Multiscale approaches to biological modeling

29 February 2008

Mark Alber
Center for the Study of Biocomplexity
University of Notre Dame


The multiscale models typical of systems biology tend to mix continuous, discrete, deterministic, and probabilistic approaches.

In the first half of this talk a multiscale model will be described for studying formation of a clot (thrombus) in a blood vessel, consisting of components for modeling viscous, incompressible blood plasma; non-activated and activated platelets; blood cells; activating chemicals; fibrinogen; vessel walls and their interactions. The macroscale dynamics of the blood flow is described by the continuum Navier-Stokes equations. The microscale interactions are described through an extended stochastic discrete cellular Potts model (CPM). Simulation results demonstrate development of an inhomogeneous internal structure of the clot, which is confirmed by the preliminary experimental data [1].

We will also describe a continuous limit of a discrete CPM for cells moving in a medium and reacting to each other through direct contact, cell-cell adhesion, and chemotaxis. A general multiscale approach has been applied to simulating spongy bone formation, suggesting that self-organizing physical mechanisms can account for this developmental process [2].


  1. Z Xu, N Chen, M M Kamocka, E D Rosen, M.S. Alber,"Multiscale model of thrombus development", J Roy Soc Interface (in press)
  2. M Alber, N Chen, P Lushnikov, S Newman, "Continuous macroscopic limit of a discrete stochastic model for interaction of living cells", Phys Rev Lett 99:168102 2007. PubMed

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