Mathematical modeling of the impact of radiation and oxidative stress on cancer development 35 Faculty of Natural and Applied Sciences Journal of Scientific Innovations Print MATHEMATICAL MODELING OF THE IMPACT OF RADIATION AND OXIDATIVE STRESS ON CANCER DEVELOPMENT * 1 Nkuturum

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 also as the enabler of the cancer cells proliferation rate indicating a compromised immune system of the organism. Introduction The application of a mathematical model to investigate how the various state variables such as irradiation, and stress-strains constitutive relationship trigger cellular damage through initiation, growth, and coalescence of tumor (cancer) is studied in detail in this paper with the view to providing requisite insight into existing knowledge on the subject. Mathematical model has become a veritable tool in various fields of human endeavour particularly aiding our understanding of many real-life phenomena is known to many authors. For example, Bradly and Enderling (2019), and Chamseddine and Rejniak, (2019) provided an excellent review of mathematical models used for different treatments of cancer. Moreira and Deutsch, (2002), Araujo and McElwain, (2004), and Lowengrub et al. (2010) reviewed tumor growth models and radiation effects. Hsu (1968) investigated the effect of radiation on the spatiotemporal distribution of oxygen inside tumour. They extended the model of Greenspan, (1972) for tumor growth and hypoxia with a linear quadratic model representing cell death due to radiotherapy. Enderling, Anderson, Chaplain, Munro and Vaidya, (2006) developed a mathematical approach for surgery and radiation treatment in early breast cancer, based on a partial differential equation and a linear-quadratic model. Many mathematical models can incorporate a large volume of quantitative information that can describe the complexity of a cell's biological pathway. Even complex biological processes can be best understood by a computational and mathematical model.