes involved in hemostasis/thrombosis are being integrated to simulate the development of the thrombus simultaneously in time and space.
Recent advances in computational modeling of fibrin clot formation: A review
Computational Biology and Chemistry
The study of thrombosis is crucial to understand and develop new therapies for diseases like deep vein thrombosis, diabetes related strokes, pulmonary embolism etc. The last two decades have seen an exponential growth in studies related to the blood clot formation using computational tools and through experiments. Despite of this growth, the complete mechanism behind thrombus formation and hemostasis is not known yet. 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 the blood clots. In this review, we will attempt to list out all major strategies attempted by researchers so far to model the blood clot formation using existing computational techniques. This review classifies them into continuum level, system level, discrete particles and multi-scale methods. We will also discuss the strength and weakness of various methods and possible future directions in which the computational blood clot research can thrive.
Modeling thrombosis in silico: Frontiers, challenges, unresolved problems and milestones
Physics of Life Reviews, 2018
Hemostasis is a complex physiological mechanism that functions to maintain vascular integrity under any conditions. Its primary components are blood platelets and a coagulation network that interact to form the hemostatic plug, a combination of cell aggregate and gelatinous fibrin clot that stops bleeding upon vascular injury. Disorders of hemostasis result in bleeding or thrombosis, and are the major immediate cause of mortality and morbidity in the world. Regulation of hemostasis and thrombosis is immensely complex, as it depends on blood cell adhesion and mechanics, hydrodynamics and mass transport of various species, huge signal transduction networks in platelets, as well as spatiotemporal regulation of the blood coagulation network. Mathematical and computational modelling has been increasingly used to gain insight into this complexity over the last 30 years, but the limitations of the existing models remain profound. Here we review state-of-the-art-methods for computational
Study of blood flow impact on growth of thrombi using a multiscale model
Soft Matter, 2009
An extended multiscale model is introduced for studying the formation of platelet thrombi in blood vessels. The model describes the interplay between viscous, incompressible blood plasma, activated and non-activated platelets, as well as other blood cells, activating chemicals, fibrinogen and vessel walls. The macroscale dynamics of the blood flow is represented by the continuous submodel in the form of the Navier-Stokes equations. The microscale cell-cell interactions are described by the stochastic Cellular Potts Model (CPM). Simulations indicate that increase in flow rates leads to greater structural heterogeneity of the clot. As heterogeneous structural domains within the clot affect thrombus stability, understanding the factors influencing thrombus structure is of significant biomedical importance.
A Mechano-Chemical Computational Model of Deep Vein Thrombosis
Frontiers in Physics
Computational models of deep vein thrombosis (DVT) typically account for either the mechanical or biochemical factors involved in thrombus formation. Developing a model that accounts for both factors will improve our understanding of the coagulation process in this particular disease. The work presented in this study details the development of a CFD model that considers the biochemical reactions between thrombin and fibrinogen, pulsatile blood flow, and clot growth within a three-dimensional patient-specific common femoral vein. Thrombin is released into the bloodstream from an injury zone on the wall of the vein. The Michaelis–Menten equation is used to represent the conversion of thrombin and fibrinogen to fibrin, the final product of the coagulation process. The model development starts with a two-dimensional idealized geometry. At this stage, the model is used to conduct a parametric study to determine the effects of varying parameters such as inlet velocity, vein diameter, and ...
