Journal of Vascular Surgery
Volume 37, Issue 5 , Pages 1118-1128, May 2003

Computational modeling of arterial biomechanics: Insights into pathogenesis and treatment of vascular disease☆☆☆★★★

London and Toronto, Canada; and Pittsburgh, Pa

From Imaging Research Laboratories, Robarts Research Institute, and Departments of Medical Biophysics and Diagnostic Radiology, University of Western Ontario,a the Departments of Surgery and Bioengineering, and McGowan Institute for Regenerative Medicine, University of Pittsburgh,b and the Department of Mechanical and Industrial Engineering, and Institute of Biomaterials and Biomedical Engineering, University of Toronto.c

Received 30 April 2002; accepted 15 August 2002.

Article Outline

Abstract 

We review how advances in computational techniques are improving our understanding of the biomechanical behavior of the healthy and diseased cardiovascular system. Numerical modeling of biomechanics is being used in a wide variety of ways, including assessment of effects of mural and hemodynamically induced stresses on atherogenesis, development of risk measures for aneurysm rupture, improvement in interpretation of medical images, and quantification of oxygen transport in diseased and healthy arteries. Although not amenable to routine clinical use, numerical modeling of cardiovascular biomechanics is a powerful research tool. (J Vasc Surg 2003;37:1118-28.)

 

Thanks to remarkable advances in computer technology, engineers now routinely solve problems on desktop personal computers that would have been nearly intractable 20 years ago. This has enabled researchers to use new and powerful computational techniques to understand the role of biomechanical factors in the healthy and diseased cardiovascular system. We describe specific examples of how computational technology is being used to unravel the interplay of biology and mechanics present in vivo.

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Background 

Mechanical effects are important in the cardiovascular system in two ways.

First, cells sense and respond to their biomechanical environment. This almost certainly has a key role in arterial disease, including atherogenesis1, 2 and development, enlargement, and rupture of aneurysms. For example, endothelial cells respond to shearing forces from flowing blood and mechanical stretch from arterial pulsation, whereas mural smooth muscle cells experience stretch and also shearing forces due to transmural filtration.3 Platelets can be activated by shear stress, and biomechanical effects are important in rolling and adhesion of monocytes.4 Unfortunately, the specific causative link between biomechanical factors and arterial pathogenesis remains to be identified,5 in part because of the substantial complexity of the highly unsteady, three-dimensional biomechanical environment within the arteries. Computational technology enables us to simulate and quantify this biomechanical environment in otherwise inaccessible locations. In fact, as described in more detail below, the combination of simulation and medical imaging enables us to quantify the in vivo biomechanical environment within arteries with comparable or better accuracy than is possible with direct, invasive measurement.6, 7, 8 Such techniques, in conjunction with appropriately designed experiments, are helping us better understand the links between biomechanics and arterial disease.

Second, the performance of implanted prosthetic vascular devices depends in part on biomechanical factors, including device fatigue life and hemodynamic perturbations induced by the device. Computing, in conjunction with suitable experimental data, can be important here by helping us understand the complex relationship between biomechanics and device failure and by aiding in design of better devices while shortening design cycle time. This field is in its infancy, and is only briefly discussed here.

Here we examine the recent literature on computational analysis of wall stresses and hemodynamic patterns in large arteries. Finally, we discuss computational studies of mass transfer in arteries as related to arterial pathophysiology.

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Computational analysis of arterial wall stresses 

The arterial wall deforms as a result of pulsatile pressure over each cardiac cycle and other mechanical loads. This deformation creates forces within the vascular wall, which when normalized by cross-sectional area are referred to as wall stresses. Experiments show that mechanical wall stresses and deformation influence vascular cell physiology and also have a role in vascular wall disease,9, 10, 11, 12 including the two clinically relevant problems of atherosclerosis and aneurysm.

