Analysis of physiological pulsating flow of fractional Maxwell fluid in a locally narrow artery

The purpose of this paper is to provide a novel reference for the early diagnosis and treatment of atherosclerosis. Two-dimensional governing equations of fractional-order Maxwell fluid flow in a local stenotic artery are established, taking real physiological pulsating blood flow at inlet into consideration. Drawing support from the finite difference method as well as the L1 formula, vorticity and stream functions are introduced to acquire numerical solutions for velocity, stream function, and pressure. The distribution of blood flow in narrowed arteries within a real physiological pulse cycle is discussed. Furthermore, the influences of the degree of stenosis delta, the stenosis length parameter L0, fractional order parameter alpha, and relaxation time lambda on crucial medical indicators, including the time average of the wall shear stress, oscillatory shear index, relative residence time, and pressure distribution are revealed. The results show that the deceleration and reversal phases of real physiological pulsatile flow critically affect the progression of arterial stenosis, and increasing the fractional order parameter alpha weakens the development of stenosis, while increasing lambda has the opposite effect. This study is expected to serve as a reference for formulating standards of key medical indicators in the early diagnosis of vascular stenosis.