Modeling Articular Cartilage Growth With a Cartilage Growth Finite Element Model

The objective of this work was to develop a cartilage growth finite element model (CGFEM) to solve non-homogeneous and time-dependent growth boundary value problems. Due to the different time scales of growth and applied mechanical loading, the computational approach separated the solution of the growth boundary-value problem into two parts: one that describes the actual mechanical loading with a time scale on the order of seconds, and another that describes the resulting growth of the tissue with a time scale (i.e. increment) of 1 day. A commercial finite element code (ABAQUS) was used with tissue stress-strain and growth & remodeling algorithms implemented in its user-defined material subroutine (UMAT) to solve the non-homogeneous time-dependent growth boundary value problem in an incremental fashion.

The CGFEM has been used to simulate in vitro growth of articular cartilage explants subjected to dynamic confined compression and unconfined compression loading protocols and steady-state permeation. The results illustrated that the CGFEM can be used to predict the evolution of non-uniform tissue composition, residual stress, and mechanical properties due to differential and non-uniform growth.

Publications

  • Yamauchi KA, Raub CB, Chen AC, Sah RL, Hazelwood SJ, Klisch SM. Glycosaminoglycan and collagen remodeling during in vitro dynamic compression of articular cartilage: experiments and finite element modeling. Transactions of the ASME Summer Bioengineering Conference, 2013.
  • Ficklin TP, Davol A, Klisch SM. Simulating the growth of articular cartilage explants in a permeation bioreactor to aid in experimental protocol design. Journal of Biomechanical Engineering, 131:041008, 2009.ABSTRACT PDF
  • Davol A, Bingham MS, Sah RL, Klisch SM. A nonlinear finite element model of cartilage growth. Biomechanics and Modeling in Mechanobiology, 7:295-307, 2008.ABSTRACT PDF
  • Klisch SM. Continuum Models of growth with special emphasis on articular cartilage. In: Mechanics of Biological Tissue. Eds. Holzapfel GA, Ogden RW, Springer, Berlin-Heidelberg-New York, 2006.
  • Klisch SM, Van Dyke TJ, Hoger A.  A theory of volumetric growth for compressible elastic biological materials. Mathematics and Mechanics of Solids 6:551-575, 2001.ABSTRACT PDF

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