Biomechanics of Coronary Artery and Bypass Graft Disease: Potential New Approaches

The contribution of biomechanical factors to the incidence and distribution of coronary artery and bypass graft disease is underrecognized. This review examined the literature to determine which factors were relevant and the evidence for their importance. It identified two primary biomechanical factors that predispose to disease: (1) low-wall shear stress and (2) high-wall mechanical stress or strain. A range of secondary biomechanical factors have also been identified and include: vessel geometry; vessel movement; vessel wall characteristics and the presence of reflection waves. Potential surgical approaches for minimizing these effects are discussed. The contribution of biomechanical factors to the incidence and distribution of coronary artery and bypass graft disease is underrecognized. This review examined the literature to determine which factors were relevant and the evidence for their importance. It identified two primary biomechanical factors that predispose to disease: (1) low-wall shear stress and (2) high-wall mechanical stress or strain. A range of secondary biomechanical factors have also been identified and include: vessel geometry; vessel movement; vessel wall characteristics and the presence of reflection waves. Potential surgical approaches for minimizing these effects are discussed. There is vast literature on the cause and biology of coronary artery disease. However, two observations suggest that the importance of at least one potential factor has been underestimated. The first is that the recognized risk factors for coronary artery disease can only explain half its variability [1Pearson T.A. Coronary arteriography in the study of the epidemiology of coronary disease.Epidemiol Rev. 1984; 6: 140-166Crossref PubMed Scopus (109) Google Scholar]. The second is that its distribution is usually discrete and it's not generalized. This suggests that other predisposing factors whose effects vary with location may be important. It is possible that the “missing” factors may be biomechanical. To date, there has been relatively little emphasis on the relevance of biomechanical factors to coronary artery disease. The “‘Achilles’ heal” of bypass graft surgery is graft disease. Considerable efforts have been made to improve long-term patency, including the use of arterial conduits. However, the long saphenous vein is still extensively used and may be subject to early graft disease. It is probable that biomechanical factors contribute to this. However, no modifications to coronary surgical practice have been made or suggested yet to specifically reduce this effect. The aim of this review is to increase the awareness among cardiac surgeons of the possible importance of biomechanical factors to both native vessel and graft disease. It is also speculated as to how coronary surgery may minimize them in the future to improve graft patency.MethodsA computerized literature search for abstracts was performed using MEDLINE and the Cochrane Library from the earliest available date to March 2008. The initial Key words were: “fluid mechanics and coronary arteries;” “biomechanics and coronary arteries;” “shear stress and coronary arteries;” “anatomy and coronary artery disease;” “intramuscular coronary arteries;” “external stenting of grafts;” “wave reflection;” and “coronary artery movement.” All relevant full articles were reviewed.Definition of Relevant Terms UsedWall StressStress is a force that acts on a unit area. When the force acts directly on the measured area, then it is known as normal stress. Wall stress is normal stress that acts on a vessel wall (Fig 1). It may be internal normal stress, such as that generated by a pressure wave acting on the vessel wall, or external normal stress, such as that caused by external compression.Wall StrainNormal stress (either internal or external) will cause a deformation of the vessel wall it acts on. Wall strain is a measure of that deformation and it is defined as the