Robust nonrigid registration to capture brain shift from intraoperative MRI

Abstract

We present a new algorithm to register 3-D preoperative magnetic resonance (MR) images to intraoperative MR images of the brain which have undergone brain shift. This algorithm relies on a robust estimation of the deformation from a sparse noisy set of measured displacements. We propose a new framework to compute the displacement field in an iterative process, allowing the solution to gradually move from an approximation formulation (minimizing the sum of a regularization term and a data error term) to an interpolation formulation (least square minimization of the data error term). An outlier rejection step is introduced in this gradual registration process using a weighted least trimmed squares approach, aiming at improving the robustness of the algorithm. We use a patient-specific model discretized with the finite element method in order to ensure a realistic mechanical behavior of the brain tissue. To meet the clinical time constraint, we parallelized the slowest step of the algorithm so that we can perform a full 3-D image registration in 35 s (including the image update time) on a heterogeneous cluster of 15 personal computers. The algorithm has been tested on six cases of brain tumor resection, presenting a brain shift of up to 14 mm. The results show a good ability to recover large displacements, and a limited decrease of accuracy near the tumor resection cavity.

Fig. 1

The 0.5 T open magnet system (Signa SP, GE Medical Systems) of the Brigham and Women’s Hospital

Fig. 2

Overview of the steps involved in the registration process.

Fig. 3

Illustration of the pre-operative processes. (A) pre-operative image. (B) segmentation of the brain and 3D mesh generation (we only represent the surface mesh for visualization convenience). (C) Example of block selection, choosing 5% of the total brain voxels as blocks centers. Only the central voxel of the selected blocks is displayed. (D) Structure tensor visualization as ellipsoids (zoom on the red square), the color of the tensors demonstrates the fractional anisotropy.

Fig. 4

Block matching-based displacements estimation. Top left: slice of the pre-operative MR image. Top right: intra-operative MR image. Bottom: the sparse displacement field estimated with the block matching algorithm and superposed to the gradient of the pre-operative image (5% block selection, using the coefficient of correlation). The color scale encodes the norm of the displacement, in millimeters.

Fig. 5

Solving the registration problem using the approximation formulation (shown on the same slice as Figure 4). Left: dense displacement computed as the solution of Equation 8. Right: gradient of the target image superimposed on the pre-operative deformed image using the computed displacement field. We can observe a systematic error on large displacements.

Fig. 6

Solving the registration problem using the interpolation formulation leads to poor matches. Top left: intra-operative MR image intersecting the tumor. Top right: result of the registration of the pre-operative on the intra-operative image using the interpolation formulation (Equation 14). Middle left: estimated displacement using the block matching algorithm (same slice). Middle right: norm of the recovered displacement field using the interpolation formulation. Bottom: zoom on the registration displacement field around the tumor region (red box) indicates disturbed displacements.

Fig. 7

Solving the registration problem using the proposed iterative approach (Algorithm 1). Top left: result of the registration of the pre-operative on the intra-operative image using the iterative formulation (same slice as Figure 6). Top right: norm of the recovered displacement field. Bottom: zoom on the registration displacement field around the tumor region (red box) indicates realistic displacements.

Fig. 8

Visualization of the block-rejection step on the same patient as Figure 6 (2.5% of blocks rejected per iteration). Left: initial matches. Middle: after 5 iterations (12.5% rejection). Right: final selected matches after 10 iterations of block rejection (25% of the total blocks are rejected). The region around the tumor seems to have a larger rejection rate than the rest of the brain (especially below the tumor). A closer look at this region (bottom row) reveals that lots of matches around the tumor point toward a wrong direction.

Fig. 9

Result of the non-rigid registration of the pre-operative image on the intra-operative image. For each patient: (top left) pre-operative image; (top right) intra-operative image; (bottom left) result of the registration: deformation of the pre-operative image on the intra-operative image; (bottom right) gradient of the intra-operative image superimposed on the result image. The enhanced region on patient’s 4 image indicates that the resection is incomplete. The white dotted line shows where the outline of the tumour is predicted to be after deformation (top right). It shows a reasonable matching with the tumor margin in the deformed image (bottom right).

Fig. 10

Measure of the registration error for 54 landmarks as a function of the initial error (i.e. as a function of the real displacement of tissue, estimated with the landmarks).

Fig. 11

Measure of the registration error for 54 landmarks as a function of the distance to the tumor margin.