×

Open problems in computational vascular biomechanics: hemodynamics and arterial wall mechanics. (English) Zbl 1229.76120

Summary: The vasculature consists of a complex network of vessels ranging from large arteries to arterioles, capillaries, venules, and veins. This network is vital for the supply of oxygen and nutrients to tissues and the removal of carbon dioxide and waste products from tissues. Because of its primary role as a pressure-driven chemomechanical transport system, it should not be surprising that mechanics plays a vital role in the development and maintenance of the normal vasculature as well as in the progression and treatment of vascular disease. This review highlights some past successes of vascular biomechanics, but emphasizes the need for research that synthesizes complementary advances in molecular biology, biomechanics, medical imaging, computational methods, and computing power for purposes of increasing our understanding of vascular physiology and pathophysiology as well as improving the design of medical devices and clinical interventions, including surgical procedures. That is, computational mechanics has great promise to contribute to the continued improvement of vascular health.

MSC:

76Z05 Physiological flows
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
92C10 Biomechanics
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
92-02 Research exposition (monographs, survey articles) pertaining to biology
PDF BibTeX XML Cite
Full Text: DOI Link

References:

[1] Young, T., Hydraulic investigations, subservient to an intended Croonian lecture on the motion of the blood, Philos. trans. roy. soc. (London), 98, 164-186, (1808)
[2] Roy, C.S., The elastic properties of the arterial wall, J. physiol., 3, 125-159, (1881)
[3] Pries, A.R.; Secomb, T.W.; Gaehtgens, P., Design principles of vascular beds, Circ. res., 77, 5, 1017-1023, (1995)
[4] Olufsen, M.S., Structured tree outflow condition for blood flow in larger systemic arteries, Am. J. physiol., 276, 1 Pt 2, H257-H268, (1999)
[5] Kassab, G.S.; Rider, C.A.; Tang, N.J.; Fung, Y.C., Morphometry of pig coronary arterial trees, Am. J. physiol., 265, 1 Pt 2, H350-H365, (1993)
[6] Nichols, W.W.; O’Rourke, M.F., Mcdonald’s blood flow in arteries: theoretical, experimental and clinical principles, (2005), Oxford University Press
[7] Davies, P.F., Flow-mediated endothelial mechanotransduction, Physiol. rev., 75, 3, 519-560, (1995)
[8] Strauss, B.H.; Rabinovitch, M., Adventitial fibroblasts: defining a role in vessel wall remodeling, Am. J. respir. cell mol. biol., 22, 1, 1-3, (2000)
[9] Levy, B.I.; Tedgui, A., Biology of the arterial wall, (1999), Kluwer Academic Publishers Dordrecht
[10] Humphrey, J.D., Cardiovascular solid mechanics: cells, tissues, and organs, (2002), Springer New York
[11] Greenwald, S.E., Ageing of the conduit arteries, J. pathol., 211, 2, 157-172, (2007)
[12] O’Rourke, M.F.; Hashimoto, J., Mechanical factors in arterial aging: a clinical perspective, J. am. coll. cardiol., 50, 1, 1-13, (2007)
[13] Laurent, S.; Tropeano, A.I.; Boutouyrie, P., Pulse pressure reduction and cardiovascular protection, J. hypertens. suppl., 24, 3, S13-S18, (2006)
[14] Humphrey, J.D., Vascular adaptation and mechanical homeostasis at tissue, cellular, and sub-cellular levels, Cell biochem. biophys., 50, 2, 53-78, (2008)