Atherosclerosis 

Computational stress modeling has helped in our understanding of atherogenesis and its sequelae. Computational analyses13, 14, 15, 16, 17, 18, 19, 20 show that atherosclerotic plaques, and other heterogeneities, lead to increased local stress in the artery wall. This is clinically significant, because the so-called stress concentration within the plaque region increases the probability of plaque rupture, which can lead to sudden thrombotic occlusion or distal embolization. Further, when blood flows through a stenosis there is a decrease in pressure, because of the Bernoulli effect, which can cause local collapse of the artery and further stress concentration within the artery wall.21

In addition to increasing the probability of plaque rupture, arterial wall stresses may promote development of atherosclerotic plaques. For example, plaques form particularly frequently near the carotid bifurcation, where computational analyses have revealed a complex wall stress distribution,22, 23 with peak stress occurring on the lateral walls, where plaque preferentially forms (Fig 1).

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  • Fig. 1. 

    Computed stress patterns within walls of a carotid bifurcation at pressure of 120 mm Hg. In this calculation, maximum stress variation across the artery wall occurred on the lateral walls of the bifurcation in the sinus. Light blue areas, minimum stress; green areas, higher stress. Subdivision of artery wall into finite elements, required for analysis, is seen. (Reprinted from Delfino A, Stergiopulos N, Moore JE Jr, Meister JJ. Residual strain effects on the stress field in a thick wall finite element model of the human carotid bifurcation. J Biomech 1997;30:777-86. Copyright 1997, with permission from Elsevier Science.)

Another example is the coronary arteries, with a biomechanical environment that is rather unusual because of the large deformation these arteries undergo as a result of their attachment to the moving myocardium.24, 25 Stein et al26 used computational methods to demonstrate that wall stress is increased in the coronary arteries, which may contribute to plaque formation at this disease-prone site.

Two common treatment methods for atherosclerotic occlusive disease are arterial stenting or bypass grafting. It is believed that the stress-induced injury to the arterial wall at the site of stent placement or bypass graft anastomosis promotes intimal hyperplasia and potential restenosis. A computational analysis of stent deployment27 demonstrated that the stress injury is highly dependent on inflation (deployment) pressure and geometry of the stent struts (eg, opening size). Compliance mismatch, ie, the relative rigidity of presently used vascular graft materials as compared with the host arterial tissue, has been implicated as one cause of vascular graft failure. This disparity in compliance causes chronic stretching or stress at the junction between the graft and the artery19, 28, 29, 30 (Fig 2).

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  • Fig. 2. 

    Stress distribution within walls of an end-to-side anastomosis between an artery and a Dacron bypass graft under pressure of 100 mm Hg. Colors denote stress values. Note large spatial gradient in stress at the suture line, and extreme stress values at the suture locations. (Reprinted from Ballyk PD, Walsh C, Butany J, Ojha M. Compliance mismatch may promote graft-artery intimal hyperplasia by altering suture-line stresses. J Biomech 1998;31:229-37. Copyright 1998, with permission from Elsevier Science.)

Abdominal aortic aneurysm 

At present there is no reliable basis on which to evaluate susceptibility to rupture of a particular abdominal aortic aneurysm (AAA). AAA rupture is a biomechanical phenomenon that occurs when the stress within the aneurysm wall exceeds the tensile strength of the wall. Therefore, evaluation of wall stress or wall strength distribution for a particular AAA may provide a predictor of its risk for rupture. Early studies used idealized, symmetric geometries for computational stress analyses of AAA.31, 32, 33 However, actual AAA geometry is too complex to be reliably approximated with idealized representations,34 implying that clinical decisions must be based on the actual “irregular” geometry of an individual AAA. By using spiral computed tomography (CT) data to create three-dimensional reconstructions of the abdominal aorta, or “virtual AAA” (Fig 3), Raghavan et al8 evaluated the stress distribution within 6 virtual AAA and 1 nonaneurysmal aorta (Fig 4).

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  • Fig. 3. 

    Creation of a “virtual AAA” for computational analyses based on three-dimensional reconstruction of clinical CT scans of a representative subject. A “point cloud” or “wire frame” model derived from stacking of two-dimensional boundary contours (A) is fit with a rough skin surface (B) and then smoothed to remove artifact (C). (Reprinted with permission from Raghavan ML et al. J Vasc Surg 2000;31:760-9.)

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  • Fig. 4. 

