Limiting Fiber Extensibility as Parameter for Damage in Venous Wall
An inflation–extension test with human vena cava
inferior was performed with the aim to fit a material model. The vein
was modeled as a thick–walled tube loaded by internal pressure and
axial force. The material was assumed to be an incompressible
hyperelastic fiber reinforced continuum. Fibers are supposed to be
arranged in two families of anti–symmetric helices. Considered
anisotropy corresponds to local orthotropy. Used strain energy
density function was based on a concept of limiting strain
extensibility. The pressurization was comprised by four pre–cycles
under physiological venous loading (0 – 4kPa) and four cycles under
nonphysiological loading (0 – 21kPa). Each overloading cycle was
performed with different value of axial weight. Overloading data
were used in regression analysis to fit material model. Considered
model did not fit experimental data so good. Especially predictions
of axial force failed. It was hypothesized that due to
nonphysiological values of loading pressure and different values of
axial weight the material was not preconditioned enough and some
damage occurred inside the wall. A limiting fiber extensibility
parameter Jm was assumed to be in relation to supposed damage.
Each of overloading cycles was fitted separately with different values
of Jm. Other parameters were held the same. This approach turned out
to be successful. Variable value of Jm can describe changes in the
axial force – axial stretch response and satisfy pressure – radius
dependence simultaneously.
[1] J. V. Psaila, and J. Melhuish, "Viscoelastic properties and collagen
content of the long saphenous vein in normal and varicose veins," B. J.
Surg., vol. 76, no. 1, pp. 37-40, January 1989.
[2] T. Azuma, and M. Hasegawa, "Distensibility of the vein: From the
architectural point of view", Biorheology, vol. 10, pp. 469-479, 1973.
[3] V. Milesi, A. Rebolledo, F. A. Paredes, et al., "Mechanical properties of
human saphenosu veins from normotensive and hypertensive patients,"
Ann. Thorac. Surg., vol. 66, no. 2, pp. 455-461, August 1998.
[4] R. L. Wesly, R. N. Vaishnav, J. C. Fuchs, D. J. Patel, and J. C.
Greenfield, Jr., "Static linear and nonlinear elastic properties of normal
and arterialized venous tissue in dog and man," Circ. Research, vol. 37,
no. 4, pp. 509-520, 1975.
[5] H. W. Weizsacker, "Passive elastic properties of the rat abdominal vena
cava," Pfluger Archs., vol. 412, no. 1-2, pp. 147-154, July 1988.
[6] R. Rezakhaniha, and N. Stergiopulos, "A structural model of the venous
wall considering elastin anisotropy," J. Biomech. Eng. - Trans. ASME,
vol. 130, no. 3, article no. 031017, Jun 2008.
[7] C. O. Horgan, and G. Saccomandi, "A description of arterial wall
mechanics using limiting chain extensibility constitutive models,"
Biomechan. Model. Mechanobiol., vol. 1, no. 4, pp. 251-266, Aprile
2003.
[8] C. O. Horgan, and G. Saccomandi, "A new constitutive theory for fiber-
reinforced incompressible nonlinear elastic solids," J. Mech. Phys.
Solids, vol. 53, no. 9, pp. 1985-2015, September 2005.
[9] A. N. Gent, "New constitutive relation for rubber," Rub. Chem.
Technol., vol. 69, no. 1, pp. 59-61, Mach-April 1996.
[10] G. A. Holzapfel, Nonlinear solid mechanics - A continuum approach for
engineering. Chichester: John Wiley & Sons, 2000, ch. 6.
[11] L. Horny, R. Zitny, and H. Chlup, "Strain energy function for arterial
walls based on limiting fiber extensibility," Proceedings of 4th European
Congress for Medical and Biomedical Engineering 2008, 23-27 Nov
2008 Antwerp, Belgium, IFBME (Accepted for publication).
[1] J. V. Psaila, and J. Melhuish, "Viscoelastic properties and collagen
content of the long saphenous vein in normal and varicose veins," B. J.
Surg., vol. 76, no. 1, pp. 37-40, January 1989.
