Fung’s Model Constants for Intracranial Blood Vessel of Human Using Biaxial Tensile Test Results
Mechanical properties of cerebral arteries are, due to their relationship with cerebrovascular diseases, of clinical worth. To acquire these properties, eight samples were obtained from middle cerebral arteries of human cadavers, whose death were not due to injuries or diseases of cerebral vessels, and tested within twelve hours after resection, by a precise biaxial tensile test device specially developed for the present study considering the dimensions, sensitivity and anisotropic nature of samples. The resulting stress-stretch curve was plotted and subsequently fitted to a hyperelastic three-parameter Fung model. It was found that the arteries were noticeably stiffer in circumferential than in axial direction. It was also demonstrated that the use of multi-parameter hyperelastic constitutive models is useful for mathematical description of behavior of cerebral vessel tissue. The reported material properties are a proper reference for numerical modeling of cerebral arteries and computational analysis of healthy or diseased intracranial arteries.
[1] R. J. Coulson, M. J. Cipolla, L .Vitullo, N. C. Chesler, “Mechanical
properties of rat middle cerebral arteries with and without myogenic
tone,” J. Biomech Eng, 2004, 126, pp. 76-81.
[2] G. A. Holzapfel, T. C. Gasser, R. W. Ogden, “A new constitutive
framework for arterial wall mechanics and a comparative study of
material models,” J. Elasticity, 2000, 61, pp. 1-48.
[3] V. Gourisankaran, M. G. Sharma, “The finite element analysis of
stresses in atherosclerotic arteries during balloon angioplasty,” Crit Rev
Biomed Eng, 2000, 28 (1-2), pp. 47-51.
[4] Y. Feng, S. Wada, K. Tsubota, T. Yamaguchi, “ Growth of intracranial
aneurysms arising from curved vessels under the influence of elevated
wall shear stress a computer simulation study,” JSME Int. J. Ser. C,
2004, Series C. 2004, 47(4), pp. 1035–1042.
[5] W. S. Aronow, K.S. Schwartz, M. Koenigsberg, “ Correlation of serum
lipids calcium, and phosphorus, diabetes mellitus and history of systemic
hypertension with presence or absence of calcified or thickened aortic
cusps or root in elderly patients,” Am J Cardiol 1987, 59 (9), pp. 998-9.
[6] M. Lindroos, M. Kupari, J. Heikkila, R. Tuilvis, “Prevalence of aortic
valve abnormalities in the elderly: An echocardiography study of a
random population sample,” Am J Cardiol, 1993, 21(5), pp. 1220-5.
[7] K. Ourie, “Peripheral Arterial Disease,” Lancet, 2001, 358(9289), pp.
1257-64.
[8] C. Ally, A. J. Reid, P. J. Prendergast, “Elastic behavior of porcine
coronary artery tissue under uniaxial and equibiaxial tension,” Ann
Biomed Eng, 2004, 32(10), pp. 1355-64.
[9] S. A. Dixon, R. G. Heikes, R. P. Vito, “Constitutive modeling of porcine
coronary arteries using designed experiments,” J. Biomech Eng, 2003,
125(2), pp. 274-9.
[10] S. H. Lu, M. S. Sacks, S. Y. Chung, D. C. Gloeckner, R. Pruchnic, J.
Huard, W. C. Degroat, M. B. Chancellor, “Biaxial mechanical properties
of muscle derived cell seeded small intestinal submucosa for bladder
wall reconstitution,” Biomaterials, 2005,26(4), pp. 443-9.
[11] J. C. Criscione, M. S. Sacks, W. C. Hunter, “Experimentally tractable
pseudoelastic constitutive law for biomembranes,” J. Biomech Eng,
2003, 125 (1), pp. 94-9.
[12] R. J. Okamoto, J. E. Wagenseil, W. R. Delong, S. J. Peterson, N. T.
Kouchoukos, “Mechanical properties of dilated human ascending aorta,”
Ann Biomed Eng, 2002, 30(5), pp. 624-35.
[13] G. J. L'Italien, N. R. Chandrasekar, G. M. Lamuraglia, W. C. Pevec, S.
