Track 14. Cardiovascular Mechanics

5981 We, 09:30-09:45 (P28) Sensitivity of flow dynamics to reconstruction errors in systemic and coronary vessels ?. Radaelli, A. Gambarutto, K. Lee, S. Giordana, J. Peir6, D.J. Doorly, S.J. Sherwin. Bioflow Group, Department of Aeronautics, Imperial College London, UK

Advances in medical imaging have made anatomically accurate images of both arterial and coronary vessels possible which has necessarily promoted associated studies of the flow dynamics within these vessels. Although there are numerous examples of these types of reconstructions and simulations in the literature there is comparatively small amount of discussion on the inherent errors associated with these anatomical reconstructions and the sensitivity of the flow dynamics to these errors. We have therefore focused our recent research efforts in this area on addressing the issue of flow sensitivity to reconstruction errors. We have considered both gradient and standard thresholding image segmen- tation techniques to determine the vessel lumen. Subsequently we have used reconstruction techniques based on the use of an implicit surface interpolation to recover the closed lumen in a repeatable manner. Using this technology we have reconstructed geometries from MR images with both good and poor contrast-to-noise ratios, as well as considering phantom geometries of known dimensions, to study the influence of variations in the reconstruction parameters on both the geometric definition and the flow characteristics. The talk will present the application of this analysis of sensitivity to simulations of flows in systemic and coronary vessels.

4249 We, 11:00-11:30 (P31 ) Implications of 3D vascular geometry C. Caro, N. Cheshire, D. Ellis, M. Cerini, S. Cremers. Imperial College London, UK

The geometry of blood vessels influences their local blood flow pattern and, in turn, their biology and development of pathology. Arterial geometry is commonly three-dimensional (Caro et al, 2002; Ellis et al, 2005) and may be helical (Frazin et al, 1990). In vivo and model studies indicate that features of the associated flow include swirling, in-plane mixing, a relatively uniform dis- tribution of wall shear and residence times, and suppression of flow separation and flow instability. We report relevant studies, including flow in small amplitude helical (SMAHT) conduits. We report in addition, results obtained in a preliminary in vivo porcine study, in which common carotid-to-jugular vein shunts were created bilaterally (Caro et al, 2005); the shunt was a conventional ePTFE graft on one side and a SMAHT ePTFE graft on the other. There was markedly less thrombus and intimal hyperplasia with the SMAHT than conventional grafts. We attempt to interpret the findings in the light of continuing studies of the geometry, flow and biology, and consider the implications for cardiovascular interventions.

References Frazin L J, Lanza G, Vonesh M, et al. (1990). Functional chiral asymmetry in

descending thoracic aorta. Circulation 82, 1985-1994. Caro CG, Doorly D J, Tarnawski M, et al. (1996). Non-planar curvature and branch-

ing of arteries and non-planar-type flow. Proc. Roy. Soc. A. 452, 185-197. Caro CG, Cheshire NH, Watkins N (2005). Preliminary comparative study of small

amplitude helical and conventional ePTFE arteriovenous shunts in pigs. J. R. Soc. Interface 2: 261-266.

Ellis D, Cheshire N J, Caro CG (2005). Non-planar, tortuous coronary arteries are associated with favourable blood flow patterns: Implications for infra-inguinal and aortocoronary bypass grafts. (Submitted for presentation at Vascular Surgical Society of Great Britain and Ireland).

4202 We, 11:30-11:45 (P31 ) Asynchronous stretch and shear affect endothelial phenotype in the coronary arteries M. Dancu, J.M. Tarbell. Department of Biomedical Engineering, The City College of New York, New York, NY, USA

The proximal coronary arteries are exposed to a unique mechanical environ- ment because the cyclic mechanical strain induced by the pulse pressure is highly asynchronous with the wall shear stress driven by blood flow that is maximal during diastole when the pressure is minimal. Asynchronous circumferential strain and wall shear stress also occur in other disease prone regions of the circulation such as the carotid sinus. To determine the role of this asynchronous mechanical environment on endothelial cell phenotype, we exposed bovine aortic endothelial cells (BAECs) plated on the inner surface of elastic tubes to a highly asynchronous mechanical environment characteristic of coronary arteries, and we observed a significant inhibition of eNOS and enhancement of ET-1 gene expression relative to companion synchronous controls that would suggest a pathologic phenotype induced by asynchronous forces. To look for this phenotype in vivo, cells were extracted from the coronary

