Annals of Biomedical Engineering

, Volume 30, Issue 4, pp 483–497

Image-Based Computational Fluid Dynamics Modeling in Realistic Arterial Geometries

  • David A. Steinman
Article

Abstract

Local hemodynamics are an important factor in atherosclerosis, from the development of early lesions, to the assessment of stroke risk, to determining the ultimate fate of a mature plaque. Until recently, our understanding of arterial fluid dynamics and their relationship to atherosclerosis was limited by the use of idealized or averaged artery models. Recent advances in medical imaging, computerized image processing, and computational fluid dynamics (CFD) now make it possible to computationally reconstruct the time-varying, three-dimensional blood flow patterns in anatomically realistic models. In this paper we review progress, made largely within the last five years, towards the routine use of anatomically realistic CFD models, derived from in vivo medical imaging, to elucidate the role of local hemodynamics in the development and progression of atherosclerosis in large arteries. In addition to describing various image-based CFD studies carried out to date, we review the medical imaging and image processing techniques available to acquire the necessary geometric and functional boundary conditions. Issues related to accuracy, precision, and modeling assumptions are also discussed. © 2002 Biomedical Engineering Society.

PAC2002: 8719Uv, 8757Gg, 8710+e

Computational fluid dynamics Hemodynamics Medical imaging 3D reconstruction Finite-element method 

