Journal of Mechanics in Medicine and Biology Vol. 8, No. 3 (2008) 395–420 c  World Scientiﬁc Publishing Company UNSTEADY RESPONSE OF BLOOD FLOW THROUGH A COUPLE OF IRREGULAR ARTERIAL CONSTRICTIONS TO BODY ACCELERATION NORZIEHA MUSTAPHA ∗ , SANTABRATA CHAKRAVARTY † , PRASHANTA K. MANDAL †,‡ and NORSARAHAIDA AMIN ∗ ∗ Department of Mathematics, Faculty of Science Universiti Teknologi Malaysia, Skudai, Johor, Malaysia † Department of Mathematics, Visva-Bharati University Santiniketan, West Bengal, India ‡ pkmind02@yahoo.co.uk Received 15 December 2007 Accepted 25 December 2007 A two-dimensional (2D) nonlinear mathematical model to study the response of the pulsatile ﬂow of blood through a couple of irregular stenoses inﬂuenced by externally imposed periodic body acceleration is developed. The model is 2D and axisymmetric with an outline of the stenosis obtained from the three-dimensional (3D) casting of a mildly stenosed artery. The combined inﬂuence of an asymmetric shape and surface irregularities of the constrictions is explored in a computational study of blood ﬂow through arterial stenoses with 48% areal occlusion. The arterial wall is treated as an elastic (moving wall) cylindrical tube having a couple of stenoses in its lumen, while the streaming blood is considered to be Newtonian. Solutions of the time-dependent non- linear Navier–Stokes equations in the cylindrical coordinate system are obtained using a ﬁnite diﬀerence method based on the nonuniform and nonstaggered grids. The ﬁnite diﬀerence approximation helps to estimate the eﬀects of body acceleration on the doubly constricted ﬂow phenomena through several graphical representations quantitatively in order to validate the applicability of the present, improved mathematical model. Keywords : Multiple stenoses; Navier–Stokes equations; ﬁnite diﬀerence scheme; body acceleration; moving wall. 1. Introduction Atherosclerosis is an arterial disease caused by intravascular plaques leading to malfunction of the cardiovascular system, and is of major concern to most of the Western world. Such plaques or arterial constrictions usually disturb normal blood ﬂow through the artery, and there is considerable evidence that hydrodynamic factors can play a signiﬁcant role in the development and progression of these lesions. It has been established that once a mild stenosis is developed inside the ‡ Corresponding author. 395