Track 14. Cardiovascular Mechanics 14.7 Coronary Circulation $613

14.7 Coronary Circulation 6855 Mo-Tu, no. 42 (P65) Validation of the numerical coronary flow simulation through LDA-measurements L. Goubergrits 1 , EO. Bartz 2, Ch.N. Nayeri 2, C.O. Paschereit 2, U. Kertzscher 1 , K. Affeld 1 . 1Biofluidmechanics Lab, Charit~ - Universit&tsmedizin Berlin, Germany, 2 Hermann-F6ttinger Institut, TU Berlin, Germany

Assessing flow parameters, especially the distribution of the wall shear stress, in arteries is extremely important for the analysis of pathological changes in the vessel wall (e.g. atherosclerosis), as well as for the investigation of the atherosclerotic lesions genesis. Numerical flow simulations using realistic clinical data (e.g. MRI, angiography, CT) could be very helpful or even the only possible research method for clinically relevant studies. A fundamental or preliminary question is to validate the numerical flow computations. In this study, two 2.5-fold enlarged models of the left coronary vessel made of transparent silicon rubber were used to validate the flow computations. The first model is a simplified model of the main bifurcation of the left coronary artery generated according to the literature data. The second model was produced on the basis of a real vessel cast. Numerically, the flow was simulated with the program FLUENT6 (Fluent Inc., USA) under the same boundary conditions as the experimental tests. Initially, the mesh independence of the solution was examined. The results show that in order to ascertain the near wall flow and the wall shear stress correctly a very high near wall mesh resolution is needed (at least 1/1000 th of the vessel diameter). Experimentally, the stationary and pulsatile flows in both models were measured at six separate cross-sections with the help of a two-component-LDA-system from the firm DANTEC. A glycerine/water mixture was used for the adjustment of the silicone refraction index n = 1.4. The resulting kinematic viscosity of the mixture at a room temperature of 23°C was 3.55 10 -6 m2/s. The velocity profiles were then compared to the numerical results. The results showed a very good correlation between experimental and numerical results with a mean deviation of about 5%.

6839 Mo-Tu, no. 43 (P65) Wall shear stress prof i l ing o f the coronary flow: choosing a parameter of f low characterization L. Goubergrits 1 , E. Wellnhofer 2, U. Kertzscher 1 , K. Affeld 1 . 1Biofluid Mechanics Laboratory, Charit~-Universit~tsmedizin Berlin, Germany, 2 German Heart Institute of Berlin, Berlin, Germany

Clinical studies suggest that local wall shear stress (WSS) patterns influence the site and the progression of atherosclerotic lesions. Computational fluid dynamics methods based on in-vivo three-dimensional (3D) vessel reconstruc- tions have been recently shown to provide prognostically relevant WSS data. One of the questions that have to be solved for such studies is - Which method or parameters may be used for WSS characterisation? The method should allow a comparison between different vessels with different geometries. Differ- ent geometries imply that a point by point comparison between two different WSS distributions is not feasible. Mean values are not sufficient to characterize complex WSS patterns. We propose to generate distribution histograms to quantify differences between resulting WSS distributions,. The whole range of calculated wall shear stress values is divided into 100 classes. For each class the area with respect to the WSS range is calculated and normalized as percent of the total wall surface area. Cross-correlations and Chi-square tests may be used to compare these distribution histograms. Furthermore, histograms may be characterized by mean and peak values, median and skew. This method of WSS characterization was applied to three different right coronary arteries: one normal coronary artery, one with "obstructive" and one with "dilated" coronary atherosclerosis were compared. The geometries were reconstructed from a previously validated angiographic 3D reconstruction. The numerical solution of Navier-Stokes equations governing the fluid motion under defined boundary conditions was solved in FLUENT 6 (Fluent Inc., USA). The results show that WSS histograms within whole segments or vessels might identify different patterns of remodeling associated with characteristic changes in the distribution of WSS and quantify the extent and diffuseness of coronary artery disease.

