Predicting tumor location by modeling the deformation of the breast

Breast cancer is one of the biggest killers in the western world, and early diagnosis is essential for improved prognosis. The shape of the breast varies hugely between the scenarios of magnetic resonance (MR) imaging (patient lies prone, breast hanging down under gravity), X-ray mammography (breast strongly compressed) and ultrasound or biopsy/surgery (patient lies supine), rendering image fusion an extremely difficult task. This paper is concerned with the use of the finite-element method and nonlinear elasticity to build a 3-D, patient-specific, anatomically accurate model of the breast. The model is constructed from MR images and can be deformed to simulate breast shape and predict tumor location during mammography or biopsy/surgery. Two extensions of the standard elasticity problem need to be solved: an inverse elasticity problem (arising from the fact that only a deformed, stressed, state is known initially), and the contact problem of modeling compression. The model is used for craniocaudal mediolateral oblique mammographic image matching, and a number of numerical experiments are performed.