[2] T. Azuma, and M. Hasegawa, "Distensibility of the vein: From the
architectural point of view", Biorheology, vol. 10, pp. 469-479, 1973.
[3] V. Milesi, A. Rebolledo, F. A. Paredes, et al., "Mechanical properties of
human saphenosu veins from normotensive and hypertensive patients,"
Ann. Thorac. Surg., vol. 66, no. 2, pp. 455-461, August 1998.
[4] R. L. Wesly, R. N. Vaishnav, J. C. Fuchs, D. J. Patel, and J. C.
Greenfield, Jr., "Static linear and nonlinear elastic properties of normal
and arterialized venous tissue in dog and man," Circ. Research, vol. 37,
no. 4, pp. 509-520, 1975.
[5] H. W. Weizsacker, "Passive elastic properties of the rat abdominal vena
cava," Pfluger Archs., vol. 412, no. 1-2, pp. 147-154, July 1988.
[6] R. Rezakhaniha, and N. Stergiopulos, "A structural model of the venous
wall considering elastin anisotropy," J. Biomech. Eng. - Trans. ASME,
vol. 130, no. 3, article no. 031017, Jun 2008.
[7] C. O. Horgan, and G. Saccomandi, "A description of arterial wall
mechanics using limiting chain extensibility constitutive models,"
Biomechan. Model. Mechanobiol., vol. 1, no. 4, pp. 251-266, Aprile
2003.
[8] C. O. Horgan, and G. Saccomandi, "A new constitutive theory for fiber-
reinforced incompressible nonlinear elastic solids," J. Mech. Phys.
Solids, vol. 53, no. 9, pp. 1985-2015, September 2005.
[9] A. N. Gent, "New constitutive relation for rubber," Rub. Chem.
Technol., vol. 69, no. 1, pp. 59-61, Mach-April 1996.
[10] G. A. Holzapfel, Nonlinear solid mechanics - A continuum approach for
engineering. Chichester: John Wiley & Sons, 2000, ch. 6.
[11] L. Horny, R. Zitny, and H. Chlup, "Strain energy function for arterial
walls based on limiting fiber extensibility," Proceedings of 4th European
Congress for Medical and Biomedical Engineering 2008, 23-27 Nov
2008 Antwerp, Belgium, IFBME (Accepted for publication).
@article{"International Journal of Medical, Medicine and Health Sciences:60500", author = "Lukas Horny and Rudolf Zitny and Hynek Chlup and Tomas Adamek and Michal Sara", title = "Limiting Fiber Extensibility as Parameter for Damage in Venous Wall", abstract = "An inflation–extension test with human vena cava
inferior was performed with the aim to fit a material model. The vein
was modeled as a thick–walled tube loaded by internal pressure and
axial force. The material was assumed to be an incompressible
hyperelastic fiber reinforced continuum. Fibers are supposed to be
arranged in two families of anti–symmetric helices. Considered
anisotropy corresponds to local orthotropy. Used strain energy
density function was based on a concept of limiting strain
extensibility. The pressurization was comprised by four pre–cycles
under physiological venous loading (0 – 4kPa) and four cycles under
nonphysiological loading (0 – 21kPa). Each overloading cycle was
performed with different value of axial weight. Overloading data
were used in regression analysis to fit material model. Considered
model did not fit experimental data so good. Especially predictions
of axial force failed. It was hypothesized that due to
nonphysiological values of loading pressure and different values of
axial weight the material was not preconditioned enough and some
damage occurred inside the wall. A limiting fiber extensibility
parameter Jm was assumed to be in relation to supposed damage.
Each of overloading cycles was fitted separately with different values
of Jm. Other parameters were held the same. This approach turned out
to be successful. Variable value of Jm can describe changes in the
axial force – axial stretch response and satisfy pressure – radius
dependence simultaneously.", keywords = "Constitutive model, damage, fiber reinforcedcomposite, limiting fiber extensibility, preconditioning, vena cavainferior.", volume = "2", number = "8", pages = "314-4", }