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

TL;DR

This paper extends the MLBI mechanistic model of cellular growth to a broader class of interactions, linking microscopic biological mechanisms to macroscopic growth behaviors, with implications for understanding cancer growth.

Contribution

It generalizes the MLBI model to include arbitrary biologically plausible cell interactions and establishes a relationship between microscopic interactions and macroscopic growth rates.

Findings

The MLBI model encompasses main phenomenological growth models.

A new relationship links microscopic interactions to macroscopic growth.

The approach aids in assessing biological plausibility of cancer growth models.

Abstract

In this paper we study and extend the mechanistic mean field theory of growth of cellular populations proposed by Mombach et al in (Mombach J. C. M. et al., Europhysics Letter, 59 (2002) 923) (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 \emph{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.