The Mathematical Institute, University of Oxford, Eprints Archive

A Comparison of Numerical Methods used for
Finite Element Modelling of Soft Tissue
Deformation

Pathmanathan, P. and Whiteley, J. P. and Gavaghan, D. J. (2009) A Comparison of Numerical Methods used for
Finite Element Modelling of Soft Tissue
Deformation.
Not specified . (Submitted)

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Abstract

Soft tissue deformation is often modelled using incompressible nonlinear elasticity, with solutions computed using the finite element method. There are a range of options available when using the finite element method, in particular, the polynomial degree of the basis functions used for interpolating position and pressure, and the type of element making up the mesh. We investigate the effect of these choices on the accuracy of the computed solution, using a selection of model problems motivated by typical deformations seen in soft tissue modelling. We set up model problems with discontinuous material properties (as is the case for the breast), steeply changing gradients in the body force (as found in contracting cardiac tissue), and discontinuous first derivatives in the solution at the boundary, caused by a discontinuous applied force (as in the breast during mammography). We find that the choice of pressure basis functions are vital in the presence of a material interface, higher-order schemes do not perform as well as may be expected when there are sharp gradients, and in general that it is important to take the expected regularity of the solution into account when choosing a numerical scheme.

Item Type:Article
Subjects:H - N > Numerical analysis
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:814
Deposited By:Dr M. Stoll
Deposited On:24 Sep 2009 13:39
Last Modified:24 Sep 2009 13:39

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