change in length of the wall acted on divided by its original length. It is dimensionless.Wall Shear RateBlood flow within arteries is usually laminar. In laminar flow, the blood may be considered as a series of concentric “cylinders” that move in the same direction but at different velocities. The “cylinder” of blood flowing along the center of the vessel has the greatest velocity and that “cylinder” adjacent to the wall itself is stationary. The velocity profile across a transverse section of a blood vessel is therefore parabolic (Fig 2). A velocity gradient may be used to describe this profile. This is a measure of the change in velocity with change in distance from the vessel wall. The velocity gradient adjacent to the vessel wall itself is called the wall shear rate. Figure 3 illustrates velocity profiles with high-wall and low-wall shear rates.Fig 2The velocity profile of laminar flow in a vessel. (Left) Transverse section of a vessel. (Right) Cross section of a vessel. (D = distance from the vessel wall; V = velocity, and the longer the arrow the greater the velocity.)View Large Image Figure ViewerDownload (PPT)Fig 3Transverse section of a vessel showing typical velocity profiles for (left) high-wall shear rate and (right) low-wall shear rate.View Large Image Figure ViewerDownload (PPT)Wall Shear StressShear stress acts parallel to the face of the relevant material as compared with normal stress that acts directly on it. The shear stress of a flowing fluid is due to the frictional forces acting between adjacent concentric “cylinders” of fluid. The wall shear stress is the product of the wall shear rate with the viscosity of blood.It is important not to confuse wall shear stress with wall stress. The former acts parallel to the vessel wall, whereas the latter acts directly on it (Fig 4).Fig 4The direction of action of (left) wall stress (normal to the vessel wall) and (right) wall shear stress (parallel to the vessel wall).View Large Image Figure ViewerDownload (PPT)Biomechanical FactorsBiomechanical factors may be divided into those relating to fluid dynamics and those relating to wall mechanics. Biomechanical factors associated with an increased local incidence of disease were identified and termed “primary biomechanical factors.” In addition, “secondary biomechanical factors,” which contribute to disease by directly affecting the primary biomechanical factors were identified. These are summarized in Figure 5.Fig 5Summary of the interaction of primary and secondary biomechanical factors together with their effect on the vessel wall.View Large Image Figure ViewerDownload (PPT)Primary Biomechanical FactorsFluid dynamicsWall shear stress variation is an important factor in determining disease distribution. The mean wall shear stress of human coronary arteries is approximately 0.7 N/m2 [2Doriot P.A. Dorsaz P.A. Dorsaz L. De Benedetti E. Chatelain P. Delafontaine P. In-vivo measurements of wall shear stress in human coronary arteries.Coron Artery Dis. 2000; 11: 495-502Crossref PubMed Scopus (93) Google Scholar]. It is inversely related to age, systolic blood pressure and body mass index [3Gnasso A. Carallo C. Irace C. et al.Association between intima-media thickness and wall shear stress in common carotid arteries in healthy male subjects.Circulation. 1996; 94: 3257-3262Crossref PubMed Scopus (280) Google Scholar]. Although some have considered that high-wall shear stress is a risk factor [4Fry D.L. Certain histological and chemical responses of the vascular interface to acutely induced mechanical stress in the aorta of the dog.Circ Res. 1969; 24: 93-108Crossref PubMed Scopus (323) Google Scholar], most consider that low-wall shear stress is instead associated with disease [5Shaaban A.M. Duerinckx A.J. Wall shear stress and early atherosclerosis: a review.Am J Roent. 