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From microscopic to macroscopic description of multicellular systems and biological growing tissues

Bellomo, Nicola and Bellouquid, Abdelghani and Herrero, Miguel A. (2007) From microscopic to macroscopic description of multicellular systems and biological growing tissues. Computers & Mathematics with Applications , 53 (3-4). pp. 647-663. ISSN 0898-1221

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Abstract

This paper presents an asymptotic theory for a large class of Boltzmann-type equations suitable to model the evolution of multicellular systems in biology. The mathematical approach described herein shows how various types of diffusion phenomena, linear and nonlinear, can be obtained in suitable asymptotic limits. Time scaling related to cell movement and biological activity are shown to play a crucial role in determining the macroscopic equations corresponding to each case.


Item Type:Article
Uncontrolled Keywords:Kinetic theory; multicellular systems; asymptotic limits; nonlinear problems; bacterial chemotaxis; asymptotic analysis; mathematical-model; diffusion limit; kinetic-models; equations; aggregation; dictyostelium; angiogenesis; invasion
Subjects:Medical sciences > Biology > Biomathematics
Sciences > Mathematics > Operations research
ID Code:16308
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