[15] Jeffery, T.K.; Wanstall, J.C., Pulmonary vascular remodeling: a target for therapeutic intervention in pulmonary hypertension, Pharmacol. ther., 92, 1, 1-20, (2001)
[16] Mandegar, M.; Fung, Y.C.; Huang, W.; Remillard, C.V.; Rubin, L.J.; Yuan, J.X., Cellular and molecular mechanisms of pulmonary vascular remodeling: role in the development of pulmonary hypertension, Microvasc. res., 68, 2, 75-103, (2004)
[17] Burrowes, K.S.; Hunter, P.J.; Tawhai, M.H., Anatomically based finite element models of the human pulmonary arterial and venous trees including supernumerary vessels, J. appl. physiol., 99, 2, 731-738, (2005)
[18] Spilker, R.L.; Feinstein, J.A.; Parker, D.W.; Reddy, V.M.; Taylor, C.A., Morphometry-based impedance boundary conditions for patient-specific modeling of blood flow in pulmonary arteries, Ann. biomed. engrg., 35, 4, 546-559, (2007)
[19] Caro, C.G.; Fitz-Gerald, J.M.; Schroter, R.C., Atheroma arterial wall shear. observation, correlation and proposal of a shear dependent mass transfer mechanism for atherogenesis, Proc. roy. soc. London B: biol. sci., 177, 46, 109-159, (1971)
[20] Friedman, M.H.; Hutchins, G.M.; Bargeron, C.B.; Deters, O.J.; Mark, F.F., Correlation between intimal thickness and fluid shear in human arteries, Atherosclerosis, 39, 3, 425-436, (1981)
[21] Zarins, C.K.; Giddens, D.P.; Bharadvaj, B.K.; Sottiurai, V.S.; Mabon, R.F.; Glagov, S., Carotid bifurcation atherosclerosis. quantitative correlation of plaque localization with flow velocity profiles and wall shear stress, Circ. res., 53, 4, 502-514, (1983)
[22] Humphrey, J.D.; Canham, P., Structure, properties, and mechanics of intracranial saccular aneurysms, J. elast., 61, 49-81, (2000) · Zbl 0973.92016
[23] Vorp, D.A., Biomechanics of abdominal aortic aneurysm, J. biomech., 40, 9, 1887-1902, (2007)
[24] Humphrey, J.D.; Taylor, C.A., Intracranial and abdominal aortic aneurysms: similarities, differences, and need for a new class of computational models, Annu. rev. biomed. engrg., 10, 221-246, (2008)
[25] Baek, S.; Rajagopal, K.R.; Humphrey, J.D., A theoretical model of enlarging intracranial fusiform aneurysms, J. biomech. engrg., 128, 1, 142-149, (2006)
[26] Kroon, M.; Holzapfel, G.A., A model for saccular cerebral aneurysm growth by collagen fibre remodelling, J. theor. biol., 247, 4, 775-787, (2007)
[27] Dalman, R.L.; Tedesco, M.M.; Myers, J.; Taylor, C.A., AAA disease: mechanism, stratification, and treatment, Ann. New York acad. sci., 1085, 92-109, (2006)
[28] Anand, M.; Rajagopal, K.; Rajagopal, K.R., A model for the formation, growth, and lysis of clots in quiescent plasma. A comparison between the effects of antithrombin III deficiency and protein c deficiency, J. theor. biol., 253, 4, 725-738, (2008) · Zbl 1398.92065
[29] Guy, R.D.; Fogelson, A.L.; Keener, J.P., Fibrin gel formation in a shear flow, Math. med. biol., 24, 1, 111-130, (2007) · Zbl 1115.92017
[30] Wootton, D.M.; Ku, D.N., Fluid mechanics of vascular systems, diseases, and thrombosis, Annu. rev. biomed. engrg., 1, 299-329, (1999)
[31] Kiousis, D.E.; Gasser, T.C.; Holzapfel, G.A., A numerical model to study the interaction of vascular stents with human atherosclerotic lesions, Ann. biomed. engrg., 35, 11, 1857-1869, (2007)
