Current work on blood clot
modeling.
Abstract for paper in
progress:
The body heals injured blood vessels and prevents bleeding by clotting
the blood. Clots are primarily made of blood-borne cells and a fibrous
material that is assembled at the site of injury in flowing blood. Clot
composition and structure change with local chemistry and fluid
dynamics, which in turn alters the flow. To better understand this
fluid-structure coupling, we have created a mathematical model to
simulate the formation of a blood clot in a dynamic fluid environment.
The growing clot is represented as a mixed porous medium whose
permeability is dependent on the coagulation chemistry within it. We
developed a method using regularized periodic fundamental solutions for
the equations of porous media flow to calculate the permeability of the
clot for different internal structures. The flow field resulting from a
clot with specific calculated permeability and size can then be
recovered by solving the Navier-Stokes equations with an added friction
term. We report on how this complex fluid-structure interaction affects
the limiting factor(s) of blood clot growth.
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