Stress-dependent finite growth in soft elastic tissues

https://doi.org/10.1016/0021-9290(94)90021-3Get rights and content

Abstract

Growth and remodeling in tissues may be modulated by mechanical factors such as stress. For example, in cardiac hypertrophy, alterations in wall stress arising from changes in mechanical loading lead to cardiac growth and remodeling. A general continuum formulation for finite volumetric growth in soft elastic tissues is therefore proposed. The shape change of an unloaded tissue during growth is described by a mapping analogous to the deformation gradient tensor. This mapping is decomposed into a transformation of the local zero-stress reference state and an accompanying elastic deformation that ensures the compatibility of the total growth deformation. Residual stress arises from this elastic deformation. Hence, a complete kinematic formulation for growth in general requires a knowledge of the constitutive law for stress in the tissue. Since growth may in turn be affected by stress in the tissue, a general form for the stress-dependent growth law is proposed as a relation between the symmetric growth-rate tensor and the stress tensor. With a thick-walled hollow cylinder of incompressible, isotropic hyperelastic material as an example, the mechanics of left ventricular hypertrophy are investigated. The results show that transmurally uniform pure circumferential growth, which may be similar to eccentric ventricular hypertrophy, changes the state of residual stress in the heart wall. A model of axially loaded bone is used to test a simple stress-dependent growth law in which growth rate depends on the difference between the stress due to loading and a predetermined growth equilibrium stress.

References (40)

  • K. Takamizawa et al.

    Strain energy density function and uniform strain hypothesis for arterial mechanics

    J. Biomechanics

    (1987)
  • D.R. Carter et al.

    The compressive behavior of bone as a two-phase porous material

    J. Bone Jt Surg.

    (1977)
  • C.J. Choung et al.

    Residual stress in arteries

  • K.D. Costa et al.

    Three-dimensional residual strain in canine left ventricle

    FASEB J.

    (1993)
  • S.C. Cowin

    The mechanical and stress adaptive properties of bone

    Ann. biomed. Engng

    (1983)
  • S.C. Cowin

    Wolff's law of trabecular architecture at remodeling equilibrium

    ASME J. biomech. Engng

    (1986)
  • K. Firoozbakhsh et al.

    The effect of stress concentration on bone remodeling: theoretical predictions

    ASME J. biomech. Engng

    (1989)
  • Y.C. Fung
  • B.K.D. Gairola

    Nonlinear elastic problems

  • W. Grossman

    Cardiac hypertrophy: useful adaptation or pathologic process?

    Am. J. Med.

    (1980)
  • Cited by (0)

    View full text