Selection of optimal hyper-parameters for estimation of uncertainty in MRI-TRUS registration of the prostate

Transrectal ultrasound (TRUS) facilitates intra-treatment delineation of the prostate gland (PG) to guide insertion of brachytherapy seeds, but the prostate substructure and apex are not always visible which may make the seed placement sub-optimal. Based on an elastic model of the prostate created from MRI, where the prostate substructure and apex are clearly visible, we use a Bayesian approach to estimate the posterior distribution on deformations that aligns the pre-treatment MRI with intra-treatment TRUS. Without apex information in TRUS, the posterior prediction of the location of the prostate boundary, and the prostate apex boundary in particular, is mainly determined by the pseudo stiffness hyper-parameter of the prior distribution. We estimate the optimal value of the stiffness through likelihood maximization that is sensitive to the accuracy as well as the precision of the posterior prediction at the apex boundary. From a data-set of 10 pre- and intra-treatment prostate images with ground truth delineation of the total PG, 4 cases were used to establish an optimal stiffness hyper-parameter when 15% of the prostate delineation was removed to simulate lack of apex information in TRUS, while the remaining 6 cases were used to cross-validate the registration accuracy and uncertainty over the PG and in the apex.