Fractal growth of tumors and other cellular populations: Linking the mechanistic to the phenomenological modeling and vice versa

Alberto d'Onofrio

Research output: Contribution to journalArticle

Abstract

In this paper we study and extend the mechanistic mean field theory of growth of cellular populations proposed by Mombach et al. [Mombach JCM, Lemke N, Bodmann BEJ, Idiart MAP. A mean-field theory of cellular growth. Europhys Lett 2002;59:923-928] (MLBI model), and we demonstrate that the original model and our generalizations lead to inferences of biological interest. In the first part of this paper, we show that the model in study is widely general since it admits, as particular cases, the main phenomenological models of cellular growth. In the second part of this work, we generalize the MLBI model to a wider family of models by allowing the cells to have a generic unspecified biologically plausible interaction. Then, we derive a relationship between this generic microscopic interaction function and the growth rate of the corresponding macroscopic model. Finally, we propose to use this relationship in order to help the investigation of the biological plausibility of phenomenological models of cancer growth.

Original languageEnglish
Pages (from-to)875-880
Number of pages6
JournalChaos, Solitons and Fractals
Volume41
Issue number2
DOIs
Publication statusPublished - Jul 30 2009

ASJC Scopus subject areas

  • Mathematics(all)

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