ABSTRACT

Abstract

This paper investigates the mathematical modelling of blood flow through a stenosed human carotid artery. Constraints of blood flow in human carotid arteries are known as stenosis which may ends up into hypertension/stoke and heart failure. Also, the deposits of cholesterol on the arterial wall and proliferation of connective tissue are responsible for abnormal growth in the lumen of an artery. This work investigates the mathematical modelling of the effect of multistenosis in relation to shear stress, pressure gradient and viscosity of constricted human carotid arterial blood flow and its aftermath on the heart and general human health. The governing equations of blood flow in the human carotid artery were derived. The equations that were involved are the variables of interest such as number (n) of stenosis, percentage of Hematocrit (H) of red blood cels in the blood and the length (z) of the artery. Guided by medical data collected in the constraint of blood flow in a stenosed human carotid arteries, the governing equations were used to check the effects of pressure gradients, wall shear stress, velocity and volumetric flow rate of blood in human carotid arteries with the help of the boundary conditions. Observations revealed that; as Hematocrit and viscosity increase, the arterial wall shear stress decreases, an indication of increase in human heart pressure. However, increase in Hematocrit (H) and the length of the artery (z = 1) is inversely proportional to the arterial wall shear stress, this signifies the damage of veins around the arteries. The blood pressure gradient increases, which is directly proportional to the length of the artery (z) and Hematocrit, this suggest clotting of blood in human heart which can lead to death.