[32] LaDisa, J.F.; Guler, I.; Olson, L.E.; Hettrick, D.A.; Kersten, J.R.; Warltier, D.C.; Pagel, P.S., Three-dimensional computational fluid dynamics modeling of alterations in coronary wall shear stress produced by stent implantation, Ann. biomed. engrg., 31, 8, 972-980, (2003)
[33] Rogers, C.; Edelman, E.R., Endovascular stent design dictates experimental restenosis and thrombosis, Circulation, 91, 12, 2995-3001, (1995)
[34] Finn, A.V.; Nakazawa, G.; Joner, M.; Kolodgie, F.D.; Mont, E.K.; Gold, H.K.; Virmani, R., Vascular responses to drug eluting stents: importance of delayed healing, Arterioscler. thromb. vasc. biol., 27, 7, 1500-1510, (2007)
[35] Fogarty, T.J.; Arko, F.R.; Zarins, C.K., Endograft technology: highlights of the past 10years, J. endovasc. ther., 11, Suppl. 2, II192-II199, (2004)
[36] Linfante, I.; Wakhloo, A.K., Brain aneurysms and arteriovenous malformations: advancements and emerging treatments in endovascular embolization, Stroke, 38, 4, 1411-1417, (2007)
[37] Yoganathan, A.P.; He, Z.; Casey Jones, S., Fluid mechanics of heart valves, Annu. rev. biomed. engrg., 6, 331-362, (2004)
[38] Simon, M.A.; Watson, J.; Baldwin, J.T.; Wagner, W.R.; Borovetz, H.S., Current and future considerations in the use of mechanical circulatory support devices, Annu. rev. biomed. engrg., 10, 59-84, (2008)
[39] Ross, R., Atherosclerosis – an inflammatory disease, New engl. J. med., 340, 2, 115-126, (1999)
[40] Gijsen, F.J.; Allanic, E.; van de Vosse, F.N.; Janssen, J.D., The influence of the non-Newtonian properties of blood on the flow in large arteries: unsteady flow in a 90 degrees curved tube, J. biomech., 32, 7, 705-713, (1999)
[41] Perktold, K.; Resch, M.; Peter, R.O., Three-dimensional numerical analysis of pulsatile flow and wall shear stress in the carotid artery bifurcation, J. biomech., 24, 6, 409-420, (1991)
[42] Figueroa, C.A.; Vignon-Clementel, I.E.; Jansen, K.C.; Hughes, T.J.R.; Taylor, C.A., A coupled momentum method for modeling blood flow in three-dimensional deformable arteries, Comput. methods appl. mech. engrg., 195, 41-43, 5685-5706, (2006) · Zbl 1126.76029
[43] Perktold, K.; Rappitsch, G., Computer simulation of local blood flow and vessel mechanics in a compliant carotid artery bifurcation model, J. biomech., 28, 7, 845-856, (1995)
[44] Ethier, C.R., Computational modeling of mass transfer and links to atherosclerosis, Ann. biomed. engrg., 30, 4, 461-471, (2002)
[45] Taylor, C.A.; Hughes, T.J.R.; Zarins, C.K., Finite element modeling of blood flow in arteries, Comput. methods appl. mech. engrg., 158, 155-196, (1998) · Zbl 0953.76058
[46] Taylor, C.A.; Draney, M.T., Experimental and computational methods in cardiovascular fluid mechanics, Annu. rev. fluid mech., 36, 197-231, (2004) · Zbl 1125.76414
[47] Vignon-Clementel, I.E.; Figueroa, C.A.; Jansen, K.E.; Taylor, C.A., Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries, Comput. methods appl. mech. engrg., 195, 29-32, 3776-3796, (2006) · Zbl 1175.76098
[48] Fung, Y.C., Biomechanics: motion, flow, stress, and growth, (1990), Springer New York · Zbl 0743.92007
[49] Holzapfel, G.A.; Gasser, T.C.; Ogden, R.W., A new constitutive framework for arterial wall mechanics and a comparative study of material models, J. elast., 61, 1-48, (2000) · Zbl 1023.74033
[50] A. Valentin, L. Cardamone, S. Baek, J.D. Humphrey, Complementary vasoactivity and matrix remodelling in arterial adaptations to altered flow and pressure, J. R. Soc. Interface (2009), in press.
