Multiscale modeling approach typical of systems biology tends to mix continuous, discrete, \
deterministic, and probabilistic submodels. To prevent the loss of blood following a break \
in blood vessels, components in blood and the vessel wall interact rapidly to form a clot t\
o limit hemorrhage. In this talk we will describe a multiscale hybrid model of thrombus for\
mation consisting of components for modeling viscous, incompressible blood plasma; coagulat\
ion pathway; quiescent and activated platelets; blood cells; activating chemicals; fibrinog\
en; the vessel walls and their interactions. At macro scale blood flow is described by the \
incompressible Navier-Stokes equations and is numerically solved using the projection metho\
d. At micro scale, cell movement, cell-cell adhesion, cell-flow and cell-vessel wall intera\
ctions are described through an extended stochastic discrete Cellular Potts Model (CPM). Si\
mulation results show development of an inhomogeneous internal structure of the clot confir\
med by the preliminary experimental data. It is also demonstrated that dependence of the cl\
ot size on the blood flow rate in simulations is close to the one observed experimentally.
In the second half of the talk a continuous limit will be discussed of a two-dimensional st\
ochastic CPM describing cells moving in a medium and reacting to each other through direct \
contact, cell-cell adhesion, and long range chemotaxis. Contrary to classical Keller-Segel \
model, solutions of the obtained equation do not collapse in finite time and can be used ev\
en when relative volume occupied by cells is quite large. A very good agreement was demonst\
rated between CPM Monte Carlo simulations and numerical solutions of the obtained macroscop\
ic nonlinear diffusion equation. Combination of microscopic and macroscopic models was used\
to simulate growth of structures similar to early vascular networks.
Xu, Z., Chen, N., Kamocka, M.M., Rosen, E.D., and M.S. Alber [2008], Multiscale Model of Th\
rombus Development, Journal of the Royal Society Interface 5 705-722.
Alber, M., Chen, N., Lushnikov, P., and S. Newman [2007], Continuous macroscopic limit of a\
discrete stochastic model for interaction of living cells, Physical Review Letters 99 1681\
02.
Lushnikov, P.P., Chen, N., and M.S. Alber, Macroscopic dynamics of biological cells interac\
ting via chemotaxis and direct contact, Physical Review E (to appear).