2000; : 1657-1665Crossref PubMed Scopus (207) Google Scholar, 6Krams R. Wentzel J.J. Oomen J.A.F. et al.Evaluation of endothelial shear stress and 3D geometry as factors determining the development of atherosclerosis and remodelling in human coronary arteries in vivo.Arterioscler Thromb Vasc Biol. 1997; 17: 2061-2065Crossref PubMed Scopus (246) Google Scholar, 7Sabbah H.N. Khaja F. Hawkins E.T. et al.Relation of atherosclerosis to arterial wall shear in the left anterior descending artery of man.Am Heart J. 1986; 112: 453-458Abstract Full Text PDF PubMed Scopus (54) Google Scholar, 8Caro C.G. Fitz-Gerald J.M. Schroter R.C. Arterial wall shear stress and distribution of early atheroma in man.Nature. 1969; 223: 1159-1161Crossref PubMed Scopus (503) Google Scholar, 9Caro C.G. Fitz-Gerald J.M. Schroter R.C. Proposal of a shear dependent mass transfer mechanism for atherogenesis.Clin Sci. 1971; 40: 5PPubMed Google Scholar, 10Friedman M.H. Hutchins G.M. Bargeron C.B. Deters O.J. Mark F.F. Correlations between intimal thickness and fluid shear in human arteries.Atherosclerosis. 1981; 39: 425-436Abstract Full Text PDF PubMed Scopus (290) Google Scholar, 11Ojha M. Ethier C.R. Johnston K. Cobbold R. Steady and pulsatile flow fields in an end-to-side arterial anastomotic model.J Vasc Surg. 1990; 12: 747-753Abstract Full Text Full Text PDF PubMed Scopus (100) Google Scholar, 12Gibson C.M. Diaz L. Kandarpa K. Relation of vessel wall shear stress to atherosclerosis progression in human coronary arteries.Arterioscler Thromb. 1993; 13: 310-315Crossref PubMed Google Scholar, 13Wahle A. Lopez J.J. Olszewski M.E. Vigmostad S.C. Chandran K.B. Rossen J.D. Sonka M. Plaque development, vessel curvature and wall shear stress in coronary arteries assessed by X-ray angiography and intravascular ultrasound.Med Image Anal. 2006; 10: 615-631Abstract Full Text Full Text PDF PubMed Scopus (84) Google Scholar, 14Stone P.H. Coskun A.U. Kinlay S. et al.Regions of low endothelial shear stress are the sites where coronary plaque progresses and vascular remodelling occurs in humans: an in vivo serial study.Eur Heart J. 2007; 28: 705-710Crossref PubMed Scopus (143) Google Scholar]. In a computational fluid dynamics model of the right coronary artery, an inverse relationship between wall shear stress and the plaque thickness was reported [6Krams R. Wentzel J.J. Oomen J.A.F. et al.Evaluation of endothelial shear stress and 3D geometry as factors determining the development of atherosclerosis and remodelling in human coronary arteries in vivo.Arterioscler Thromb Vasc Biol. 1997; 17: 2061-2065Crossref PubMed Scopus (246) Google Scholar]. Early plaque development seems to be associated with low-wall shear stress [13Wahle A. Lopez J.J. Olszewski M.E. Vigmostad S.C. Chandran K.B. Rossen J.D. Sonka M. Plaque development, vessel curvature and wall shear stress in coronary arteries assessed by X-ray angiography and intravascular ultrasound.Med Image Anal. 2006; 10: 615-631Abstract Full Text Full Text PDF PubMed Scopus (84) Google Scholar]. In addition, low-wall shear stress is associated with increased atherosclerosis progression [12Gibson C.M. Diaz L. Kandarpa K. Relation of vessel wall shear stress to atherosclerosis progression in human coronary arteries.Arterioscler Thromb. 1993; 13: 310-315Crossref PubMed Google Scholar]. Rapidly changing shear stress has also been linked with the development of atherosclerosis [5Shaaban A.M. Duerinckx A.J. Wall shear stress and early atherosclerosis: a review.Am J Roent. 2000; : 1657-1665Crossref PubMed Scopus (207) Google Scholar].There are a number of reasons why low-wall shear stress may encourage atherosclerosis. One possibility is a direct effect on endothelial cells. These cells in the canine aorta elongate and align along the direction of flow when subjected to high-wall shear stress, but they remain more rounded, without a preferred alignment when subjected to low-wall shear stress [15Levesque M.J. Liepsch D. Moravec S. Nerem R.M. Correlation of endothelial cell shape and wall shear stress in a stenosed dog aorta.Arteriosclerosis. 