Introduction

Tissue deformation and shift that occur during neurosurgery during removal of a tumor results in a loss of the spatial relation established between the patient (brain) and the MR/CT image volumes acquired prior to surgery. This relation between the patient and the MR/CT scans is the basis for accurate neuronavigation-based procedures. Due to the inhomogeneous nature of the brain, the displacements will vary from point to point based on local elasticity and intra-cranial pressure. Therefore, the magnitude of the brain shift will be dependent on the size and location of the tumor. A large brain shift, if not corrected, will result in inaccuracies in surgical procedures and has the potential to cause damage to normal tissue. Detection and correction of brain shift during surgery is essential to the preservation of neuronavigation accuracy. This work aims to utilize intra-operative CT imaging to monitor and correct preoperative MR/CT scans for brain shift.

A method has been developed for registration and tracking of brain structures in intraoperative CT image volumes and mapping these volumes to MR/CT image volumes acquired prior to surgery and used as input for neuronavigation systems. This registration and tracking process makes it possible to correct deformations and displacements of various brain structures, and enables neuronavigation in the coordinate system that is set up between the patient (brain) and the pre-surgical scans. In the following, the details of the method are given and examples demonstrating its capabilities are presented.

Problem Description

It is assumed that an MR_p image and a CT_p image of a patient’s brain taken prior to the surgery are available. It is also assumed that k CT images CT₁, CT₂, . . CT_k of the patient taken during surgery are available. a) We want to rigidly register the pre-surgical images (MR_p and CT_p) so that knowing the coordinates of points in the CT_p image, we will know the coordinates of the corresponding points in the MR_p image. b) We want to nonrigidly register image CT_p with image CT₁, nonrigidly register image CT₁ with image CT₂, and so on until finally images CT_k-1 and CT_k are nonrigidly registered. This sequence of nonrigid registrations makes it possible to trace coordinates of points in any intraoperatively obtained CT image back to the CT or MR image acquired prior to surgery, and consequently correct the coordinates of brain that has been displaced as a result of the surgery.

Approach

A)  Rigid Registration

Rigid registration is achieved by selecting the fifteen most unique and spatially distributed spherical templates in the MR_p image volume and searching for them in the CT_p image volume using mutual information as the similarity measure. Among the fifteen matches, four that produce the most accurate rigid registration are chosen, and the transformation obtained from them is used to relate coordinates of points in MR_p and CT_p images. A key characteristic of this method is that since it discards the inaccurate matches, the pre-surgical MR_p and CT_p volumes may have significant differences and by using only templates from similar areas in the images the process will find the rigid transformation. The example in Fig. 1 shows a registration case where the CT image volume contains a head holder, while the MR data was acquired without a head holder. The rigid registration is automatic, robust, and fast. It takes only a few minutes to register two typical pre-surgical MR_p and CT_p image volumes.

B)   Nonrigid Registration

The nonrigid registration step matches two consecutive CT images (CT_i and CT_i+1) with nonlinear geometric differences. To account for local geometric differences between the volumes, a large number of correspondences is used. Moreover, an elastic transformation is applied that adapts to the local geometric differences between the volumes.

Nonrigid registration is achieved in a coarse to fine fashion. At the coarse level, the resolution of the volumes is reduced by a factor of 4. Second derivative edges are located, and correspondence is established between the edges. The geometry and intensity of edges are used to achieve the matching. To filter out the possible mismatches, various constraints are used. From the coordinates of corresponding edge points in the images at the coarse resolution, a transformation function is estimated to map CT_i+1 to CT_i at mid-resolution (original volumes reduced by a factor of 2).  This resampling globally aligns the images and compensates for deformations that are extended globally over the image domain.

The nonrigid registration is repeated on the mid-resolution CT_i and the resampled mid-resolution CT_i+1. The obtained transformation is used to resample the original CT_i+1 image to align with the original CT_i image. This step further corrects the geometry of CT_i+1 to resemble that of CT_i. This transformation compensates for deformations that cover rather large local neighborhoods.

To correct for fine local deformations, the process is repeated, this time registering the resampled CT_i+1 with CT_i at fine resolution. The coarse-to-fine registration process gradually corrects CT_i+1 to take the geometry of CT_i. The gradual deformation improves the edge matching accuracy. At the coarse resolution, local geometric differences between the images are smoothed so edges in the images will have similar geometries, resulting in a high match rating. Gradually, the complexity of the images is increased while changing the geometry of one image to take the geometry of the other image. Therefore, the process compensates for large geometric differences between the images by gradually deforming one image and matching with the other image.

