A mathematical model for platelet thrombus growth with shear-induced diffusion of platelets (in Russian) (original) (raw)

Modelling of thrombus growth and growth stop in flow by the method of dissipative particle dynamics

Russian Journal of Numerical Analysis and Mathematical Modelling, 2012

Platelet aggregation at the site of vascular injury leads to formation of a hemostatic plug covering the injury site, or a thrombus in the pathological case. The mechanisms that control clot growth and which lead to growth arrest are not yet completely understood. In order to study these mechanisms theoretically, we use the Dissipative Particle Dynamics method which allows us to model individual platelets in the flow and in the clot. The model takes into account different stages of platelet adhesion process. First, a platelet is captured reversibly by the aggregate, and then it activates and adheres firmly becoming a part of its core. We suggest that the core of the clot is composed of platelets unable to attach new platelets from the flow due to activation by thrombin and/or wrapping by the fibrin mesh. The simulations are in a good agreement with the experimental results . Modelling shows that stopping of growth of a hemostatic plug (and thrombus) can result from removing its exterior part by flow and exposing its non-adhesive core to the flow.

Fluid shear as a possible mechanism for platelet diffusivity in flowing blood

Journal of Biomechanics, 1986

Platelet transport theory is based on convection diffusion and describes adequately the influence of wail shear rate, platelet concentration and axial (down stream) position. Until now, the influence of the predominant factors affecting platelet adherence, the hematocrit and the red cell size, was not included in this theory. Their role remained hidden in the platelet diffusivity (Dv), which was assumed to be related to the shear rate (7) expressed in s-' by a power law function D, = m;", in which m and n were thought to be constants.

An estimated shape function for drift in a platelet-transport model

Biophysical Journal, 1994

Pnor work has shown that concentraton profiles of platelets in flowing whole blood and of platelet-sized beads in fowing blood suspensxios can include near-wall excesses. A moder to describe this phernoenon was built about a singlecomponent convective diffusion equation. To irporate redistribui to peferred sites by shear flows of red cell suspensions, the model used a drift shape furton (in addition to the commonly used augmented difusion coefficnt). This paper reports experiments that provide an average concentration profile from which the shape function for that model is calculated; the experiments and shape funcion are for the parublar codtons of 40% hematocrit, platelet-sized latex beads (2.5 pm diameter), tube ID of 217 pm, and a wall shear rate of 555 s-1. Less precise estimates of the shape function obtained from data of previous studies indicate that the shape furtion is similar for the hematocrit of 15%.

The Influence of Hindered Transport on the Development of Platelet Thrombi Under Flow

Bulletin of Mathematical Biology, 2013

Vascular injury triggers two intertwined processes, platelet deposition and coagulation, and can lead to the formation of an intravascular clot (thrombus) that may grow to occlude the vessel. Formation of the thrombus involves complex biochemical, biophysical, and biomechanical interactions that are also dynamic and spatially-distributed, and occur on multiple spatial and temporal scales. We previously developed a spatial-temporal mathematical model of these interactions and looked at the interplay between physical factors (flow, transport to the clot, platelet distribution within the blood) and biochemical ones in determining the growth of the clot. Here, we extend this model to include reduction of the advection and diffusion of the coagulation proteins in regions of the clot with high platelet number density. The effect of this reduction, in conjunction with limitations on fluid and platelet transport through dense regions of the clot can be profound. We found that hindered transport leads to the formation of smaller and denser clots compared to the case with no protein hindrance. The limitation on protein transport confines the important activating complexes to small regions in the interior of the thrombus and greatly reduces the supply of substrates to these complexes. Ultimately, this decreases the rate and amount of thrombin production and leads to greatly slowed growth and smaller thrombus size. Our results suggest a possible physical mechanism for limiting thrombus growth.

A multiscale model for multiple platelet aggregation in shear flow

Biomechanics and Modeling in Mechanobiology, 2021

We developed a multiscale model for simulating aggregation of multiple, free-flowing platelets in low-intermediate shear viscous flow, in which aggregation is mediated by the interaction of α IIb β 3 receptors on the platelets membrane and fibrinogen (Fg). This multiscale model uses coarse grained molecular dynamics (CGMD) for platelets at the microscales, and dissipative particle dynamics (DPD) for the shear flow at the macroscales, employing our hybrid aggregation force field for modeling molecular level receptor ligand bonds. We define an aggregation tensor and use it to quantify the molecular level contact characteristics between platelets in an aggregate. We perform numerical studies under different flow conditions for platelet doublets and triplets and evaluate the contact area, detaching force, and minimum distance between different pairs of platelets in an aggregate. We also present the dynamics of applied stress and velocity magnitude distributions on the platelet membrane during aggregation and quantify the increase in stress in the contact region under different flow conditions. Integrating the knowledge from our previously validated models, together with new aggregation scenarios, our model can dynamically quantify aggregation characteristics and map stress and velocity distribution on the platelet membrane which are difficult to measure in vitro, thus providing an insight into mechanotransduction bond formation response of platelets to flow induced shear stresses. This modeling framework, together with the tensor method for quantifying inter-platelet contact, can be extended to simulate and analyze larger aggregates and their adhesive properties.