1986; 6: 220-229Crossref PubMed Google Scholar]. A more obvious potential link with atherosclerosis is the effect on lipids. Low-wall shear stress may result in increased uptake of atherogenic particles due to increased residence time [16Glagov S. Zarins C. Giddens D.P. Ku D.N. Hemodynamics and atherosclerosis Insights and perspectives gained from studies of human arteries.Arch Pathol Lab Med. 1988; 112: 1018-1031PubMed Google Scholar]. A computer simulation suggested that low-wall shear stress results in a flow-dependent concentration polarization of low-density lipoprotein creating a hypercholesterolemic environment [17Wada S. Karino T. Theoretical prediction of low-density lipoproteins concentration at the luminal surface of an artery with a multiple bend.Ann Biomed Eng. 2002; 30: 778-791Crossref PubMed Scopus (122) Google Scholar]. A further mechanism is its possible effect on oxygen flux. A correlation between low-wall shear stress and decreased oxygen flux into the vessel wall has been reported [18Perktold K. Leuprecht A. Prosi M. et al.Fluid dynamics, wall mechanics, and oxygen transfer in peripheral bypass anastomoses.Ann Biomed Eng. 2002; 30: 447-460Crossref PubMed Scopus (56) Google Scholar]. Alternately, high-wall shear stress may be atheroprotective. There is in vitro evidence that an acute increase in wall shear stress activates a signaling cascade in endothelial cells, which results in the release of the vasodilators nitric oxide and prostacyclin [19Ballermann B.J. Dardik A. Eng E. Liu A. Shear stress and the endothelium.Kidney Int Suppl. 1998; 67: 5100-5108Google Scholar]. Nitric oxide may be the key mediator of the atheroprotective effect of high-wall shear stress [20Traub O. Berk B.C. Laminar shear stress: mechanisms by which endothelial cells transducer an atheroprotective force.Arterioscler Thromb Vasc Biol. 1998; 18: 677-685Crossref PubMed Scopus (917) Google Scholar].Gene regulation and molecular responses may also play a role. It seems that integrins and the vascular endothelial growth factor Flk-1 can sense shear stress and that sustained shear stress results in down regulation of atherogenic genes such as monocyte chemotactic protein-1 [21Chien S. Molecular and mechanical bases of focal lipid accumulation in arterial wall.Prog Biophys Mol Biol. 2003; 83: 131-151Crossref PubMed Scopus (118) Google Scholar]. Another potentially relevant cellular response to high shear stress is a decrease in levels of endothelin-1 peptide, which has a constricting and mitogenic effect on vascular smooth muscle [22Sharefkin J.B. Diamond S.L. Eskin S.G. McIntyre L.V. Dieffenbach C.W. Fluid flow decreases preproendothelin mRNA and suppresses endothelin-1 peptide release in cultured human endothelial cells.J Vasc Surg. 1999; 14: 1-9Abstract Full Text Full Text PDF Scopus (192) Google Scholar]. Prolonged oscillatory wall shear stress has been reported to induce endothelial leukocyte adhesion molecule expression [23Chappell D.C. Varner S.E. Nerem R.M. Medford R.M. Alexander R.W. Oscillatory shear stress stimulates adhesion molecule expression in cultured human endothelium.Circ Res. 1998; 82: 532-539Crossref PubMed Scopus (467) Google Scholar], which is relevant to the location of leukocytes in the arterial wall.Low-wall shear stress or highly oscillatory wall shear stress seems to be primary biomechanical factors associated with disease location. However, it should also be noted that a high shear stress may not be benign, and if beyond the normal physiological range, it may damage blood elements as well as contribute to plaque rupture.Vessel Wall MechanicsWall stress and strain are either related to cardiac movement or to the generated pressure wave within the coronary arteries. Even if there are relatively small differences at different sites, they are significantly increased by the repetitive nature of the cardiac cycle. For example, if a site experiences a force that is 1% greater than the surrounding regions after each cardiac pulsation, then over the course of 1 year it is subjected to a total force that is more than 300,000 times greater. If vessel wall stress and strain predispose to atherosclerosis, then this variable topography of peak values may contribute to the actual distribution of disease.The importance of stress and strain is suggested by the localization of disease where they are maximal. In the carotid artery regions of localized stress concentration at the bifurcation and over the sinus bulb are also sites susceptible to atherosclerosis [24Salzar R.S. Thubrikar M.J. Eppink R.T. Pressure-induced mechanical stress in the carotid artery bifurcation: a possible correlation to atherosclerosis.J Biomech. 