6397 Mo-Tu, no. 44 (P65) Hemodynamic effects of a distal high-grade stenosis on a vulnerable plaque Z. Aronis, S. Einav. Biomedical Engineering Department, TeI-Aviv University, Tel Aviv, Israel

Vulnerable atherosclerotic plaques (VP), defined as low-grade stenoses with rich inflamed lipid cores and thin fibrous caps, are assumed to cause about 80% of deadly myocardial infarctions (MI). Angioscopic finding show that in

MI patients all three major coronary arteries are widely diseased and have multiple nondisrupted plaques. What causes some plaques to rupture while other stay intact is still unknown. In previous studies a high prevalence of rupture sites existed proximal to the minimum lumen area, which raised the question weather the existence of two distinct adjacent plaques, from which the distal plaque causes a higher narrowing, may give rise to hemodynamic forces that will push the non-stenotic plaque to rupture. Models of the coronary arteries with one and two eccentric and concentric stenotic narrowings were connected to a closed flow loop. The single stenosis model consisted of a 75% area reduction narrowing (representing the VP) with relevant elastic properties, and the double stenoses models included an additional distal 84% area reduction narrowing. The flow in the area between the two stenoses was recorded and analyzed using CDPIV, and the hydrostatic pressure acting on the proximal plaque was measured. Results show that compared to a single stenosis model, higher flow oscillations exist on the distal shoulder of the VP, accompanied by high wall shear stress temporal gradients, in an eccentric double-stenotic model. Higher maximal pressures and higher pressure drop were also measured on the VP with the distal high-grade stenosis, as the total pressure rise was in the order of 15mmHg. The combined shear rates and pressure effects in a model with a significant distal stenosis can contribute to the increase in plaque instability by LDL and macrophages' enhanced uptake, resulting from the highly oscillatory nature of the disturbed flow near the shoulder of the VP, thus enriching its lipid soft core, and the higher hydrostatic pressures applied on the same lesion in this geometry can induce high internal maximal stresses that may trigger the rupture of the plaque.

6850 Mo-Tu, no. 45 (P65) Pulse wave propagation in blood vessels: theoretical investigation and clinical applications

I. Barbieri 1 , G. Belmonte 1 , L. Coli 2, G. Donati 2, G.L. Gardini 3, G. Pallotti 1 , P. Pettazzoni 1 , D. Salcito 3, I. Selezov 4, A. Tedesco 3, O. Zvonareva 5. 1Faculty of Medicine and Surgery, University of Bologna "Alma Mater Studiorum", Bologna, Italy, 2 Nephrology Dyalisis and Renal Transplantation Unit, S.Orsola Hospital, Bologna, Italy, 3Villa Torri Hospital, Bologna, Italy, 4Department of Wave Process, Institute of Hydrodynamics NASU, Kiev, Ukraine, 5 Transport University, Dnepropetrovsk, Ukraine

A general investigation of the heart pulse propagation in blood vessel as been done and this research has been conducted for the blood flow in physiological conditions; then also the problems connected to new surgical techniques and also necessary in the organs transplantations. In particular in the presence of insertion at some distance from the input is investigated and also the effects of the connection of vascular segments with different mechanical properties increses the risk of generation of blood turbolence fluxes and involves, in the arterial vessels. The development of complications such as artherosclerosis and stenotic process have been considered. It is assumed that the vessel material has of great arteries has the following mechanical properties: viscoelasticity with the presence of a Coulombian resistence, while the blood is a viscoelastic fluid. Therefore mechanical models of cardiovascular system have been studied and the effects considered in clinical applications.

4714 Mo-Tu, no. 46 (P65) Comparison of flow and wall shear stress in normal and stenotic coronary arteries

R. Torii 1 , A. Dowsey 2, N. Wood 1 , G.-Z. Yang 2, A. Hughes 3, A. Wright 4, D. Firmin 5, S. Thom 3, X.'~ Xu 1 . 1Department of Chemical Engineering, 2Department of Computing, 3Department of NHLI, International Centre for Circulatory Health, 4Department of Radiology, St Mary's Hospital, 5National Heart and Lung Institute, CMR Unit, Royal Brompton Hospital, Imperial College London, UK

The mechanisms linking haemodynamics to atherogenesis have been studied for many years, providing evidence for the role of wall shear stress (WSS) [1,2]. Although a number of studies have been carried out on coronary blood flow [3, 4], comparisons between disease-free and stenotic coronary arteries are sparse [5]. We aim to gain better understanding of the effects of atherosclerotic lesions on coronary haemodynamics by comparing flow patterns and resulting WSS for both lesion-free and atherosclerotic arteries. The right coronary arter- ies (RCA) of three subjects were examined in this study, one RCA was lesion- free while the other two had stenoses. Subject-specific coronary geometries were reconstructed based on CT images and geometries corresponding to a diastolic phase were used in flow simulations. Pulsatile velocity profiles derived from a waveform measured with a Doppler flow wire in a RCA were applied as the inlet boundary condition for all subjects. Results show that WSS in the stenosed arteries was considerably lower than 1 Pa in the post-stenotic zone,