[51] Alastrue, V.; Pena, E.; Martinez, M.A.; Doblare, M., Assessing the use of the “opening angle method” to enforce residual stresses in patient-specific arteries, Ann. biomed. engrg., 35, 10, 1821-1837, (2007)
[52] Delfino, A.; Stergiopulos, N.; Moore, J.E.; Meister, J.J., Residual strain effects on the stress field in a thick wall finite element model of the human carotid bifurcation, J. biomech., 30, 8, 777-786, (1997)
[53] Stalhand, J.; Klarbring, A.; Karlsson, M., Towards in vivo aorta material identification and stress estimation, Biomech. model mechanobiol., 2, 3, 169-186, (2004)
[54] Masson, I.; Boutouyrie, P.; Laurent, S.; Humphrey, J.D.; Zidi, M., Characterization of arterial wall mechanical behavior and stresses from human clinical data, J. biomech., (2008)
[55] Hughes, T.J.R.; Liu, W.K.; Zimmermann, T.K., Lagrangian – eulerian finite element formulation for incompressible viscous flows, Comput. methods appl. mech. engrg., 29, 329-349, (1981) · Zbl 0482.76039
[56] Wolinsky, H.; Glagov, S., Comparison of abdominal and thoracic aortic medial structure in mammals. deviation of man from the usual pattern, Circ. res., 25, 6, 677-686, (1969)
[57] Tarbell, J.M., Mass transport in arteries and the localization of atherosclerosis, Annu. rev. biomed. engrg., 5, 79-118, (2003)
[58] Shadden, S.C.; Taylor, C.A., Characterization of coherent structures in the cardiovascular system, Ann. biomed. engrg., 36, 7, 1152-1162, (2008)
[59] Dajnowiec, D.; Langille, B.L., Arterial adaptations to chronic changes in haemodynamic function: coupling vasomotor tone to structural remodelling, Clin. sci. (London), 113, 1, 15-23, (2007)
[60] Buerk, D.G., Can we model nitric oxide biotransport? A survey of mathematical models for a simple diatomic molecule with surprisingly complex biological activities, Annu. rev. biomed. engrg., 3, 109-143, (2001)
[61] Rachev, A., A model of arterial adaptation to alterations in blood flow, J. elast., 61, 83-111, (2000) · Zbl 1071.74660
[62] Taber, L.A., A model for aortic growth based on fluid shear and fiber stresses, J. biomech. engrg., 120, 3, 348-354, (1998)
[63] Humphrey, J.D.; Rajagopal, K.R., A constrained mixture model for growth and remodeling of soft tissues, Math. model method appl. sci., 12, 407-430, (2002) · Zbl 1021.74026
[64] Watton, P.N.; Hill, N.A.; Heil, M., A mathematical model for the growth of the abdominal aortic aneurysm, Biomech. model mechanobiol., 3, 2, 98-113, (2004)
[65] Baek, S.; Gleason, R.L.; Rajagopal, K.R.; Humphrey, J.D., Theory of small on large: potential utility in computations of fluid – solid interactions in arteries, Comput. methods appl. mech. engrg., 196, 3070-3078, (2007) · Zbl 1127.74026
[66] Figueroa, C.A.; Baek, S.; Taylor, C.A.; Humphrey, J.D., A computational framework for coupled fluid – solid growth modeling in cardiovascular simulations, Comput. methods appl. mech. engrg., 3583-3602, (2008) · Zbl 1229.74097
[67] Moore, J.A.; Rutt, B.K.; Karlik, S.J.; Yin, K.; Ethier, C.R., Computational blood flow modeling based on in vivo measurements, Ann. biomed. engrg., 27, 5, 627-640, (1999)
[68] Taylor, C.A.; Draney, M.T.; Ku, J.P.; Parker, D.; Steele, B.N.; Wang, K.; Zarins, C.K., Predictive medicine: computational techniques in therapeutic decision-making, Comput. aided surg., 4, 5, 231-247, (1999)
[69] Long, Q.; Xu, X.Y.; Ariff, B.; Thom, S.A.; Hughes, A.D.; Stanton, A.V., Reconstruction of blood flow patterns in a human carotid bifurcation: a combined CFD and MRI study, J. magn. reson. imaging, 11, 3, 299-311, (2000)