1995; 28: 1333-1340Abstract Full Text PDF PubMed Scopus (97) Google Scholar]. There are a number of reported observations that indicate why disease may be associated with increased vessel wall stress or strain. Mechanical deformation of the arterial wall stimulates the generation of reactive oxygen species and results in the upregulation of redox-sensitive pro-inflammatory gene products [25Taylor W.R. Mechanical deformation of the arterial wall in hypertension: a mechanism for vascular pathology.Am J Med Sci. 1998; 316: 156-161Crossref PubMed Scopus (19) Google Scholar]. In the long saphenous vein it was reported that pressure distension resulted in the upregulation of endothelial adhesion molecules, together with a subsequent increase in endothelial neutrophil adhesion [26Chello M. Mastroroberto P. Frati G. et al.Pressure distension stimulates the expression of endothelial adhesion molecules in the human saphenous vein graft.Ann Thorac Surg. 2003; 76: 453-458Abstract Full Text Full Text PDF PubMed Scopus (41) Google Scholar]. In an in vitro study, pulsatile stretch stimulated the proliferation of long saphenous vein smooth muscle cells [27Predel H.G. Yang Z. von Segesser L. Turina M. Bühler F.H. Lüscher T.F. Implication of pulsatile stretch on growth of saphenous vein and mammary artery smooth muscle.Lancet. 1992; 340: 878-879Abstract PubMed Scopus (122) Google Scholar].High vessel wall stress or strain seems to be a primary biomechanical factor associated with disease location.Secondary Biomechanical FactorsThese are other biomechanical factors that have been implicated in the cause of atherosclerosis that seem to act by modifying one of the primary factors.Vessel GeometryThe major determinant of individual variation in coronary artery anatomy is the presence of branches. They are associated with an increased incidence of atherosclerosis. Lesions tend to occur eccentrically at the lateral walls of the origins of smaller branches [28Endoh R. Hommah T. Furihata Y. Susaki Y. Fukushima T. A morphometric study of the distribution of early atherosclerosis using arteriography.Artery. 1988; 15: 192-202PubMed Google Scholar]. The angle a branch makes also seems to be relevant. A positive correlation has been reported between this angle and the maximum thickness of the intima and media [29Friedman M.H. Baker P.B. Ding Z. Kuban B.D. Relationship between the geometry and quantitative morphology of the left anterior descending artery.Atherosclerosis. 1996; 125: 183-192Abstract Full Text PDF PubMed Scopus (69) Google Scholar, 30Friedman M.H. Ding Z. Relation between the structural asymmetry of coronary branch vessels and the angle at their origin.J Biomech. 1998; 31: 273-278Abstract Full Text Full Text PDF PubMed Scopus (30) Google Scholar]. Vessel curvature is also relevant with atherosclerosis being more common along the inner wall of curved segments [7Sabbah H.N. Khaja F. Hawkins E.T. et al.Relation of atherosclerosis to arterial wall shear in the left anterior descending artery of man.Am Heart J. 1986; 112: 453-458Abstract Full Text PDF PubMed Scopus (54) Google Scholar].The anatomy of the left main stem coronary artery has been particularly investigated. Fibrous plaques are more common on the outer walls of the bifurcation, whereas the flow divider and inner walls downstream are relatively disease free [31Svindland A. The localisation of sudanophilic and fibrous plaques in the main left coronary bifurcation.Atherosclerosis. 