A density‐dependent FEM‐FCT algorithm with application to modeling platelet aggregation

Abstract

Upon injury to a blood vessel, flowing platelets will aggregate at the injury site, forming a plug to prevent blood loss. Through a complex system of biochemical reactions, a stabilizing mesh forms around the platelet aggregate forming a blood clot that further seals the injury. Computational models of clot formation have been developed to a study intravascular thrombosis, where a vessel injury does not cause blood leakage outside the blood vessel but blocks blood flow. To model scenarios in which blood leaks from a main vessel out into the extravascular space, new computational tools need to be developed to handle the complex geometries that represent the injury. We have previously modeled intravascular clot formation under flow using a continuum approach wherein the transport of platelet densities into some spatial location is limited by the platelet fraction that already reside in that location, i.e., the densities satisfy a maximum packing constraint through the use of a hindered transport coefficient. To extend this notion to extravascular injury geometries, we have modified a finite element method flux‐corrected transport (FEM‐FCT) scheme by prelimiting antidiffusive nodal fluxes. We show that our modified scheme, under a variety of test problems, including mesh refinement, structured vs unstructured meshes, and for a range of reaction rates, produces numerical results that satisfy a maximum platelet‐density packing constraint.

A Mathematical Model of Platelet Aggregation in an Extravascular Injury Under Flow

“…The geometric configuration for the 2D model is the 'H' domain as depicted in Figure 1A and as described in detail in our previous work [7]. Briefly, there are two vertical channels through which blood and wash (buffer) flow.…”

“…The term −µα(θ B ) u represents a frictional resistance to the fluid motion due to the presence of the platelet aggregate with volume fraction of bound platelets, θ B . Equations (A.9)-(A.10) are solved numerically using the rotational projection method, as described previously [7,45]. We assume a functional form of the friction term, α(θ B ), that follows the Carman-Kozeny relation and the particular value of C K is specified in Appendix C.2.…”

“…+ k coh η(x) P max P m,a , (A. 13) where θ T = P m,u +P m,a +P b,a Pmax θ max , and D p , k adh (x), k coh , and W (θ T ) are the platelet diffusion coefficient, spatially-dependent adhesion rate, cohesion rate coefficient, and hindered platelet flux coefficient, all used as previously described [7,24]. The parameter, η(x) is a local approximation to the bound platelet fraction that indicates both the location and density of bound platelets to mobile platelets as part of the cohesion rate; the cohesion rate is enhanced where the local bound platelet fraction is increased.…”

“…To our knowledge, the model we present here is the first mathematical model to incorporate key biophysical and biochemical mechanisms of primary hemostasis in the framework of an extravascular injury. Our model is based on ODEs and is calibrated and validated using analogous experimental (Appendix A.2) and PDE (Appendix A.4) models [7,40].…”

Study of Reversible Platelet Aggregation Model by Nonlinear Dynamics

“…The mechanistic models take into account the mechanical forces of platelet interactions and the Navier-Stokes equation for the interaction between platelets and blood plasma. Typically, these models are two-dimensional [6][7][8][9], and even then they have a large set of required parameters (31 [6], >10 [7], >50 [9]). The first three-dimensional model of platelet aggregation published in 2019 also had a large number of parameters (>28) [10].…”