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REFERENCES

  1. 1.
    Aoki, S., K. Aoki, S. Ohsawa, H. Nakajima, H. Kumagai, and T. Araki. Dynamic MR imaging of the carotid wall. J. Magn. Reson. Imaging 9:420–427, 1999.Google Scholar
  2. 2.
    Augst, A. D., D. C. Barratt, A. D. Hughes, S. A. Thom, and X. Y. Xu. CFD model of a human carotid artery bifurcation reconstructed from 3D ultrasound data. Proceedings of the 5th International Symposium on Computer Methods in Biomechanics and Biomedical Engineering, 2001 (unpublished).Google Scholar
  3. 3.
    Bao, X., C. Lu, and J. A. Frangos. Temporal gradient in shear but not steady shear stress induces PDGF-A and MCP-1 expression in endothelial cells: Role of NO, NF kappa B, and egr-1. Arterioscler., Thromb., Vasc. Biol. 19:996–1003, 1999.Google Scholar
  4. 4.
    Stroud, J. S., S. A. Berger, and D. Saloner. Numerical analysis of flow through a severely stenotic carotid artery bifurcation. J. Biomech. Eng. 124:9–20, 2002.Google Scholar
  5. 5.
    Bergeron, P., R. Carrier, D. Roy, N. Blais, and J. Raymond. Radiation doses to patients in neurointerventional procedures. AJNR Am. J. Neuroradiol. 15:1809–1812, 1994.Google Scholar
  6. 6.
    Botnar, R., G. Rappitsch, M. B. Scheidegger, D. Liepsch, K. Perktold, and P. Boesiger. Hemodynamics in the carotid artery bifurcation: A comparison between numerical simulations and in vitro MRI measurements. J. Biomech. 33:137–144, 2000.Google Scholar
  7. 7.
    Caro, C. G., J. M. Fitz-Gerald, and R. C. Schroter. Atherosclerosis and arterial wall shear: Observations, correlation, and proposal of a shear-dependent mass transfer mechanism for atherogenesis. Proc. R. Soc. London, Ser. B 177:109, 1971.Google Scholar
  8. 8.
    Caro, C. G., J. M. Fitz-Gerald, and R. C. Schroter. Proposal of a shear-dependent mass transfer mechanism for atherogenesis. Clin. Sci. 40:5P, 1971.Google Scholar
  9. 9.
    Cebral, J. R., R. Lohner, and J. E. Burgess. Computer simulation of cerebral artery clipping: Relevance to aneurysm neurosurgery planning. Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering, 2000 (unpublished).Google Scholar
  10. 10.
    Cebral, J. R., R. Lohner, P. L. Choyke, and P. J. Yim. Merging of intersecting triangulations for finite-element modeling. J. Biomech. 34:815–819, 2001.Google Scholar
  11. 11.
    Cebral, J. R., R. Lohner, O. Soto, and P. J. Yim. On the modeling of carotid artery blood flow from magnetic resonance images. ASME Bioeng. Conf. 50:619–620, 2001.Google Scholar
  12. 12.
    Cebral, J. R., P. J. Yim, R. Lohner, O. Soto, H. Marcos, and P. J. Choyke. New methods for computational fluid dynamics modeling of carotid artery from magnetic resonance angiography. Proc. SPIE 4321:177–187, 2001.Google Scholar
  13. 13.
    Chandran, K. B., M. J. Vonesh, A. Roy, S. Greenfield, B. Kane, R. Greene, and D. D. McPherson. Computation of vascular flow dynamics from intravascular ultrasound images. Med. Eng. Phys. 18:295–304, 1996.Google Scholar
  14. 14.
    Clingan, P. A., and M. H. Friedman. The effect of celiac and renal artery outflows on near-wall velocities in the porcine iliac arteries. Ann. Biomed. Eng. 28:302–308, 2000.Google Scholar
  15. 15.
    Fahrig, R., A. J. Fox, S. Lownie, and D. W. Holdsworth. Use of a C-arm system to generate true three-dimensional computed rotational angiograms: Preliminary in vitro and in vivo results. AJNR Am. J. Neuroradiol. 18:1507–1514, 1997.Google Scholar
  16. 16.
    Fenster, A., D. B. Downey, and H. N. Cardinal. Three-dimensional ultrasound imaging. Phys. Med. Biol. 46:R67–R99, 2001.Google Scholar
  17. 17.
    Foutrakis, G. N., G. Burgreen, H. Yonas, and R. J. Sclabassi. Construction of 3D arterial volume meshes from magnetic resonance angiography. Neurol. Res. 18:354–360, 1996.Google Scholar
  18. 18.
    Frayne, R., D. A. Steinman, C. R. Ethier, and B. K. Rutt. Accuracy of MR phase contrast velocity measurements for unsteady flow. J. Magn. Reson. Imaging 5:428–431, 1995.Google Scholar
  19. 19.
    Friedman, M. H., C. B. Bargeron, O. J. Deters, G. M. Hutchins, and F. F. Mark. Correlation between wall shear and intimal thickness at a coronary artery branch. Atherosclerosis (Berlin) 68:27–33, 1987.Google Scholar
