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Stochastic
modeling of platelet aggregation
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 We
developed a computational stochastic model of platelet aggregation in 3D
blood flows by accounting for the movements of all platelets individually
involved. The model incorporates information about platelet adhesion
molecule behavior, cell mechanics, and fibrinogen formation. To make
simulations of thousands platelets tractable, we employed spectal/hp element discretization of the unsteady
Stokes equations in combination with the Force Coupling Method (FCM), in
which platelets are represented as force envelopes based on a spatial
distribution of finite force multipoles. Thrombus
growth rates are affected by the velocity of the blood flow, but do no
simply increase with it. As the velocity increases, the growth rates
exhibit a maximum, and subsequently decrease. Our simulations demonstrated
the dependence of thrombus growth rate on blood velocity as found
experimentally by Begent & Born (Nature,1970).
Platelet aggregation movie (Quicktime,
10MB): Thrombus growing on a blood vessel due to accumulation of platelets. Blue
denotes inactivated platelets and green denotes triggered platelets, which
convert to activated (red) platelets after a characteristic delay time.
Three-dimensional parallel simulations were performed to resolve the blood
flow and the platelets dynamics.
Related publications:
I.V. Pivkin, P.D. Richardson, and G.E. Karniadakis, “Blood flow velocity effects and role of
activation delay time on growth and form of platelet thrombi”, Proceedings
of National Academy of Sciences of the United States of America, vol.
103, pp. 17164-17169, 2006.
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Coarse-grained
stochastic molecular dynamics simulations
 Dissipative particle dynamics
(DPD) is a new, potentially very effective approach in simulating mesoscale hydrodynamics. It can simulate efficiently
complex liquids and dense suspensions using only a few thousand virtual
particles and at speed-up factors of more than one hundred thousand
compared to molecular dynamics. The DPD model consists of particles which
correspond to coarse-grained entities, thus representing molecular clusters
rather than individual atoms. DPD can be thought of as a coarse-grained
version of Molecular Dynamics (MD), but it employs dissipative and
stochastic forces to account for the eliminated degrees of freedom. Similar
to the effort that has been going on with the lattice Boltzmann method
(LBM), another mesoscopic simulation technique, a
systematic verification and validation of DPD is required to evaluate its
accuracy, efficiency and robustness. In a series of papers we analyzed the
fundamental modeling ideas of DPD. Unlike an MD simulation where the choice
of potential is based on a theoretical model of the physical system to be
simulated, a DPD simulation involves potentials of a form independent of
the physical system. We proposed a process of choosing the DPD parameters
and determining the DPD length and time scales for different levels of
coarse-graining such that the DPD simulations correspond to an MD
simulation of a Lennard-Jones (LJ) liquid. We
investigated and identified the limits of coarse-graining procedure in DPD.
Unlike the MD method, the soft repulsion between DPD particles cannot
prevent fluid particles from penetrating solid boundaries, and thus extra
effort is required to impose accurately the no-slip wall boundary
condition. We developed an adaptive method to impose no-slip conditions and
to control anomalous density fluctuations near the solid walls in DPD
simulations. The formalism of this method is not restricted to DPD but it
could remedy a similar pathology in other particle-based simulations.
Related publications:
I.V. Pivkin and
G.E. Karniadakis, “Controlling
density fluctuations in wall-bounded DPD systems”, Physical Review Letters, vol. 96,
p. 206001, 2006.
I.V. Pivkin and
G.E. Karniadakis, “Coarse-graining
limits in open and wall-bounded DPD systems", Journal of Chemical Physics, vol. 124,
p.184101, 2006.
E.E. Keaveny, I.V. Pivkin, M. Maxey, and G.E. Karniadakis,
“A
comparative study between dissipative particle dynamics and molecular
dynamics for simple- and complex-geometry flows”, Journal of Chemical Physics, vol. 123,
p. 104107, 2005.
I.V. Pivkin and G.E. Karniadakis,
“A
new method to impose no-slip boundary conditions in dissipative particle
dynamics”, Journal of Computational
Physics, vol. 207, pp. 114-128, 2005.
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Biomembranes and cell biomechanics
 In this project we develop a
coarse-grained model of the red blood cell (RBC) membrane to simulate the
motion and deformation of the RBCs under
physiological flow conditions. The RBC wall comprises a phospholipid
bilayer, cholesterol molecules, transmembrane proteins and an underlying spectrin network which is tethered to the membrane.
These structural components collectively determine the deformation behavior
of the RBC, in addition to performing their normal biological functions.
A two-dimensional network of
interacting particles is embedded in a three-dimensional closed surface to
represent the membrane. By using the worm-like-chain (WLC) model to
describe the nonlinear force-displacement behavior of spectrin
molecules, the deformation characteristics of the RBC membrane are obtained
by incorporating the effects of spontaneous curvature of the lipid bilayers material, structural relaxation of the
in-plane shear energy, and geometrical constraints of fixed surface area
and fixed enclosed volume. The model allows us to simulate the blood flow
in the presence of RBCs at physiological hematocrit, as well as to investigate the motion and
deformation of the RBCs in the microcirculation.
RBC
biconcave shape movie (AVI, 2.5MB): Sphere
is deflated to 65% of its volume to get biconcave shape
RBC
in microchannel movie (AVI, 5MB): Single RBC is placed into the microchannel
of 9 microns in diameter. The pressure gradient is applied and later turned
off.
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