Our research on biomechanical modelling of soft tissue has two aims:
- efficient and accurate computation of the solution of the governing equations; and
- simplification of the model whilst maintaining physical realisticity.
There are currently two areas of application: the heart; and the breast. In each of these application areas the deformations seen are too large to be modelled by linear elasticity, and so we apply the theory of finite deformation elasticity to these problems. The tissues are usually modelled as being incompressible, with incompressibility being enforced using Lagrange multipliers. A further complication is that most biological tissues have a preferred direction for stretching. These problems are three-dimensional, and the incompressibility constraint introduces several numerical complications when solving the governing equations. An accurate and efficient solution of the governing equations offers a significant computational challenge.
This work is in collaboration with The Bioenginnering Institute at the University of Auckland as part of the Integrative Biology project for whole heart modelling. We and our collaborators aim to couple soft tissue, cellular and fluid dynamics models of the heart.
There are a range of techniques that may be used for locating cancerous tumours within the breast. For each of these techniques the breast is in a different position: for Magnetic Resonance (MR) imaging the woman is lying face down; for mammography (X-rays) the breast is tightly compressed; and for ultrasound the woman lies half on her side or face up. A further complication is that during surgery the woman may lie in yet another position. Combining the information from these different imaging modalities and then providing the surgeon with an accurate location of the tumour during surgery requires a robust soft tissue model of the breast.
A problem associated with soft tissue modelling that is of particular relevance when studying the breast is that of solving the inverse problem. For all the imaging modalities described above the breast is in a deformed position. The calculation of the position of the undeformed breast, by solving the inverse problem, is necessary if information from these different imaging modalities is to be fused.
- P. Pathmanathan, D.J. Gavaghan, J.P. Whiteley and J.M. Brady. Predicting the deformation of the breast with a 3D finite element model for image matching and tumour location. International Workshop on Digital Mammography, Chapel Hill, North Carolina, USA, 2004.
- P. Pathmanathan, D.J. Gavaghan, J.P. Whiteley, J.M. Brady, M.P. Nash, P.M.F. Nielsen and V. Rajagopal. Predicting tumour location by simulating large deformations of the breast using a 3D finite element model and nonlinear elasticity. Proceedings of MICCAI 2004, Lecture Notes in Computer Science 3217, 217-224, 2004.
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