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Determination of in vivo velocity and endothelial shear stress patterns with phasic flow in human coronary arteries: A methodology to predict progression of coronary atherosclerosis
Progress in Cardiology
Determination of in vivo velocity and endothelial shear stress patterns with phasic flow in human coronary arteries: A methodology to predict progression of coronary atherosclerosis Charles L. Feldman, ScD,a Olusegun J. Ilegbusi, PhD,b Zhenjun Hu, PhD,b Richard Nesto, MD,c Sergio Waxman, MD,c and Peter H. Stone, MDa Boston, Mass
Background Although the coronary arteries are equally exposed to systemic risk factors, coronary atherosclerosis is focal and eccentric, and each lesion evolves in an independent manner. Variations in shear stress elicit markedly different humoral, metabolic, and structural responses in endothelial cells. Areas of low shear stress promote atherosclerosis, whereas areas of high shear stress prevent atherosclerosis. Characterization of the shear stresses affecting coronary arteries in humans in vivo may permit prediction of progression of coronary disease, prediction of which plaques might become vulnerable to rupture, and prediction of sites of restenosis after percutaneous coronary intervention.
Methods To determine endothelial shear stress, the 3-dimensional anatomy of a segment of the right coronary artery was determined immediately after directional atherectomy by use of a combination of intracoronary ultrasound and biplane coronary angiography. The geometry of the segment was represented in curvilinear coordinates and a computational fluid dynamics technique was used to investigate the detailed phasic velocity profile and shear stress distribution. The results were analyzed with several conventional indicators and one novel indicator of disturbed flow. Results Our methodology identified areas of minor flow reversals, significant swirling, and large variations of local velocity and shear stress—temporally, axially, and cirumferentially—within the artery, even in the absence of significant luminal obstruction.
Conclusions We have described a system that permits, for the first time, the in vivo determination of pulsatile local velocity patterns and endothelial shear stress in the human coronary arteries. The flow phenomena exhibit characteristics consistent with the focal nature of atherogenesis and restenosis. (Am Heart J 2002;143:931-9.) Local hemodynamic factors, especially alterations of arterial wall shear stress, have an enormous impact on endothelial function and atherogenesis.1,2 The local nature of atherosclerosis is underscored by the observations that within each patient, each coronary obstruction progresses or regresses in an entirely independent manner, including regions subjected to percutaneous revascularization.3,4 Mechanical stresses are transmitted to the vascular wall as a combination of compressive pressure forces, tensile stretch forces, and tangential frictional (or shear) stresses.5 Mechani-
From the aCardiovascular Division, Brigham and Women’s Hospital, the bDepartment of Mechanical, Industrial and Manufacturing Engineering, Northeastern University, and the cCardiovascular Division, Beth Israel Deaconess Medical Center, Boston, Mass. Submitted April 11, 2001; accepted January 17, 2002. Reprint requests: Peter H. Stone, MD, Cardiovascular Division, Brigham and Women’s Hospital, 75 Francis St, Boston, MA 02115. E-mail: [email protected] © 2002, Mosby, Inc. All rights reserved. 0002-8703/2002/$35.00 ⫹ 0 4/1/123118 doi:10.1067/mhj.2002.123118
cal forces in general, and fluid shear stress in particular, elicit a large number of humoral, metabolic and structural responses in endothelial cells.2,5 The initiating stages of arterial plaque formation (ie, fatty streaks and fibrous plaque) occur preferentially in regions where the endothelial shear stress is low or retrograde for at least part of the cardiac cycle.6-9 Areas of low shear stress (ie, ⬍6 dynes/cm2) are atherogenic in that they are associated with increased uptake of lipoproteins, cause leukocyte adhesion molecules to appear on the surface of endothelial cells, cause leukocyte transmigration, cause secretion of chemotactic and growth factors, promote the accumulation of lipids as well as free and esterified cholesterol, and are prothrombotic.2,5,10-13 High shear stress (ie, ⬎70 dynes/ cm2), on the other hand, can produce endothelial damage,14 promote platelet deposition,15 and may promote plaque rupture.14 The relationships between hemodynamics (shear stress) and coronary arterial wall structure and function are likely to be extremely dynamic and selfamplifying. As coronary atherosclerosis progresses at a
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single site, different hemodynamic environments develop and lead to the creation of new hemodynamic environments, which, in turn, lead to dramatically different cellular and structural responses.16,17 The relationship between rapidly evolving flow/shear stress profile and plaque growth may be the critical element responsible for converting a quiescent plaque to an active, unstable, vulnerable plaque that may lead to an acute ischemic syndrome. Intravascular flow patterns and wall shear stress are largely determined by arterial geometry (branches and curvature) and by other factors such as flow pulsatility, flow rates, and divisions among the branches, with blood rheology and vessel wall compliance playing a secondary role.8,18-21 Experiments to elucidate the interactions between flow variables and endothelium can be readily conducted in vitro, but understanding the clinical significance of these basic interactions is dependent on developing suitable methodologies for calculating and measuring intracoronary flow in vivo, and on understanding the relationships between flow variables and the formation, morphology, and composition of complex plaque forms. The nature and effect of the changing shear stresses existing along the longitudinal axis of the coronary artery have not been previously studied in detail and may be extremely important in identifying the natural history of a particular coronary plaque and its likelihood to become vulnerable and rupture.22,23 Our purpose was to create a system for determining 3-dimensional (3-D) luminal and plaque geometry of the human coronary artery and provide detailed intravascular phasic flow characteristics in vivo. The goal of the system is to facilitate the study of plaque growth and the relationships between local hemodynamic factors and atherogenesis, thrombosis, and restenosis.
Methods The methods employed for this study are similar to those we employed for investigations of steady flow and are described in detail elsewhere.24 The study protocol was approved by the investigational review board of the Beth Israel Deaconess Medical Center and written informed consent was obtained. Data were obtained on a patient receiving an atherectomy and subsequent intracoronary ultrasound (ICUS) for clinical reasons. Briefly, the 3-D anatomy of the artery is reconstructed from simultaneous ICUS images and biplane coronary angiography (BCA). The lumen geometry is then represented in curvilinear coordinates and resampled at regular intervals to form a grid structure suitable for numerical computation. The detailed intravascular flow characteristics are obtained by solving the coupled transport equations by use of a finite-domain, fully implicit numeric technique.