Dhara, D. F. Warnock, W. M. Abbott, “Biaxial elastic properties of rat
arteries in vivo: Influence of vascular wall cells on anisotropy,” Am J
Physiol, 1994, 267(2 Pt 2), pp. H574-9.
[14] G. A. Holzapfel, R. Eberlein, P. Wriggers,, H. Weizsacker, “Large strain
analysis of soft biological membranes: Formulation and finite element
analysis,” Comput Methods Appl Mech Eng, 1996, 132(1-2), pp. 45-61.
[15] R. W. Ogden, Nonlinear Elastic Deformations, 1st Ed, New York, Dover
Publication,1997.
[16] M. A. Zulliger, P. Fridez, K. Hayashi, N. Stergiopulos, “A strain energy
function for arteries accounting for wall composition and structure,” J.
Biomech, 2004, 37(7), pp. 989-1000.
[17] T. C. Gasser, C. A. Schulze-Bauer, G. A. Holzapfel, “A three
dimensional finite element model for arterial clamping,” J. Biomech
Eng, 2002,124.
[18] J. D. Humphrey, R. K. Strumpf, F. C. P. Yin, “Determination of a
constitutive relation for passive myocardium: a new functional form,” J.
Biomech Eng, 1990,112.
[19] J. D. Humphrey, R. K. Strumpf, F. C. P. Yin, “Determination of a
constitutive relation for passive myocardium: II. Parameter estimation,”
J . Biomech Eng, 1990, 112(3), pp. 340-6.
[20] W. E. Stehbens, “Pathology of the Cerebral Blood Vessels,” St Louis,
MO: CV Mosby, 1972, pp. 351–470
[21] D. E. Busby, A. C. Burton, “The effect of age on the elasticity of the
major brain arteries,” Can J Appl Physiol Pharmacol, 1965, 43(2),pp.
185-202.
[22] J. J. Hu, S. Baek, J. D. Humphrey, “Strain behavior of the passive basilar
artery in normotension and hypertension,” J. Biomech, 2007, 40(11), pp.
2559-63.
[23] J. J. Hu, T. W. Fossum, M. W. Miller, H . Xu, J. C. Liu, J. D.
Humphrey, “Biomechanics of the porcine basilar artery in
hypertension,” Ann Biomed Eng, 2006, 35, pp. 19-29.
[24] B. K. Wicker, H. P. Hutchens, Q. Wu, A. T. Yeh, J. D. Humphrey,
“Normal basilar artery structure and biaxial mechanical behavior,”
Comput Methods Biomech Biomed Engin, 2008, 11, pp. 539–551.
[25] S. Nagasawa, H. Handa, Y. Naruo, K. Moritake, K. Hayashi,
“Experimental cerebral vasospasm arterial wall mechanics and
connective tissue composition,” Stroke, 1982, 13, pp. 595-600.
[26] K. Monson, Mechanical and failure properties of human cerebral blood
vessels, Ph.D. Thesis, University of California, Berkeley, USA, 2001.
[27] S. Scott, G. G. Fergosun, M. R. Roach, “Comparison of the elastic
properties of human intracranial arteries and aneurysms,” Can J Appl
Physiol Pharmacol, 1972, 50, pp. 328-32.
[28] P. Seshaiyer, F. P. K. Hsu, A. D. Shah, S. K. Kyriacou, J. D. Humphrey,
“Multiaxial mechanical behavior of human saccular aneurysms,”
Comput Methods Biomech Biomed Engin, 2001, 4, pp. 281-289.
[29] K. Toth, “Analysis of the mechanical parameters of human brain
aneurysm,” Acta Bioeng Biomech, 2005, 7,pp. 1-21.
[30] K. L. Monson, N. M. Barbaro, G. T. Manley, “Biaxial response of
passive human cerebral arteries,” Ann Biomed Eng, 2008, 36, pp. 28-41.
[31] Y. C. Fung, K. Fronek, P. Patitucci, “Pseudoelasticity of arteries and the
choice of its mathematical expression,” Am J Physiol, 1979, 237, pp.
620–631.
[1] R. J. Coulson, M. J. Cipolla, L .Vitullo, N. C. Chesler, “Mechanical
properties of rat middle cerebral arteries with and without myogenic
tone,” J. Biomech Eng, 2004, 126, pp. 76-81.