  20. 20.
    Friedman, M. H., O. J. Deters, C. B. Bargeron, G. M. Hutchins, and F. F. Mark. Shear-dependent thickening of the human arterial intima. Atherosclerosis (Berlin) 60:161–171, 1986.Google Scholar
  21. 21.
    Fry, D. L. Acute vascular endothelial changes associated with increased blood velocity gradients. Circ. Res. 22:165–197,1968.Google Scholar
  22. 22.
    Gibson, C. M., L. Diaz, K. Kandarpa, F. M. Sacks, R. C. Pasternak, T. Sandor, C. Feldman, and P. H. Stone. Relation of vessel wall shear stress to atherosclerosis progression in human coronary arteries. Arterioscler. Thromb. 13:310–315,1993.Google Scholar
  23. 23.
    Gill, J. D., H. M. Ladak, D. A. Steinman, and A. Fenster. Accuracy and variability assessment of a semiautomatic technique for segmentation of the carotid arteries from three-dimensional ultrasound images. Med. Phys. 27:1333–1342, 2000.Google Scholar
  24. 24.
    Gnasso, A., C. Carallo, C. Irace, V. Spagnuolo, N. G. De, P. L. Mattioli, and A. Pujia. Association between intima-media thickness and wall shear stress in common carotid arteries in healthy male subjects. Circulation 94:3257–3262, 1996.Google Scholar
  25. 25.
    Gnasso, A., C. Irace, C. Carallo, F. M. De, C. Motti, P. L. Mattioli, and A. Pujia. In vivo association between low wall shear stress and plaque in subjects with asymmetrical carotid atherosclerosis. Stroke 28:993–998, 1997.Google Scholar
  26. 26.
    Goldman, D., and A. S. Popel. Computational modeling of oxygen transport from complex capillary networks. Relation to the microcirculation physiome. Adv. Exp. Med. Biol. 471:555–563, 1999.Google Scholar
  27. 27.
    Goldman, D., and A. S. Popel. A computational study of the effect of capillary network anastomoses and tortuosity on oxygen transport. J. Theor. Biol. 206:181–194, 2000.Google Scholar
  28. 28.
    Guadagni, G., F. Migliavacca, G. Dubini, and E. L. Bove. Simulations of surgical planning for fontan procedures. Proc. ASME Bioeng. Conf. 50:911–912, 2001.Google Scholar
  29. 29.
    Holdsworth, D. W., C. J. Norley, R. Frayne, D. A. Steinman, and B. K. Rutt. Characterization of common carotid artery blood-flow wave forms in normal human subjects. Physiol. Meas. 20:219–240, 1999.Google Scholar
  30. 30.
    Huang, H., R. Virmani, H. Younis, A. P. Burke, R. D. Kamm, and R. T. Lee. The impact of calcification on the biomechanical stability of atherosclerotic plaques. Circulation 103:1051–1056, 2001.Google Scholar
  31. 31.
    Hyun, S., C. Kleinstreuer, and J. P. Archie, Jr. Computer simulation and geometric design of endarterectomized carotid artery bifurcations. Crit. Rev. Biomed. Eng. 28:53–59, 2000.Google Scholar
  32. 32.
    Hyun, S., C. Kleinstreuer, and J. P. Archie, Jr. Hemodynamics analyses of arterial expansions with implications to thrombosis and restenosis. Med. Eng. Phys. 22:13–27, 2000.Google Scholar
  33. 33.
    Hyun, S., C. Kleinstreuer, and J. P. Archie, Jr. Computational particle-hemodynamics analysis and geometric reconstruction after carotid endarterectomy. Comput. Biol. Med. 31:365–384, 2001.Google Scholar
  34. 34.
    Ilegbusi, O. J., Z. Hu, R. Nesto, S. Waxman, D. Cyganski, J. Kilian, P. H. Stone, and C. L. Feldman. Determination of blood flow and endothelial shear stress in human coronary artery in vivo. J. Invasive Cardiol. 11:667–674, 1999.Google Scholar
  35. 35.
    Jespersen, S. K., J. E. Wilhjelm, and H. Sillesen. Multiangle compound imaging. Ultrason. Imaging 20:81–102, 1998.Google Scholar
  36. 36.
    Kaazempur-Mofrad, M. R., and C. R. Ethier. Mass transport in an anatomically realistic human right coronary artery. Ann. Biomed. Eng. 29:121–127, 2001.Google Scholar
  37. 37.
    Karner, G., K. Perktold, M. Hofer, and D. Liepsch. Flow characteristics in an anatomically realistic compliant carotid artery bifurcation model. Comput. Methods Biomech. Biomed. Eng. 2:171–185, 1999.Google Scholar
  38. 38.
