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Title of Journal: J Math Biol

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Abbravation: Journal of Mathematical Biology

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Springer-Verlag

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1432-1416

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Stochastic modelling of biased cell migration and

Authors: Andreas Groh Alfred K Louis
Publish Date: 2009/12/10
Volume: 61, Issue: 5, Pages: 617-647
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Abstract

Matrix dynamics plays a crucial role in several physiological and pathological processes In this paper we develop a model framework which describes the temporal fibre network evolution depending on the influence of migrating fibroblasts The cells are regarded as discrete objects in the plane whose velocities are determined by a generalised Langevin equation For its solution we verify existence and uniqueness The courses of the trajectories are affected by two external impulses chemotaxis and contact guidance respectively The extracellular matrix is described by a continuous vector field which contains both information on density and orientation of the fibrous material Modelling dynamic interaction between the discrete and the continuum variables is an essential point of this paper In particular the smoothing of the fluctuating paths plays a key role Besides a detailed description of the formulated equations we also supply the condensed pseudo code of the algorithm We investigate several examples and present results both from artificial and real data

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  2. Mathematical analysis of Mayer waves
  3. “Classical” Electropermeabilization Modeling at the Cell Scale
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  15. A hybrid mathematical model for self-organizing cell migration in the zebrafish lateral line
  16. A Diffusion Approach to Approximating Preservation Probabilities for Gene Duplicates
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