Image acquisition and fusion ICUS (Endosonics, Rancho Cordova, Calif) was performed with controlled pullback at approximately one millimeter per second with simultaneous BCA. The guidewire used for ICUS was also recorded on the angiograms and later used to define the path of the ICUS transducer during pullback. The arterial lumen was reconstructed from end-diastolic ICUS frames because the majority of coronary blood flow occurs during diastole. End-diastolic frames were selected by visual observation as that frame immediately before the start of ventricular contraction. This largely eliminated the problem of heart motion during the cardiac cycle. To perform real-time visualization of intravascular flow characteristics, a digital image processing technique was developed to reconstruct the 3-D luminal geometry from digitized ICUS images and BCA.24 The ICUS and angiography data were stored as video images. Subsequently, a video clip capture was performed to transfer a sequence of video frames to disk files by use of a Broadway digital video system (Broadway MPEG Capture/ Compression, Version 1.0, Data Translation, Marlboro, Mass). The images were enhanced to overcome low contrast and to sharpen the edges of plaque and lumen by use of a Gaussian smoothing filter and a squared gradient filter. Edge detection and boundary extraction were combined into a single semiautomated procedure by developing an active contour algorithm, as described previously.24-26 To reconstruct the luminal geometry, the locus of the guidewire of the ICUS was first obtained from the information provided by the BCA. The guidewire track in 3 dimensions can be determined from its track in each of 2 perpendicular planes. Because any value of the vertical coordinate (z) is common to both the frontal and sagittal planes, each z value unambiguously links together an x value in the frontal plane with a y value in the sagittal plane. The path of the guidewire can thus be measured from the angiogram with appropriate scaling and knowledge of the spatial relationships. The guidewire served as the stem on which to rebuild the 3-D geometry. The corresponding point of the guidewire on each frame was determined from the transducer pullback speed and the video frame rate. The normal direction of each frame was determined from the corresponding tangential direction of the guidewire because the ICUS image is perpendicular to the catheter axis. The plane of the frame was therefore uniquely determined. The rotation of the frame was determined by reference to an arterial branch27 and the spatial position of a point on the luminal boundary was determined. The boundary points of each frame were connected by a spline curve to rebuild the luminal geometry in Cartesian coordinate. Spline interpolation was used specifically to smooth the boundary profile. Three frames were inserted between 2 successive frames by use of linear interpolation. Each frame was divided into small patches that were in turn connected between frames to form the computational control volumes.
Hemodynamic calculations A semiautomatic adaptive grid-generation code was developed to discretize the complete segment into small control
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volumes. An essential feature of this code is its ability to model the highly irregular cross section of the diseased artery. Because of this unpredictable irregularity, a manual check is still needed at present to ensure approximate orthogonality of the generated grids. A total of 136 by 12 ⫻ 12 grid nodes were employed along and across the artery, respectively. It was assumed that the arterial wall is stiff and blood is incompressible, homogeneous, and Newtonian. These assumptions have been demonstrated by several investigators15,18-20 to be reasonable for intracoronary hemodynamics. Pulsatile laminar blood flow in the artery can therefore be described by a set of transport equations and boundary conditions for mass and momentum conservation as previously described.24 Because we were unable to directly measure either the spatial or temporal coronary flow profile, a uniform velocity cross-sectional profile was assumed across the inlet and the phasic flow variation was assumed to be a typical phasic inflow coronary velocity waveform, as described previously (Figure 1).28 The equations were solved by use of a fully-implicit, upwind numerical scheme embodied in the PHOENICS computer code.29 The numerical accuracy of the results was ensured by systematic grid refinement until the maximum change in the characteristic velocity was ⬍1%. The computation was considered converged when the maximum difference in the final velocity between 2 successive iterations was ⬍1%. After the velocity field was calculated, a quadratic equation was fit to the axial velocity abutting the wall. The axial velocity gradient was calculated and the shear stress at the luminal surface of the artery was calculated as the product of viscosity and the velocity gradient at the wall. Thus, we were able to directly calculate shear stress and shear stress gradient throughout the vessel for each point in the cardiac cycle. In addition, a variety of flow-related parameters were calculated: normalized wall shear stress (WSS), normalized wall shear stress gradient (WSSG), oscillatory shear index (OSI), swirl number (Sw), and swirl oscillatory shear index (SOSI), as described in the Appendix. Finally, to separate regions of mixing from regions without mixing, massless particles were introduced into the flow at the inlet and tracked as they transited the artery. Particles that coursed a relatively straight path showed regions without mixing, whereas those that were subject to irregular paths demonstrated regions where mixing took place.
Results The right coronary artery was evaluated after successful directional atherectomy and balloon angioplasty (Figure 2). Only minor luminal irregularities are evident by angiography.
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Figure 1
Empirically derived waveform of coronary artery inlet blood velocity during phasic flow.28
flow condition during systole (T3). The change in flow pattern occurs before reversal of the inlet flow direction. There are recirculation bubbles (regions of reversed laminar flow) both upstream and downstream of the local minor stenosis. It should be noted that because of the complexity of the luminal geometry, only part of the flow is reversed, resulting in a complex vortex distribution within the arterial segment. Figure 4 shows the endothelial shear stress distribution on the “inner” and “outer” walls of the arterial segment at 5 different times during the cardiac cycle, starting with mid-diastole. “Inner” and “outer” refer to the half “cylinders” closer to and further away from the viewer, respectively. In Figure 4, the scale has been expanded to show more detail. A region of this atherectomized coronary artery (marked by an arrow) that experiences reversed shear stress and a border zone of stasis—negligible flow and negligible shear stress—throughout the cardiac cycle is quite apparent. Conversely, very high shear stresses occur at the stenosis itself during peak diastolic flow. Figure 5 displays the endothelial shear stress averaged over the cardiac cycle in the region of the minor stenosis. This is nearly identical to the shear stress distribution calculated from an assumed steady flow.24
Flow pattern and shear stress during the cardiac cycle
Flow indicators
Figure 3 shows the predicted velocity vectors at several stages of the cardiac cycle for the y-midplane of the region of interest. The flow patterns do not change significantly except near the reversed inlet
Figures 6 and 7 show the distribution of the Sw and SOSI, respectively, for the arterial segment under consideration. SOSI is displayed for “inner wall” and “outer wall” of the endothelial surface by use of the same
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Figure 2
Arterial segment investigated: original (A); processed (B); and reconstructed geometry (C).
convention as previously described. SOSI (and the underlying OSI) is low except in the vicinity of the atherectomy where the luminal wall has been rendered highly irregular. Sw is defined only for each cross section of the lumen and not at the wall. The strength of the swirling flow is estimated from the variation of the Sw along the arterial segment, as shown in Figure 6. During diastole (T5 and T1), the Sw increases rapidly after about one third of the artery length (which corresponds to the location of the atherectomy). The Sw then reaches 2 peaks downstream of the atherectomy with a maximum value of about 0.02, which may be considered relatively high. The characteristics during systole (T2, T3, and T4) are somewhat different. The Sw is smaller during systole because the flow itself is low. However, the Sw at peak systole is relatively high, despite negligible flow, reflecting the intense mixing taking place during this phase of the cardiac cycle.
Flow mixing As we have shown previously for steady flow,24 there is considerable swirl in the section of coronary artery under investigation. To investigate this phenomenon for pulsatile flow, we have numerically tracked the paths of massless particles (tracers) introduced
into the artery at the inlet. The results are presented as particle pathlines in Figure 8. Figure 8, A and B, shows the pathlines near the wall at systole and diastole respectively. Figure 8, C and D, gives results along the centerline of the artery for systole and diastole. The highly intermingled lines just before systole in Figure 8, A, are consistent with the complex flow pattern and vortex structure that exist in this segment of coronary artery. The pathlines near the centerline of the artery at diastole (Figure 8, C ) are essentially straight upstream of the atherectomy, indicating uniform flow. Distal to the atherectomy, the pathlines become chaotic, indicating enhanced mixing. The path of tracers introduced near the wall is relatively straight proximal to the atherectomy during both systole and diastole but becomes diffuse and twisted distal to the atherectomy (Figure 8, C and D). The paths of these tracers indicate there is a swirling flow and enhanced blood mixing in the artery in the region of and distal to the atherectomy.