    Kornet, L., A. P. Hoeks, J. Lambregts, and R. S. Reneman. In the femoral artery bifurcation, differences in mean wall shear stress within subjects are associated with different intima-media thicknesses. Arterioscler., Thromb., Vasc. Biol. 19:2933–2939, 1999.Google Scholar
  39. 39.
    Kornet, L., J. Lambregts, A. P. Hoeks, and R. S. Reneman. Differences in near-wall shear rate in the carotid artery within subjects are associated with different intima-media thicknesses. Arterioscler., Thromb., Vasc. Biol. 18:1877–1884, 1998.Google Scholar
  40. 40.
    Krams, R., J. J. Wentzel, J. A. Oomen, R. Vinke, J. C. Schuurbiers, P. J. de Feyter, P. W. Serruys, and C. J. Slager. Evaluation of endothelial shear stress and 3D geometry as factors determining the development of atherosclerosis and remodeling in human coronary arteries in vivo. Combining 3D reconstruction from angiography and IVUS (ANGUS) with computational fluid dynamics. Arterioscler., Thromb., Vasc. Biol. 17:2061–2065, 1997.Google Scholar
  41. 41.
    Ku, D. N., D. P. Giddens, C. K. Zarins, and S. Glagov. Pulsatile flow and atherosclerosis in the human carotid bifurcation. Positive correlation between plaque location and low oscillating shear stress. Arteriosclerosis (Dallas) 5:293–302, 1985.Google Scholar
  42. 42.
    Ladak, H. M., J. S. Milner, and D. A. Steinman. Rapid three-dimensional segmentation of the carotid bifurcation from serial MR images. J. Biomech. Eng. 122:96–99, 2000.Google Scholar
  43. 43.
    Ladak, H. M., J. B. Thomas, J. R. Mitchell, B. K. Rutt, and D. A. Steinman. A semiautomatic technique for measurement of arterial wall from black blood MRI. Med. Phys. 28:1098–1107, 2001.Google Scholar
  44. 44.
    Lei, M., C. Kleinstreuer, and G. A. Truskey. A focal stress gradient-dependent mass transfer mechanism for atherogenesis in branching arteries. Med. Eng. Phys. 18:326–332, 1996.Google Scholar
  45. 45.
    Liu, Y., Y. Lai, A. Nagaraj, B. Kane, A. Hamilton, R. Greene, D. D. McPherson, and K. B. Chandran. Pulsatile flow simulation in arterial vascular segments using intravascular ultrasound images. Med. Eng. Phys. 23:583–595, 2001.Google Scholar
  46. 46.
    Long, Q., X. Y. Xu, B. Ariff, S. A. Thom, A. D. Hughes, and A. V. Stanton. Reconstruction of blood flow patterns in a human carotid bifurcation: A combined CFD and MRI study. J. Magn. Reson. Imaging 11:299–311, 2000.Google Scholar
  47. 47.
    Long, Q., X. Y. Xu, M. Bourne, and T. M. Griffith. Numerical study of blood flow in an anatomically realistic aorto-iliac bifurcation generated from MRI data. Magn. Reson. Med. 43:565–576, 2000.Google Scholar
  48. 48.
    Long, Q., X. Y. Xu, M. W. Collins, M. Bourne, and T. M. Griffith. Magnetic resonance image processing and structured grid generation of a human abdominal bifurcation. Comput. Methods Programs Biomed. 56:249–259, 1998.Google Scholar
  49. 49.
    Long, Q., X. Y. Xu, M. W. Collins, T. M. Griffith, and M. Bourne. The combination of magnetic resonance angiography and computational fluid dynamics: A critical review. Crit. Rev. Biomed. Eng. 26:227–274, 1998.Google Scholar
  50. 50.
    Malek, A. M., S. L. Alper, and S. Izumo. Hemodynamic shear stress and its role in atherosclerosis. J. Am. Med. Assoc. 282:2035–2042, 1999.Google Scholar
  51. 51.
    Meairs, S., J. Rother, W. Neff, and M. Hennerici. New and future developments in cerebrovascular ultrasound, magnetic resonance angiography, and related techniques. J. Clin. Ultrasound 23:139–149, 1995.Google Scholar
  52. 52.
    Milner, J. S., J. A. Moore, B. K. Rutt, and D. A. Steinman. Hemodynamics of human carotid artery bifurcations: Computational studies with models reconstructed from magnetic resonance imaging of normal subjects. J. Vasc. Surg. 28:143–156, 1998.Google Scholar
  53. 53.
    Moore, J. A., B. K. Rutt, S. J. Karlik, K. Yin, and C. R. Ethier. Computational blood flow modeling based on in vivo measurements. Ann. Biomed. Eng. 27:627–640, 1999.Google Scholar
  54. 54.
    Moore, J. A., D. A. Steinman, and C. R. Ethier. Computational blood flow modeling: Errors associated with reconstructing finite-element models from magnetic resonance images. J. Biomech. 31:179–184, 1998.Google Scholar
  55. 55.
