TY - JOUR
T1 - Fractal growth of tumors and other cellular populations
T2 - Linking the mechanistic to the phenomenological modeling and vice versa
AU - d'Onofrio, Alberto
PY - 2009/7/30
Y1 - 2009/7/30
N2 - 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.
AB - 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.
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U2 - 10.1016/j.chaos.2008.04.014
DO - 10.1016/j.chaos.2008.04.014
M3 - Article
AN - SCOPUS:67349108817
VL - 41
SP - 875
EP - 880
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
SN - 0960-0779
IS - 2
ER -