Post by David Feder on Jun 11, 2009 18:25:09 GMT -5
Stability and phase transitions in a mathematical model of
Duchenne muscular dystrophy
Guido Dell’Acqua and Filippo Castiglione
Institute for Computing Applications “M. Picone”,
National Research Council (CNR),
Viale del Policlinico 137, 00161 - Rome, Italy
{g.dellacqua,f.castiglione}@iac.cnr.it
June 9, 2009
Abstract
We present a mathematical model to investigate the role of the immune system in the Duchenne
muscular dystrophy disease. It is based on the assumption that the immune system contributes to the
tissue damage and indeed its interaction with the muscle tissue after an initial endogenous damage can
be described as a predator-prey system showing typical oscillations. In this article we investigate the
dynamical properties of the system. We find that, for a biologically relevant parameters range, it shows
two phase-transitions between qualitative different behaviors corresponding to complete recover or to a
state where muscle regeneration and degeneration coexist
Duchenne muscular dystrophy
Guido Dell’Acqua and Filippo Castiglione
Institute for Computing Applications “M. Picone”,
National Research Council (CNR),
Viale del Policlinico 137, 00161 - Rome, Italy
{g.dellacqua,f.castiglione}@iac.cnr.it
June 9, 2009
Abstract
We present a mathematical model to investigate the role of the immune system in the Duchenne
muscular dystrophy disease. It is based on the assumption that the immune system contributes to the
tissue damage and indeed its interaction with the muscle tissue after an initial endogenous damage can
be described as a predator-prey system showing typical oscillations. In this article we investigate the
dynamical properties of the system. We find that, for a biologically relevant parameters range, it shows
two phase-transitions between qualitative different behaviors corresponding to complete recover or to a
state where muscle regeneration and degeneration coexist