Mathematical study and simulation on stenosed carotid arteries with the help of a two-phase blood flow model

The present study is focused on a medical problem called stenosed carotid artery. The problem is formulated with the help of a two-phase blood flow model. The non-Newtonian nature of blood is considered that hold power law. Physical quantities were expressed in tensorial form. Analytical and numerical methods are used to solve equations under given boundary conditions. The effects of various parameters on blood flow like stenosis size, flow flux, resistance, haematocrit, pressure drop, etc. were studied and shown through various graphs. Parameter $k$, which ensures that the fluid is Newtonian or non-Newtonian; its impact on pressure drop; resistance to flow; and flow flux were obtained during the disease and presented through the graph. A relationship between pressure drop and haematocrit was obtained, which was helpful to predict fluctuation in blood flow during stenosis. We have also given a medical use for this model with the help of pathological data. We also analyzed steady and laminar flow in a carotid artery for different heights of stenosis. The study of various physiological parameters has been performed on the basis of blockage percentage and concentration of haematocrit. The nature of the red blood corpuscle (RBC) phase is considered liquid packets in a semi-permeable membrane, which makes this model close to reality.