Biomedical Engineering Reference
In-Depth Information
Fluid-platelets interaction models
A model that accounts for the influence of fluid motion and hemodynamic forces on
the aggregation process, activation of platelets by chemicals, platelet-platelet and
platelet-wall interactions, as well as the feedback role of aggregate growth on the
fluid dynamics, has been considered in [23] (see also [24]). This model was devel-
oped to describe the formation of platelet thrombi in coronary-artery-sized blood
vessels and is a follow up of earlier models of platelet aggregation (with no in-
fluence of the fluid dynamics), [21, 22], along with computational results, [64]. It
gives an important contribution to better understand the interactions between local
geometry, fluid dynamics, and aggregate growth. This continuum model involves
two spatial scales, the microscale of the platelets and the macroscale of the vessel,
using as a major tool the Immersed Boundary method (IB) introduced by Peskin
(see [95]. More precisely, the microscopic scale tracks individual platelets, their de-
tection and response to chemical activators, and mechanical interactions among the
platelets, fluid and the vascular wall. The macroscopic scale tracks the dynamics
of the same interactions on a larger scale; it follows the evolution of density func-
tions that describe the distribution of nonactivated and activated platelets and of their
links.
The model involves a large number of coupled nonlinear partial differential equa-
tions where the dynamics of the fluid is described by the Navier-Stokes equations; it
involves a mix of Eulerian and Lagrangian communicating descriptions; steep spa-
tial gradients appear due to the combination of rapid localized reactions and small
diffusion coefficients; transport of platelets and chemicals needs to be confined to
the portions of the domain inside of the immersed boundaries used to represent the
vessel walls; the fluid - wall and fluid - platelet interactions can be stiff and present
difficulties in achieving stable calculations. Appropriate numerical methods have
been used to meet these challenges and numerical simulations have shown that it is
possible to capture important behaviours in the platelet aggregation process during
blood clotting, including vessel occlusion by thrombi growth.
This model does not include Thrombin which is an important platelet activator
produced on the surface of activated platelets. Three-dimensional simulations at both
micro- and macroscales are computationally very expensive.
Models incorporating the mechanical activation of platelets
Anand et al [2] developed a phenomenological mathematical model of the hemo-
static system that takes into account biochemical, physiologic and rheological fac-
tors playing an important role in the formation, growth and lysis of blood clots (see
also [3]). It models blood as a non-Newtonian fluid, namely as a shear-thinning vis-
coelastic fluid with a shear dependent relaxation time, and the clot as such a fluid with
much higher viscosity. The extrinsic pathway of enzymatic cascade of reactions that
leads to clot formation and growth was modelled by a set of 23 coupled convection-
reaction-diffusion partial differential equations, and the system was closed by appro-
priate initial and flux boundary conditions, reflecting the injury to the vessel wall. A
method for tracking the boundary between the growing clot and normal blood was
