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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.

Original publication

DOI

10.1093/imammb/dqm006

Type

Journal article

Journal

Math Med Biol

Publication Date

09/2007

Volume

24

Pages

327 - 345

Keywords

Algorithms, Biomechanical Phenomena, Breast, Computer Simulation, Elasticity, Female, Gravitation, Humans, Hypergravity, Models, Biological, Specific Gravity, Stress, Mechanical