    Moore, J. A., D. A. Steinman, D. W. Holdsworth, and C. R. Ethier. Accuracy of computational hemodynamics in complex arterial geometries reconstructed from magnetic resonance imaging. Ann. Biomed. Eng. 27:32–41, 1999.Google Scholar
  56. 56.
    Moore, J. A., D. A. Steinman, S. Prakash, K. W. Johnston, and C. R. Ethier. A numerical study of blood flow patterns in anatomically realistic and simplified end-to-side anastomoses. J. Biomech. Eng. 121:265–272, 1999.Google Scholar
  57. 57.
    Myers, J. G., J. A. Moore, M. Ojha, K. W. Johnston, and C. R. Ethier. Factors influencing blood flow patterns in the human right coronary artery. Ann. Biomed. Eng. 29:109–120, 2001.Google Scholar
  58. 58.
    Myers, J. G., M. Ojha, K. W. Johnston, and C. R. Ethier. Influence of branches, curvature, and caliber on blood flow patterns in the human right coronary artery. Comput. Methods Biomech. Biomed. Eng. (in press).Google Scholar
  59. 59.
    Olufsen, M. S. Structured tree outflow condition for blood flow in larger systemic arteries. Am. J. Physiol. 276:H257–H268, 1999.Google Scholar
  60. 60.
    Pedersen, E. M., S. Oyre, M. Agerbaek, I. B. Kristensen, S. Ringgaard, P. Boesiger, and W. P. Paaske. Distribution of early atherosclerotic lesions in the human abdominal aorta correlates with wall shear stresses measured in vivo. Eur. J. Vasc. Endovasc. Surg. 18:328–333, 1999.Google Scholar
  61. 61.
    Perktold, K., and M. Hofer. Mathematical modeling of flow effects and transport processes in arterial bifurcation models. In The Haemodynamics of Arterial Organs—Comparison of Computational Predictions with In vivo and In vitro Data, edited by X. Y. Xu and M. W. Collins. Southampton, UK: WIT, 1999, pp. 43–84.Google Scholar
  62. 62.
    Perktold, K., M. Hofer, G. Rappitsch, M. Loew, B. D. Kuban, and M. H. Friedman. Validated computation of physiologic flow in a realistic coronary artery branch. J. Biomech. 31:217–228, 1998.Google Scholar
  63. 63.
    Perktold, K., A. Leuprecht, M. Prosi, T. Berk, M. Czerny, W. Trubel, and H. Schima. Fluid dynamics, wall mechanics, and oxygen transfer in peripheral bypass anastomoses: Computer studies on various designs. Ann. Biomed. Eng. (in press).Google Scholar
  64. 64.
    Prakash, S., and C. R. Ethier. Enhanced error estimator for adaptive finite-element analysis of 3D incompressible flow. Comput. Methods Appl. Mech. Eng. 190:5413–5426, 2001.Google Scholar
  65. 65.
    Prakash, S., and C. R. Ethier. Requirements for mesh resolution in 3D computational hemodynamics. J. Biomech. Eng. 123:134–144, 2001.Google Scholar
  66. 66.
    Raghavan, M. L., D. A. Vorp, M. P. Federle, M. S. Makaroun, and M. W. Webster. Wall stress distribution on three-dimensionally reconstructed models of human abdominal aortic aneurysm. J. Vasc. Surg. 31:760–769, 2000.Google Scholar
  67. 67.
    Rutt, B. K., D. W. Holdsworth, S. Naik, D. H. Lee, and A. J. Fox. Ultra-high-resolution three-dimensional carotid MRA: Validation of ceMRA and MOTSA with CRA. Proceedings of the International Society for Magnetic Resonance in Medicine 9th Scientific Meeting, 2001, p. 399.Google Scholar
  68. 68.
    Shpilfoygel, S. D., R. A. Close, D. J. Valentino, and G. R. Duckwiler. X-ray videodensitometric methods for blood flow and velocity measurement: A critical review of literature. Med. Phys. 27:2008–2023, 2000.Google Scholar
  69. 69.
    Steinman, D. A., C. R. Ethier, and B. K. Rutt. Combined analysis of spatial and velocity displacement artifacts in phase contrast measurements of complex flows. J. Magn. Reson. Imaging 7:339–346, 1997.Google Scholar
  70. 70.
    Steinman, D. A., and B. K. Rutt. On the nature and reduction of plaque-mimicking flow artifacts in black blood MRI of the carotid bifurcation. Magn. Reson. Med. 39:635–641, 1998.Google Scholar
  71. 71.
    Steinman, D. A., J. B. Thomas, H. M. Ladak, J. S. Milner, J. G. Merino, and J. D. Spence. Use of a patient-specific computational hemodynamic model to explain conflicting Doppler and B-mode ultrasound assessments of carotid stenosis. Proceedings of the 2nd World Congress on Medical Physics and Biomedical Engineering, 2000 (unpublished).Google Scholar
  72. 72.
