Alexandra Fronville, Abdoulaye Sarr and Vincent Rodin.
Viability kernel algorithm for shapes equilibrium.
Cell and Tissue Engineering,
American Institute of Mathematical Sciences (AIMS),
1(2):118-139, September 2017.
Abstract:
Viability is a very important feature of dynamic systems under state
constraints whose initial value problem does not ensure uniqueness of
solutions.
In this paper, we introduce an hybrid automaton to address the question
of viability of a cellular tissue.
This hybrid automaton couples two dynamical models: differential equations
manage the energy of the system and morphological equations govern the
growth of the tissue.
The cells can proliferate when they have enough access to oxygen and nutrient
to produce the energy, remain quiescent when this energy is between two levels,
or die when this energy is too low.
The constraint we choose is to maintain the number of cells of the tissue
during a certain time horizon. We have shown that for all the 1029 2D-tissues
of 16 cells with an associate genotype, only 5 are viable for this constraint
in a long time horizon.
Moreover, for all these tissues, they renew there cells periodically.
These periodic shapes are like periodic limit cycles in the state space of
shapes.
Keywords:
Engineered tissues, hybrid automata, computational modeling,
mutational analysis, viability theory, epigenetics.
[doi:10.3934/celltissue.2017.2.118]
[pdf]
[Fronville17b.pdf]