[2] G. A. Holzapfel, T. C. Gasser, R. W. Ogden, “A new constitutive
framework for arterial wall mechanics and a comparative study of
material models,” J. Elasticity, 2000, 61, pp. 1-48.
[3] V. Gourisankaran, M. G. Sharma, “The finite element analysis of
stresses in atherosclerotic arteries during balloon angioplasty,” Crit Rev
Biomed Eng, 2000, 28 (1-2), pp. 47-51.
[4] Y. Feng, S. Wada, K. Tsubota, T. Yamaguchi, “ Growth of intracranial
aneurysms arising from curved vessels under the influence of elevated
wall shear stress a computer simulation study,” JSME Int. J. Ser. C,
2004, Series C. 2004, 47(4), pp. 1035–1042.
[5] W. S. Aronow, K.S. Schwartz, M. Koenigsberg, “ Correlation of serum
lipids calcium, and phosphorus, diabetes mellitus and history of systemic
hypertension with presence or absence of calcified or thickened aortic
cusps or root in elderly patients,” Am J Cardiol 1987, 59 (9), pp. 998-9.
[6] M. Lindroos, M. Kupari, J. Heikkila, R. Tuilvis, “Prevalence of aortic
valve abnormalities in the elderly: An echocardiography study of a
random population sample,” Am J Cardiol, 1993, 21(5), pp. 1220-5.
[7] K. Ourie, “Peripheral Arterial Disease,” Lancet, 2001, 358(9289), pp.
1257-64.
[8] C. Ally, A. J. Reid, P. J. Prendergast, “Elastic behavior of porcine
coronary artery tissue under uniaxial and equibiaxial tension,” Ann
Biomed Eng, 2004, 32(10), pp. 1355-64.
[9] S. A. Dixon, R. G. Heikes, R. P. Vito, “Constitutive modeling of porcine
coronary arteries using designed experiments,” J. Biomech Eng, 2003,
125(2), pp. 274-9.
[10] S. H. Lu, M. S. Sacks, S. Y. Chung, D. C. Gloeckner, R. Pruchnic, J.
Huard, W. C. Degroat, M. B. Chancellor, “Biaxial mechanical properties
of muscle derived cell seeded small intestinal submucosa for bladder
wall reconstitution,” Biomaterials, 2005,26(4), pp. 443-9.
[11] J. C. Criscione, M. S. Sacks, W. C. Hunter, “Experimentally tractable
pseudoelastic constitutive law for biomembranes,” J. Biomech Eng,
2003, 125 (1), pp. 94-9.
[12] R. J. Okamoto, J. E. Wagenseil, W. R. Delong, S. J. Peterson, N. T.
Kouchoukos, “Mechanical properties of dilated human ascending aorta,”
Ann Biomed Eng, 2002, 30(5), pp. 624-35.
[13] G. J. L'Italien, N. R. Chandrasekar, G. M. Lamuraglia, W. C. Pevec, S.
Dhara, D. F. Warnock, W. M. Abbott, “Biaxial elastic properties of rat
arteries in vivo: Influence of vascular wall cells on anisotropy,” Am J
Physiol, 1994, 267(2 Pt 2), pp. H574-9.
[14] G. A. Holzapfel, R. Eberlein, P. Wriggers,, H. Weizsacker, “Large strain
analysis of soft biological membranes: Formulation and finite element
analysis,” Comput Methods Appl Mech Eng, 1996, 132(1-2), pp. 45-61.
[15] R. W. Ogden, Nonlinear Elastic Deformations, 1st Ed, New York, Dover
Publication,1997.
[16] M. A. Zulliger, P. Fridez, K. Hayashi, N. Stergiopulos, “A strain energy
function for arteries accounting for wall composition and structure,” J.
Biomech, 2004, 37(7), pp. 989-1000.
[17] T. C. Gasser, C. A. Schulze-Bauer, G. A. Holzapfel, “A three
dimensional finite element model for arterial clamping,” J. Biomech
Eng, 2002,124.
[18] J. D. Humphrey, R. K. Strumpf, F. C. P. Yin, “Determination of a
constitutive relation for passive myocardium: a new functional form,” J.
