Journal Article

Non-linear modelling of breast tissue

Jonathan P. Whiteley, David J. Gavaghan, S. Jonathan Chapman and J. Michael Brady

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 24, issue 3, pages 327-345
Published in print September 2007 | ISSN: 1477-8599
Published online September 2007 | e-ISSN: 1477-8602 | DOI:
Non-linear modelling of breast tissue

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  • Applied Mathematics
  • Biomathematics and Statistics


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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

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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