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Ann Thorac Surg 2009;87:331-338. doi:10.1016/j.athoracsur.2008.07.023
© 2009 The Society of Thoracic Surgeons
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Right arrow Coronary disease

Review

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

Lindsay C.H. John, MD, FRCS*

Department of Cardiothoracic Surgery, Kings College Hospital, London, United Kingdom

* Address correspondence to Dr John, Department of Cardiothoracic Surgery, Kings College Hospital, Denmark Hill, London, SE5 9RS, United Kingdom (Email: lindsay.john{at}kch.nhs.uk).


   Abstract
Top
 Abstract
Introduction
 Methods
 Definition of Relevant Terms...
 Conclusion
 References
 
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.


   Introduction
Top
 Abstract
 Introduction
Methods
 Definition of Relevant Terms...
 Conclusion
 References
 
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 [1]. 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.


   Methods
Top
 Abstract
 Introduction
 Methods
Definition of Relevant Terms...
 Conclusion
 References
 
A 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 Used
Top
 Abstract
 Introduction
 Methods
 Definition of Relevant Terms...
Conclusion
 References
 
Wall Stress
Stress 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.


Figure 1
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  		Fig 1. (Left) Internal wall stress and (right) external wall stress causing deformation.

 
Wall Strain
Normal 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 Rate
Blood 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.


Figure 2
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  		Fig 2. The 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.)

 

Figure 3
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  		Fig 3. Transverse section of a vessel showing typical velocity profiles for (left) high-wall shear rate and (right) low-wall shear rate.

 
Wall Shear Stress
Shear 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).


Figure 4
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  		Fig 4. The direction of action of (left) wall stress (normal to the vessel wall) and (right) wall shear stress (parallel to the vessel wall).

 
Biomechanical Factors
Biomechanical 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.


Figure 5
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  		Fig 5. Summary of the interaction of primary and secondary biomechanical factors together with their effect on the vessel wall.

 
Primary Biomechanical Factors
Fluid dynamics
Wall 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 [2]. It is inversely related to age, systolic blood pressure and body mass index [3]. Although some have considered that high-wall shear stress is a risk factor [4], most consider that low-wall shear stress is instead associated with disease [5–14]. In a computational fluid dynamics model of the right coronary artery, an inverse relationship between wall shear stress and the plaque thickness was reported [6]. Early plaque development seems to be associated with low-wall shear stress [13]. In addition, low-wall shear stress is associated with increased atherosclerosis progression [12]. Rapidly changing shear stress has also been linked with the development of atherosclerosis [5].

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 [15]. 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 [16]. A computer simulation suggested that low-wall shear stress results in a flow-dependent concentration polarization of low-density lipoprotein creating a hypercholesterolemic environment [17]. 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 [18]. 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 [19]. Nitric oxide may be the key mediator of the atheroprotective effect of high-wall shear stress [20].

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 [21]. 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 [22]. Prolonged oscillatory wall shear stress has been reported to induce endothelial leukocyte adhesion molecule expression [23], 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 Mechanics
Wall 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 [24]. 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 [25]. 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 [26]. In an in vitro study, pulsatile stretch stimulated the proliferation of long saphenous vein smooth muscle cells [27].

High vessel wall stress or strain seems to be a primary biomechanical factor associated with disease location.

Secondary Biomechanical Factors
These 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 Geometry
The 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 [28]. 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 [29, 30]. Vessel curvature is also relevant with atherosclerosis being more common along the inner wall of curved segments [7].

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 [31]. The angle made by the bifurcation of the left main stem also seems to be relevant. It has been reported [32] 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 [6, 33] 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 [34]. 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 [35]. 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 [24], 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 [36].

Coronary Artery Movement
The 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 [37]. 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 [38]. Attempts have been made to classify these movements. In one such classification [39], 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 [38, 39. Changes in curvature are 40% greater in coronary arteries that overlie actively contracting myocardium compared with those in the atrioventricular groove [40]. The left anterior descending artery undergoes less displacement than the right coronary artery [41], but it is subject to greater axial variability in torsion [38]. 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 [42], 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 [43]. In a study [44] 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° [44]. Movement also affects the fluid dynamics within the coronary arteries [45–50]. Flow seems to be more affected by change in vessel curvature than by torsion [51]. The wall shear stress patterns are strongly dependent on the frequency of curvature variation [48]. Therefore, it is likely that coronary artery movement has an effect on disease location through the two biomechanical factors which are low wall shear stress and increased vessel wall stress or strain.

