Incorporating Folding, Unfolding, Denaturation in a Mathematical Model for Cancer Spreading
T. A. Atabong *
Department of Mathematics, College of Science and Technology, Florida A&M University, 1516 Martin Luther King Bld, Fl 32307, USA.
M. O. Oyesanya
Department of Mathematics, University of Nigeria, Nsukka, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
World known biological protein materials like arteries, bones, and tendons are constantly in a state of continuous stress due to their respective activities within the body. This stress will result in an increase in tissue residual temperature and consequently denaturation. The effects of denaturation on tumor initiation and progression are considered. All the parameters are integrated into a 9 step computational procedure, later transformed into a series of partial differential equations in time and space. A program was written to retrieve the steady states using parameters mined from existing and related models. The non-significant stable trivial steady state was observed to be driven unstable with an increase in the diffusion coefficient of the denatured cells. As denaturation increases, the progression of a tumor is exponential given a maker that denaturation favors the tumor population doubling model observed in many mathematical and biomedical studies. The outcome of this research can as well fit into other classes of tumors and will go a long way to contribute to the eventual eradication of tumor by suggesting elimination of stress of all forms in the body.
Keywords: Numerical algorithm, soft tissue, biological protein material, folding, denaturation.