Eur. Phys. J. Plus (2015) 130: 159
https://doi.org/10.1140/epjp/i2015-15159-4

Regular Article

Mimic therapeutic actions against keloid by thermostatted kinetic theory methods

¹ Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Universités, UPMC Univ Paris 06, UMR 7600, 4, place Jussieu, case courrier 121, 75252, Paris cedex 05, France
² CNRS, UMR 7600 LPTMC, Paris, France

^* e-mail: bianca@lptmc.jussieu.fr

Received: 15 June 2015
Accepted: 10 July 2015
Published online: 5 August 2015

Abstract

This paper deals with the modeling of a wound-healing disease under a therapeutic action by employing the methods of the thermostatted kinetic theory for active particles. In particular, in order to test therapeutic actions against keloid formation and the possible development of a cancer, an external force field coupled to a Gaussian thermostat is introduced into a mathematical model recently proposed. Specifically the model depicts the competition of the immune system cells with a virus, the mutated fibroblast cells, and the cancer cells. Employing a computational analysis, the effects of three different external forces mimic therapeutic actions are analyzed: A vaccine for the virus, the PUVA therapy for the keloid and a vaccine for the cancer. The results are in agreement with the evidence that the sole action of the immune system is not sufficient to obtain a total depletion of keloid thus requiring the definition of a therapy. Further refinements and developments of the model are also discussed in the paper.