A three dimensional finite element method for biological active soft tissue Formulation in cylindrical polar coordinates

Christian Bourdarias; Stéphane Gerbi; Jacques Ohayon

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 37, Issue: 4, page 725-739
  • ISSN: 0764-583X

Abstract

top
A hyperelastic constitutive law, for use in anatomically accurate finite element models of living structures, is suggested for the passive and the active mechanical properties of incompressible biological tissues. This law considers the passive and active states as a same hyperelastic continuum medium, and uses an activation function in order to describe the whole contraction phase. The variational and the FE formulations are also presented, and the FE code has been validated and applied to describe the biomechanical behavior of a thick-walled anisotropic cylinder under different active loading conditions.

How to cite

top

Bourdarias, Christian, Gerbi, Stéphane, and Ohayon, Jacques. "A three dimensional finite element method for biological active soft tissue Formulation in cylindrical polar coordinates." ESAIM: Mathematical Modelling and Numerical Analysis 37.4 (2010): 725-739. <http://eudml.org/doc/194188>.

@article{Bourdarias2010,
abstract = { A hyperelastic constitutive law, for use in anatomically accurate finite element models of living structures, is suggested for the passive and the active mechanical properties of incompressible biological tissues. This law considers the passive and active states as a same hyperelastic continuum medium, and uses an activation function in order to describe the whole contraction phase. The variational and the FE formulations are also presented, and the FE code has been validated and applied to describe the biomechanical behavior of a thick-walled anisotropic cylinder under different active loading conditions. },
author = {Bourdarias, Christian, Gerbi, Stéphane, Ohayon, Jacques},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Constitutive law; finite element method; biological tissue; hyperelasticity; nonlinear partial differential equations; anisotropic material.; hyperelastic continuum medium; thick-walled anisotropic cylinder},
language = {eng},
month = {3},
number = {4},
pages = {725-739},
publisher = {EDP Sciences},
title = {A three dimensional finite element method for biological active soft tissue Formulation in cylindrical polar coordinates},
url = {http://eudml.org/doc/194188},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Bourdarias, Christian
AU - Gerbi, Stéphane
AU - Ohayon, Jacques
TI - A three dimensional finite element method for biological active soft tissue Formulation in cylindrical polar coordinates
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 4
SP - 725
EP - 739
AB - A hyperelastic constitutive law, for use in anatomically accurate finite element models of living structures, is suggested for the passive and the active mechanical properties of incompressible biological tissues. This law considers the passive and active states as a same hyperelastic continuum medium, and uses an activation function in order to describe the whole contraction phase. The variational and the FE formulations are also presented, and the FE code has been validated and applied to describe the biomechanical behavior of a thick-walled anisotropic cylinder under different active loading conditions.
LA - eng
KW - Constitutive law; finite element method; biological tissue; hyperelasticity; nonlinear partial differential equations; anisotropic material.; hyperelastic continuum medium; thick-walled anisotropic cylinder
UR - http://eudml.org/doc/194188
ER -

References

top
  1. W.M. Bayliss, On the local reaction of the arterial wall to changes of internal pressure. J. Physiol. London28 (1902) 220-231.  
  2. J. Berntsen, T.O. Espelid and A. Genz, Algorithm 698: DCUHRE: An adaptive multidimensional integration routine for a vector of integrals. ACM Trans. Math. Softw.17 (1991) 452-456.  Zbl0900.65053
  3. P.H.M. Bovendeerd, T. Arts, J.M. Huyghe, D.H. van Campen and R.S. Reneman, Dependance of local left ventricular wall mechanics on myocardial fiber orientation: a model study. J. Biomech.25 (1992) 1129-1140.  
  4. P.G. Ciarlet, The finite element method for elliptic problems, Vol. 4 of Studies in Mathematics and its Applications. North-Holland, Amsterdam-New York (1980).  Zbl0511.65078
  5. K.D. Costa, P.J. Hunter, J.S. Wayne, L.K. Waldman, J.M. Guccione and A.D. McCulloch, A three-dimensional finite element method for large elastic deformations of ventricular myocardium: Part I. Cylindrical and spherical polar coordinates. ASME J. Biomech. Eng.118 (1996) 452-463.  
  6. R. Glowinski and P. LeTallec, Augmented lagrangian and operator-splitting methods in nonlinear mechanics. SIAM, Philadelphia, PA (1989).  
  7. D.H.S. Lin and F.C.P. Yin, A multiaxial constitutive law for mammalian left ventricular myocardium in steady-state barium contracture or tetanus. J. Biomech. Eng.120 (1998) 504-517.  
  8. L.E. Malvern, Introduction to the mechanics of a continuous medium. Prentice-Hall (1969).  Zbl0181.53303
  9. A.D. McCulloch, L.K. Waldman, J. Rogers and J. Guccione, Large scale finite element analysis of the beating heart. Crit. Rev. Biomed. Eng.20 (1992) 427-449.  
  10. J.J. Morge, B.S. Garbow and K.E. Hillstrom, User Guide for MINPACK-1. Technical Report ANL-80-74, Argonne National Laboratory (March 1980).  
  11. J.T. Oden, Finite elements of nonlinear continua. McGraw-Hill, New York (1972).  Zbl0235.73038
  12. J. Ohayon and R.S. Chadwick, Effects of collagen microstructure on the mechanics of the left ventricle. Biophys. J.54 (1988) 1077-1088.  
  13. M.J.D. Powell, A hybrid method for nonlinear equations, in Numerical methods for nonlinear algebraic equations, P. Rabinowitz Ed. Gordon and Breach, New York (1970) 87-114.  
  14. A. Quarteroni and A. Valli, Numerical approximation of partial differential equations, Vol. 23 of Springer Series in Computational Mathematics. Springer Verlag, Berlin (1994).  Zbl0803.65088
  15. G.M. Rubanyi, Mechanoreception by the vascular wall. Futura Publishing Company, Inc. (1993).  
  16. L.A. Taber, On a nonlinear theory for muscle shells: Part II. Application to the beating left ventricle. J. Biomech. Eng.113 (1991) 63-71.  
  17. P. Teppaz, J. Ohayon and R. Herbin, Interaction fluide-structure active : écoulement artériel. C.R. Acad. Sci. Paris324 (1997) 37-45.  Zbl0873.76099
  18. T.P. Usyk, Omens J.H. and A.D. McCulloch, Regional septal dysfunction in a three-dimensional computational model of focal myofiber dissaray. Am. J. Physiol. Heart Circ. Physiol.281 (2001) 506-514.  
  19. J. Zhang and C. Xu, A class of indefinite dogleg path mehods for unconstrained minimization. SIAM J. Optim.9 (1999) 646-667.  Zbl0953.90053

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.