1983; 48: 139-145Abstract Full Text PDF PubMed Scopus (62) Google Scholar]. The angle made by the bifurcation of the left main stem also seems to be relevant. It has been reported [32Friedman M.H. Brinkman A.M. Qin J.J. Seed W.A. Relation between coronary artery geometry and the distribution of early sudophilic lesions.Atherosclerosis. 1993; 98: 193-199Abstract Full Text PDF PubMed Scopus (70) Google Scholar] that there is a negative correlation between this angle and the presence of proximal disease in the left anterior descending and circumflex coronary arteries.It is probable that these anatomical features are associated with disease because of their effect on the primary biomechanical factors. Blood velocity would be expected to be greater along the outer wall of a curved vessel. Therefore, wall shear stress is least along the inner wall. This has been confirmed by observations both in canine and human coronary arteries [6Krams R. Wentzel J.J. Oomen J.A.F. et al.Evaluation of endothelial shear stress and 3D geometry as factors determining the development of atherosclerosis and remodelling in human coronary arteries in vivo.Arterioscler Thromb Vasc Biol. 1997; 17: 2061-2065Crossref PubMed Scopus (246) Google Scholar, 33Bell D.R. Sabbah H.N. Stein P.D. Profiles of velocity in coronary arteries of dogs indicate lower shear rate along inner arterial curvature.Arteriosclerosis. 1985; 9: 167-175Google Scholar] and would explain the increased incidence of atherosclerosis along the inner wall of curved segments. The association of disease with branch anatomy is probably related to its effect on both fluid dynamics and wall mechanics. Where there is a sudden change in vessel diameter or an abrupt branching, then the streamlines of flow may loose their attachment to the wall and form a “jet.” The region between the vessel wall and the “jet” is associated with “stagnant” flow. Such regions have a low-wall shear stress [34Mac Isaac A.I. Thomas J.D. Topol E.J. Towards the quiescent plaque, review article.JACC. 1993; 22: 1228-1241Abstract Full Text PDF PubMed Scopus (140) Google Scholar]. Where the branching or bifurcation is less extreme, there are also changes in the fluid dynamics. Low-wall shear stress occurs at bifurcations in regions opposite the flow divider, whereas high-wall shear stress occurs at all flow dividers [35Soulis J.V. Farmakis T.M. Giannoglu G.D. Louridas G.E. Wall shear stress in normal left coronary artery tree.J Biomech. 2006; 39: 742-749Abstract Full Text Full Text PDF PubMed Scopus (128) Google Scholar]. This distribution in low-wall shear stress fits with the observed distribution of disease and is consistent with its role as a primary biomechanical factor. Branches are also sites of increased vessel wall stress and strain [24Salzar R.S. Thubrikar M.J. Eppink R.T. Pressure-induced mechanical stress in the carotid artery bifurcation: a possible correlation to atherosclerosis.J Biomech. 1995; 28: 1333-1340Abstract Full Text PDF PubMed Scopus (97) Google Scholar], which is the other primary biomechanical factor associated with disease. It has been suggested that it is the combination of both low-wall shear stress and high-wall strain at the same site that predisposes to atherosclerosis [36Zhao S.Z. Ariff B. Long Q. et al.Inter-individual variations in wall shear stress and mechanical stress distributions at the carotid artery bifurcation of healthy humans.J Biomech. 2002; 35: 1367-1377Abstract Full Text Full Text PDF PubMed Scopus (107) Google Scholar].Coronary Artery MovementThe movement of coronary arteries has important biomechanical consequences. The coronary arteries are unique among the cardiovascular system in that they are subject to large dynamic variations during each cardiac cycle [37Schilt S. Moore J.E. Delfino A. Meister J.J. The effects of time-varying curvature on velocity profiles in a model of the coronary arteries.J Biomech. 