Annals of Biomedical Engineering

, Volume 38, Issue 3, pp 1178–1187

Flow Interactions with Cells and Tissues: Cardiovascular Flows and Fluid–Structure Interactions

Sixth International Bio-Fluid Mechanics Symposium and Workshop, March 28–30, 2008, Pasadena, California
  • Morton H. Friedman
  • Rob Krams
  • Krishnan B. Chandran
Position Paper


Interactions between flow and biological cells and tissues are intrinsic to the circulatory, respiratory, digestive and genitourinary systems. In the circulatory system, an understanding of the complex interaction between the arterial wall (a living multi-component organ with anisotropic, non-linear material properties) and blood (a shear-thinning fluid with 45% by volume consisting of red blood cells, platelets, and white blood cells) is vital to our understanding of the physiology of the human circulation and the etiology and development of arterial diseases, and to the design and development of prosthetic implants and tissue-engineered substitutes. Similarly, an understanding of the complex dynamics of flow past native human heart valves and the effect of that flow on the valvular tissue is necessary to elucidate the etiology of valvular diseases and in the design and development of valve replacements. In this paper we address the influence of biomechanical factors on the arterial circulation. The first part presents our current understanding of the impact of blood flow on the arterial wall at the cellular level and the relationship between flow-induced stresses and the etiology of atherosclerosis. The second part describes recent advances in the application of fluid–structure interaction analysis to arterial flows and the dynamics of heart valves.