Discussion These results describe, for the first time, the in vivo determination of local velocity patterns and endothelial shear stress within the epicardial human coronary arteries with phasic flow. We describe these parameters
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at each point within the coronary artery under study for each time during the cardiac cycle. In addition, we have been able to calculate several important indices of the flow within the coronary artery and illustrate the artery’s patterns of mixing. Even in the absence of significant luminal obstruction angiographically, the shear stress profile in the arterial segment indicates the presence of virtual stasis, marked flow reversal, and low and oscillating shear stress, characteristics that strongly promote thrombosis, atherogenesis, and accelerating atherosclerosis. Because each atherosclerotic lesion evolves in an independent manner,3,4 one could potentially use the shear stress profiling method in vivo to identify those minor luminal irregularities or revascularized segments that have local flow characteristics indicating a high likelihood of progression. Identification of atherosclerotic plaques likely to become high risk in the future could lead to an early local intervention to avoid the adverse natural history of such high-risk plaque. Although it is impossible to directly validate the results, qualitatively they are in agreement with intuitive expectations. Furthermore, the shear stress pattern averaged over the cardiac cycle is in close quantitative agreement with the results obtained during steady flow,24 ensuring that the phasic calculations did not introduce any artifact of its own and suggesting that details of the phasic flow waveform are not critical. The effects of assuming uniform velocity across the inlet section will introduce errors only within a few diameters of the inlet; further downstream, the flow pattern is independent of the assumed inlet condition. Serial longitudinal studies currently underway will be necessary to confirm that the flow characteristics of a minor obstruction at one point in time will predict changes in the obstruction, its morphology and its constituents, at a later point in time. The most dramatic feature of the velocity distribution is a large region of very low, slightly reversed flow immediately proximal to the mildly narrowed section of vessel (Figure 3) that persists throughout the cardiac cycle. The blood in this region is nearly static, suggesting the possibility of enhanced thrombogenicity and clot formation in the absence of plaque rupture or erosion as observed by Virmani et al.30 There is also a smaller region in which reversed flow occurs only during systole and a complex vortex develops with increased velocity opposite the narrowing. These features are reflected in the corresponding shear stress distributions (Figure 4), implying highly heterogeneous endothelial function and dysfunction, and suggesting localizing patterns typical of atherosclerotic plaque progression and restenosis. The presence of significant Sws (Figure 6) in the region of and distal to the region of the atherectomy for at least part of the cardiac cycle is consistent with
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Figure 3
Flow pattern in coronary artery during cardiac cycle. The individual time points during the cardiac cycle are illustrated as T1-T5.
well-known pathology data31 that describe spiral patterns of atheroma in coronary arteries. Although the primary component of endothelial shear stress is along the longitudinal axis of the artery, swirl will produce a tangential shear stress component. It will also produce small differential concentrations of blood components of different densities as a result of the centrifugal force of the swirling motion. Whether those concentration gradients are sustainable will be determined by the mixing patterns (Figure 8). A new flow indicator, SOSI, has been introduced here (Figure 7). The need for a new indicator has been addressed by Nerem,32 who argued that the focal nature of atherosclerosis may result not only from low shear stress, but also from other factors including oscillation of shear stress during the cardiac cycle, increased resident time, increased local concentration of atherogenic macromolecules resulting from flow mixing, and increased deposition of these materials resulting from the centrifugal force induced by blood flow. It appears that SOSI may integrate many of these contributing factors as follows: SOSI conserves the basic characteristics of OSI, indicating regions where shear stress is oscillating during the cardiac cycle; it includes
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Figure 4
Shear stress distribution during the cardiac cycle. Note that the scale has been changed at each point in the cardiac cycle to retain detail.
the possible enhancement of deposition of important particles on the arterial wall resulting from the centrifugal force induced by the swirling flow; and it includes the contribution of particle resident time, which is increased by swirling. In summary, the results of our shear stress profiling are in accordance with our general knowledge of coronary anatomy, intracoronary flow patterns, and atherogenesis. The luminal geometry reconstructed from ICUS is consistent with the observed arterial geometry obtained from angiography. Minor flow reversals, significant swirling flow, and large variations of local velocity and shear stress, both axially and circumferentially, were found within the short segment of right coronary artery under investigation. The measured flow pattern exhibits characteristics consistent with the focal nature of atherogenesis and restenosis. Of particular interest is the region of essentially static flow just proximal to the atherectomy. Virmani et al30 have observed that up to 50% of myocardial infarctions caused by occlusive thrombus may occur without underlying plaque rupture or plaque erosion. For the first
time, this work has demonstrated a region of blood stasis that may act as a nidus for occlusive clot. The addition of phasic flow to our previous work, which assumed steady flow,24 underscores the feasibility of determining phasic as well as steady flow characteristics. The effects of the assumption of rigid arteries and Newtonian fluid still remain to be explored.
Conclusion The work presented here demonstrates that the technology now exists to determine the true 3-D luminal geometry of human coronary arteries and predict the local phasic variations in flow fields and endothelial shear stress in vivo, providing a powerful new tool for investigating both the development and progression of native vessel atherosclerosis and restenosis after percutaneous coronary interventions. The structural insights and predictive power gained from this flow-profiling methodology may also be complementary with other novel diagnostic modalities, such as thermography,33 optical coherence tomography,34 and near infrared spectroscopy,35 which may identify in
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Figure 5
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Figure 7
Distribution of time-averaged WSS in the artery segment for phasic flow. Distribution of SOSI in the artery segment.
Figure 8
Figure 6
Change of Sw along the artery at different time points during the cardiac cycle.
Particle pathlines at different time points during the cardiac cycle.
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vivo the development of other characteristics of the vulnerable plaque. Identification of an early raised plaque likely to develop subsequently into a vulnerable plaque could lead to an early “prophylactic” intervention to avert the development of vulnerable plaque and the subsequent adverse natural history.