1996; 29: 469-474Abstract Full Text PDF PubMed Scopus (41) Google Scholar]. As this movement can potentially modify both wall mechanics and vessel fluid dynamics, it has been suggested that it may have an important role in atherosclerosis [38Ding Z. Friedman M.H. Dynamics of human coronary arterial motion and its potential role in coronary atherogenesis.J Biomech Eng. 2000; 122: 488-492Crossref PubMed Scopus (62) Google Scholar]. Attempts have been made to classify these movements. In one such classification [39Konta T. Bett J.H.N. Patterns of coronary artery movement and the development of coronary atherosclerosis.Circ J. 2003; 67: 846-850Crossref PubMed Scopus (19) Google Scholar], ten patterns were grouped into three classes: (1) the bend type in which the coronary artery flexes into a curve, (2) the compression type in which there is segmental shortening, and (3) the displacement type in which the location of the coronary artery changes without any change in the segmental length or shape. These movement patterns of coronary arteries differ between individuals and between coronary arteries [38Ding Z. Friedman M.H. Dynamics of human coronary arterial motion and its potential role in coronary atherogenesis.J Biomech Eng. 2000; 122: 488-492Crossref PubMed Scopus (62) Google Scholar, 39Konta T. Bett J.H.N. Patterns of coronary artery movement and the development of coronary atherosclerosis.Circ J. 2003; 67: 846-850Crossref PubMed Scopus (19) Google Scholar. Changes in curvature are 40% greater in coronary arteries that overlie actively contracting myocardium compared with those in the atrioventricular groove [40Liao R. Chen S.Y. Messenger J.C. Grooves B.M. Burchenal J.E. Carroll J.D. Four-dimensional analysis of cyclic changes in coronary artery shape.Catheter Cardiovasc Interv. 2002; 55: 344-354Crossref PubMed Scopus (23) Google Scholar]. The left anterior descending artery undergoes less displacement than the right coronary artery [41Shechter G. Resar J.R. McVeigh E.R. Displacement and velocity of the coronary arteries: cardiac and respiratory motion.IEEE Trans Med Imaging. 2006; 25: 369-375Crossref PubMed Scopus (128) Google Scholar], but it is subject to greater axial variability in torsion [38Ding Z. Friedman M.H. Dynamics of human coronary arterial motion and its potential role in coronary atherogenesis.J Biomech Eng. 2000; 122: 488-492Crossref PubMed Scopus (62) Google Scholar]. This variation may be relevant to the differing incidence and distribution of coronary artery disease.There have been a number of reports suggesting a relationship between different coronary artery movements and atherosclerosis. In one study [42Zhu H. Friedman M.H. Relationship between the dynamic geometry and wall thickness of a human coronary artery.Arterioscler Thromb Vasc Biol. 2003; 23: 2260Crossref PubMed Scopus (45) Google Scholar], time averaged values of curvature and torsion of the right coronary artery were found to correlate with maximum wall thickness. Coronary artery locations subjected to higher torsions are more likely to be diseased [43Ding Z. Zhu H. Friedman M.H. Coronary artery dynamics in vivo.Ann Biomed Eng. 2002; 30: 419-429Crossref PubMed Scopus (54) Google Scholar]. In a study [44Stein P.D. Hamid M.S. Shivkumar K. Davis T.P. Khaja F. Henry J.W. Effects of cyclic flexion of coronary arteries on progression of atherosclerosis.Am J Cardiol. 1994; 73: 431-437Abstract Full Text PDF PubMed Scopus (70) Google Scholar] that examined the angiograms of 33 patients taken at two different times it was reported that plaque progression was increased with greater flexion angles.Coronary artery movement affects both vessel-wall mechanics and fluid dynamics. Many of the types of coronary artery movement associated with disease, such as torsion, compression, and flexion, increase vessel wall stress and strain. It has been shown by mathematical modeling that wall stresses are increased by 1.5-fold to 1.9-fold when the flexion angle increases from 10° to 20° [44Stein P.D. Hamid M.S. Shivkumar K. Davis T.P. Khaja F. Henry J.W. Effects of cyclic flexion of coronary arteries on progression of atherosclerosis.Am J Cardiol. 1994; 73: 431-437Abstract Full Text PDF PubMed Scopus (70) Google Scholar]. 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