Mathematical Model of Platelet Deposition under Flow Conditions

Abstract

Platelet deposition in resting blood is well researched and understood. However, the influence of hemodynamic parameters such as wall shear rate is less clear. Clinical experience and experiments show an interaction between flow and platelet deposition. But a complete understanding of the flow influence and hence a quantification has not yet been achieved. A well defined experiment of flow dependant platelet depositions is the stagnation point flow. This kind of flow is ubiquitous in the circulatory system, to be found in every bifurcation and recirculation region. These are the areas where thrombus formations are likely to occur if other conditions are also met. First, experiments were performed in a stagnation point flow chamber. A simplified blood model, platelet rich plasma, was used as a test fluid. With a microscope the platelet deposition was observed and recorded. Platelets deposit in a characteristic pattern showing the influence of the flow. An analysis of this pattern is the objective of this study and is achieved with the help of a numerical model, which is based on a convective diffusive transport. The model results in a platelet deposition pattern, which in its shape and temporal development is very similar to experimental results. Hence it is concluded that the assumed transport processes are causal for platelet depositions and thrombus formation.

Mathematical Models of Blood Coagulation and Platelet Adhesion: Clinical Applications

“…Adhesion of platelets to the vessel wall was assumed to increase the probability of adhesion/activation for other platelets thus imitating the effect of platelet activators release. These models showed good agreement with experimental data [44][45][46] and provided an insight into the role of platelet margination by red blood cells. David et al [44] found that the rate of platelet interaction with the vessel wall should depend on the shear rate.…”

“…In particular, a formula was suggested to estimate thrombotic risk by determining the time to vessel occlusion T occlusion : A number of studies used a stagnation point assumption to simulate platelet adhesion both analytically and computationally [44][45][46]. This type of flow is often present in the circulation, in particular, in the recirculation regions.…”

“…In contrast, the model [46], based on the Monte-Carlo simulation method, neglected platelet diffusion and considered the platelet adhesion process in the boundary layer as probabilistic. Adhesion of platelets to the vessel wall was assumed to increase the probability of adhesion/activation for other platelets thus imitating the effect of platelet activators release.…”

“…David et al [44] found that the rate of platelet interaction with the vessel wall should depend on the shear rate. The model of Affeld et al [46] can be used in the design of artificial organs to predict the regions of thrombus formation.…”

“…In addition to platelet deposition, the model considered the roles of thrombin, prothrombin and AT-III, and was able to predict effects of anticoagulants (heparin and PPACK) on the kinetics of platelet thrombus growth on the collagen surface. More detailed models of platelet adhesion, which consider the stagnation point flow, the feedback effect of thrombus on the flow, thrombus shape change under the flow, etc., have been proposed since then [44][45][46][47]75] as discussed in the section "Analysis of disease basis", but they were not applied for studies of biomaterials.…”