  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.