It is also probable that movement has an effect on graft patency. Although speculative, this may explain the decreased long-term patency observed in grafts to the distal circumflex or right coronary arteries. The presence of the proximal anastomosis on the aorta for vein grafts may contribute an additional biomechanical risk factor for graft disease. It is a junction between the stationary aorta and the partially mobile graft and may therefore be subject to increased local wall stresses and strains. Also, as one end of the graft is fixed in position (proximal anastomosis) and the other end is mobile (distal anastomosis), the graft is subjected to a repeated torsional or pendular movement depending on the site of the anastomosis. This may result in resonance if the heart rate is similar to the natural frequency of the vein graft. This previously unrecognized possibility could contribute to graft disease by significantly increasing graft wall stress and strain.

Local Variation in Coronary Artery/Graft Wall Characteristics
A common observation is the absence of disease in intramyocardial coronary artery segments. This effect is probably due to a modification of one or both primary biomechanical factors associated with atherosclerosis. As the myocardium contracts, the pressure external to the vessel increases; this results in a decrease in the transmural pressure gradient and hence reduces vessel wall stress. This may protect the intramyocardial segment from disease [52]. Others have proposed that an effect on fluid dynamics is relevant [53]. In one study [54] that used finite element analysis to investigate the effect of external tissue contraction, it was concluded that changes in flow velocity and wall shear stress were less important than reduction in circumferential stress and strain.

There has been a long history of the experimental use of external stents as a potential method for reducing the progression of graft disease. The stents used have included a wide range of materials [55–59]. The majority of such studies have reported a beneficial effect including a reduction in graft wall cellular damage [58], intimal foam cells [60], intimal and neointimal hyperplasia [57, 58, 60], medial thickening [57, 61], loss of smooth muscle cells [57], and apoptosis [60]. However, some studies have reported a decrease in graft lumen due to neointimal formation [55, 61]. This may be a consequence of stents interrupting flow through the vasa vasorum and causing graft hypoxia [62]. The use of porous or oversized grafts may reduce this problem [56, 57]. A further approach is to use biodegradable external sheaths [63] to reduce the long-term risks of infection and mechanical complications.

There seems to be clear experimental evidence that external supporting of grafts reduces disease. It probably does so by modifying either one or both of the two primary biomechanical factors associated with disease. External stents reduce graft wall stress [57, 60, 61] reportedly by almost a half [64]. They also increase shear stress within grafts [60] by as much as fivefold [64]. A number of relevant biological effects have also been reported, including decreased tyrosine kinase activity [64], decreased upregulation of vascular adhesion molecules [56, 65], and decreased platelet-derived growth factor expression [66].

Wave Reflection
Wave reflection has been used to explain the general form of the intravascular pressure and flow waves. However its possible effect on fluid and wall mechanics on a smaller scale in localized vascular systems, such as the coronary artery tree, has not been well described. The pressure wave is propagated throughout the coronary tree. At any particular site, the maximum wall stress will correspond with the peak of the pressure wave, and the maximum strain with the associated peak of circumferential expansion. In a uniform nonbranching vessel without any wave reflection, such a pressure wave would subject each wall location to the same maxima and minima of stress or strain. However, because of the complex anatomy of the coronary artery tree and the likely presence of reflected waves [67], different locations are subjected to different peaks of stress and strain. Wall shear stress is very sensitive to the impedance phase angle [68], which is a measure of wave reflection. Wave reflection seems to locally modify both primary biomechanical factors associated with atherosclerosis.

