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Mathematical Medicine and Biology Advance Access originally published online on September 22, 2007
Mathematical Medicine and Biology 2007 24(3):327-345; doi:10.1093/imammb/dqm006
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© The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Non-linear modelling of breast tissue

Jonathan P. Whiteley{dagger} and David J. Gavaghan

Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, UK

S. Jonathan Chapman

Mathematical Institute, University of Oxford, 24–29 St Giles, Oxford OX1 3LB, UK

J. Michael Brady

Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK

{dagger} Email: jonathan.whiteley{at}comlab.ox.ac.uk

Received on December 29, 2005. Revised on February 21, 2007. Accepted on July 15, 2007.

Previous approaches to modelling the large deformation of breast tissue, as occurs, e.g. in imaging using magnetic resonance imaging or mammography, include using linear elasticity and pseudo-non-linear elasticity, in which case the non-linear deformation is approximated by a series of small linear isotropic deformations, with the (constant) Young's modulus of each linear deformation an exponential function of the total non-linear strain. In this paper, these two approaches are compared to the solution of the full non-linear elastic problem for tissue with an exponential relationship between stress and strain. Having formulated each model and related the coefficients between the models, numerical simulations are performed on a block of incompressible material. These demonstrate that the simpler models may not be appropriate even in the case of modelling deformations of the human breast under gravity.

Keywords: nonlinear elasticity; linear elasticity; breast modelling


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