Assimilating intraoperative data with brain shift modeling using the adjoint equations

Biomechanical models of brain deformation are increasingly being used to nonrigidly register preoperative MR (pMR) images of the brain to the surgical scene. These model estimates can potentially be improved by incorporating sparse displacement data available in the operating room (OR), but integrating the intraoperative information with model calculations is a nontrivial problem. We present an inverse method to estimate the unknown boundary and volumetric forces necessary to achieve a least-squares fit between the model and the data that is formulated in terms of the adjoint equations, which are solved directly by the method of representers. The scheme is illustrated in a 2D simulation and in a 2D approximation based on a patient case using actual OR data.