A new approach for the in-vivo characterization of the biomechanical behavior of the breast and the cornea

Abstract

The characterization of the mechanical behavior of soft living tissues is a big challenge in Biomechanics. The difficulty arises from both the access to the tissues and the manipulation in order to know their physical properties. Currently, the biomechanical characterization of the organs is mainly performed by testing ex-vivo samples or by means of indentation tests. In the first case, the obtained behavior does not represent the real behavior of the organ. In the second case, it is only a representation of the mechanical response of the indented areas. The purpose of the research reported in this thesis is the development of a methodology to in-vivo characterize the biomechanical behavior of two different organs: the breast and the cornea. The proposed methodology avoids invasive measurements to obtain the mechanical response of the organs and is able to completely characterize of the biomechanical behavior of them.

The research reported in this thesis describes a methodology to in-vivo characterize the biomechanical behavior of the breast and the cornea. The estimation of the elastic constants of the constitutive equations that define the mechanical behavior of these organs is performed using an iterative search algorithm which optimizes these parameters. The search is based on the iterative variation of the elastic constants of the model in order to increase the similarity between a simulated deformation of the organ and the real one. The similarity is measured by means of a volumetric similarity function which combines overlap-based coefficients and distance-based coefficients. Due to the number of parameters to be characterized as well as the non-convergences that the solution may present in some regions, genetic heuristics were chosen to drive the search algorithm.

In the case of the breast, the elastic constants of an anisotropic hyperelastic neo-Hookean model proposed to simulate the compression of the breast during an MRI-guided biopsy were estimated. Results from this analysis showed that the proposed algorithm accurately found the elastic constants of the proposed model, providing an average relative error below 10%. The methodology was validated using breast software phantoms. Nevertheless, this methodology can be easily transferred into its use with real breasts. In the case of the cornea, the elastic constants of a hyperelastic second-order Ogden model were estimated for 24 corneas corresponding to 12 patients. The finite element method was applied in order to simulate the deformation of the human corneas due to non-contact tonometry. The iterative search was applied in order to estimate the elastic constants of the model which approximates the most the simulated deformation to the real one. Results showed that these constants can be estimated with an error of about 5%.

After the results obtained for both organs, it can be concluded that the iterative search methodology presented in this thesis allows the \textit{in-vivo} estimation the patient-specific elastic constants of the constitutive biomechanical models that govern the biomechanical behavior of these two organs.