References 1. Sabbah HN, Khaja F, Brymer JF, et al. Blood velocity in the right coronary artery: relation to the distribution of atherosclerosis lesions. Am J Cardiol 1984;53:1008-12. 2. Malek AM, Alper SL, Izumo S. Hemodynamic shear stress and its role in atherosclerosis. JAMA 1999;282:2035-42. 3. Gibson CM, Kuntz RE, Nobuyoshi M, et al. Lesion-to-lesion independence of restenosis after treatment by conventional angioplasty, stenting, or direction atherectomy: validation of lesion-based restenosis analysis. Circulation 1993;87:1123-9. 4. Sacks FM, Pasternak RC, Gibson MC, et al. For the Harvard Atherosclerosis Reversibility Project (HARP) Group. Lancet 1994;344: 1182-6. 5. Barakat et al. Mechanisms of shear stress transmission and transduction in endothelial cells. Chest 1998;114(1 Suppl):58-63S. 6. Asakura T, Karino T. Flow patterns and spatial distribution of atherosclerotic lesions in human coronary arteries. Circ Res 1990;66: 1045-66. 7. Ku DN, Giddens DO, Zarins CZ, et al. Pulsatile flow and atherosclerosis in the human carotid bifurcation: positive correlation between plaque location and low and oscillating shear stress. Arteriosclerosis 1985;5:293-302. 8. Gertz SD, Roberts WC. Hemodynamic shear force in rupture of coronary arterial atherosclerotic plaques. Am J Cardiol 1990:66: 1368-72. 9. Nakashima Y, Plump AS, Raines EW, et al. ApoE-deficient mice develop lesions of all phases of atherosclerosis throughout the arterial tree. Arterioscler Thromb 1994;14:133-40. 10. Traub O, Berk BC. Laminar shear stress: mechanisms by which endothelial cells transduce an atheroprotective force. Arterioscler Thromb Vasc Biol 1998;18:677-85. 11. Tardy Y, Resnick N, Nagel T, et al. Shear stress gradients remodel endothelial monolayers in vitro via a cell proliferation-migrationloss cycle. Arterioscler Thromb Vasc Biol 1997;17:3102-6. 12. Chappell, Varner S, Nerem R, et al. Oscillatory shear stress stimulates adhesion molecule expression in cultured human endothelium. Circ Res 1998;82:532-9. 13. Topper JN, Cai J, Falb D, et al. Identification of vascular endothelial genes differentially responsive to fluid mechanical stimuli: cyclooxygenase-2, manganese superoxide dismutase, and endothelial cell nitric oxide synthase are selectively up-regulated by steady laminar shear stress. Proc Natl Acad Sci USA 1996;93:10417-22. 14. Badimon L, Badimon JJ, Galvez A, et al. Influence of arterial damage and wall shear rate on platelet deposition: ex vivo study in a swine model. Arteriosclerosis 1986;6:312-20. 15. Bassiouny HS, Liever BB, Giddens DP, et al. Differential effect of wall shear stress on intimal thickness in the critical and subcritical stenosis [abstract]. Circulation 1988;78(2 Suppl):II394. 16. Stary HC, Chandler AB, Dinsmore RE, et al. A definition of advanced types of atherosclerotic lesions and a histological classification of atherosclerosis: a report from the Committee on Vascular Lesions of the Council on Arteriosclerosis, American Heart Association. Circulation 1995;92:1355-74.
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17. Guyton JR, Klemp KF. Development of the lipid-rich core in human atherosclerosis. Arterioscler Thromb Vasc Biol 1996;16:4-11. 18. Constantinides P. Experimental atherosclerosis. Amsterdam: Elsevier; 1965. p. 17. 19. Texon M. Hemodynamic basis of atherosclerosis. New York: Hemisphere; 1980. p. 13-8. 20. Friedman MH, Bargeron CB, Duncan DD, et al. Effects of arterial compliance and non-Newtonian rhelogy on correlation between intimal thickness and wall shear. J Biomech Eng 1992:114:31720. 21. Perktold K, Peter RO, Resh M, et al. Pulsatile non-Newtonian blood flow in three-dimensional carotid bifurcation models: a numerical study of flow phenomena under different bifurcation angles. J Biomed Eng 1991;13:507-15. 22. Nosovitsky VA, Ilegbusi OJ, Jiang J, et al. Effects of curvature and stenosis-like narrowing on wall shear stress in a coronary artery model with phasic flow. J Biomech 1997;9:575-80. 23. Tricot O, Mallat Z, Heymes C, et al. Relation between endothelial cell apoptosis and blood flow direction in human atherosclerotic plaques. Circulation 2000;101:2450-3. 24. Ilegbusi OJ, Hu Z, Nesto R, et al. Determination of blood flow and endothelial shear stress in human coronary artery in vivo. J Invasive Cardiol 1999;11:667-74. 25. Laban M, Oomen JA, Slager CJ, et al. ANGUS: a new approach to three-dimensional reconstruction of coronary vessels by combined use of angiography and intravascular ultrasound. IEEE Comput Cardiol 1995;22:325-8. 26. Prause GPM, Dejong SC, McKay CR, et al. Semi-automated segmentation and 3-D reconstruction of coronary trees: biplane angiography and intravascular ultrasound fusion. Society of Photooptical and Image Engineers Proceedings: Medical Imaging 1996-Physiology and Function. 1996;2709:82-92. 27. Prause GPM, Dejong SC, Sonka M. Geometrically correct 3-D reconstruction of coronary wall and plaque: combining biplane angiography and intravascular ultrasound. Comput Cardiol 1996; 23:325-8. 28. Cokelet GR, Merrill EW, Gilliland ER, et al. The rheology of human blood-measurements near and at zero shear rate. Trans Soc Rheol 1963;7:303-16. 29. Rosten H, Spauling DC. A Guide to the PHOENICS Input Language. Technical Report, TR/100. Wimbleton (UK): CHAM Ltd; 1986. 30. Virmani R, Kolodgie FD, Burke AP, et al. Lessons from sudden coronary death. Atheroscler Thromb Vasc Biol 2000;20:126275. 31. Fox B, James K, Morgan B. Distribution of fatty and fibrous plaques in young human coronary arteries. Atherosclerosis 1982; 41:337-47. 32. Nerem RM. Vascular fluid mechanics, the arterial wall, and atherosclerosis. J Biomech Eng 1992;114:274-82. 33. Casscells W, Hathorn B, David M, et al. Thermal detection of cellular infiltrates in living atherosclerotic plaques: possible implications for plaque rupture and thrombosis. Lancet 1996;347:144751. 34. Fujimoto JG, Boppart SA, Tearney GJ, et al. High resolution in vivo intra-arterial imagine with optical coherence tomography. Heart 1999;82:128-33. 35. Charash WE, Lodder RA, Moreno PR, et al. Detection of simulated vulnerable plaque using a novel near infrared spectroscopy catheter [abstract]. J Am Coll Cardiol 2000;35(A Suppl):38.
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Appendix Calculations of flow related parameters: 1. OSI (oscillatory shear index) is defined as
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where U is the average inlet velocity, m is the direction of the maximum mean temporal wall shear stress, n is normal to m, and m and n are the wall shear stress components along the m and n directions, respectively. 4. Sw (swirl number) is defined as
where G and Gx are the angular momentum and axial momentum, respectively, calculated as in which T is the period of the cardiac cycle. This parameter indicates the regions where the endothelial shear stress changes between positive and negative values during the cardiac cycle. 2. WSS (normalized wall shear stress) is defined as
This parameter expresses the shear stress at any point on the lumen wall averaged over the cardiac cycle as a fraction of the average kinetic forces in the stream—a way of looking at the shear stress that is independent of the actual value of blood velocity. 3. WSSG (normalized wall shear stress gradient) is defined as
where V and W are angular velocity and axial velocity, respectively. As the name and definition implies, Sw expresses the swirling component of fluid momentum (or velocity) as a fraction of the axial momentum (or velocity). 5. SOSI (swirl oscillatory shear index), introduced here for the first time, is defined as the product of the timeaveraged Sw and OSI. Thus:
A high value of SOSI reflects a region of endothelium subject to both oscillating axial shear stress and highly swirling flow at that cross section.
