×

zbMATH — the first resource for mathematics

A 3-D framework for arterial growth and remodeling in response to altered hemodynamics. (English) Zbl 1231.76369
Summary: We present a three-dimensional mathematical framework for modeling the evolving geometry, structure, and mechanical properties of a representative straight cylindrical artery subjected to changes in mean blood pressure and flow. We show that numerical predictions recover prior findings from a validated two-dimensional framework, but extend those findings by allowing effects of transmural gradients in wall constituents and vasoactive molecules to be simulated directly. Of particular note, we show that the predicted evolution of the residual stress related opening angle in response to an abrupt, sustained increase in blood pressure is qualitatively similar to measured changes when one accounts for a nonlinear transmural distribution of pre-stretched elastin. We submit that continuum-based constrained mixture models of arterial adaptation hold significant promise for deepening our basic understanding of arterial mechanobiology and thus for designing improved clinical interventions to treat many different types of arterial disease and injury.

MSC:
76Z05 Physiological flows
92C35 Physiological flow
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alford, P.W.; Humphrey, J.D.; Taber, L.A., Growth and remodeling in a thick-walled artery model: effects of spatial variations in wall constituents, Biomech. model. mechanobiol., 7, 245-262, (2008)
[2] Baek, S.; Rajagopal, K.R.; Humphrey, J.D., A theoretical model of enlarging intracranial fusiform aneurysms, J. biomech. eng., 128, 142-149, (2006)
[3] Baek, S.; Valentín, A.; Humphrey, J.D., Biochemomechanics of cerebral vasospasm and its resolution: II. constitutive relations and model simulations, Ann. biomed. eng., 35, 1498-1509, (2007)
[4] D. Bergel, The visco-elastic properties of the arterial wall, PhD Thesis, University of London, London, UK, 1960.
[5] Cardamone, L.; Valentín, A.; Eberth, J.F.; Humphrey, J.D., Origin of axial prestretch and residual stress in arteries, Biomech. model. mechanobiol., 8, 431-446, (2009)
[6] Cardamone, L.; Valentín, A.; Eberth, J.F.; Humphrey, J.D., Modelling carotid artery adaptations to dynamic alterations in pressure and flow over the cardiac cycle, Math. med. biol., (2010) · Zbl 1203.92019
[7] Dorrington, K.L.; McCrum, N.G., Elastin as a rubber, Biopolymers, 16, 1201-1222, (1977)
[8] Driessen, N.J.B.; Cox, M.A.J.; Bouten, C.V.C.; Baaijens, F.P.T., Remodelling of the angular collagen fiber distribution in cardiovascular tissues, Biomech. model. mechanobiol., 7, 93-103, (2008)
[9] Fridez, P.; Zulliger, M.; Bobard, F.; Montorzi, G.; Miyazaki, H.; Hayashi, K.; Stergiopulos, N., Geometrical, functional, and histomorphometric adaptation of rat carotid artery in induced hypertension, J. biomech., 36, 671-680, (2003)
[10] Fung, Y., On the foundations of biomechanics, J. appl. mech., 50, 1003, (1983)
[11] Hariton, I.; de Botton, G.; Gasser, T.C.; Holzapfel, G.A., Stress-driven collagen fiber remodeling in arterial walls, Biomech. model. mechanobiol., 6, 163-175, (2007)
[12] 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
[13] Hu, J.-J.; Ambrus, A.; Fossum, T.W.; Miller, M.W.; Humphrey, J.D.; Wilson, E., Time courses of growth and remodeling of porcine aortic media during hypertension: a quantitative immunohistochemical examination, J. histochem. cytochem., 56, 359-370, (2008)
[14] Hu, J.-J.; Fossum, T.W.; Miller, M.W.; Xu, H.; Liu, J.-C.; Humphrey, J.D., Biomechanics of the porcine basilar artery in hypertension, Ann. biomed. eng., 35, 19-29, (2007)
