MIND Demons for MR-to-CT Deformable Image Registration In Image-Guided Spine Surgery

Abstract

Purpose: Localization of target anatomy and critical structures defined in preoperative MR images can be achieved by means of multi-modality deformable registration to intraoperative CT. We propose a symmetric diffeomorphic deformable registration algorithm incorporating a modality independent neighborhood descriptor (MIND) and a robust Huber metric for MR-to-CT registration.

Method: The method, called MIND Demons, solves for the deformation field between two images by optimizing an energy functional that incorporates both the forward and inverse deformations, smoothness on the velocity fields and the diffeomorphisms, a modality-insensitive similarity function suitable to multi-modality images, and constraints on geodesics in Lagrangian coordinates. Direct optimization (without relying on an exponential map of stationary velocity fields used in conventional diffeomorphic Demons) is carried out using a Gauss-Newton method for fast convergence. Registration performance and sensitivity to registration parameters were analyzed in simulation, in phantom experiments, and clinical studies emulating application in image-guided spine surgery, and results were compared to conventional mutual information (MI) free-form deformation (FFD), local MI (LMI) FFD, and normalized MI (NMI) Demons.

Result: The method yielded sub-voxel invertibility (0.006 mm) and nonsingular spatial Jacobians with capability to preserve local orientation and topology. It demonstrated improved registration accuracy in comparison to the reference methods, with mean target registration error (TRE) of 1.5 mm compared to 10.9, 2.3, and 4.6 mm for MI FFD, LMI FFD, and NMI Demons methods, respectively. Validation in clinical studies demonstrated realistic deformation with sub-voxel TRE in cases of cervical, thoracic, and lumbar spine.

Conclusions: A modality-independent deformable registration method has been developed to estimate a viscoelastic diffeomorphic map between preoperative MR and intraoperative CT. The method yields registration accuracy suitable to application in image-guided spine surgery across a broad range of anatomical sites and modes of deformation.

Keywords: CT; Demons algorithm; MIND; MRI; deformable image registration; image-guided surgery; multimodality image registration; symmetric diffeomorphism.

Figure 1

Lagrangian description of the diffeomorphisms (ϕ₀, ϕ₁, and ψ) and their associated time-dependent velocity fields.

Figure 2

MIND stencil configurations used in this work. (a, b) Stencil for 2D and 3D images, respectively. (c) Corresponding coronal slices of the 3D stencil in (b). Gray voxels mark members of the stencil, and the black voxel marks the voxel for which MIND is computed.

Figure 3

Flowchart for the MIND Demons algorithm.

Figure 4

2D Simulated images emulating simple coronal curvature (scoliosis) of the spine, each with 31 target points. (a) T₂-weighted MR moving image (I₀). (b) CT fixed image (I₁).

Figure 5

Ovine spine phantom. (a) Phantom assembly – spine encased in polyvinyl alcohol (PVA) hydrogel within a flexible cylinder. (b) CT images with the scoliotic spine (I₀) and the straight spine (I₁). (c) T₂-weighted MR images with the scoliotic spine (I₀) and the straight spine (I₁).

Figure 6

Clinical MR and CT image data. (a) T₂-weighted MR (I₀) and (b) CT (I₁) images of the cervical spine. (c, d) The same, in the thoracic spine. (e, f) The same, in the lumbar spine.

Figure 7

Simulation study results. Transformed I₀ image following (a) MI FFD, (b) LMI FFD, (c) NMI Demons, and (d) MIND Demons. Note the reduced TRE (alignment of cyan target points) and robustness against spurious distortion for the MIND method.

Figure 8

MR-to-CT registration of the ovine spine phantom. (a–c) TRE, 𝒥, and 𝒟 as a function of registration methods.

Figure 9

MR-to-CT registration of the ovine spine phantom. (Top) Semi-opaque surface rendering of the pink MR moving image I₀ and the cyan fixed CT image I₁ after registration. Cyan spheres represent the target points in I₁ and yellow lines mark distances between corresponding target points in I₀ and I₁ after registration. (Bottom) Superposition of yellow Canny edges of the MR moving image I₀ after registration on the MR fixed image I₁. (a, f) NMI rigid registration. (b, g) MI FFD. (c, h) LMI FFD. (d, i) NMI Demons. (e, j) MIND Demons.

Figure 10

MR-to-CT registration in clinical studies. (a–c) TRE, 𝒥, and 𝒟 as a function of the spinal sections: cervical, thoracic, and lumbar spines.

Figure 11

MR-to-CT registration in clinical studies. (Top) Semi-opaque surface rendering of the pink MR moving image I₀ and the cyan fixed CT image I₁ after NMI rigid and MIND Demons registration for each spinal section. Cyan spheres represent the target points in I₁ and yellow lines mark distances between corresponding target points in I₀ and I₁ after registration. (Middle) Superposition of yellow Canny edges of the CT fixed image I₁ on the MR moving image I₀ after NMI rigid and MIND Demons registration for each spinal section. (Bottom) Checkerboard images between the MR moving image I₀ and the CT fixed image I₁ after NMI rigid and MIND Demons registration.