Determination of in vivo velocity and endothelial shear stress patterns with phasic flow in human coronary arteries: A methodology to predict progression of coronary atherosclerosis Charles L. Feldman, ScD,a Olusegun J. Ilegbusi, PhD,b Zhenjun Hu, PhD,b Richard Nesto, MD,c Sergio Waxman, MD,c and Peter H. Stone, MDa Boston, Mass
Background Although the coronary arteries are equally exposed to systemic risk factors, coronary atherosclerosis is focal and eccentric, and each lesion evolves in an independent manner. Variations in shear stress elicit markedly different humoral, metabolic, and structural responses in endothelial cells. Areas of low shear stress promote atherosclerosis, whereas areas of high shear stress prevent atherosclerosis. Characterization of the shear stresses affecting coronary arteries in humans in vivo may permit prediction of progression of coronary disease, prediction of which plaques might become vulnerable to rupture, and prediction of sites of restenosis after percutaneous coronary intervention.
Methods To determine endothelial shear stress, the 3-dimensional anatomy of a segment of the right coronary artery was determined immediately after directional atherectomy by use of a combination of intracoronary ultrasound and biplane coronary angiography. The geometry of the segment was represented in curvilinear coordinates and a computational fluid dynamics technique was used to investigate the detailed phasic velocity profile and shear stress distribution. The results were analyzed with several conventional indicators and one novel indicator of disturbed flow. Results Our methodology identified areas of minor flow reversals, significant swirling, and large variations of local velocity and shear stress—temporally, axially, and cirumferentially—within the artery, even in the absence of significant luminal obstruction.
Conclusions We have described a system that permits, for the first time, the in vivo determination of pulsatile local velocity patterns and endothelial shear stress in the human coronary arteries. The flow phenomena exhibit characteristics consistent with the focal nature of atherogenesis and restenosis. (Am Heart J 2002;143:931-9.) Local hemodynamic factors, especially alterations of arterial wall shear stress, have an enormous impact on endothelial function and atherogenesis.1,2 The local nature of atherosclerosis is underscored by the observations that within each patient, each coronary obstruction progresses or regresses in an entirely independent manner, including regions subjected to percutaneous revascularization.3,4 Mechanical stresses are transmitted to the vascular wall as a combination of compressive pressure forces, tensile stretch forces, and tangential frictional (or shear) stresses.5 Mechani-
From the aCardiovascular Division, Brigham and Women’s Hospital, the bDepartment of Mechanical, Industrial and Manufacturing Engineering, Northeastern University, and the cCardiovascular Division, Beth Israel Deaconess Medical Center, Boston, Mass. Submitted April 11, 2001; accepted January 17, 2002. Reprint requests: Peter H. Stone, MD, Cardiovascular Division, Brigham and Women’s Hospital, 75 Francis St, Boston, MA 02115. E-mail: [email protected] © 2002, Mosby, Inc. All rights reserved. 0002-8703/2002/$35.00 ⫹ 0 4/1/123118 doi:10.1067/mhj.2002.123118
cal forces in general, and fluid shear stress in particular, elicit a large number of humoral, metabolic and structural responses in endothelial cells.2,5 The initiating stages of arterial plaque formation (ie, fatty streaks and fibrous plaque) occur preferentially in regions where the endothelial shear stress is low or retrograde for at least part of the cardiac cycle.6-9 Areas of low shear stress (ie, ⬍6 dynes/cm2) are atherogenic in that they are associated with increased uptake of lipoproteins, cause leukocyte adhesion molecules to appear on the surface of endothelial cells, cause leukocyte transmigration, cause secretion of chemotactic and growth factors, promote the accumulation of lipids as well as free and esterified cholesterol, and are prothrombotic.2,5,10-13 High shear stress (ie, ⬎70 dynes/ cm2), on the other hand, can produce endothelial damage,14 promote platelet deposition,15 and may promote plaque rupture.14 The relationships between hemodynamics (shear stress) and coronary arterial wall structure and function are likely to be extremely dynamic and selfamplifying. As coronary atherosclerosis progresses at a
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single site, different hemodynamic environments develop and lead to the creation of new hemodynamic environments, which, in turn, lead to dramatically different cellular and structural responses.16,17 The relationship between rapidly evolving flow/shear stress profile and plaque growth may be the critical element responsible for converting a quiescent plaque to an active, unstable, vulnerable plaque that may lead to an acute ischemic syndrome. Intravascular flow patterns and wall shear stress are largely determined by arterial geometry (branches and curvature) and by other factors such as flow pulsatility, flow rates, and divisions among the branches, with blood rheology and vessel wall compliance playing a secondary role.8,18-21 Experiments to elucidate the interactions between flow variables and endothelium can be readily conducted in vitro, but understanding the clinical significance of these basic interactions is dependent on developing suitable methodologies for calculating and measuring intracoronary flow in vivo, and on understanding the relationships between flow variables and the formation, morphology, and composition of complex plaque forms. The nature and effect of the changing shear stresses existing along the longitudinal axis of the coronary artery have not been previously studied in detail and may be extremely important in identifying the natural history of a particular coronary plaque and its likelihood to become vulnerable and rupture.22,23 Our purpose was to create a system for determining 3-dimensional (3-D) luminal and plaque geometry of the human coronary artery and provide detailed intravascular phasic flow characteristics in vivo. The goal of the system is to facilitate the study of plaque growth and the relationships between local hemodynamic factors and atherogenesis, thrombosis, and restenosis.
Methods The methods employed for this study are similar to those we employed for investigations of steady flow and are described in detail elsewhere.24 The study protocol was approved by the investigational review board of the Beth Israel Deaconess Medical Center and written informed consent was obtained. Data were obtained on a patient receiving an atherectomy and subsequent intracoronary ultrasound (ICUS) for clinical reasons. Briefly, the 3-D anatomy of the artery is reconstructed from simultaneous ICUS images and biplane coronary angiography (BCA). The lumen geometry is then represented in curvilinear coordinates and resampled at regular intervals to form a grid structure suitable for numerical computation. The detailed intravascular flow characteristics are obtained by solving the coupled transport equations by use of a finite-domain, fully implicit numeric technique.
