Mathematical modeling of the impact of radiation and oxidative stress on cancer development

Abstract

In this paper, the damage mechanic model of cancer caused by radiation and oxidative stress refers to the application of a mathematical model to investigate how the various state variables such as irradiation, stress-strain constitutive relationship trigger cellular damage through initiation, growth, and coalescence of tumor (cancer) with the view to providing requisite insight into the study. Three non-linear differential equations were coupled to undertake the study. The solutions to the equations indicate that the Extracellular Matrix density ????????(????????,????????), Cell density ????????????????(????????,????????) and Cell displacement ????????(????????,????????) are the functions of time and position. Furthermore, the solutions obtained to the model equations indicate the steady-state solutions implying that the secretion surface is activating the growth or proliferation rate of cancer cells in the body of the organisms in this instance we refer to the solid tumor (cancer). The stable solutions indicated the presence of cancer cells which in a steady state grows exponentially and if unchecked defile all medication or treatment protocol employed due to the actions of radiation and oxidative stress. The established results indicated the presence of radiation and oxidative stress in the injured area acting