[70] Steinman, D.A., Image-based computational fluid dynamics modeling in realistic arterial geometries, Ann. biomed. engrg., 30, 4, 483-497, (2002)
[71] Gijsen, F.J.; Wentzel, J.J.; Thury, A.; Lamers, B.; Schuurbiers, J.C.; Serruys, P.W.; van der Steen, A.F., A new imaging technique to study 3-d plaque and shear stress distribution in human coronary artery bifurcations in vivo, J. biomech., 40, 11, 2349-2357, (2007)
[72] Tang, B.T.; Cheng, C.P.; Draney, M.T.; Wilson, N.M.; Tsao, P.S.; Herfkens, R.J.; Taylor, C.A., Abdominal aortic hemodynamics in Young healthy adults at rest and during lower limb exercise: quantification using image-based computer modeling, Am. J. physiol. heart circ. physiol., 291, 2, H668-H676, (2006)
[73] Cebral, J.R.; Castro, M.A.; Burgess, J.E.; Pergolizzi, R.S.; Sheridan, M.J.; Putman, C.M., Characterization of cerebral aneurysms for assessing risk of rupture by using patient-specific computational hemodynamics models, AJNR - am. J. neuroradiol., 26, 10, 2550-2559, (2005)
[74] Jou, L.D.; Wong, G.; Dispensa, B.; Lawton, M.T.; Higashida, R.T.; Young, W.L.; Saloner, D., Correlation between lumenal geometry changes and hemodynamics in fusiform intracranial aneurysms, AJNR - am. J. neuroradiol., 26, 9, 2357-2363, (2005)
[75] Shojima, M.; Oshima, M.; Takagi, K.; Torii, R.; Hayakawa, M.; Katada, K.; Morita, A.; Kirino, T., Magnitude and role of wall shear stress on cerebral aneurysm: computational fluid dynamic study of 20 middle cerebral artery aneurysms, Stroke, 35, 11, 2500-2505, (2004)
[76] Wilson, N.M.; Wang, K.C.; Dutton, R.W.; Taylor, C.A., A software framework for creating patient specific geometric models from medical imaging data for simulation based medical planning of vascular surgery, Lect. notes comput. sci., 2208, 449-456, (2001) · Zbl 1041.68783
[77] Bekkers, E.J.; Taylor, C.A., Multiscale vascular surface model generation from medical imaging data using hierarchical features, IEEE trans. med. imaging, 27, 3, 331-341, (2008)
[78] Cebral, J.R.; Castro, M.A.; Appanaboyina, S.; Putman, C.M.; Millan, D.; Frangi, A.F., Efficient pipeline for image-based patient-specific analysis of cerebral aneurysm hemodynamics: technique and sensitivity, IEEE trans. med. imaging, 24, 4, 457-467, (2005)
[79] Zhang, Y.; Bazilevs, Y.; Goswami, S.; Bajaj, C.L.; Hughes, T.J.R., Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow, Comput. methods appl. mech. engg., 196, 29-30, 2943-2959, (2007) · Zbl 1121.76076
[80] Moore, J.A.; Steinman, D.A.; Ethier, C.R., Computational blood flow modeling: errors associated with reconstructing finite element models from magnetic resonance images, J. biomech., 31, 2, 179-184, (1998)
[81] Marsden, A.L.; Vignon-Clementel, I.E.; Chan, F.P.; Feinstein, J.A.; Taylor, C.A., Effects of exercise and respiration on hemodynamic efficiency in CFD simulations of the total cavopulmonary connection, Ann. biomed. engrg., 35, 2, 250-263, (2007)
[82] Migliavacca, F.; Dubini, G.; Bove, E.L.; de Leval, M.R., Computational fluid dynamics simulations in realistic 3-d geometries of the total cavopulmonary anastomosis: the influence of the inferior caval anastomosis, J. biomech. engrg., 125, 6, 805-813, (2003)
[83] Marsden, A.L.; Feinstein, J.A.; Taylor, C.A., A computational framework for derivative-free optimization of cardiovascular geometries, Comput. methods appl. mech. engrg., 197, 21-24, 1890-1905, (2008) · Zbl 1194.76296
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.