Whiteley Jonathan P, Gavaghan David J, Chapman S Jonathan, Brady J Michael
Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, UK.
Math Med Biol. 2007 Sep;24(3):327-45. doi: 10.1093/imammb/dqm006. Epub 2007 Sep 22.
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.
以往对乳腺组织大变形进行建模的方法，例如在磁共振成像或乳腺摄影成像中出现的情况，包括使用线性弹性和伪非线性弹性，在这种情况下，非线性变形由一系列小的线性各向同性变形近似表示，每个线性变形的（常数）杨氏模量是总非线性应变的指数函数。在本文中，将这两种方法与应力和应变呈指数关系的组织的完全非线性弹性问题的解进行了比较。在建立了每个模型并关联了模型之间的系数之后，对一块不可压缩材料进行了数值模拟。这些模拟表明，即使在模拟重力作用下人体乳房变形的情况下，较简单的模型也可能不合适。