    Computed stress distribution in artery walls in 6 patients with AAA and 1 control subject (bottom left) under patient-specific systolic pressure. Colors denote stress values, from smallest (blue) to largest (red). Each pair of images shows anterior and posterior views of the same arterial segment. Note higher stress in the aortas of patients with AAA. (Reprinted with permission from Raghavan ML et al. J Vasc Surg 2000;31:760-9.)

The disparity in peak and average wall stress values between the nonaneurysmal aorta and the AAA, and the complex distribution of wall stresses in AAA, were notable features of this work. More recent work has focused on developing a way to estimate AAA wall tensile strength distribution35, 36 and the rupture potential of a specific AAA.36

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Computational analysis of blood flow 

The biomechanics community has had long-standing interest in understanding hemodynamic patterns in large arteries, given their important role in vascular diseases such as atherosclerosis37 and intimal hyperplasia.38 Previous studies relied on either idealized vessel geometry, which can only be applied in a general sense to the human circulation,39 or casts of postmortem specimens.40 More recently the combination of high-resolution medical imaging (typically, magnetic resonance angiography [MRA], but also x-ray angiography and ultrasound), sophisticated image processing techniques, and high-performance desktop workstations has made it possible to simulate physiologically pulsatile flow patterns in anatomically realistic arterial geometry with computational fluid dynamics (CFD) modeling techniques. Such “image-based” CFD analyses have clearly demonstrated the importance of subject-specific geometry, and to a lesser extent subject-specific flow rates (typically measured with phase contrast magnetic resonance imaging (MRI) or Doppler ultrasound scanning), in determining the local hemodynamic environment.41

Recent efforts have focused on elucidating the relationship between specific hemodynamic factors and the presence or absence of vascular disease. For example, Zhao et al42 coupled CFD and structural modeling techniques to demonstrate an association between low wall shear stress and high wall mechanical stress at the carotid bulb (Fig 5), in this case using ultrasound to provide estimates of the wall thickness in the various vessel branches.

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  • Fig. 5. 

    Results of numerical simulation of both blood flow patterns and mural stress distribution (coupled fluid-structure interaction) in a carotid bifurcation. Note correspondence between low wall shear stress (blue) (left) and high mechanical stress (red) (right) where atherosclerotic plaques are known to develop. (Reprinted with permission from Holden C [editor]. Science 2000;290:1291.)

Krams et al44 used angiography and intravascular ultrasound (ANGUS) to demonstrate a significant inverse relationship between wall shear stress and wall thickening in a segment of coronary artery under assumed steady flow conditions. Though highly invasive and thus applicable only in animal models or patients already referred for cardiac catheterization, this ANGUS-based approach has nevertheless proved valuable for identifying how stresses at and within the vessel wall regulate the remodeling process after vascular interventions.45, 46 A noninvasive alternative was recently presented by Steinman et al,47 who used the combination of black blood MRI and CFD to identify a correspondence between low and oscillating shear and wall thickness at the carotid bulbs in both a patient with early atherosclerosis and a healthy subject (Fig 6).
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  • Fig. 6. 

    Comparison of wall thickness (mm) (a, d), cycle-averaged wall shear stress (dynes/cm2) (b, e), and oscillatory wall shear stress index (c, f) in the carotid bifurcation in a patient with early atherosclerosis (top illustrations) and a healthy volunteer (bottom illustrations). Wall thickness (intima plus media) was measured in vivo with high-resolution MRI, whereas shear stresses were computed based on in vivo geometry and flow rates, determined from the same MRI study. Correspondence between wall thickening and low and oscillating wall shear stress is observed in both subjects. (Reprinted with permission from Steinman DA, Thomas JB, Ladak HM, Milner JS, Rutt BK, Spence JD. Reconstruction of carotid bifurcation hemodynamics and wall thickness using computational fluid dynamics and MRI. Magn Reson Med 2002;47:149-59. Copyright 2002, Wiley-Liss, Inc, a subsidiary of John Wiley & Sons, Inc.)

It is interesting that this study failed to find a significant relationship between wall thickness and wall shear stress variables when considering data from the whole carotid bifurcation, hinting at a more complex relationship between local hemodynamic factors and atherosclerosis that will no doubt be the subject of further scrutiny with these novel techniques.