Image acquisition and fusion ICUS (Endosonics, Rancho Cordova, Calif) was performed with controlled pullback at approximately one millimeter per second with simultaneous BCA. The guidewire used for ICUS was also recorded on the angiograms and later used to define the path of the ICUS transducer during pullback. The arterial lumen was reconstructed from end-diastolic ICUS frames because the majority of coronary blood flow occurs during diastole. End-diastolic frames were selected by visual observation as that frame immediately before the start of ventricular contraction. This largely eliminated the problem of heart motion during the cardiac cycle. To perform real-time visualization of intravascular flow characteristics, a digital image processing technique was developed to reconstruct the 3-D luminal geometry from digitized ICUS images and BCA.24 The ICUS and angiography data were stored as video images. Subsequently, a video clip capture was performed to transfer a sequence of video frames to disk files by use of a Broadway digital video system (Broadway MPEG Capture/ Compression, Version 1.0, Data Translation, Marlboro, Mass). The images were enhanced to overcome low contrast and to sharpen the edges of plaque and lumen by use of a Gaussian smoothing filter and a squared gradient filter. Edge detection and boundary extraction were combined into a single semiautomated procedure by developing an active contour algorithm, as described previously.24-26 To reconstruct the luminal geometry, the locus of the guidewire of the ICUS was first obtained from the information provided by the BCA. The guidewire track in 3 dimensions can be determined from its track in each of 2 perpendicular planes. Because any value of the vertical coordinate (z) is common to both the frontal and sagittal planes, each z value unambiguously links together an x value in the frontal plane with a y value in the sagittal plane. The path of the guidewire can thus be measured from the angiogram with appropriate scaling and knowledge of the spatial relationships. The guidewire served as the stem on which to rebuild the 3-D geometry. The corresponding point of the guidewire on each frame was determined from the transducer pullback speed and the video frame rate. The normal direction of each frame was determined from the corresponding tangential direction of the guidewire because the ICUS image is perpendicular to the catheter axis. The plane of the frame was therefore uniquely determined. The rotation of the frame was determined by reference to an arterial branch27 and the spatial position of a point on the luminal boundary was determined. The boundary points of each frame were connected by a spline curve to rebuild the luminal geometry in Cartesian coordinate. Spline interpolation was used specifically to smooth the boundary profile. Three frames were inserted between 2 successive frames by use of linear interpolation. Each frame was divided into small patches that were in turn connected between frames to form the computational control volumes.
Hemodynamic calculations A semiautomatic adaptive grid-generation code was developed to discretize the complete segment into small control
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volumes. An essential feature of this code is its ability to model the highly irregular cross section of the diseased artery. Because of this unpredictable irregularity, a manual check is still needed at present to ensure approximate orthogonality of the generated grids. A total of 136 by 12 ⫻ 12 grid nodes were employed along and across the artery, respectively. It was assumed that the arterial wall is stiff and blood is incompressible, homogeneous, and Newtonian. These assumptions have been demonstrated by several investigators15,18-20 to be reasonable for intracoronary hemodynamics. Pulsatile laminar blood flow in the artery can therefore be described by a set of transport equations and boundary conditions for mass and momentum conservation as previously described.24 Because we were unable to directly measure either the spatial or temporal coronary flow profile, a uniform velocity cross-sectional profile was assumed across the inlet and the phasic flow variation was assumed to be a typical phasic inflow coronary velocity waveform, as described previously (Figure 1).28 The equations were solved by use of a fully-implicit, upwind numerical scheme embodied in the PHOENICS computer code.29 The numerical accuracy of the results was ensured by systematic grid refinement until the maximum change in the characteristic velocity was ⬍1%. The computation was considered converged when the maximum difference in the final velocity between 2 successive iterations was ⬍1%. After the velocity field was calculated, a quadratic equation was fit to the axial velocity abutting the wall. The axial velocity gradient was calculated and the shear stress at the luminal surface of the artery was calculated as the product of viscosity and the velocity gradient at the wall. Thus, we were able to directly calculate shear stress and shear stress gradient throughout the vessel for each point in the cardiac cycle. In addition, a variety of flow-related parameters were calculated: normalized wall shear stress (WSS), normalized wall shear stress gradient (WSSG), oscillatory shear index (OSI), swirl number (Sw), and swirl oscillatory shear index (SOSI), as described in the Appendix. Finally, to separate regions of mixing from regions without mixing, massless particles were introduced into the flow at the inlet and tracked as they transited the artery. Particles that coursed a relatively straight path showed regions without mixing, whereas those that were subject to irregular paths demonstrated regions where mixing took place.
Results The right coronary artery was evaluated after successful directional atherectomy and balloon angioplasty (Figure 2). Only minor luminal irregularities are evident by angiography.
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Figure 1
Empirically derived waveform of coronary artery inlet blood velocity during phasic flow.28
flow condition during systole (T3). The change in flow pattern occurs before reversal of the inlet flow direction. There are recirculation bubbles (regions of reversed laminar flow) both upstream and downstream of the local minor stenosis. It should be noted that because of the complexity of the luminal geometry, only part of the flow is reversed, resulting in a complex vortex distribution within the arterial segment. Figure 4 shows the endothelial shear stress distribution on the “inner” and “outer” walls of the arterial segment at 5 different times during the cardiac cycle, starting with mid-diastole. “Inner” and “outer” refer to the half “cylinders” closer to and further away from the viewer, respectively. In Figure 4, the scale has been expanded to show more detail. A region of this atherectomized coronary artery (marked by an arrow) that experiences reversed shear stress and a border zone of stasis—negligible flow and negligible shear stress—throughout the cardiac cycle is quite apparent. Conversely, very high shear stresses occur at the stenosis itself during peak diastolic flow. Figure 5 displays the endothelial shear stress averaged over the cardiac cycle in the region of the minor stenosis. This is nearly identical to the shear stress distribution calculated from an assumed steady flow.24
Flow pattern and shear stress during the cardiac cycle
Flow indicators
Figure 3 shows the predicted velocity vectors at several stages of the cardiac cycle for the y-midplane of the region of interest. The flow patterns do not change significantly except near the reversed inlet
Figures 6 and 7 show the distribution of the Sw and SOSI, respectively, for the arterial segment under consideration. SOSI is displayed for “inner wall” and “outer wall” of the endothelial surface by use of the same
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Figure 2
Arterial segment investigated: original (A); processed (B); and reconstructed geometry (C).
convention as previously described. SOSI (and the underlying OSI) is low except in the vicinity of the atherectomy where the luminal wall has been rendered highly irregular. Sw is defined only for each cross section of the lumen and not at the wall. The strength of the swirling flow is estimated from the variation of the Sw along the arterial segment, as shown in Figure 6. During diastole (T5 and T1), the Sw increases rapidly after about one third of the artery length (which corresponds to the location of the atherectomy). The Sw then reaches 2 peaks downstream of the atherectomy with a maximum value of about 0.02, which may be considered relatively high. The characteristics during systole (T2, T3, and T4) are somewhat different. The Sw is smaller during systole because the flow itself is low. However, the Sw at peak systole is relatively high, despite negligible flow, reflecting the intense mixing taking place during this phase of the cardiac cycle.
Flow mixing As we have shown previously for steady flow,24 there is considerable swirl in the section of coronary artery under investigation. To investigate this phenomenon for pulsatile flow, we have numerically tracked the paths of massless particles (tracers) introduced
into the artery at the inlet. The results are presented as particle pathlines in Figure 8. Figure 8, A and B, shows the pathlines near the wall at systole and diastole respectively. Figure 8, C and D, gives results along the centerline of the artery for systole and diastole. The highly intermingled lines just before systole in Figure 8, A, are consistent with the complex flow pattern and vortex structure that exist in this segment of coronary artery. The pathlines near the centerline of the artery at diastole (Figure 8, C ) are essentially straight upstream of the atherectomy, indicating uniform flow. Distal to the atherectomy, the pathlines become chaotic, indicating enhanced mixing. The path of tracers introduced near the wall is relatively straight proximal to the atherectomy during both systole and diastole but becomes diffuse and twisted distal to the atherectomy (Figure 8, C and D). The paths of these tracers indicate there is a swirling flow and enhanced blood mixing in the artery in the region of and distal to the atherectomy.
