Physiological flow analysis in significant human coronary artery stenoses

Article type: Research Article

Authors: Banerjee, Rupak K.^; | Back, Lloyd H. | Back, Martin R. | Cho, Young I.

Affiliations: Department of Mechanical, Industrial and Nuclear Engineering, University of Cincinnati, Cincinnati, OH, USA | Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA | Division of Vascular & Endovascular Surgery, University of South Florida, College of Medicine, Tampa, FL, USA | Mechanical Engineering and Mechanics Department, Drexel University, Philadelphia, PA, USA

Note: [] Address for correspondence: R.K. Banerjee, Dept. of Mechanical, Industrial and Nuclear Engineering, 598 Rhodes Hall, PO Box 210072, Cincinnati, OH 45221‐0072, USA. Tel.: +1 513 556 2124; Fax: +1 513 556 3390; E‐mail: [email protected].

Abstract: To evaluate the local hemodynamics in flow limiting coronary lesions, computational hemodynamics was applied to a group of patients previously reported by Wilson et al. (1988) with representative pre‐angioplasty stenosis geometry (minimal lesion size dm=0.95 mm; 68% mean diameter stenosis) and with measured values of coronary flow reserve (CFR) in the abnormal range (2.3±0.1). The computations were at mean flow rates ($\widetilde{Q}$) of 50, 75 and 100 ml/min (the limit of our converged calculations). Computed mean pressure drops Δ$\tilde{p}$ were ∼9 mmHg for basal flow (50 ml/min), ∼27 mmHg for elevated flow (100 ml/min) and increased to an extrapolated value of ∼34 mmHg for hyperemic flow (115 ml/min), which led to a distal mean coronary pressure $\tilde{p}$rh of ∼55 mmHg, a level known to cause ischemia in the subendocardium (Brown et al., 1984), and consistent with the occurrence of angina in the patients. Relatively high levels of wall shear stress were computed in the narrow throat region and ranged from about 600 to 1500 dyn/cm2, with periodic (phase shifted) peak systolic values of about 3500 dyn/cm2. In the distal vessel, the interaction between the separated shear layer wave, convected downstream by the core flow, and the wall shear layer flow, led to the formation of vortical flow cells along the distal vessel wall during the systolic phase where Reynolds numbers Ree(t) were higher. During the phasic vortical mode observed at both basal and elevated mean flow rates, wide variations in distal wall shear stress occurred, distal transmural pressures were depressed below throat levels, and pressure recovery was larger farther along the distal vessel. Along the constriction (convergent) and throat segments of the lesion the pulsatile flow field was principally quasi‐steady before flow separation occurred. The flow regimes were complex in the narrow mean flow Reynolds number range $\widetilde{\mathrm{R}}$ee=100–230 and a frequency parameter of αe=2.25. The shear layer flow disturbances diminished in strength due to viscous damping along the distal vessel at these relatively low values of $\widetilde{\mathrm{R}}$ee, typical of flow through diseased epicardial coronary vessels. The distal hyperemic flow field was likely to be in an early stage of turbulent flow development during the peak systolic phase.

Journal: Biorheology, vol. 40, no. 4, pp. 451-476, 2003