Mathematical Modeling for Keloid Formation Triggered by Virus: Malignant Effects and Immune System Competition

Abstract

This paper deals with the modeling of a wound healing disease, the keloid, which may provoke onset of malignant cells with higher progression feature, thus generating cells with heterogeneous phenotype. According to medical hypothesis, it is assumed that viruses and the genetic susceptibility of patients are the main causes that trigger the formation. The mathematical model is developed by means of the tools of the kinetic theory for active particles. The competition of the immune system cells with viruses, keloid¯broblast cells, and malignant cells is taken into account. Numerical simulations, obtained by considering the sensitivity analysis of the parameters in the model, show the emerging phenomena that are typical of this disease. Math. Models Methods Appl. Sci. 2011.21:389-419. Downloaded from www.worldscientific.com by MONASH UNIVERSITY on 12/15/14. For personal use only.result of age-related loss of regulatory control. The process and the risk factors that can a®ect the normal organ repair and wound healing are brie°y reviewed in this paper in view of the mathematical modeling approach. Indeed, the main aim of this paper is to develop a mathematical model which can be tuned according to the patient data provided by medics.The construction of mathematical models for biological systems of the life sciences is a hot theme of this new century that involves experts coming from di®erent sci-enti¯c¯elds: mathematics, physics and bioinformatics. Mathematical models attempt to describe, by equations, the dynamics in time and space of real systems that, in the case under consideration, belong to the living matter. All mathematical models (predictive or explorative) need the identi¯cation of the parameters that appear in the equations. Once this assessment has been properly performed, the model can be used to provide an approximate description of physical reality. In some special cases, the model can even depict emerging behaviors only partially shown by empirical data. Finally, it contributes to the re¯nement of experiments.The modeling of biological systems needs to tackle the additional di±culty generated by the peculiarities of the living matter. Among various issues, the lack of invariance principles that are typical of systems of the inert matter. A critical analysis of these issues is developed in the papers by Herrero, 20 May 25 and Reed. 30 Hartwell et al. 19 propose a deep insight into the above issues. The main conceptual idea is that invariance principles are modi¯ed by the ability of living systems to express speci¯c strategies that depend on survival purposes and adaptation to environmental conditions. Therefore, living systems have the ability of extracting energy for their own bene¯t. Moreover, their adaptation ability generates mutations, which occur at the molecular scale of genes and induce phenotype mutations. This evolution may even be very rapid in some speci¯c pathologies.Recently, various complex systems in the life and applied sciences such as cancer disease, tra±c, social systems, behavioral...

On the Asymptotic Theory From Microscopic to Macroscopic Growing Tissue Models: An Overview With Perspectives

“…23 for the immune competition between cancer and immune cells, and in Ref. 24 to model the onset of keloids triggered by a virus and contrasted by the immune system. Moreover, it is useful dealing with open systems, 15 where external therapeutical actions are applied to an inner multicellular system.…”

Towards a unified approach in the modeling of fibrosis: A review with research perspectives

“…Bearing all above in mind, a kinetic for active particles-based model has been proposed in [194] and further analyzed in [195]. Specifically the model is developed assuming that the keloid formation involves four interacting functional subsystems: Normal-fibroblast cells, activated viruses, keloid fibroblast cells, malignant cells and immune system cells.…”

On the modeling of nonlinear interactions in large complex systems

“…(1.2), for modeling complex systems in the life sciences; see Refs. [2,[5][6][7]9], and many others. An interesting problem consists in analyzing the role of nonlinear interactions, namely how these can modify the output of the overall collective dynamics.…”

“…An account of the literature in the field is offered by paper [1], which reports on the mathematical approach of the so-called kinetic theory for active particles, for short KTAP theory, that has been specifically developed for modeling complex systems. This method has been applied in several fields of natural and applied sciences such as immune competition (see [2,3], which refer to [4]), epidemics [5], wound healing and diseases [6], social dynamics [7,8], and psychological interactions [9].…”