Journal of Mechanical Science and Technology 23 (2009) 1650~1669 www.springerlink.com/content/1738-494x DOI 10.1007/s12206-009-0355-y Journal of Mechanical Science and Technology Two -fluid nonlinear mathematical model for pulsatile blood flow through catheterized arteries † D. S. Sankar and Usik Lee * Department of Mechanical Engineering, Inha University, 253 Yonghyun-Dong, Nam-Gu, Incheon 402-751, Republic of Korea (Currently working at the School of Mathematical Sciences, University Science Malaysia, 11800 Penang, Malaysia) (Manuscript Received February 25, 2008; Revised October 8, 2008; Accepted February 25, 2009) -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Abstract The pulsatile flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a Herschel-Bulkley fluid and the peripheral region of plasma as a Newtonian fluid. The resulting system of the nonlinear implicit system of partial differential equations is solved by perturbation method. The expressions for shear stress, velocity, flow rate, wall shear stress and longitudinal impedance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio, amplitude, pulsatile Rey- nolds number ratio and peripheral layer thickness are discussed. The velocity and flow rate are observed to decrease, and the wall shear stress and resistance to flow increase when the yield stress increases. The plug flow velocity and flow rate decrease, and the longitudinal impedance increases when the catheter radius ratio increases. The velocity and flow rate increase while the wall shear stress and longitudinal impedance decrease with the increase of the peripheral layer thickness. The estimates of the increase in the longitudinal impedance are significantly lower for the present two- fluid model than those of the single-fluid model. Keywords: Two-fluid model; Herschel-bulkley fluid; Newtonian fluid; Pulsatile flow; Catheterized artery; Longitudinal impedance -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction Catheters are used extensively in modern medicine. Typically, a catheter consists of a long flexible cylin- drical tube at the tip of which various functional tools (pressure transducers, flow meters, inflatable balloons, etc.) are positioned. The purpose of catheters is to accurately measure the arterial pressure or pressure gradient, or to clear short occlusions from the walls of the stenosed artery [1]. The method of catheterization is to insert the catheter-tool device into a peripheral artery and then position the device in the desired part of the arterial network by passing an appropriate length of the catheter through the artery [2]. The in- sertion of a catheter into an artery leads to the forma- tion of an annular region between the catheter wall and the arterial wall. The insertion of a catheter into an artery alters the flow field, modifies the pressure distribution and hence increases the resistance to flow [3]. Thus, the pressure or pressure gradient recorded by a transducer attached to the catheter will differ from that of an uncatheterized artery and hence, it is essential to know the catheter-induced error [4]. Back [5] and Back et al. [6] have studied the im- portant hemodynamic characteristics like the wall shear stress, pressure drop and frictional resistance in catheterized coronary arteries under the normal and pathological situation of a stenosis present. The effect of catheterization on various flow quantities in a curved artery is studied by Karahalios [7] and Jayaraman and Tiwari [8]. Daripa and Dash [1] have performed a numerical study of pulsatile blood flow in an eccentric catheterized artery using a fast algo- †This paper was recommended for publication in revised form by Associate Editor Gihun Son * Corresponding author. Tel.: +82 32 860 7318, Fax.: +82 32 866 1434 E-mail address: ulee@inha.ac.kr (U. Lee) © KSME & Springer 2009