Another important application of image-based CFD relates to the treatment of vascular disease. In particular, attention has been focused on elucidating the role of hemodynamics in complications associated with surgical procedures such as carotid endarterectomy48 and bypass grafting.49 For example, Hyun et al50 used a quasi-realistic carotid bifurcation CFD model as a platform to demonstrate that the presence of a sharp or even smoothed common carotid artery step increases a number of “disturbed flow” indicators and thus the potential for postoperative complications. Leuprecht et al51 used a coupled fluid dynamics and structural analysis approach to investigate the effect of end-to-side anastomosis technique (conventional vs Miller cuff) on flow dynamics, using anatomically realistic geometry derived from casts of bypass grafts implanted into sheep. Generally similar flow patterns were observed between the two models (Fig 7); however, the Miller cuff geometry displayed more pronounced vortical flow and wall deformation, but less pronounced stagnation point motion, in the anastomotic region.

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  • Fig. 7. 

    Computed velocity patterns for unsteady flow in conventional (A) and Miller cuff (B) anastomosis geometry. C, Selected axial velocity profiles. D, Secondary velocity vectors at indicated sections. Axial velocity refers to velocity directed along the axis of the artery; secondary velocity vectors are the two velocity components at right angles to the axial direction. Pronounced skewing of axial velocity profiles and strong secondary flow are evident in both anastomoses. (Reprinted from Perktold K, Leuprecht A, Prosi M, Berk T, Czerny M, Trubel W, et al. Fluid dynamics, wall mechanics and oxygen transfer in peripheral bypass anastomoses: computer studies on various designs. Ann Biomed Eng 2002:35:225-36. Copyright 2002, with permission from Elsevier Science.)

Morphometric analysis of corresponding grafts explanted 6 months after surgery revealed little difference in bed hyperplasia, suggesting only a minor role for flow dynamics in bed hyperplasia. Conversely, structural analysis revealed a strong relationship between suture line intimal thickening and compliance mismatch.

With improved understanding of how local blood flow dynamics affect outcome of vascular interventions, it might eventually be possible to plan vascular procedures in a patient-specific manner. Taylor et al53 are leading proponents of this “predictive medicine” approach. Their group pioneered the use of CFD techniques for computer-assisted planning of bypass surgery. Similar approaches have also been proposed for optimizing treatment of congenital heart defects54 and cerebral aneurysms.55, 56 It is important to note, however, that, although possible, these simulation-based techniques are not yet practical for use in routine surgical or intervention planning. Moreover, it remains to be seen whether such sophisticated planning techniques will have a measurable effect on outcome and whether the potential costs of such an approach outweigh any added benefits.

Finally, CFD analysis has proved valuable in explaining how complex blood flow alters the appearance of medical images. A practical example of this was presented by Steinman and Rutt,57 who coupled CFD analysis of carotid bifurcation hemodynamics to a model of MRI physics to explain the origin of, and propose a simple means to reduce, plaque-mimicking flow artifacts in black blood MRI. Similar techniques have also been used to explain artifacts in conventional MRA58 and inherent errors in phase contrast MRI velocimetry of complex flow such as occurs at bypass graft anastomoses.59

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Mass transfer in arterial system 

In the context of the cardiovascular system, mass transfer refers to exchange of substances between blood and the arterial wall. Substances of interest include oxygen, low-density lipoprotein (LDL), and platelet-derived cytokines, as well as potential therapeutic agents designed for local delivery by intravascular infusion. In additional to endothelial permeability, mass transfer patterns depend on local hemodynamics. Thus modeling of mass transfer first requires computation of blood flow patterns, followed by solution of equations governing mass transport. Most mass transfer “action” occurs in a thin layer next to the arterial wall. This leads to computational difficulties,60, 61 but also makes the mass transport process sensitively dependent on near-wall hemodynamics and thus local arterial geometry. For example, Qiu and Tarbell62 showed that modest amounts of curvature in an idealized artery lead to significant differences in local mass transfer rates. This effect is even more drastic in realistic curved arteries, eg, the coronary arteries, where small local variations in curvature and caliber lead to huge local variations in mass transfer61 (Fig 8).

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  • Fig. 8. 

