IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 17, Issue 1 Ser. I (Jan. – Feb. 2021), PP 48-54 www.iosrjournals.org DOI: 10.9790/5728-1701014854 www.iosrjournals.org 48 | Page Mathematical Model of Cellular Injury Nkuturum Christiana Ph.D Department of Mathematics/Statistics Ignatius Ajuru University of Education Rivers State, Port Harcourt Onwubuya, M. N. Department of Statistics Delta State Polytechnic, Oghara Abstract This study revealed that ischemia and hypoxia are the forms of stress present in soft tissue cells that can lead to cellular injury. The study also explained that cellular injuries exhibit viscoelastic properties in the body of the living organisms as cells are damaged. The analytic solution showed that the magnitude of ischemia and hypoxia that led to cellular injury was kN 270 and the time taken for the dead cells to escalate was three months and one week. The solution showed that the environmental factor that affected the cellular injury that led to escalation of dead cells to cellular injury was temperature given as  between 0 0 100 80  c. The model result also showcased that the amplitude of the hypoxia in the cell damage that led to cellular injury was kN 2300 and the time taken to enlarge was three months. Finally, the solution to the model ascertained that it took between two –three months for ischemia and hypoxia to act on a tissue cell before it ruptures and become cellular injury. All these results were determined from the graphs when plotted the parameter values given in the discussion of results. Finally, the analytic solution of the study illustrates that dead cells exist right in the rock-solid form as a result of oxidative stress (ischemia and hypoxia) losing its bonding power. The study explicate that the model equations were found in the flesh existing in a local syndrome called ‘‘Orolla’’. The system showed significant effect and was found to be stable with escalating dead cells in living organism. Keywords: Cellular Injury, Stress, Ischemia, Hypoxia, Apotosis, Necrosis, Cell death. --------------------------------------------------------------------------------------------------------------------------------------- Date of Submission: 14-01-2021 Date of Acceptance: 29-01-2021 --------------------------------------------------------------------------------------------------------------------------------------- I. Introduction Cellular injury also known as cell injury or cell damage is a variety of changes of stress that a cell suffers due to external and internal environmental changes. Among other causes, this can be due to physical, chemical, infectious, biological, nutritional or immunological factors [55]. Cellular injury is also caused by stimuli which includes immunological reactions such as immune deficiency, autoimmune reactions, hypersensitivity reaction to foreign agents; nutritional imbalances such as malnutrition in protein calorie, excess intake of carbonhydrates, proteins and fats; and genetic defects such as inborn errors in metabolism [57] The causes of cellular injury are irradiation, ischemia and hypoxia as a result of oxidative stress loosing its bonding power. Hypoxia is a deficiency of oxygen which causes cell injury by reducing aerobic oxidative respiration [2,54]. It is an extremely important and common cause of cell injury and cell death. In cell biology and pathophysiology, cellular adaptation refers to changes made by a cell in response to adverse environmental changes. The adaptation may be physiological normal or pathological abnormal [56]. Five minor types of adaptation include atrophy, hypertrophy, hyperplasia, dysplasia, and metaplasia.The most important goal is to gain a general understanding of cellular adaptations or cell injury [3, 39]. The two types of cellular injury are necrosis (irreversible cellular injury) and apoptosis (reversible cellular injury or degeneration). In reversible cellular injury, stress in the cell is mild to moderate and the injured cells may recover while there is persistent and severe cell injury that can lead to cell death [1, 29]. In necrosis, mitochondria swell, lysosomes swell, plasma membrane is damaged and the lysosomal membranes lead to enzyme leakage; and there occurs acidosis protection by inhibiting enzymatic reactions [4, 20]. Cell damage depends on the extent of injury and the cellular response may be adaptive and if possible, homeostasis is restored. The study of cell injury and cell death is the basis for the understanding of disease mechanisms. Based on this cell damage, the method of damage mechanics model was adopted as to profer solution to the problem [5,40]. Thus, damage mechanics is the study done power-driven variables of the tools involved in the deterioration of materials or tissues when subjected to loading [23-26]. Damage mechanics illustrates the typical engineering methodology to model complex phenomena cellular injury. Damage mechanics shows the idea of propagation, initiation and coalescence of dead cells through the cell microenvironment under the influence of