Arterial endothelium Atherosclerosis Heart valve dynamics 



Arbitrary Lagrangian–Eulerian


Computational fluid dynamics


Computed tomography


Fluid–structure interaction


Low-density lipoprotein


Matrix metalloproteinase


Magnetic resonance


Magnetic resonance imaging


Oxidized low-density lipoprotein




  1. 1.
    Ateshain, G. A., and M. H. Friedman. Integrative biomechanics: a paradigm for clinical applications of fundamental mechanics. J. Biomech. 42:1444–1451, 2009.CrossRefGoogle Scholar
  2. 2.
    Bluestein, D., Y. Alemu, I. Avrahami, M. Gharib, K. Dumont, J. J. Ricotta, and S. Einav. Influence of microcalcifications on vulnerable plaque mechanics using Fsi modeling. J. Biomech. 41:1111–1118, 2008.CrossRefPubMedGoogle Scholar
  3. 3.
    Bluestein, D., K. Dumont, M. D. Beule, J. Ricotta, P. Impellizzeri, B. Verhegghe, and P. Verdonck. Intraluminal thrombus and risk of rupture inpatient specific abdominal aortic aneurysm. Comput. Methods Biomech. Biomed. Eng. First article:1–9, 2008.Google Scholar
  4. 4.
    Caro, C. G., J. M. Fitz-Gerald, and R. C. Schroter. Atheroma and arterial wall shear observation, correlation and proposal of a shear dependent mass transfer mechanism for stherogenesis. Proc. R. Soc. Lond. B Biol. Sci. 177:109–159, 1971.CrossRefPubMedGoogle Scholar
  5. 5.
    Chatzizisis, Y. S., A. U. Coskun, M. Jonas, E. R. Edelman, C. L. Feldman, and P. H. Stone. Role of endothelial shear stress in the natural history of coronary atherosclerosis and vascular remodeling: molecular, cellular, and vascular behavior. J. Am. Coll. Cardiol. 49:2379–2393, 2007.CrossRefPubMedGoogle Scholar
  6. 6.
    de Hart, J., G. W. Peters, P. J. Schreurs, and F. P. Baaijens. A two-dimensional fluid–structure interaction model of the aortic valve [correction of value]. J. Biomech. 33:1079–1088, 2000.CrossRefPubMedGoogle Scholar
  7. 7.
    de Hart, J., G. W. Peters, P. J. Schreurs, and F. P. Baaijens. A three-dimensional computational analysis of fluid–structure interaction in the aortic valve. J. Biomech. 36:103–112, 2003.CrossRefPubMedGoogle Scholar
  8. 8.
    de Korte, C. L., G. Pasterkamp, A. F. van der Steen, H. A. Woutman, and N. Bom. Characterization of plaque components with intravascular ultrasound elastography in human femoral and coronary arteries in vitro. Circulation 102:617–623, 2000.PubMedGoogle Scholar
  9. 9.
    de Korte, C. L., M. J. Sierevogel, F. Mastik, C. Strijder, J. A. Schaar, E. Velema, G. Pasterkamp, P. W. Serruys, and A. F. van der Steen. Identification of atherosclerotic plaque components with intravascular ultrasound elastography in vivo: a Yucatan Pig Study. Circulation 105:1627–1630, 2002.CrossRefPubMedGoogle Scholar
  10. 10.
    Dumont, K., J. M. Stijnen, J. Vierendeels, F. N. van de Vosse, and P. R. Verdonck. Validation of a fluid–structure interaction model of a heart valve using the Dynamic Mesh Method in Fluent. Comput. Methods Biomech. Biomed. Eng. 7:139–146, 2004.CrossRefGoogle Scholar
  11. 11.
    Dumont, K., J. Vierendeels, R. Kaminsky, G. van Nooten, P. Verdonck, and D. Bluestein. Comparison of the hemodynamic and thrombogenic performance of two bileaflet mechanical heart valves using a Cfd/Fsi model. J. Biomech. Eng. 129:558, 2007.CrossRefPubMedGoogle Scholar
  12. 12.
    Feintuch, A., P. Ruengsakulrach, A. Lin, J. Zhang, Y. Q. Zhou, J. Bishop, L. Davidson, D. Courtman, F. S. Foster, D. A. Steinman, R. M. Henkelman, and C. R. Ethier. Hemodynamics in the mouse aortic arch as assessed by Mri, ultrasound, and numerical modeling. Am. J. Physiol. Heart Circ. Physiol. 292:H884–H892, 2007.CrossRefPubMedGoogle Scholar