A transformation function developed in this project is used in the nonrigid registration. A characteristic of this transformation function is that it does not require a uniform density of point correspondences and a highly varying density of point correspondences may be used to register the images. This property is a requirement as the density of edge points used in the matching changes with the local structure of images and varies greatly across the image domain. Another characteristic of this transformation function is that it has a rigidity parameter that can be adjusted to the magnitude of geometric differences between the images.

The software developed in this project allows registration of complete volumes, or registration of subvolumes of interest in two images. If there is a need to register only subvolumes of interest in two images, after rigidly registering the images, the subvolume of interest may be selected manually with the mouse. This is shown in the left image in Fig. 2. The entire images are then replaced with the selected subvolumes and coregistered. An example of this is shown in the right image in Fig. 2.

Results

In this section a number of examples are given, demonstrating the capabilities and properties of the newly developed software.

A)  Registration of synthetic images

In order to determine the accuracy of the method, a number of synthetic images were generated. An example of this is shown in Fig. 3. One of the images is a real one. The second image is generated from the first by removing a spherical area of a desired radius and shifting the remaining image points towards the center of the removed area by amounts nonlinearly proportional to their distances to the center of region. More specifically, point (x,y) in the synthetic image is shifted by aexp{-[(x-x_r)² +(y-y_i)²]/2s²} in the direction connecting point (x,y) to point (x_r,y_r), where a is the maximum shift, (x_r,y_r) is the center of the removed area, and s shows the inverse rate the deformation fades away with respect to the center of the removed region. The smaller the s, the higher the rate the deformation fades away. By comparing the true magnitude and direction of shift of each image point with the magnitude and direction of shift estimated by the registration process, the maximum (MAX) and root-mean-squared (RMS) errors between the true and the estimated shifts can be computed. Table 1 shows MAX and RMS errors of the nonrigid registration under various magnitudes and rates of deformation. All numbers are in voxels. The registration res
ult when s = a = 5 voxels is shown in Fig. 3. Only the subvolume of interest containing deformation was processed in this example.

(a)                                                                                                                                     (b)

(c)                                                                                                                                     (d)

B)   Registration of intraoperative CT data

To determine the quality of registration for real images, one of intraoperative CT images available to us were used. Fig. 4. shows the rigid registration step. The nonrigid registration step did not work on these images because of the considerable intensity differences between them caused by streak artifacts from surgical instruments used during the surgery (pins to fix the head). The nonrigid registration, however, works rather well when a subvolume that does not contain the artifacts is selected from the images and registered. This is depicted in Fig. 5.

C)  Computational complexity

The rigid registration step takes only a few minutes to complete. The nonrigid registration consists of times to register the images at coarse, mid, and fine resolutions. These times are 15, 23, and 30 minutes, respectively, for images of size 256X256X200. If time is critical, the user may stop after the coarse or mid-resolution step. If time is available, one should register the images at fine resolution to account for local deformations of one image with respect to the other. Since registration of entire images may not be necessary intraoperatively, one may choose an area of interest in the rigidly registered space and register the subvolumes at fine resolution in a relatively short amount of time. The time needed to register an area of size 100X100X100 is about 5 minutes. All times reported here are measured using a PC with a 2 GHz processor.

Conclusions

A method for registering pre-surgical MR/CT scans taken preoperatively to images taken intraoperatively has been designed and implemented. The method has the following characteristics:

1. It consists of a rigid and and multiple nonrigid registration steps.
2. 2.The rigid registration step is robust and fast. It can register images with considerable intensity differences as well as some local geometric differences in just a few minutes.
3. The nonrigid registration is achieved from coarse to fine in three steps. The coarse registration, which takes about 15 minutes, compensates for global nonlinear geometric differences between the images. The mid-resolution registration takes 23 minutes and compensates for deformations that exist over rather large local areas. And finally, the fine resolution takes 30 minutes and accounts for deformations that only exist in small neighborhoods. Subvolume of size 100X100X100 take only 5 minutes to register. The process can register images with a combination of local and global geometric differences.
4. To achieve high speed while maintaining high accuracy in registration, a mechanism has been implemented that allows the user to select an area of interest in rigidly registered space and register corresponding areas in the images nonrigidly at fine resolution.
5. The developed system, in addition to image registration, supports imaging capabilities that are essential in reviewing and saving of images. The software allows quick and easy reviewing of images individually or in synchronization after a registration. It allows overlaying of image edges to visually evaluate the quality of registration. It generates 3-D flow diagrams that visualize the amount and direction of shift across the image domain. The software can read a variety of file formats including DICOM and save images in a new lossless compressed format.
6. The methodology and the developed software are believed to be unique, providing imaging capabilities that are not found elsewhere.

Further results on registration of pre- and post-surgical MR brain images are shown here.

For more information contact A. Goshtasby (agoshtas@cs.wright.edu).

Last modified:7/28/03.