Biomech Eng, 1990,112.
[19] J. D. Humphrey, R. K. Strumpf, F. C. P. Yin, “Determination of a
constitutive relation for passive myocardium: II. Parameter estimation,”
J . Biomech Eng, 1990, 112(3), pp. 340-6.
[20] W. E. Stehbens, “Pathology of the Cerebral Blood Vessels,” St Louis,
MO: CV Mosby, 1972, pp. 351–470
[21] D. E. Busby, A. C. Burton, “The effect of age on the elasticity of the
major brain arteries,” Can J Appl Physiol Pharmacol, 1965, 43(2),pp.
185-202.
[22] J. J. Hu, S. Baek, J. D. Humphrey, “Strain behavior of the passive basilar
artery in normotension and hypertension,” J. Biomech, 2007, 40(11), pp.
2559-63.
[23] J. J. Hu, T. W. Fossum, M. W. Miller, H . Xu, J. C. Liu, J. D.
Humphrey, “Biomechanics of the porcine basilar artery in
hypertension,” Ann Biomed Eng, 2006, 35, pp. 19-29.
[24] B. K. Wicker, H. P. Hutchens, Q. Wu, A. T. Yeh, J. D. Humphrey,
“Normal basilar artery structure and biaxial mechanical behavior,”
Comput Methods Biomech Biomed Engin, 2008, 11, pp. 539–551.
[25] S. Nagasawa, H. Handa, Y. Naruo, K. Moritake, K. Hayashi,
“Experimental cerebral vasospasm arterial wall mechanics and
connective tissue composition,” Stroke, 1982, 13, pp. 595-600.
[26] K. Monson, Mechanical and failure properties of human cerebral blood
vessels, Ph.D. Thesis, University of California, Berkeley, USA, 2001.
[27] S. Scott, G. G. Fergosun, M. R. Roach, “Comparison of the elastic
properties of human intracranial arteries and aneurysms,” Can J Appl
Physiol Pharmacol, 1972, 50, pp. 328-32.
[28] P. Seshaiyer, F. P. K. Hsu, A. D. Shah, S. K. Kyriacou, J. D. Humphrey,
“Multiaxial mechanical behavior of human saccular aneurysms,”
Comput Methods Biomech Biomed Engin, 2001, 4, pp. 281-289.
[29] K. Toth, “Analysis of the mechanical parameters of human brain
aneurysm,” Acta Bioeng Biomech, 2005, 7,pp. 1-21.
[30] K. L. Monson, N. M. Barbaro, G. T. Manley, “Biaxial response of
passive human cerebral arteries,” Ann Biomed Eng, 2008, 36, pp. 28-41.
[31] Y. C. Fung, K. Fronek, P. Patitucci, “Pseudoelasticity of arteries and the
choice of its mathematical expression,” Am J Physiol, 1979, 237, pp.
620–631.
@article{"International Journal of Biological, Life and Agricultural Sciences:65443", author = "Mohammad Shafigh and Nasser Fatouraee and Amirsaied Seddighi", title = "Fung’s Model Constants for Intracranial Blood Vessel of Human Using Biaxial Tensile Test Results", abstract = "Mechanical properties of cerebral arteries are, due to their relationship with cerebrovascular diseases, of clinical worth. To acquire these properties, eight samples were obtained from middle cerebral arteries of human cadavers, whose death were not due to injuries or diseases of cerebral vessels, and tested within twelve hours after resection, by a precise biaxial tensile test device specially developed for the present study considering the dimensions, sensitivity and anisotropic nature of samples. The resulting stress-stretch curve was plotted and subsequently fitted to a hyperelastic three-parameter Fung model. It was found that the arteries were noticeably stiffer in circumferential than in axial direction. It was also demonstrated that the use of multi-parameter hyperelastic constitutive models is useful for mathematical description of behavior of cerebral vessel tissue. The reported material properties are a proper reference for numerical modeling of cerebral arteries and computational analysis of healthy or diseased intracranial arteries.
", keywords = "Anisotropic Tissue, Cerebral Blood Vessels, Fung Model, Nonlinear Material, Plain Stress.", volume = "7", number = "3", pages = "237-5", }