Modelling fibrinolysis: a 3D stochastic multiscale model
Mathematical Medicine and Biology, 2012
Fibrinolysis, the proteolytic degradation of the fibrin fibres that stabilize blood clots, is initiated when tissue-type plasminogen activator (tPA) activates plasminogen to plasmin, the main fibrinolytic enzyme. Many experiments have shown that coarse clots made of thick fibres lyse more quickly than fine clots made of thin fibres, despite the fact that individual thick fibres lyse more slowly than individual thin fibres. The generally accepted explanation for this is that a coarse clot with fewer fibres to transect will be degraded faster than a fine clot with a higher fibre density. Other experiments show the opposite result. The standard mathematical tool for investigating fibrinolysis has been deterministic reaction-diffusion models, but due to low tPA concentrations, stochastic models may be more appropriate. We develop a 3D stochastic multiscale model of fibrinolysis. A microscale model representing a fibre cross section and containing detailed biochemical reactions provides information about single fibre lysis times, the number of plasmin molecules that can be activated by a single tPA molecule and the length of time tPA stays bound to a given fibre cross section. Data from the microscale model are used in a macroscale model of the full fibrin clot, from which we obtain lysis front velocities and tPA distributions. We find that the fibre number impacts lysis speed, but so does the number of tPA molecules relative to the surface area of the clot exposed to those molecules. Depending on the values of these two quantities (tPA number and surface area), for given kinetic parameters, the model predicts coarse clots lyse faster or slower than fine clots, thus providing a possible explanation for the divergent experimental observations.
Grow with the flow: a spatial-temporal model of platelet deposition and blood coagulation under flow
Mathematical Medicine and Biology, 2010
The body's response to vascular injury involves two intertwined processes: platelet aggregation and coagulation. Platelet aggregation is a predominantly physical process, whereby platelets clump together, and coagulation is a cascade of biochemical enzyme reactions. Thrombin, the major product of coagulation, directly couples the biochemical system to platelet aggregation by activating platelets and by cleaving fibrinogen into fibrin monomers that polymerize to form a mesh that stabilizes platelet aggregates. Together, the fibrin mesh and the platelet aggregates comprise a thrombus that can grow to occlusive diameters. Transport of coagulation proteins and platelets to and from an injury is controlled largely by the dynamics of the blood flow. To explore how blood flow affects the growth of thrombi and how the growing masses, in turn, feed back and affect the flow, we have developed the first spatial-temporal mathematical model of platelet aggregation and blood coagulation under flow that includes detailed descriptions of coagulation biochemistry, chemical activation and deposition of blood platelets, as well as the two-way interaction between the fluid dynamics and the growing platelet mass. We present this model and use it to explain what underlies the threshold behaviour of the coagulation system's production of thrombin and to show how wall shear rate and near-wall enhanced platelet concentrations affect the development of growing thrombi. By accounting for the porous nature of the thrombus, we also demonstrate how advective and diffusive transport to and within the thrombus affects its growth at different stages and spatial locations.
Modelling fibrinolysis: 1D continuum models
Mathematical Medicine and Biology, 2012
Fibrinolysis is the enzymatic degradation of the fibrin mesh that stabilizes blood clots. Experiments have shown that coarse clots made of thick fibres sometimes lyse more quickly than fine clots made of thin fibres, despite the fact that individual thick fibres lyse more slowly than individual thin fibres. This paper aims at using a 1D continuum reaction-diffusion model of fibrinolysis to elucidate the mechanism by which coarse clots lyse more quickly than fine clots. Reaction-diffusion models have been the standard tool for investigating fibrinolysis, and have been successful in capturing the wave-like behaviour of lysis seen in experiments. These previous models treat the distribution of fibrin within a clot as homogeneous, and therefore cannot be used directly to study the lysis of fine and coarse clots. In our model, we include a spatially heterogeneous fibrin concentration, as well as a more accurate description of the role of fibrin as a cofactor in the activation of the lytic enzyme. Our model predicts spatio-temporal protein distributions in reasonable quantitative agreement with experimental data. The model also predicts observed behaviour such as a front of lysis moving through the clot with an accumulation of lytic proteins at the front. In spite of the model improvements, however, we find that 1D continuum models are unable to accurately describe the observed differences in lysis behaviour between fine and coarse clots. Features of the problems that lead to the inaccuracy of 1D continuum models are discussed. We conclude that higher-dimensional, multiscale models are required to investigate the effect of clot structure on lysis behaviour.