Mathematical Modeling and Computational Simulation of the Diffusive Behavior of Adenocarcinoma Biomarker Particles

Colorectal adenocarcinoma is one of the carcinogenic diseases that most affects the health of the world population. This disease is manifested biologically by the segregation of biomarker substances in the human system. This paper presents the development of a numerical-mathematical model for the study of the diffuse behavior of particles segregated by this type of cancer. Flow conditions, characteristics and properties of the diffusive medium are determined, and the study domain is defined. A mathematical description is elaborated to represent the behavior of the phenomenon by means of constitutive laws of the biosystem. A numerical-computational algorithm is constructed that makes possible the analysis of the different behavioral conditions; in this paper one of the multiples settings is showed. The computational implementation is done using Taylor series defined by finite differences with a refinement of the grid that can be controlled by the user. In addition, a structural element is incorporated with which it is intended to evaluate the level of concentration in the structure-substance contact zone. As a platform for the implementation of the algorithm, Matlab program is used. The results have been plotted by surface curves. Concentration levels are obtained at three points of interest, including concentrations at the structure-substance contact point, with concentration values of \(1*10^{-6} \frac{\mathrm{kg}}{\mathrm{m}^{3}}\). The research is oriented in the search of an alternative that allows the detection of colorectal cancer in its early phase.