Potential Future Developments
Increasing the use of arterial grafts may improve overall graft patency, but long saphenous vein grafts are still used extensively. Part of the rationale for this review was to identify potential methods for improving graft patency, in particular, of long saphenous vein grafts by minimizing biomechanical factors associated with disease. Unfortunately, relatively little is known regarding the biomechanics of bypass grafts and that which is known has mainly been based on mathematical and computer modeling studies. Although these mathematical simulations are likely to improve and provide more relevant information, it is likely that changes in practice would only occur if relevant biomechanical effects can be demonstrated in vivo. Therefore, there is a need for more clinical studies with direct measurement of relevant biomechanical measurements. We are not yet at the stage in which randomized trials would be useful, as we have not refined the routine measurement of these factors nor indeed is their significance generally appreciated. One useful study would be the measurement of the natural frequencies of bypass graft conduits to assess the possibility of graft resonance. However, despite this relative lack of data on graft biomechanics, potential methods for reducing biomechanical factors that increase disease, or future studies to determine how to do this can be considered.

Anastomosis Geometry
Computational models [69] have demonstrated that end-to-side grafts to coronary arteries result in altered fluid dynamics. Potential variables include the graft angle, the caliber ratio of the graft and native vessel, and the anastomosis length. An established view is that the latter should be 1.5 times greater than the smallest structure. By relevant in vivo measurements, in the future the optimum geometry could be determined to minimize areas of low-wall shear stress.

Anastomosis Site
The current belief is that the greater the "run-off" for a graft, the longer it is likely to remain patent. This encourages the siting of grafts proximal to major branches. However, it seems that branches are the sites for both altered fluid dynamics and reflection waves. It is possible that the siting of grafts at a "critical" distance proximal to a branch with a "critical" angle could result in an adverse biomechanical effect and compromise patency. In the future this could be determined by appropriate in vivo measurements.

Graft Geometry
Graft geometry can vary in a number of ways, which includes its curvature. In a curved vessel the wall shear stress is least along the inner curvature. This effect becomes greater as the curvature increases. To reduce such regions of low-wall shear stress, which are associated with disease, grafting strategies that minimize the graft curvatures can be considered. This would only be possible for those grafts with alternative routes between the proximal and distal anastomosis.

Graft Movement
Adverse effects of graft movement are likely to be related to regions of high vessel wall stress. Consideration needs to be given to graft orientation to minimize flexion points.

Graft Wall Characteristics
Different grafts have different wall characteristics that determine their response to wall stress and strain. As far as arterial grafts are concerned, one choice that the surgeon has is whether they should be skeletonized. Studies have not clearly demonstrated decreased patency with this approach. This may be because the peri-arterial tissue is not sufficient to reduce wall stress or other factors that may outweigh any biomechanical advantage. The relative disadvantages and advantages of such an approach need to be considered by the surgeon. For the saphenous vein, the use of peri-graft stents remains a potential option. However, despite their long experimental use, presently there has been no large scale clinical use to date. One option that might be considered is the placement of peri-graft "reinforcement" at specific "at risk" sites of a graft, such as at unavoidable flexion points. Care would need to be taken that in doing so two new flexion points are not introduced.

There is also the possibility that alternative surgical approaches could be developed, such as local peri-artery "reinforcement" to directly minimize adverse biomechanical factors in the coronary arteries themselves. However, this would require a clearer knowledge of "at risk" anatomy than we have presently, and the ability to routinely measure coronary artery biomechanical factors in vivo.


   Conclusion
Top
 Abstract
 Introduction
 Methods
 Definition of Relevant Terms...
 Conclusion
References
 
Biomechanical factors are likely to contribute to the development of both coronary artery and bypass graft disease. In general, these factors have not been well appreciated. Our knowledge of them is as yet imperfect and only likely to be improved by studies with more direct relevant in vivo measurements. However, what we do know allows us to consider ways in which we may improve graft patency by minimizing their adverse effect. "Mechanical problems need a mechanical solution" is an expression that some have described as the raison d'être of cardiac surgery. In the case of coronary artery disease, the mechanical problem is an obstruction, and the mechanical solution is to bypass it. Unfortunately this situation is not a static one. This review has highlighted that disease progression may at least be due partly to a mechanical process. If cardiac surgery could develop approaches that provide mechanical solutions for this process, then it may be able to contribute more than the palliation of current coronary artery bypass surgery.


   References
Top
 Abstract
 Introduction
 Methods
 Definition of Relevant Terms...
 Conclusion
 References
 

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H. Nordgaard, A. Swillens, D. Nordhaug, I. Kirkeby-Garstad, D. Van Loo, N. Vitale, P. Segers, R. Haaverstad, and L. Lovstakken
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