Computational Simulation of Platelet Deposition and Activation: I. Model Development and Properties

Annals of Biomedical Engineering, 1999

To better understand the mechanisms leading to the formation and growth of mural thrombi on biomaterials, we have developed a two-dimensional computational model of platelet deposition and activation in flowing blood. The basic formulation is derived from prior work by others, with additional levels of complexity added where appropriate. It is comprised of a series of convection-diffusion-reaction equations which simulate platelet-surface and platelet-platelet adhesion, platelet activation by a weighted linear combination of agonist concentrations, agonist release and synthesis by activated platelets, platelet-phospholipid-dependent thrombin generation, and thrombin inhibition by heparin. The model requires estimation of four parameters to fit it to experimental data: shear-dependent platelet diffusivity and resting and activated platelet-surface and platelet-platelet reaction rate constants. The model is formulated to simulate a wide range of biomaterials and complex flows. In this article we present the basic model and its properties; in Part II (Sorensen et al., Ann. Biomed. Eng. 27:449–458, 1999) we apply the model to experimental results for platelet deposition onto collagen. © 1999 Biomedical Engineering Society. PAC99: 8719Uv, 8380Lz, 8717Aa, 8710+e, 8768+z

A computational model of chemically and mechanically induced platelet plug formation

ObjectivesThrombotic deposition is a major consideration in the development of implantable cardiovascular devices. Recently, it has been experimentally demonstrated that localized changes in the blood shear rate -i.e. shear gradients-play a critical role in thrombogenesis. The goal of the present work is to develop a predictive computational model of platelet plug formation that can be used to assess the thrombotic burden of cardiovascular devices, introducing for the first time the role of shear gradients. We have developed a comprehensive model of platelet-mediated thrombogenesis which includes platelet transport in the blood flow, platelet activation and aggregation induced by both biochemical and mechanical factors, kinetics and mechanics of platelet adhesion, and changes in the local fluid dynamics due to the thrombus growth.MethodsA 2D computational model was developed using the multi-physics finite element solver COMSOL 5.6. The model can be described by a coupled set of conv...

Modelling platelet-blood flow interaction using the subcellular element Langevin method

Journal of The Royal Society Interface, 2011

In this paper, a new three-dimensional modelling approach is described for studying fluid–viscoelastic cell interaction, the subcellular element Langevin (SCEL) method, with cells modelled by subcellular elements (SCEs) and SCE cells coupled with fluid flow and substrate models by using the Langevin equation. It is demonstrated that: (i) the new method is computationally efficient, scaling as 𝒪( N ) for N SCEs; (ii) cell geometry, stiffness and adhesivity can be modelled by directly relating parameters to experimentally measured values; (iii) modelling the fluid–platelet interface as a surface leads to a very good correlation with experimentally observed platelet flow interactions. Using this method, the three-dimensional motion of a viscoelastic platelet in a shear blood flow was simulated and compared with experiments on tracking platelets in a blood chamber. It is shown that the complex platelet-flipping dynamics under linear shear flows can be accurately recovered with the SCEL ...

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.

Numerical simulation of blood flows with non-uniform distribution of erythrocytes and platelets

Russian Journal of Numerical Analysis and Mathematical Modelling, 2000

Blood cell interactions present an important mechanism in many processes occurring in blood. Due to different blood cell properties, cells of different types behave differently in the flow. One of observed behaviours is segregation of erythrocytes, which group near the flow axis, and platelets, which migrate towards the blood vessel wall. In this work, a three dimensional model based on Dissipative Particle Dynamics method is used to study the interaction of erythrocytes and platelets in a flow inside a cylindrical channel. The erythrocytes are modelled as elastic highly deformable membranes, while platelets are modelled as elastic spherical membranes which tend to preserve their spherical shape. As the result of modelling, the separation of erythrocytes and platelets in a cylindrical vessel flow is shown for vessels of different diameters. Erythrocyte and platelet distribution profiles in vessel cross-section are in good agreement with existing experimental results. The described 3-D model can be used for further modelling of blood flow-related problems.