Stochastic Correction of Boundary Conditions during Liver Surgery

Boundary conditions play an essential role in form-ing the predictive capacity of a biomechanical model of liver, which is used to facilitate the intra-operative navigation during surgery operation. However, these conditions are determined mainly by ligaments, and its the properties cannot be measured reliably. Therefore, the idea is to propose a data assimilation approach, where the deformation of the liver tissue is used to estimate the organ attachments. The behavior of liver can be captured on stereo camera, ultrasound, or some other modality, but, due to the observational errors, there is a high amount of uncertainty in the system. One possible option is to model the boundary conditions as stochastic parameters and to use the Kalman filtering method for their estimation. This filter obtains the result as iterative process based on computation of the weighted average between observed data and the physically-based model that simulates behavior of liver. Based on an approach previously proposed in [1], this work is focused on estimation of the modified boundary conditions, which is needed when ligaments are cut during surgery process. This estimation incorporates changes in liver shape movement under various manipulations. The method is evaluated using synthetic data in two scenarios: the deformation of parallelepiped mesh under single direction straight forward deformation and the deformation of liver model under more complex movements.