Rheologica Acta Rheol Acta 27:418-427 (1988) Response of blood flow through an artery under stenotic conditions S. Chakravarty and A. Ghosh Chowdhury Department of Mathematics, Visva-Bharati University, Santiniketan (India) Abstract: This paper presents an analytical study on the behavoiur of blood flow in an artery having a stenosis. This is basically formulated through the use of a suitable mathematical model. The arterial segment under consideration is simulated by an anisotropically elastic cylindrical tube filled with a viscous incompressible fluid repre- senting blood. The analysis is carried out for an artery with mild local narrowing in its lumen forming a stenosis. Particular emphasis has been paid to the effect of the surrounding connective tissues on the motion of the arterial wall. Blood is treated as a Newtonian fluid. The analysis is restricted to propagation of small amplitude harmonic waves, generated due to the flow of blood whose wave length is large compared to the radius of the arterial segment. The effect of the shape of stenosis on the resistance to blood flow has been well illustrated quantitatively through numerical computations of the resulting expressions. A quantitative analysis is also made for the variation of the phase velocity, as well as the velocity of wave propagation and the flow rate, in order to illustrate the applicability of the model. Key words: _Bloodflow, _artery, stenosis, _elasticcylindrical tube 1. Introduction In recent years quite a few analytical and experimental investigations with different perspectives related to blood flow have already been carried out. Major attention has been focused in this specific area of Biomechanics with the advent of the discovery that many cardiovascular diseases viz. atherosclerosis, atherogenesis, atheroma etc. are closely associated with the flow conditions in the blood vessels. The deposit of cholesterol and prolifera- tion of connective tissues in the arterial wall form plaques which grow inward and restrict the blood flow. This causes the appearance of atherosclerosis, a very common disease of advanced age, and may lead to cerebral throm- bosis, myocardial infarction, angina pectoris etc. Thus the presence of stenosis, the coarctation of the aorta in the arterial lumen, is solely responsible for the cause of such diseases. In order to have a fuller understanding of the development of these diseases, an accurate knowledge of the mechanical properties of the vascular wall together with the flow characteristics of blood are indispensable. Thus relevant information is deemed to be of great help in the treatment of vascular diseases and also to bioen- gineers who are engaged in the design and construction of improved artificial organs. 285 Perhaps the actual cause of abnormal growth in an artery is not completely clear to the theoretical investigators but its effect over the cardiovascular system has been determined by studying the flow characteristics of blood in the stenosed area. Although the applicability of a purely mechanical model for such a phy- siological problem has obvious limitations, vascular rheology to- gether with haemodynamic factors are predominant in the devel- opment and progression of arterial stenosis. An attempt towards a systematic study of the flow around a stenosis seems to have been started by Young [I]. Fry [2] pointed out from his study of fluid mechanics in arteries that endothelial wall deterioration and growth is closely related to the shear stress acting on the vascular wall. The effects of flow separation were examined by Forrester and Young [3] as well as by Lee and Funs [4]. Young and Tsai [5] performed an experiment on the models of arterial stenoses by considering the steady flow of blood and reported that the hydrodynamic factors play a significant role in the development and progression of the arterial stenosis. Several researchers (cf. Young [61, Morgan and Young [7], Deshpande et al. [8], Perkkio and Keskinen [9]) have studied analyticallythe flow characteristics of blood in an artery with mild stenosis while the fluid representing blood has been considered to be Newtoni- an. Although blood shows a non-Newtonian behaviour at low shear rates in tubes of smaller diameters (cf. Hershey et al. [10], Hucaba et al. [11], Merrill [12], Charm and Kurland [13], Whit- more [14], Hart and Barnett [15]), but at high shear rates, com- monly found in the larger arteries (above 1 mm in diameter), blood behaves like a Newtonian fluid as reported by Taylor [16]. Many other investigators carried out a good number of theoret- ical studies on various aspects of wall deformation and blood