Current work on blood clot
modeling.
Abstract for paper in
progress:
The body's response to vascular injury involves two intertwined
processes: platelet aggregation and coagulation. Platelet aggregation
is a predominantly physical process whereby platelets clump together
and coagulation is a cascade of biochemical enzyme
reactions. Thrombin, the major product of coagulation, directly
couples the biochemical system to platelet aggregation by activating
platelets and by cleaving fibrinogen into fibrin monomers which
polymerize to form a mesh that stabilizes platelet
aggregates. Together, the fibrin mesh and the platelet aggregates
comprise a thrombus which can grow to occlusive diameters. Transport
of coagulation proteins and platelets to and from an injury is
controlled largely by the dynamics of the blood flow. To explore how
blood flow affects the growth of thrombi, and how the growing masses,
in turn, feed back and affect the flow, we have developed the first
spatial-temporal mathematical model of platelet aggregation and blood
coagulation under flow that includes detailed decriptions of
coagulation biochemistry, chemical activation and deposition of blood
platelets, as well as the two-way interaction between the fluid
dynamics and the growing platelet mass. We present this model and use
it to explain what underlies the threshold behavior of the coagulation
system's production of thrombin, and to show how wall shear rate and
near-wall enhanced platelet concentrations affect the development of
growing thrombi. By accounting for the porous nature of the thrombus,
we also demonstrate how advective and diffusive transport to and
within the thrombus affects its growth at different stages and spatial
locations.
Recent work on flow through the endothelial surface layer.
Abstract from our published paper:
Flow through the endothelial surface layer (the glycocalyx and adsorbed
plasma proteins) plays an important but poorly understood role in cell
signaling through a process known as mechanotransduction.
Characterizing the flow rates and shear stresses throughout this layer
is critical for understanding how flow-induced ionic currents,
deformations of transmembrane proteins, and the convection of
extracellular molecules signal biochemical events within the cell,
including cytoskeletal rearrangements, gene activation, and the release
of vasodilators. Previous mathematical models of flow through the
endothelial surface layer are based upon the assumptions that the layer
is of constant hydraulic permeability and constant height. These models
also assume that the layer is continuous across the endothelium and
that the layer extends into only a small portion of the vessel lumen.
Results of these models predict that fluid shear stress is dissipated
through the surface layer and is thus negligible near endothelial cell
membranes. In this paper, such assumptions are removed, and the
resultant flow rates and shear stresses through the layer are
described. The endothelial surface layer is modeled as clumps of a
Brinkman medium immersed in a Newtonian fluid. The width and spacing of
each clump, hydraulic permeability, and fraction of the vessel lumen
occupied by the layer are varied. The two-dimensional Navier–Stokes
equations with an additional Brinkman resistance term are solved using
a projection method. Several fluid shear stress transitions in which
the stress at the membrane shifts from low to high values are
described. These transitions could be significant to cell signaling
since the endothelial surface layer is likely dynamic in its
composition, density, and height.
here is a glimpse of our new glycocalyx flow tank!
notice the parabolic flow in the beaded region - unexpected, but super
cool!
if you would like to watch the whole movie, please click here.
Note: this is a quicktime movie in .mov
format
Old work on bending of glycocalyx proteins