Discussion These results describe, for the first time, the in vivo determination of local velocity patterns and endothelial shear stress within the epicardial human coronary arteries with phasic flow. We describe these parameters
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at each point within the coronary artery under study for each time during the cardiac cycle. In addition, we have been able to calculate several important indices of the flow within the coronary artery and illustrate the artery’s patterns of mixing. Even in the absence of significant luminal obstruction angiographically, the shear stress profile in the arterial segment indicates the presence of virtual stasis, marked flow reversal, and low and oscillating shear stress, characteristics that strongly promote thrombosis, atherogenesis, and accelerating atherosclerosis. Because each atherosclerotic lesion evolves in an independent manner,3,4 one could potentially use the shear stress profiling method in vivo to identify those minor luminal irregularities or revascularized segments that have local flow characteristics indicating a high likelihood of progression. Identification of atherosclerotic plaques likely to become high risk in the future could lead to an early local intervention to avoid the adverse natural history of such high-risk plaque. Although it is impossible to directly validate the results, qualitatively they are in agreement with intuitive expectations. Furthermore, the shear stress pattern averaged over the cardiac cycle is in close quantitative agreement with the results obtained during steady flow,24 ensuring that the phasic calculations did not introduce any artifact of its own and suggesting that details of the phasic flow waveform are not critical. The effects of assuming uniform velocity across the inlet section will introduce errors only within a few diameters of the inlet; further downstream, the flow pattern is independent of the assumed inlet condition. Serial longitudinal studies currently underway will be necessary to confirm that the flow characteristics of a minor obstruction at one point in time will predict changes in the obstruction, its morphology and its constituents, at a later point in time. The most dramatic feature of the velocity distribution is a large region of very low, slightly reversed flow immediately proximal to the mildly narrowed section of vessel (Figure 3) that persists throughout the cardiac cycle. The blood in this region is nearly static, suggesting the possibility of enhanced thrombogenicity and clot formation in the absence of plaque rupture or erosion as observed by Virmani et al.30 There is also a smaller region in which reversed flow occurs only during systole and a complex vortex develops with increased velocity opposite the narrowing. These features are reflected in the corresponding shear stress distributions (Figure 4), implying highly heterogeneous endothelial function and dysfunction, and suggesting localizing patterns typical of atherosclerotic plaque progression and restenosis. The presence of significant Sws (Figure 6) in the region of and distal to the region of the atherectomy for at least part of the cardiac cycle is consistent with
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Figure 3
Flow pattern in coronary artery during cardiac cycle. The individual time points during the cardiac cycle are illustrated as T1-T5.
well-known pathology data31 that describe spiral patterns of atheroma in coronary arteries. Although the primary component of endothelial shear stress is along the longitudinal axis of the artery, swirl will produce a tangential shear stress component. It will also produce small differential concentrations of blood components of different densities as a result of the centrifugal force of the swirling motion. Whether those concentration gradients are sustainable will be determined by the mixing patterns (Figure 8). A new flow indicator, SOSI, has been introduced here (Figure 7). The need for a new indicator has been addressed by Nerem,32 who argued that the focal nature of atherosclerosis may result not only from low shear stress, but also from other factors including oscillation of shear stress during the cardiac cycle, increased resident time, increased local concentration of atherogenic macromolecules resulting from flow mixing, and increased deposition of these materials resulting from the centrifugal force induced by blood flow. It appears that SOSI may integrate many of these contributing factors as follows: SOSI conserves the basic characteristics of OSI, indicating regions where shear stress is oscillating during the cardiac cycle; it includes
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Figure 4
Shear stress distribution during the cardiac cycle. Note that the scale has been changed at each point in the cardiac cycle to retain detail.
the possible enhancement of deposition of important particles on the arterial wall resulting from the centrifugal force induced by the swirling flow; and it includes the contribution of particle resident time, which is increased by swirling. In summary, the results of our shear stress profiling are in accordance with our general knowledge of coronary anatomy, intracoronary flow patterns, and atherogenesis. The luminal geometry reconstructed from ICUS is consistent with the observed arterial geometry obtained from angiography. Minor flow reversals, significant swirling flow, and large variations of local velocity and shear stress, both axially and circumferentially, were found within the short segment of right coronary artery under investigation. The measured flow pattern exhibits characteristics consistent with the focal nature of atherogenesis and restenosis. Of particular interest is the region of essentially static flow just proximal to the atherectomy. Virmani et al30 have observed that up to 50% of myocardial infarctions caused by occlusive thrombus may occur without underlying plaque rupture or plaque erosion. For the first
time, this work has demonstrated a region of blood stasis that may act as a nidus for occlusive clot. The addition of phasic flow to our previous work, which assumed steady flow,24 underscores the feasibility of determining phasic as well as steady flow characteristics. The effects of the assumption of rigid arteries and Newtonian fluid still remain to be explored.
Conclusion The work presented here demonstrates that the technology now exists to determine the true 3-D luminal geometry of human coronary arteries and predict the local phasic variations in flow fields and endothelial shear stress in vivo, providing a powerful new tool for investigating both the development and progression of native vessel atherosclerosis and restenosis after percutaneous coronary interventions. The structural insights and predictive power gained from this flow-profiling methodology may also be complementary with other novel diagnostic modalities, such as thermography,33 optical coherence tomography,34 and near infrared spectroscopy,35 which may identify in
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Figure 5
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Figure 7
Distribution of time-averaged WSS in the artery segment for phasic flow. Distribution of SOSI in the artery segment.
Figure 8
Figure 6
Change of Sw along the artery at different time points during the cardiac cycle.
Particle pathlines at different time points during the cardiac cycle.
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vivo the development of other characteristics of the vulnerable plaque. Identification of an early raised plaque likely to develop subsequently into a vulnerable plaque could lead to an early “prophylactic” intervention to avert the development of vulnerable plaque and the subsequent adverse natural history.
