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

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.

Efficient numerical methods for nonlinear-facilitated transport and exchange in a blood-tissue exchange unit

The analysis of experimental data obtained by the multiple-indicator method requires complex mathematical models for which capillary blood-tissue exchange (BTEX) units are the building blocks. This study presents a new, nonlinear, two-region, axially distributed, single capillary, BTEX model. A facilitated transporter model is used to describe mass transfer between plasma and intracellular spaces. To provide fast and accurate solutions, numerical techniques suited to nonlinear convection-dominated problems are implemented. These techniques are the random choice method, an explicit Euler-Lagrange scheme, and the MacCormack method with and without flux correction. The accuracy of the numerical techniques is demonstrated, and their efficiencies are compared. The random choice, Euler-Lagrange and plain MacCormack method are the best numerical techniques for BTEX modeling. However, the random choice and Euler-Lagrange methods are preferred over the MacCormack method because they allow for the derivation of a heuristic criterion that makes the numerical methods stable without degrading their efficiency. Numerical solutions are also used to illustrate some nonlinear behaviors of the model and to show how the new BTEX model can be used to estimate parameters from experimental data.