John Dallon: Paper Abstract
Numerical Aspects of Discrete and Continuum Hybrid Models in Cell Biology
AUTHOR:
John C. Dallon
Department of Mathematics, Heriot-Watt University,
Edinburgh EH14 4AS, UK.
ABSTRACT:
In this paper we introduce a method of modeling which mixes
continuum and discrete variables, and explain two models in cell
biology that use this method. The first application deals with
wound healing, more specifically the collagen alignment in scar
tissue formation and the second models early aggregation in the
cellular slime mold Dictyostelium
discoideum. We solve these models using numerical
techniques similar to the particle-in-cell method which requires
that the discrete and continuum variables are interpolated one to
the other. The implementational and numerical details are discussed
in an informal and practical manner with particular attention given
to the problem of interpolation.
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