References 1. Sabbah HN, Khaja F, Brymer JF, et al. Blood velocity in the right coronary artery: relation to the distribution of atherosclerosis lesions. Am J Cardiol 1984;53:1008-12. 2. Malek AM, Alper SL, Izumo S. Hemodynamic shear stress and its role in atherosclerosis. JAMA 1999;282:2035-42. 3. Gibson CM, Kuntz RE, Nobuyoshi M, et al. Lesion-to-lesion independence of restenosis after treatment by conventional angioplasty, stenting, or direction atherectomy: validation of lesion-based restenosis analysis. Circulation 1993;87:1123-9. 4. Sacks FM, Pasternak RC, Gibson MC, et al. For the Harvard Atherosclerosis Reversibility Project (HARP) Group. Lancet 1994;344: 1182-6. 5. Barakat et al. Mechanisms of shear stress transmission and transduction in endothelial cells. Chest 1998;114(1 Suppl):58-63S. 6. Asakura T, Karino T. Flow patterns and spatial distribution of atherosclerotic lesions in human coronary arteries. Circ Res 1990;66: 1045-66. 7. Ku DN, Giddens DO, Zarins CZ, et al. Pulsatile flow and atherosclerosis in the human carotid bifurcation: positive correlation between plaque location and low and oscillating shear stress. Arteriosclerosis 1985;5:293-302. 8. Gertz SD, Roberts WC. Hemodynamic shear force in rupture of coronary arterial atherosclerotic plaques. Am J Cardiol 1990:66: 1368-72. 9. Nakashima Y, Plump AS, Raines EW, et al. ApoE-deficient mice develop lesions of all phases of atherosclerosis throughout the arterial tree. Arterioscler Thromb 1994;14:133-40. 10. Traub O, Berk BC. Laminar shear stress: mechanisms by which endothelial cells transduce an atheroprotective force. Arterioscler Thromb Vasc Biol 1998;18:677-85. 11. Tardy Y, Resnick N, Nagel T, et al. Shear stress gradients remodel endothelial monolayers in vitro via a cell proliferation-migrationloss cycle. Arterioscler Thromb Vasc Biol 1997;17:3102-6. 12. Chappell, Varner S, Nerem R, et al. Oscillatory shear stress stimulates adhesion molecule expression in cultured human endothelium. Circ Res 1998;82:532-9. 13. Topper JN, Cai J, Falb D, et al. Identification of vascular endothelial genes differentially responsive to fluid mechanical stimuli: cyclooxygenase-2, manganese superoxide dismutase, and endothelial cell nitric oxide synthase are selectively up-regulated by steady laminar shear stress. Proc Natl Acad Sci USA 1996;93:10417-22. 14. Badimon L, Badimon JJ, Galvez A, et al. Influence of arterial damage and wall shear rate on platelet deposition: ex vivo study in a swine model. Arteriosclerosis 1986;6:312-20. 15. Bassiouny HS, Liever BB, Giddens DP, et al. Differential effect of wall shear stress on intimal thickness in the critical and subcritical stenosis [abstract]. Circulation 1988;78(2 Suppl):II394. 16. Stary HC, Chandler AB, Dinsmore RE, et al. A definition of advanced types of atherosclerotic lesions and a histological classification of atherosclerosis: a report from the Committee on Vascular Lesions of the Council on Arteriosclerosis, American Heart Association. Circulation 1995;92:1355-74.
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17. Guyton JR, Klemp KF. Development of the lipid-rich core in human atherosclerosis. Arterioscler Thromb Vasc Biol 1996;16:4-11. 18. Constantinides P. Experimental atherosclerosis. Amsterdam: Elsevier; 1965. p. 17. 19. Texon M. Hemodynamic basis of atherosclerosis. New York: Hemisphere; 1980. p. 13-8. 20. Friedman MH, Bargeron CB, Duncan DD, et al. Effects of arterial compliance and non-Newtonian rhelogy on correlation between intimal thickness and wall shear. J Biomech Eng 1992:114:31720. 21. Perktold K, Peter RO, Resh M, et al. Pulsatile non-Newtonian blood flow in three-dimensional carotid bifurcation models: a numerical study of flow phenomena under different bifurcation angles. J Biomed Eng 1991;13:507-15. 22. Nosovitsky VA, Ilegbusi OJ, Jiang J, et al. Effects of curvature and stenosis-like narrowing on wall shear stress in a coronary artery model with phasic flow. J Biomech 1997;9:575-80. 23. Tricot O, Mallat Z, Heymes C, et al. Relation between endothelial cell apoptosis and blood flow direction in human atherosclerotic plaques. Circulation 2000;101:2450-3. 24. Ilegbusi OJ, Hu Z, Nesto R, et al. Determination of blood flow and endothelial shear stress in human coronary artery in vivo. J Invasive Cardiol 1999;11:667-74. 25. Laban M, Oomen JA, Slager CJ, et al. ANGUS: a new approach to three-dimensional reconstruction of coronary vessels by combined use of angiography and intravascular ultrasound. IEEE Comput Cardiol 1995;22:325-8. 26. Prause GPM, Dejong SC, McKay CR, et al. Semi-automated segmentation and 3-D reconstruction of coronary trees: biplane angiography and intravascular ultrasound fusion. Society of Photooptical and Image Engineers Proceedings: Medical Imaging 1996-Physiology and Function. 1996;2709:82-92. 27. Prause GPM, Dejong SC, Sonka M. Geometrically correct 3-D reconstruction of coronary wall and plaque: combining biplane angiography and intravascular ultrasound. Comput Cardiol 1996; 23:325-8. 28. Cokelet GR, Merrill EW, Gilliland ER, et al. The rheology of human blood-measurements near and at zero shear rate. Trans Soc Rheol 1963;7:303-16. 29. Rosten H, Spauling DC. A Guide to the PHOENICS Input Language. Technical Report, TR/100. Wimbleton (UK): CHAM Ltd; 1986. 30. Virmani R, Kolodgie FD, Burke AP, et al. Lessons from sudden coronary death. Atheroscler Thromb Vasc Biol 2000;20:126275. 31. Fox B, James K, Morgan B. Distribution of fatty and fibrous plaques in young human coronary arteries. Atherosclerosis 1982; 41:337-47. 32. Nerem RM. Vascular fluid mechanics, the arterial wall, and atherosclerosis. J Biomech Eng 1992;114:274-82. 33. Casscells W, Hathorn B, David M, et al. Thermal detection of cellular infiltrates in living atherosclerotic plaques: possible implications for plaque rupture and thrombosis. Lancet 1996;347:144751. 34. Fujimoto JG, Boppart SA, Tearney GJ, et al. High resolution in vivo intra-arterial imagine with optical coherence tomography. Heart 1999;82:128-33. 35. Charash WE, Lodder RA, Moreno PR, et al. Detection of simulated vulnerable plaque using a novel near infrared spectroscopy catheter [abstract]. J Am Coll Cardiol 2000;35(A Suppl):38.
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Appendix Calculations of flow related parameters: 1. OSI (oscillatory shear index) is defined as
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where U is the average inlet velocity, m is the direction of the maximum mean temporal wall shear stress, n is normal to m, and m and n are the wall shear stress components along the m and n directions, respectively. 4. Sw (swirl number) is defined as
where G and Gx are the angular momentum and axial momentum, respectively, calculated as in which T is the period of the cardiac cycle. This parameter indicates the regions where the endothelial shear stress changes between positive and negative values during the cardiac cycle. 2. WSS (normalized wall shear stress) is defined as
This parameter expresses the shear stress at any point on the lumen wall averaged over the cardiac cycle as a fraction of the average kinetic forces in the stream—a way of looking at the shear stress that is independent of the actual value of blood velocity. 3. WSSG (normalized wall shear stress gradient) is defined as
where V and W are angular velocity and axial velocity, respectively. As the name and definition implies, Sw expresses the swirling component of fluid momentum (or velocity) as a fraction of the axial momentum (or velocity). 5. SOSI (swirl oscillatory shear index), introduced here for the first time, is defined as the product of the timeaveraged Sw and OSI. Thus:
A high value of SOSI reflects a region of endothelium subject to both oscillating axial shear stress and highly swirling flow at that cross section.