Registration of Pre- and Post-Treatment Brain Images with Missing Correspondences

Abstract

Medical image registration is an important technology that can be used to align patient images from different treatment time points to a single reference frame. This process of establishing correspondences between images is important in both the clinic and research to make meaningful comparisons across scans and better understand changes that may have occurred over time. Traditional algorithms and those used in general practice assume a one-to-one correspondence between features in the images to be registered. However, this assumption is clearly violated when the images are missing correspondences, which often occurs when dealing with patient data due to treatment effects or disease progression. Standard registration methods, therefore, will likely cause misalignment of actual corresponding features, especially near regions with missing data, which are usually the locations we are most interested in aligning.

The purpose of this dissertation is to develop an automated image registration algorithm to deal with the missing correspondence problem. Our key idea is to incorporate the estimation of a label map segmenting the valid and missing correspondence voxels during the registration. We pose the registration goal as a parameter estimation problem in a maximum a posteriori framework and jointly solve for the transformation parameters and label map using the expectation-maximization (EM) algorithm. In each iteration of the algorithm, the E-step computes the probability of label assignment for valid and missing correspondences given the current transformation, while the M-step updates the registration parameters using the current label map probabilities. Under our mathematical formulation, we incorporate four models: image similarity, which defines how well the image intensities match given the registration parameters; an image intensity prior given a label map estimate; a prior on the registration parameters to constrain how an image can be deformed; and a prior on the label map segmentation.

The algorithmic framework we have developed is general and can be adapted to many missing correspondence problems by appropriate implementation of the four models. Here, we have designed implementations tailored to handle different missing correspondence situations in T1-weighted magnetic resonance images of the brain, using preoperative and postresection brain images from epilepsy patients and scans from brain tumor patients as our examples. We tested various implementations of our method against other automated intensity-based image registration algorithms and demonstrated improved alignment on both synthetic and patient data. Finally, we presented an application of our registration and labeling estimation algorithm for aiding in tracking brain metastases in a patient over time.