  13. 13.
    Figueroa, C. A., S. Baek, C. A. Taylor, and J. D. Humphrey. Models and methods in computational vascular and cardiovascular mechanics. Comput. Methods Appl. Mech. Eng. 198(45–46):3583–3602, 2009. doi:10.1016/j.cma.2008.09.013.Google Scholar
  14. 14.
    Figueroa, C. A., I. E. Vignon-Clementel, K. E. Jansen, T. J. R. Hughes, and C. A. Taylor. A coupled momentum method for modeling blood flow in three-dimensional deformable arteries. Comput. Methods Appl. Mech. Eng. 195:5685–5706, 2006.CrossRefGoogle Scholar
  15. 15.
    Friedman, M. H., O. J. Deters, F. F. Mark, C. B. Bargeron, and G. M. Hutchins. Arterial geometry affects hemodynamics. A potential risk factor for atherosclerosis. Atherosclerosis 46:225–231, 1983.CrossRefPubMedGoogle Scholar
  16. 16.
    Fry, D. L. Acute vascular endothelial changes associated with increased blood velocity gradients. Circ. Res. 22:165–197, 1968.PubMedGoogle Scholar
  17. 17.
    Gnyaneshwar, R., R. K. Kumar, and K. R. Balakrishnan. Dynamic analysis of the aortic valve using a finite element model. Ann. Thorac. Surg. 73:1122–1129, 2002.CrossRefPubMedGoogle Scholar
  18. 18.
    Goel, R., B. R. Schrank, S. Arora, B. Boylan, B. Fleming, H. Miura, P. J. Newman, R. C. Molthen, and D. K. Newman. Site-specific effects of Pecam-1 on atherosclerosis in Ldl receptor-deficient mice. Arterioscler. Thromb. Vasc. Biol. 28:1996–2002, 2008.Google Scholar
  19. 19.
    Hahn, C., and M. A. Schwartz. The role of cellular adaptation to mechanical gorces in atherosclerosis. Arterioscler. Thromb. Vasc. Biol. 28:2101–2107, 2008.CrossRefPubMedGoogle Scholar
  20. 20.
    Harry, B. L., J. M. Sanders, R. E. Feaver, M. Lansey, T. L. Deem, A. Zarbock, A. C. Bruce, A. W. Pryor, B. D. Gelfand, B. R. Blackman, M. A. Schwartz, and K. Ley. Endothelial cell Pecam-1 promotes atherosclerotic lesions in areas of disturbed flow in Apoe-deficient mice. Arterioscler. Thromb. Vasc. Biol. 28:2003–2008, 2008.CrossRefPubMedGoogle Scholar
  21. 21.
    He, X., and D. N. Ku. Pulsatile flow in the human left coronary artery bifurcation: average conditions. J. Biomech. Eng. 118:74–82, 1996.CrossRefPubMedGoogle Scholar
  22. 22.
    Himburg, H. A., and M. H. Friedman. Correspondence of low mean shear and high harmonic content in the Porcine iliac arteries. J. Biomech. Eng. 128:852–856, 2006.CrossRefPubMedGoogle Scholar
  23. 23.
    Himburg, H. A., D. M. Grzybowski, A. B. Hazel, J. A. LaMack, X. M. Li, and M. H. Friedman. Spatial comparison between wall shear stress measures and porcine arterial endothelial permeability. Am. J. Physiol. Heart Circ. Physiol. 286:H1916–H1922, 2004.CrossRefPubMedGoogle Scholar
  24. 24.
    Hunter, K. S., C. J. Lanning, S. Y. Chen, Y. Zhang, R. Garg, D. D. Ivy, and R. Shandas. Simulations of congenital septal defect closure and reactivity testing in patient-specific models of the pediatric pulmonary vasculature: a 3d numerical study with fluid–structure interaction. J. Biomech. Eng. 128:564–572, 2006.CrossRefPubMedGoogle Scholar
  25. 25.
    Kaazempur-Mofrad, M. R., A. G. Isasi, H. F. Younis, R. C. Chan, D. P. Hinton, G. Sukhova, G. M. LaMuraglia, R. T. Lee, and R. D. Kamm. Characterization of the atherosclerotic carotid bifurcation using Mri, finite element modeling, and histology. Ann. Biomed. Eng. 32:932–946, 2004.CrossRefPubMedGoogle Scholar
