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

Carlos I Andrade,Daniel E Hurtado

doi:10.3390/math9010097

Abstract

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.

Highlights

Deformable image registration (DIR) is an image-analysis technique used to determine the optimal transformation that establishes the spatial correspondence of a point between two images
We note that the elastic DIR methods suffer from spurious displacements around the sliding line that result in distorted resampled images, see Figure 5, bottom row
The inelastic deformable image registration (i-DIR) method is capable of capturing the discontinuous displacement field imposed by the sliding motion, while elastic DIR methods fail to capture the jump in displacements and result in spurious displacement fields, see Further, we have shown that for this example, the i-DIR method consistently delivers residual sum of squared differences (RSS) and target registration error (TRE) metrics that confirm the superior performance of the i-DIR method when compared to the Elastic FEM and free-form deformation (FFD) methods, see Table 2

Summary

Introduction

Deformable image registration (DIR) is an image-analysis technique used to determine the optimal transformation that establishes the spatial correspondence of a point between two images. (i) the transformation model, (ii) the regularizer, and (iii) the similarity measure [1] These elements allow for the classification of DIR methods, and the reader is referred to [2] for a complete review. In this work we are concerned with the ability of the method to capture large displacements in the optimal transformation between medical images. From this perspective, transformation models can be divided into continuous-displacement transformations [3], which are suitable for small-deformation problems, and incremental diffeomorphic transformations based on the integration of flow equations [4,5], which can capture large deformations in DIR problems. While diffeomorphic methods have proven advantageous in capturing the large-displacement kinematics in DIR, continuous displacement models have been preferred in the field of medical imaging, as they provide a simple and efficient computational framework to DIR [6]

Methods

Results

Conclusion