The objective of this work is to prevent damage of the arterial wall, using a theoretical model of hyperelastic, anisotropic, and dynamic behavior of the human arterial. This work is mainly focused on the properties of the hydrostatic stress and the evolution of stenosis. This work is mainly focused on the properties of the hydrostatic stress and the evolution of stenosis in order to understand the effect of the size of the plaque deposit, the loss of elasticity of the wall, and the increase in the density of the blood on the mechanical behavior of the human arterial wall. The great contribution of this work shows us that increasing the size of the plaque also increases arterial stress, and the radial growth of the plaque is very dangerous compared to the longitudinal growth. Furthermore, atherosclerosis promotes the loss of elasticity of the arterial wall and increases the density of blood mass. Indeed, all these subsequent phenomena increase arterial stress. All the results are in good agreement with the expected result of the literature and could play an important role in the diagnosis of the patient with an arterial injury. It will also help the doctor and the surgeon to make a good clinical decision and good treatment planning.

Based on the biological heat transfer equation of Penne, the internal temperature distribution of the biological tissue was studied, taking into account the evolution of stenosis and hematocrit. The one-dimensional simplifying cylindrical heat equation of the biological living tissues in permanent regime was solved by the FDM (finite difference method) and analytically, to assess the temperature change under the variation of stenosis, hematocrit, K (thermal conductivity), kinematic viscosity, generation of metabolic heat and the heat transfer coefficient. The main results show that the temperature increases as the stenosis and hematocrit increase in size; and the secondary results show that the heat transfer coefficient and the K lower the body temperature while metabolic heat generation increases body temperature. This is in accordance with the literature.