14.7. Coronary Circulation $299

LAD artery (asynchronous) and the descending thoracic aorta (synchronous) of rabbits and analyzed for expression of the same genes. Indeed, eNOS was significantly suppressed and ET-1 significantly enhanced in the LAD compared to the aorta, suggesting a unique EC phenotype in the LAD that was similar to that observed in BAECs exposed to asynchronous mechanical forces in vitro. To assess the wall shear stress environment in vivo, we stained EC nuclei to observe whether they were elongated and aligned in the principal flow (shear) direction. Nuclear elongation and alignment were indistinguishable between the LAD and aorta, but these were both different from nuclei around the ostia of an intercostal artery where flow is known to be disturbed. Therefore, we conclude that the unique phenotype displayed by the coronary LAD is driven by asynchronous flow, not disturbed flow.

4845 We, 11:45-12:00 (P31) Mathematical modelling of coronary artery blood flow

S.L. Waters, J.H. Siggers. Division of Applied Mathematics, University of Nottingham, University Park, Nottingham, UK

The most common arterial disease, atherosclerosis, is particularly prevalent in the coronary arteries. The distribution of atherosclerotic plaques, which characterise the disease, is correlated with regions of low mean wall shear stress (WSS) and regions where the WSS changes direction during the cardiac cycle. The coronary arteries are situated on the surface of the beating heart or penetrate the muscular heart wall and hence their geometry, represented by the curvature and torsion of the vessel's centreline, as well as its diameter and length, varies substantially with time as the heart beats. This study addresses the effect that the coronary artery curvature and motion have on the WSS distribution and the development of atherosclerosis. We develop and solve an idealized mathematical model, in which the artery is modelled as a pipe with constant circular cross-section of radius a, having a centreline lying on an arc of a circle of radius R. The curvature is finite, in contrast to many previous studies that assumed it to be asymptotically small, and varies sinusoidally with time. The blood is modelled as a Newtonian viscous fluid driven by a pulsatile axial pressure gradient. The frequency of the pressure gradient and the curvature oscillations are equal. The model solution indicates that in certain parameter regimes, curved pipes with finite, time-dependent curvature exhibit a qualitatively different solution structure from curved pipes with asymptotically small time-dependent curva- ture. Furthermore, differences in curvature can lead to substantial quantitative differences in the WSS distribution. The physiological implications of these results to coronary artery blood flow will be discussed.

5860 We, 12:00-12:15 (P31) Unstructured cartesian sharp-interface computational method for flow simulations in realistic cardiovascular anatomies D. de Zelicourt 1 , C. Wang 1 , F. Sotiropoulos 2, A. Yoganathan 1 . 1Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA, 2Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN, USA

A major challenge in numerical simulations of blood flow in realistic cardio- vascular anatomies stems from the arbitrary geometrical complexity of such configurations. Surgically generated, junction-like configurations in bypass- type surgical procedures, for instance, involve multiple blood vessels of very complex cross-sectional shape and longitudinal curvature intersecting each other at arbitrary angles to form very complex, multi-connected geometries. Unstructured grids with finite-element solvers provide a natural choice for simulating flows in such geometries. Such solvers, however, are cumbersome to implement and they are considerably more expensive than finite-difference methods on Cartesian grids. In Cartesian methods the arbitrary geometri- cal complexity can be handled using immersed-interface type algorithms in conjunction with sharp-interface, reconstruction techniques. A major limitation of such techniques, however, is that often the majority of the grid nodes of the background Cartesian mesh within which the anatomical geometry is immersed end up lying outside the computational domain. Such nodes increase significantly the memory and computational overhead of the code without enhancing numerical resolution in the region of interest. To remedy this situation, we have developed a novel computational framework that combines the versatility of unstructured grids with the simplicity and computational efficiency of a Cartesian grid solver. To demonstrate the capabilities of the method we apply it to simulate several benchmark cases involving junction- like configurations of simple shape. We also apply the method to simulate unsteady flow in realistic total cavo-pulmonary connection (TCPC) anatomies and the computed results are shown to agree well with PIV measurements. Supported by a grant from the National Heart, Lung, and Blood Institute, HL67622.