$614 Journal of Biomechanics 2006, Vol. 39 (Suppl 1) Poster Presentations

i.e. below the lower limit in normal physiological conditions [1, 2], resulting from flow separation and recirculation. Studies suggest that WSS < 0.4 Pa may be considered atherogenic [2]. In contrast, WSS for the lesion-free artery was mostly larger than 1 Pa for the entire luminal wall. Our finding that stenoses tend to produce low WSS distally implies that the lesions are likely to develop further in the post-stenotic regions.

References [1] Caro CG, et al. Proc R Soc Lond. 1971; B177: 109-159. [2] Malek AM, et al. JAMA 1999; 282: 2035-2042. [3] Zeng D, et al. Ann Biomed Eng. 2003; 31: 420-429. [4] Krams R, et al. Arterioscler Thromb Vasc Biol. 1997; 17: 2061-2065. [5] Wentzel JJ et al. J Biomech. 2005; 38: 1551-1555.

probably related to the closure of the aortic valve, also increases coronary flow. Wave timings differ at different sites in the coronary tree, revealing the com- plexity of wave propagation. Their mapping gives a fairly complete picture of wave travel in the coronary network and insight into the physiology of coronary artery flow in health and disease [2].

References [1] Sun YH, et al. Wave-intensity analysis: a new approach to coronary haemody-

namics. J Appl Physiol 2000 October; 89: 1636-44. [2] Davies JE, et al. Evidence of a dominant backward-propagating "suction" wave,

responsible for diastolic coronary filling in humans, attenuated in left ventricular hypertrophy. Circulation, accepted 2006.

4564 Mo-Tu, no. 47 (P65) Analysis of non-newtonian blood flow in symmetric consecutive constriction artery M. Navidbakhsh, Z. Rahmdel, M. Khalilian. Biomech. Lab, University of Science and Technology, Tehran, Iran

The hemodynamics behavior of the blood flow is influenced by the presence of the arterial stenosis. If the stenosis appears in an artery, normal blood flow will be disturbed, in this study, the characteristics of steady state laminar flow in the blood vessel with two stenosis with different degrees of occlusions are investigated by the finite volume method. For this purpose some available researches with different characteristics of blood flow and geometry of blood vessel structure have been studied. Since stenosis severity below 50% is considered as mild type in this disease, the effect of stenosis severity above 50% have been investigated in most of which, results which obtained from these researches can definitely led to better understanding of the flow disturbance induced by a stenosis and better decision for finding the best solution for curing this kind of disease, which is leading cause of death in many countries. Few angiographic films show more than one constrictions along one coronary artery but unfortunately not so many investigations are available in this area, due to this fact blood flow characteristics in presence of two constrictions will be discussed in this study. Occlusion rate in same situation for the both constric- tions in the range of 30% to 60% of diameter has been considered.Of course these specifications do not obey from a general rule and will differ in each patient comparing to another. Following assumptions have been considered: Laminar, steady state, Non-Newtonian complex rheological behavior of blood by Casson's model, Two dimensional asymmetric structures for blood vessels. Wall shear stress distributions for all models are presented. The results have demonstrated that shear stress distributions in second constriction are very complex.

5400 Mo-Tu, no. 48 (P65) Coronary haemodynamics in humans using wave intensity analysis

J. Aguado-Sierra 1 , J.E. Davies 2, D.P. Francis 2, Z.I. Whinnett 2, C.H. Manisty 2, K. Willson 3, R.A. Foale 2, I.S. Malik 2, A.D. Hughes 1,2, J. Mayet 2, K.H. Parker 1 . 1PFSG, Department of Bioengineering, 2International Centre for Circulatory Health and St Mary's Hospital, 3Clinical Engineering, Royal Brompton Hospital, Imperial College London, UK

