Inelastic Deformable Image Registration (i-DIR): Capturing Sliding Motion through Automatic Detection of Discontinuities

Deformable image registration (DIR) is an image-analysis method with a broad range of applications in biomedical sciences. Current applications of DIR on computed-tomography (CT) images of the lung and other organs under deformation suffer from large errors and artifacts due to the inability of standard DIR methods to capture sliding between interfaces, as standard transformation models cannot adequately handle discontinuities. In this work, we aim at creating a novel inelastic deformable image registration (i-DIR) method that automatically detects sliding surfaces and that is capable of handling sliding discontinuous motion. Our method relies on the introduction of an inelastic regularization term in the DIR formulation, where sliding is characterized as an inelastic shear strain. We validate the i-DIR by studying synthetic image datasets with strong sliding motion, and compare its results against two other elastic DIR formulations using landmark analysis. Further, we demonstrate the applicability of the i-DIR method to medical CT images by registering lung CT images. Our results show that the i-DIR method delivers accurate estimates of a local lung strain that are similar to fields reported in the literature, and that do not exhibit spurious oscillatory patterns typically observed in elastic DIR methods. We conclude that the i-DIR method automatically locates regions of sliding that arise in the dorsal pleural cavity, delivering significantly smaller errors than traditional elastic DIR methods.