  26. 26.
    Kim, H. Dynamic Finite Element Analysis of Bioprosthetic Heart Valves with an Experimentally Derived Material Model. Ph.D. thesis, University of Iowa, 2005.Google Scholar
  27. 27.
    Kim, H., K. B. Chandran, M. S. Sacks, and J. Lu. A new finite element model for heart valve dynamic simulation. Ann. Biomed. Eng. 35:30–44, 2007.CrossRefPubMedGoogle Scholar
  28. 28.
    Kim, H., J. Lu, M. S. Sacks, and K. B. Chandran. Dynamic simulation of the opening phase of pericardial bioprosthetic heart valve function. J. Biomech. Eng. 128:717–724, 2006.CrossRefPubMedGoogle Scholar
  29. 29.
    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.PubMedGoogle Scholar
  30. 30.
    Krishnan, S., H. S. Udaykumar, J. S. Marshall, and K. B. Chandran. Two-dimensional dynamic simulation of platelet activation during mechanical heart valve closure. Ann. Biomed. Eng. 34:1519–1534, 2006.CrossRefPubMedGoogle Scholar
  31. 31.
    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 5:293–302, 1985.PubMedGoogle Scholar
  32. 32.
    Kunzelman, K. S., D. R. Einstein, and R. P. Cochran. Fluid–structure interaction models of the mitral valve function in normal and pathological states. Philos. Trans. R. Soc. Lond. B Biol. Sci. 362:1393–1406, 2007.CrossRefPubMedGoogle Scholar
  33. 33.
    Kwon, G. P., J. L. Schroeder, M. J. Amar, A. T. Remaley, and R. S. Balaban. Contribution of macromolecular structure to the retention of low-density lipoprotein at arterial branch points. Circulation 117:2919–2927, 2008.CrossRefPubMedGoogle Scholar
  34. 34.
    LaMack, J. A., and M. H. Friedman. Individual and combined effects of shear stress magnitude and spatial gradient on endothelial cell gene expression. Am. J. Physiol. Heart Circ. Physiol. 293:H2853–H2859, 2007.CrossRefPubMedGoogle Scholar
  35. 35.
    Lamack, J. A., H. A. Himburg, and M. H. Friedman. Effect of hypercholesterolemia on transendothelial Ebd-albumin permeability and lipid accumulation in porcine iliac arteries. Atherosclerosis 184:255–263, 2006.CrossRefPubMedGoogle Scholar
  36. 36.
    Lee, S. W., L. Antiga, J. D. Spence, and D. A. Steinman. Geometry of the carotid bifurcation predicts its exposure to disturbed flow. Stroke 39:2341–2347, 2008.CrossRefPubMedGoogle Scholar
  37. 37.
    Leuprecht, A., K. Perktold, M. Prosi, T. Berk, W. Trubel, and H. Schima. Numerical study of hemodynamics and wall mechanics in distal end-to-side anastomoses of bypass grafts. J. Biomech. 35:225–236, 2002.CrossRefPubMedGoogle Scholar
  38. 38.
    Li, Z., and C. Kleinstreuer. Fluid–structure interaction effects on Sac-blood pressure and wall stress in a stented aneurysm. J. Biomech. Eng. 127:662–671, 2005.CrossRefPubMedGoogle Scholar
  39. 39.
    Liang, Y., H. Zhu, and M. H. Friedman. Estimation of the transverse strain tensor in the arterial wall using ivus image registration. Ultrasound Med. Biol. 34:1832–1845, 2008.CrossRefPubMedGoogle Scholar
  40. 40.
    Liang, Y., H. Zhu, T. Gehrig, and M. H. Friedman. Measurement of the transverse strain tensor in the coronary arterial wall from clinical intravascular ultrasound images. J. Biomech. 41:2906–2911, 2008.CrossRefPubMedGoogle Scholar
  41. 41.
    Peskin, C. S. Flow patterns around heart valves: a numerical method. J. Comput. Phys. 10:252, 1972.CrossRefGoogle Scholar
  42. 42.
    Peskin, C. S. The fluid-dynamics of heart-valves—experimental, theoretical, and computational methods. Ann. Rev. Fluid Mech. 14:235–259, 1982.CrossRefGoogle Scholar