Pressure and velocity data were measured simultaneously at different locations in coronaries of patients undergoing angiography. Wave intensity analysis is used to separate forward and backward waves [1]. This requires knowledge of the local wave speed (c) which is determined from the data using a new algorithm

f~ T= 0 dP 2 Pc= ' ~T=0dU 2'

where dP and dU are pressure and velocity changes between samples summed over one cardiac period (T) and # is density. A sequence of six predominant waves were identified [2]: three associated with ventricular contraction and three with relaxation. In early systole, a backward deceleration wave is generated by the myocardium squeezing the coronary microcirculation. This wave is followed by a forward acceleration wave from the aorta generated by the increase in ventricular pressure. Later in systole a backward deceleration wave results from combined effects of reflections and continuing microvasculature compression. At end systole a forward decelera- tion wave, also seen in other systemic arteries, slows coronary flow. However the relaxation of the myocardium re-establishes coronary flow as the resistance in the microcirculation decreases, generating a backward acceleration wave. This wave is the dominant feature of coronary flow causing the high diastolic flow which is unique to coronary arteries. A final forward acceleration wave,

4460 Mo-Tu, no. 49 (P65) Anatomically-accurate modeling of coronary circulation with dual-scale numerical solution scheme J. Lee, N. Smith. Bioengineering Institute, The University of Auckland, Auckland, New Zealand

There are two major challenges involved in computational modeling of coronary circulation. The first is in obtaining a detailed morphological structure of the vascular network, which is indispensable if one was to investigate the relationship between its form and function. The other difficulty arises from the fact that the problem involves multiple spatiotemporal scales, often to which the CFD solution method must be individually tailored. In this work, we have addressed these issues by combining anatomically-accurate geometries of coronary vasculature derived from high-quality medical images with efficient coupled dual-scale 1D Navier-Stokes solution scheme. Arterial and venous coronary vascular networks were fully reconstructed from micro-CT images scanned at 8~tm and 21 ~tm voxel resolution [1] using a custom-designed algorithm. The processed datasets include a full rat heart and transmural wedges of porcine cardiac tissue, to which different sized mi- crospheres had been injected. CFD meshes in centerline-radius representation were subsequently generated by extracting sub-networks of interest. Existing methods in solving network fluid flow employed an explicit finite differ- ence scheme on 1D axi-symmetric reduction of Navier-Stokes equations [2]. In this work, methodological extensions were made to account for smaller vessels (<200~tm diameter) in which the stability condition becomes too restrictive. Implicit finite difference technique was combined with Lagrangian multiplier method to yield a scheme that is highly compatible with the existing implementation. Coupling of the two schemes is achieved by overlapping the two domains partially and requires marginal additional computation. The combined approach was applied on the reconstructed meshes to determine regional perfusion distribution.

References [1] Beighley P., et al. 3D architecture of myocardial microcirculation in intact rat

heart: a study with micro-CT, in Analytical and Quantitative Cardiology. S. Sideman and R. Beyar, Editors. Plenum Press: New York. 1997; p. 165-175.

[2] Smith N., Pullan A., Hunter P. An anatomically-based model of transient coro- nary blood flow in the heart. SIAM Journal of Applied Mathematics 2002; 62: 990-1018.

5405 Mo-Tu, no. 50 (P65) The role of wave speed in wave intensity analysis: a sensitivity study in coronary arterial data J. Aguado-Sierra 1 , J. Davies 2, J. Mayet 2, D. Francis 2, A.D. Hughes 1,2, K.H. Parker 1 . 1PFSG, Department of Bioengineering, 2International Centre for Circulatory Health and St Mary's Hospital, Imperial College London, UK

Flow in arteries is established by elastic tube waves that propagate forward and backward carrying information about the state of the heart and peripheral vessels in the arterial network. One-dimensional equations of flow can be solved using the method of characteristics to describe the behaviour of these waves in the time domain [1]. Wave speed is directly related to arterial stiffness. When wave speed is known, the measured pressure and velocity waveforms can be separated into their forward and backward components. These provide information about the source of the waves and major apparent sites of reflections throughout the cardiac cycle. There are several different techniques for calculating wave speed: foot-to-foot, characteristic impedance, stiffness parameter (15) and PU-Ioop. However there is no 'gold standard' technique and some approaches are not applicable to the coronary arteries. We have compared these techniques with a new algorithm, the sum of squares (?2) method, which can be used to estimate coronary artery wave speed. The influence of errors in the determination of wave speed from simultaneous pressure and velocity data measured in human coronary arteries is explored using a sensitivity analysis. The calculated energy of forward and backward waves introduced by inaccuracies in wave speed are non-significant up to a ±30% misestimation of the wave speed, but at greater errors it is more