    Computed axial velocity profiles (left), secondary flow patterns (middle), and concentration contours (right) at two cross-sectional sections in a realistic model of a right coronary artery. Axial velocity refers to velocity directed along the axis of the artery; secondary velocity vectors are the two velocity components at right angles to the axial direction. Mass transfer effectiveness along the artery wall adjacent to the myocardium differs by a factor of 32 between the two locations (upper and lower panels), primarily because of curvature effects in the artery driving secondary flow. (Reprinted from Kaazempur-Mofrad MR, Ethier CR. Mass transport in an anatomically realistic human right coronary artery. Ann Biomed Eng 2001:29:121-7. Copyright 2001, with permission from Elsevier Science.)

Atherogenesis has been postulated to be linked to altered mass transport patterns of oxygen and LDL. Some experimental evidence suggests that local hypoxia can promote atherogenesis,63 while mural infiltration of LDL is required to create plaques. Modeling of oxygen transport is tricky, because oxygen is present in blood dissolved in plasma and bound to hemoglobin in erythrocytes, and the interchange between free oxygen and oxyhemoglobin is nonlinear. Moore and Ethier64 included these effects and showed that, as the artery wall thickens in atherosclerosis, mural oxygen consumption dominates, leading to a hypoxic plaque core, consistent with observations of central necrosis and capillary ingrowth into plaques.

Modeling of LDL transport in large arteries has been done by several groups.65, 66 They have studied an interesting way in which LDL is carried to the artery wall, through a phenomenon known as “concentration polarization.”67 This occurs because the slow transmural filtration rate (about 0.25 μm/min) is the dominant mechanism for delivery of large, slowly diffusing molecules (eg, LDL) to the endothelium. Computational modeling of this hard-to-measure effect provides one way to study its possible role in atherogenesis (Fig 9).

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  • Fig. 9. 

    Computed flow patterns (A), wall shear stresses (B), and endothelial surface concentrations of low-density lipoprotein (LDL) (C) in an idealized T-junction geometry. Complex nature of the flow is easily seen in A, which leads to large local variations in wall shear stress exerted on endothelial cells in B. Computations of LDL concentration account for both transmural filtration and flow patterns in the artery lumen. Note large local variations in LDL concentration, especially at the junction. (Reprinted with permission from Wada S, Karino T. Computational study on LDL transfer from flowing blood to arterial walls. In: Yamaguchi T, editor. Clinical applications of computational mechanics to the cardiovascular system. Tokyo: Springer-Verlag; 2000. p. 157-73. Copyright 2000 by Springer-Verlag.)

For some transported solutes, the endothelium or media control mass transfer. Transport of albumin between blood and the arterial wall has been considered, both at macroscopic60, 68 and microscopic69, 70 scales. Because endothelial permeability to albumin (and other large solutes) is particularly sensitive to local flow conditions, flow patterns indirectly control mural albumin flux through their effect on endothelial permeability. This emphasizes the need to better understand the factors that control endothelial permeability in vivo, and provides an example of how computational tools can motivate experimental questions.

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Summary 

Computational technology provides a powerful tool to probe the biomechanical behavior of arteries and other components of the cardiovascular system. It combines synergistically with medical imaging technologies to provide information that is otherwise difficult (or impossible) to get, and it enables us to study how mechanical forces may induce arterial disease, helps in design of vascular devices, and may one day be routinely used for surgical planning. We expect that use of computational technology in arterial biomechanics will continue to grow.

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☆ Competition of interest: none.

☆☆ Supported by ongoing financial assistance from the Heart and Stroke Foundation of Ontario (Grant T-4770 and a New Investigator Award [D.A.S.]); by The Whitaker Foundation, the University of Pittsburgh Medical Center, The Pittsburgh Foundation, and National Institutes of Health Grant RO1 HL60670-01A2 (D.A.V.); and by the Natural Sciences and Engineering Research Council of Canada (C.R.E.).

★ Reprint requests to: C. Ross Ethier, PhD, Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Canada M5S 3G8 (email: ethier@mie.utoronto.ca).

★★ 0741-5214/2003/$30.00 + 0

PII: S0741-5214(02)75263-4

doi:10.1067/mva.2003.122

Journal of Vascular Surgery
Volume 37, Issue 5 , Pages 1118-1128, May 2003

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