[15] Humphrey, J.; Rajagopal, K., A constrained mixture model for growth and remodeling of soft tissues, Math. models methods appl. sci., 12, 407-430, (2002) · Zbl 1021.74026
[16] Humphrey, J.D., Cardiovascular solid mechanics: cells, tissues, and organs, (2002), Springer Verlag
[17] Humphrey, J.D., Vascular adaptation and mechanical homeostasis at tissue, cellular, and sub-cellular levels, Cell biochem. biophys., 50, 53-78, (2008)
[18] Humphrey, J.D., Mechanisms of arterial remodeling in hypertension: coupled roles of wall shear and intramural stress, Hypertension, 52, 195-200, (2008)
[19] Humphrey, J.D.; Rajagopal, K.R., A constrained mixture model for arterial adaptations to a sustained step change in blood flow, Biomech. model. mechanobiol., 2, 109-126, (2003)
[20] Karsaj, I.; Sansour, C.; Soric, J., The modelling of fibre reorientation in soft tissue, Biomech. model. mechanobiol., 8, 359-370, (2009)
[21] Langille, B.L., Arterial remodeling: relation to hemodynamics, Can. J. physiol. pharmacol., 74, 834-841, (1996)
[22] Lehman, R.M.; Owens, G.K.; Kassell, N.F.; Hongo, K., Mechanism of enlargement of major cerebral collateral arteries in rabbits, Stroke, 22, 499-504, (1991)
[23] Rachev, A., Theoretical study of the effect of stress-dependent remodeling on arterial geometry under hypertensive conditions, J. biomech., 30, 819-827, (1997)
[24] Rachev, A., A model of arterial adaptation to alterations in blood flow, J. elast., 61, 83-111, (2000) · Zbl 1071.74660
[25] Rachev, A.; Hayashi, K., Theoretical study of the effects of vascular smooth muscle contraction on strain and stress distributions in arteries, Ann. biomed. eng., 27, 459-468, (1999)
[26] Rodriguez, E.K.; Hoger, A.; McCulloch, A.D., Stress-dependent finite growth in soft elastic tissues, J. biomech., 27, 455-467, (1994)
[27] Rudic, R.D.; Shesely, E.G.; Maeda, N.; Smithies, O.; Segal, S.S.; Sessa, W.C., Direct evidence for the importance of endothelium-derived nitric oxide in vascular remodeling, J. clin. invest., 101, 731-736, (1998)
[28] Taber, L.A., A model for aortic growth based on fluid shear and fiber stresses, J. biomech. eng., 120, 348-354, (1998)
[29] Taber, L.A.; Eggers, D.W., Theoretical study of stress-modulated growth in the aorta, J. theor. biol., 180, 343-357, (1996)
[30] Taylor, C.A.; Humphrey, J.D., Open problems in computational vascular biomechanics: hemodynamics and arterial wall mechanics, Comput. methods appl. mech. eng., 198, 3514-3523, (2009) · Zbl 1229.76120
[31] Vaishnav, R.; Vossoughi, J., Estimation of residual stress in aortic segments, Biomed. eng. II: recent dev., (1983), Pergamon Press New York, pp. 330-333
[32] Valentín, A.; Cardamone, L.; Baek, S.; Humphrey, J.D., Complementary vasoactivity and matrix remodelling in arterial adaptations to altered flow and pressure, J. R. soc. interface, 6, 293-306, (2009)
[33] Valentín, A.; Humphrey, J.D., Parameter sensitivity study of a constrained mixture model of arterial growth and remodeling, J. biomech. eng., 131, 101006, (2009)
[34] Valentín, A.; Humphrey, J.D., Evaluation of fundamental hypotheses underlying constrained mixture models of arterial growth and remodelling, Philos. trans. A: math. phys. eng. sci., 367, 3585-3606, (2009) · Zbl 1185.74069
[35] Wicker, B.K.; Hutchens, H.P.; Wu, Q.; Yeh, A.T.; Humphrey, J.D., Normal basilar artery structure and biaxial mechanical behaviour, Comput. methods biomech. biomed. eng., 11, 539-551, (2008)
[36] Zeinali-Davarani, S.; Choi, J.; Baek, S., On parameter estimation for biaxial mechanical behavior of arteries, J. biomech., 42, 524-530, (2009)
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.