Intensity based image registration using robust similarity measure and constrained optimization: Applications for radiation therapy.

Abstract

In radiotherapy, an x-ray beam arrangement should be planned based on a correct patient model using a planning CT (Computed Tomography) and the x-ray beam should be focused accurately to implement the plan on actual patient. Since the patient model may not be accurate due to organ motion and there is patient set-up error, the actual delivery of the x-ray may differ from the optimal one intended by a physician, thus risking damage to normal tissues and possibly delivering a suboptimal radiation dose to the tumors. Correct estimation of the patient set-up error and organ motion is important since one can retrospectively calculate the actual x-ray dose accumulation from the treatment using the estimated set-up error and organ motion. Moreover, if the set up estimate can be completed quickly before the treatment, then one can compensate for the set-up error by adjusting either the radiotherapy table or the x-ray beam position prior to treatment delivery. Also, if one can build a <italic>dynamic model</italic> of patient organ motions before treatment, the treatment plan can be established more accurately considering the motions. Image registration is a very useful technique for estimating both patient set up and organ motion for radiation therapy. Patient set up may be estimated by 3D/2D image registration, which registers planning CT image onto radiograph images from the treatment room and organ motion from one time to another may be estimated using nonrigid image registration of two images from two time instances. We investigated several rigid and nonrigid image registration methods that are useful for estimating patient set up positioning and organ motion. By conducting an experiment with anthropomorphic chest phantom, we investigated the feasibility of 3D/2D registration methods for the set-up estimation. We achieved sub-voxel accuracy using two orthogonal projection images by the sample correlation coefficient based and the MI (Mutual Information) based methods. We have proposed a novel robust image registration method based on a <italic> robust correlation coefficient</italic>, which is useful for registering images containing unexpected objects. Images from treatment rooms usually contain objects that are not present in the planning CT image, such as radiotherapy table. The statistical properties such as bias, variance and robustness of the proposed method in comparisons with the sample correlation and the MI based method have been analyzed. We also investigated a novel nonrigid image registration method in which the estimated deformation obeys the physical constraint of positive Jacobian determinant. We derived a closed form expression of possible minimum and maximum Jacobian in terms of gradient bounds analytically. To enforce the gradient bounds of the deformation in optimization, we have introduced constraint sets in the parameter space. The optimization was accomplished using the gradient projection method with Dykstra's <italic>cyclic projection</italic> method.