Breast deformation modelling: comparison of methods to obtain a patient specific unloaded configuration

In biomechanical simulations of the human breast, the analysed geometry is often reconstructed from in vivo medical imaging procedures. For example in dynamic contrast enhanced magnetic resonance imaging, the acquired geometry of the patient's breast when lying in the prone position represents a deformed configuration that is pre-stressed by typical in vivo conditions and gravity. Thus, physically realistic simulations require consideration of this loading and, hence, establishing the undeformed configuration is an important task for accurate and reliable biomechanical modelling of the breast. We compare three different numerical approaches to recover the unloaded configuration from the loaded geometry given patient-specific biomechanical models built from prone and supine MR images. The algorithms compared are:(i) the simple inversion of gravity without the consideration of pre-stresses, (ii) an inversefinite deformation approach and (iii) afixed point type iterative approach which uses only forward simulations. It is shown that the iterative and the inverse approach produce similar zero-gravity estimates, where as the simple inversion of gravity is only appropriate for small or highly constrained deformations.