Biomathematic Analysis of Epidermal Skin Cell Stratification, Differentiation, and Death

The skin is one of the most, if not the most, important organ that organisms possess because of the functions it provides for the survival of their body. Such functions include a protective barrier and divide between the internal and external environments, a body temperature regulator, a sensory information detector, and it also plays a role in the immune system. The diversity of the purposes that the skin plays is the reason why it is an essential component within the body and the reason it is studied extensively. By gaining more information of the stratification, differentiation, and death of skin cells, it will allow us to gain more knowledge about the skin that can be used in biological and medical research to better benefit the medical industry and science, therefore advancing the community. One way to obtain data is by calculating the rates at which the outermost, epidermal, layer divides and utilizing this to discover more facts about the skin, how it properly functions, and what factors contribute to its efficiency and/or deficiency. The field of biomathematics is devoted to applying the power of mathematics to biological systems and environments. Analysis and interpretation of these results can lead to conclusive reports of new evidence discovered which can be applied to existing and/or new biological processes. One method that is used to measure the rates at which these processes occur is by utilizing differential equations and the linear algebra technique of Jacobian stability analysis to determine its steady state. The variables within each differential equation will represent a component that affects the rate during either the process of reproduction, transition into a new skin cell type, or the deterioration of these skin cells. The relationships and interactions amongst these components will be shown within the differential equations and by determining the steady state of each equation will provide insight into what concentration, speed, external and internal elements, and environmental factors are necessary to maintain a constant existence state. Deviations from or disruptions to what is defined as the normal process will change these relationships and ultimately the steady state, resulting in phenotypic abnormalities and/or differences such as rashes, cancer, dry skin, etc. By manipulating the aspects of the differential equations and basically the steady state conditions, will help us to predict outcomes under varying settings, genetic mutations, and environmental factors. Not only this, but it will assist us in visualizing intercommunication amongst these components, the extent of their influence on the epidermal mechanisms, and what physical defects it can cause. Analysis of these outcomes can be useful in the medical and scientific fields. This is the procedure that was followed during this research involving epidermal skin stratification, differentiation, and death and can be described in more detail throughout the thesis