  43. 43.
    Peskin, C. S. The immersed boundary method. Acta Numer. 11:479–517, 2002.CrossRefGoogle Scholar
  44. 44.
    Ramaswamy, S. D., S. C. Vigmostad, A. Wahle, Y.-G. Lai, M. E. Olszewski, K. C. Braddy, T. M. H. Brennan, J. D. Rossen, M. Sonka, and K. B. Chandran. Fluid dynamic analysis in a human left anterior descending coronary artery with arterial motion. Ann. Biomed. Eng. 32:1628–1641, 2004.CrossRefPubMedGoogle Scholar
  45. 45.
    Ramaswamy, S. D., S. C. Vigmostad, A. Wahle, Y.-G. Lai, M. E. Olszewski, K. C. Braddy, T. M. H. Brennan, J. D. Rossen, M. Sonka, and K. B. Chandran. Comparison of left anterior descending coronary artery hemodynamics before and after angioplasty. ASME J. Biomech. Eng. 128:40–48, 2006.CrossRefGoogle Scholar
  46. 46.
    Rissland, P., Y. Alemu, S. Einav, J. Ricotta, and D. Bluestein. Abdominal aortic aneurysm risk of rupture: patient-specific Fsi simulations using anisotropic model. J. Biomech. Eng. 131:1–10, 2009.CrossRefGoogle Scholar
  47. 47.
    Salzar, R. S., M. J. Thubrikar, and R. T. Eppink. Pressure-induced mechanical stress in the carotid artery bifurcation: a possible correlation to atherosclerosis. J. Biomech. 28:1333–1340, 1995.CrossRefPubMedGoogle Scholar
  48. 48.
    Sheikh, S., M. Rahman, Z. Gale, N. T. Luu, P. C. Stone, N. M. Matharu, G. E. Rainger, and G. B. Nash. Differing mechanisms of leukocyte recruitment and sensitivity to conditioning by shear stress for endothelial cells treated with tumour necrosis factor-alpha or interleukin-1beta. Br. J. Pharmacol. 145:1052–1061, 2005.CrossRefPubMedGoogle Scholar
  49. 49.
    Slager, C. J., J. J. Wentzel, J. C. Schuurbiers, J. A. Oomen, J. Kloet, R. Krams, C. von Birgelen, W. J. van der Giessen, P. W. Serruys, and P. J. de Feyter. True 3-dimensional reconstruction of coronary arteries inpatients by fusion of angiography and ivus (Angus) and its quantitative validation. Circulation 102:511–516, 2000.PubMedGoogle Scholar
  50. 50.
    Sun, W., A. Abad, and M. S. Sacks. Simulated bioprosthetic heart valve deformation under quasi-static loading. J. Biomech. Eng. 127:905–914, 2005.CrossRefPubMedGoogle Scholar
  51. 51.
    Suo, J., D. E. Ferrara, D. Sorescu, R. E. Guldberg, W. R. Taylor, and D. P. Giddens. Hemodynamic shear stresses in mouse aortas: implications for atherogenesis. Arterioscler. Thromb. Vasc. Biol. 27:346–351, 2007.CrossRefPubMedGoogle Scholar
  52. 52.
    Tang, D., C. Yang, S. Kobayashi, J. Zheng, and R. P. Vito. Effect of stenosis asymmetry on blood flow and artery compression: a three-dimensional fluid–structure interaction model. Ann. Biomed. Eng. 31:1182–1193, 2003.CrossRefPubMedGoogle Scholar
  53. 53.
    Tang, D., C. Yang, S. Mondal, F. Liu, G. Canton, T. S. Hatsukami, and C. Yuan. A negative correlation between human carotid atherosclerotic plaque progression and plaque wall stress: in vivo Mri-based 2d/3d Fsi models. J. Biomech. 41:727–736, 2008.CrossRefPubMedGoogle Scholar
  54. 54.
    Tang, D., C. Yang, J. Zheng, P. K. Woodard, J. E. Saffitz, J. D. Petruccelli, G. A. Sicard, and C. Yuan. Local maximal stress hypothesis and computational plaque vulnerability index for atherosclerotic plaque assessment. Ann. Biomed. Eng. 33:1789–1801, 2005.CrossRefPubMedGoogle Scholar
  55. 55.
    Tang, D., C. Yang, J. Zheng, P. K. Woodard, J. E. Saffitz, G. A. Sicard, T. K. Pilgram, and C. Yuan. Quantifying effects of plaque structure and material properties on stress distributions in human atherosclerotic plaques using 3d Fsi models. J. Biomech. Eng. 127:1185–1194, 2005.CrossRefPubMedGoogle Scholar
