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

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.)

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.)

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.)

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.)

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.)

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.)

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.)

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.)

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.)