Journal of Mechanical Science and Technology 22 (2008) 1008~1018 www.springerlink.com/content/1738-494x Journal of Mechanical Science and Technology Two-fluid Herschel-Bulkley model for blood flow in catheterized arteries D. S. Sankar 1 and Usik Lee 2,* 1 Department of Mechanical Engineering, Inha University, Incheon 402-751, Republic of Korea (Presently on leave from Department of Mathematics, B. S. A. Crescent Engineering College, Vandalur, Chennai-48, India) 2 Department of Mechanical Engineering, Inha University, 253 Yonghyun-Dong, Nam-Gu, Incheon 402-751, Republic of Korea (Manuscript Received February 25, 2007; Revised October 29, 2007; Accepted January 30, 2008) -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Abstract The steady flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the core region of suspension of all the erythrocytes as a Herschel-Bulkley fluid and the peripheral region of plasma as a Newtonian fluid. The expressions for velocity, flow rate, wall shear stress and frictional resistance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio and peripheral layer thickness are discussed. It is observed that the velocity and flow rate decrease while the wall shear stress and resistance to flow increase when the yield stress or the catheter radius ratio increases when all the other parameters held constant. It is noticed that the velocity and flow rate increase while the wall shear stress and frictional resistance decrease with the increase of the peripheral layer thickness. The estimates of the increase in the frictional resistance are significantly much smaller for the present two-fluid model than those of the single-fluid model. Keywords: Two-fluid model; Steady blood flow; Catheterized artery; Herschel-Bulkley fluid; Newtonian fluid -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction With the evolution of the medical technology, catheters play a pivotal role in the modern medicine. In clinical studies, the measurement of various physiological flow quantities (such as arterial blood pressure or pressure gradient and flow velocity or flow rate) as well as the diagnosis and treatment of various arterial diseases (such as X-ray angiography, intravascular ultrasound and coronary balloon angio- plasty) are done by an appropriate catheter-tool device by inserting it into an artery and positioning it in the desired part of the arterial network [1]. Catheters are even used to clear the short occlusions from the walls of the stenosed artery. The insertion of a catheter in an artery will alter the flow field, modify the pressure distribution and hence increase the flow resistance. Thus, the pressure or pressure gradient recorded by a transducer attached to the catheter will differ from that of an uncatheterized artery and it is essential to know the catheter-induced error [2]. Even, a very small angioplasty guidewire leads to a sizable increase in flow resistance. For an angioplasty guide- wire, over the range of catheter radius ratio (ratio of catheter radius to coronary vessel radius) from 0.3 to 0.7 (which is currently used clinically), even for New- tonian fluid, the flow resistance increases by a large factor of 3-33 for concentric configurations [3]. For smaller infusion catheters, the flow resistance in- crease is less, although still appreciable. Therefore, it is meaningful to study the increase in flow resistance due to catheterization. There have been several theoretical and experi- mental attempts to study the blood flow through catheterized arteries [1-8]. Back [3] and Back et al. [6] studied important hemodynamic characteristics like wall shear stress, pressure drop and frictional resistance in catheterized coronary arteries under a normal as well as a pathological situation of a stenosis present. The effect of catheterization on various flow characteristics in a curved artery was studied by * Corresponding author. Tel.: +82 32 860 7318, Fax.: +82 32 866 1434 E-mail address: ulee@inha.ac.kr DOI 10.1007/s12206-008-0123-4