  56. 56.
    Tang, D., C. Yang, J. Zheng, P. K. Woodard, G. A. Sicard, J. E. Saffitz, and C. Yuan. 3d Mri-based multicomponent Fsi models for atherosclerotic plaques. Ann. Biomed. Eng. 32:947–960, 2004.CrossRefPubMedGoogle Scholar
  57. 57.
    Thubrikar, M. J., and F. Robicsek. Pressure-induced arterial wall stress and atherosclerosis. Ann. Thorac. Surg. 59:1594–1603, 1995.CrossRefPubMedGoogle Scholar
  58. 58.
    Tortoriello, A., and G. Pedrizzetti. Flow-tissue interaction with compliance mismatch in a model stented artery. J. Biomech. 37:1–11, 2004.CrossRefPubMedGoogle Scholar
  59. 59.
    Tzima, E., M. Irani-Tehrani, W. B. Kiosses, E. Dejana, D. A. Schultz, B. Engelhardt, G. Cao, H. DeLisser, and M. A. Schwartz. A mechanosensory complex that mediates the endothelial cell response to fluid shear stress. Nature 437:426–431, 2005.CrossRefPubMedGoogle Scholar
  60. 60.
    Vigmostad, S. A Sharp Interface Fluid–Structure Interaction for Bioprosthetic Heart Valves. Ph.D. thesis, The University of Iowa, 2007.Google Scholar
  61. 61.
    Wentzel, J. J., J. Kloet, I. Andhyiswara, J. A. Oomen, J. C. Schuurbiers, B. J. 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.PubMedGoogle Scholar
  62. 62.
    Wentzel, J. J., R. Krams, J. C. Schuurbiers, J. A. Oomen, J. Kloet, W. J. van Der Giessen, P. W. Serruys, and C. J. Slager. Relationship between neointimal thickness and shear stress after wall stent implantation in human coronary arteries. Circulation 103:1740–1745, 2001.PubMedGoogle Scholar
  63. 63.
    Wentzel, J. J., D. M. Whelan, W. J. van der Giessen, H. M. van Beusekom, I. Andhyiswara, P. W. Serruys, C. J. Slager, and R. Krams. Coronary stent implantation changes 3-D vessel geometry and 3-D shear stress distribution. J. Biomech. 33:1287–1295, 2000.CrossRefPubMedGoogle Scholar
  64. 64.
    Yang, C., D. Tang, C. Yuan, T. S. Hatsukami, J. Zheng, and P. K. Woodard. In vivo/ex vivo Mri-based 3d non-Newtonian Fsi models for human atherosclerotic plaques compared with fluid-wall-only models. CMES 19:233–245, 2007.PubMedGoogle Scholar
  65. 65.
    Younis, H. F., M. R. Kaazempur-Mofrad, C. Chung, R. C. Chan, and R. D. Kamm. Computational analysis of the effects of exercise on hemodynamics in the carotid bifurcation. Ann. Biomed. Eng. 31:995–1006, 2003.CrossRefPubMedGoogle Scholar
  66. 66.
    Zhang, J., K. A. Burridge, and M. H. Friedman. In vivo differences between endothelial transcriptional profiles of coronary and iliac arteries revealed by microarray analysis. Am. J. Physiol. Heart Circ. Physiol. 295:H1556–H1561, 2008.CrossRefPubMedGoogle Scholar
  67. 67.
    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.CrossRefPubMedGoogle Scholar
  68. 68.
    Zhu, H., J. Zhang, J. Shih, D. S. Long, F. Lopez-Bertoni, J. R. Hagaman, N. Maeda, and M. H. Friedman. Differences in aortic arch geometry, hemodynamics, and plaque patterns between C57bl/6 and 129/Svev mice. J. Biomech. Eng., 2009. doi:10.1115/1.4000168.

Copyright information

© Biomedical Engineering Society 2010

Authors and Affiliations

  • Morton H. Friedman
    • 1
  • Rob Krams
    • 2
  • Krishnan B. Chandran
    • 3
  1. 1.Department of Biomedical EngineeringDuke UniversityDurhamUSA
  2. 2.Department of BioengineeringImperial CollegeLondonUK
  3. 3.Department of Biomedical EngineeringUniversity of IowaIowa CityUSA

Personalised recommendations