    Steinman, D. A., J. B. Thomas, H. M. Ladak, J. S. Milner, B. K. Rutt, and J. D. Spence. Reconstruction of carotid bifurcation hemodynamics and wall thickness using computational fluid dynamics and MRI. Magn. Reson. Med. 47:149–159, 2002.Google Scholar
  73. 73.
    Tasciyan, T. A., R. Banerjee, Y. I. Cho, and R. Kim. Two-dimensional pulsatile hemodynamic analysis in the magnetic resonance angiography interpretation of a stenosed carotid arterial bifurcation. Med. Phys. 20:1059–1070, 1993.Google Scholar
  74. 74.
    Taylor, C. A., M. T. Draney, J. P. Ku, D. Parker, B. N. Steele, K. Wang, and C. K. Zarins. Predictive medicine: Computational techniques in therapeutic decision making. Comput. Aided Surg. 4:231–247, 1999.Google Scholar
  75. 75.
    Taylor, C. A., T. J. R. Hughes, and C. K. Zarins. Computational investigations in vascular disease. Comput. Phys. 10:224–232, 1996.Google Scholar
  76. 76.
    Thomas, J. B., B. K. Rutt, H. M. Ladak, and D. A. Steinman. Effect of black blood MR image quality on vessel wall segmentation. Magn. Reson. Med. 46:299–304, 2001.Google Scholar
  77. 77.
    Thompson, J. F., B. K. Soni, and N. P. Weatherill. Handbook of Grid Generation. Boca Raton, FL: CRC, 1998.Google Scholar
  78. 78.
    Van Langenhove, G., J. J. Wentzel, R. Krams, C. J. Slager, J. N. Hamburger, and P. W. Serruys. Helical velocity patterns in a human coronary artery: A three-dimensional computational fluid dynamic reconstruction showing the relation with local wall thickness. Circulation 102:E22–E24, 2000.Google Scholar
  79. 79.
    Vonesh, M. J., C. H. Cho, J. V. Pinto, B. J. Kane, D. S. Lee, S. I. Roth, K. B. Chandran, and D. D. McPherson. Regional vascular mechanical properties by 3D intravascular ultrasound with finite-element analysis. Am. J. Physiol. 272:H425–H437, 1997.Google Scholar
  80. 80.
    Vorp, D. A., D. A. Steinman, and C. R. Ethier. Computational modeling of arterial biomechanics. Comput. Sci. Eng. 3:51–64, 2001.Google Scholar
  81. 81.
    Wang, K. C., R. W. Dutton, and C. A. Taylor. Improving geometric model construction for blood flow modeling. IEEE Eng. Med. Biol. Mag. 18:33–39, 1999.Google Scholar
  82. 82.
    Wentzel, J. J., J. Kloet, I. Andhyiswara, J. A. Oomen, J. C. Schuurbiers, B. de Smet, M. J. Post, D. de Kleijn, G. Pasterkamp, C. Borst, C. J. Slager, and R. Krams. Shear-stress and wall-stress regulation of vascular remodeling after balloon angioplasty: Effect of matrix metalloproteinase inhibition. Circulation 104:91–96, 2001.Google Scholar
  83. 83.
    Wentzel, J. J., R. Krams, J. C. Schuurbiers, J. A. Oomen, J. Kloet, W. J. Der Giessen, P. W. Serruys, and C. J. Slager. Relationship between neointimal thickness and shear stress after Wallstent implantation in human coronary arteries. Circulation 103:1740–1745, 2001.Google Scholar
  84. 84.
    Yim, P. J., J. R. Cebral, R. Mullick, and P. L. Choyke. Vessel surface reconstruction with a tubular deformable model. IEEE Trans. Med. Imaging 20:1411–1421, 2001.Google Scholar
  85. 85.
    Zhao, S. Z., X. Y. Xu, B. Ariff, Q. Long, A. V. Stanton, A. D. Hughes, and S. A. Thom. Interindividual variations in wall shear stress and mechanical stress distributions at the carotid artery bifurcation of healthy humans. J. Biomech. (in press).Google Scholar
  86. 86.
    Zhao, S. Z., X. Y. Xu, M. W. Collins, A. V. Stanton, A. D. Hughes, and S. A. Thom. Flow in carotid bifurcations: Effect of the superior thyroid artery. Med. Eng. Phys. 21:207–214, 1999.Google Scholar
  87. 87.
    Zhao, S. Z., X. Y. Xu, A. D. Hughes, S. A. Thom, A. V. Stanton, B. Ariff, and Q. Long. Blood flow and vessel mechanics in a physiologically realistic model of a human carotid arterial bifurcation. J. Biomech. 33:975–984, 2000.Google Scholar

Copyright information

© Biomedical Engineering Society 2002

Authors and Affiliations

  • David A. Steinman
    • 1
  1. 1.Imaging Research Laboratories, The John P. Robarts Research Institute. Departments of Medical Biophysics and Diagnostic Radiology and Nuclear MedicineThe University of Western OntarioLondonCanada

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