Summary: Growth and dissipation in biological tissues
D. Ambrosi, A. Guillou,
Dipartimento di Matematica, Politecnico di Torino,
corso Duca degli Abruzzi 24, 10129 Torino, Italy.
May 2, 2007
KEYWORDS: growth, soft biological tissues, energy inequality, nutrient factors
This paper provides a unified mathematical framework so as to study the growth
of biological tissues on an energetic basis. All the contributions to growth of solute
chemicals and nutrients are here resumed in one scalar descriptor, the biochemi-
cal energy of the system. The free energy of the system accounts for both strain
and biochemical storage. The exploitation of a dissipation inequality by standard
means provides admissible couplings between growth, tension and energy. Specific
admissible constitutive equations lead back, in some cases, to classical models.
In soft biological tissues, growth takes place at a rate that may be influenced by many
factors, including genetical predisposition, mechanical stimuli and availability of nutrients.
Even when restricting the field to the macroscopic scale only, the relevant scientific liter-
ature usually focuses just on one of these mechanisms at a time; some authors consider
the mechanical aspects of growth, while others focus on the biochemical aspects associ-