Automatic Registration of Postmortem Brain Slices to MRI Reference Volume

T.-S. Kim,+ Student Member, IEEE, M. Singh,+ Senior Member, IEEE, W. Sungkarat+, C . Zarow* and H. Chui*

'Depts. of Radiology and Biomedical Engineering, *Dept. of Neurology, University of Southern California, Los Angeles, USA

ABSTRACT A new strategy to register each slice of the postmortem brain to corresponding MRI slices is presented. The approach relies on a recursive reslicing of the 3D MRI volume using non- linear polynomial transformations. Simulation studies to validate the approach and results using real data are presented. The results suggest the feasibility and practicability of second and third-order polynomials to register postmortem images on a slice-by-slice basis to corresponding MR sections. Using this method, it is possible to investigate the pathology of a disease through routinely acquired MRIs and postmortem brains.

1. INTRODUCTION

The pathology of a disease is generally investigated by analyzing postmortem brain slices. Correlations of the postmortem slices to in-vivo MR images can provide quantitative measures of pathology. For example, patients with small-vessel ischemia and Alzheimer's disease show white matter lesions (WML), hippocampal and cortical atrophy, and peculiar vascular infarction known as lacunar infarcts or lacunes [ 11. These features can usually be identified on MR scans but are often difficult to detect on postmortem slices. Registration of the post-mortem slices to MRI can help identify these features and enable further investigation of the MR signal characteristics of the underlying disease. However the postmortem brain sections are prone to geometrical distortions due to slicing and dehydration, and it is generally difficult to keep all the slices with respect to a single reference point to realign the images, making 3D volume reconstruction difficult. Although several image registration packages [6] such as Automatic Image Registration (AIR) [2] exist, these packages require a well-reconstructed high-resolution 3D volume and relatively comparable voxel characteristics such as those for PET-to-PET, MRI-to-MRI, or PET-to-MRI registration. Our initial studies suggest that registration based on these techniqucs does not work well due to extreme distortions and nonuniform pixel intensity distribution between postmortem and MR images. In this study we present the results of our studies to register any slice of the postmortem brain to its corresponding MR section using 2D- to-3D non-linear polynomial based transformations.

11. METHOD

A. Postmortem Brain Image Preparation The postmortem brains were treated in 10% neutral formalin for at least two weeks, and then each brain was sectioned into 25-30 coronal slices of 5mm thick. Each image is then digitized, and stored in the Kodak PhotoCD RGB color format at a resolution of 3072x2048 (Fig. 1), keeping an in-plane spatial resolution of approximately 0.6mm.

B. Premortem Magnetic Resonance Imaging To facilitate visualization of lacunes (which are best seen in relatively thick transaxial proton density and T2 weighted slices) and other structures such as the hippocampus (which are best seen in relatively thin T1 weighted coronal slices) three types of data sets were acquired on a GE 1.5T Signa System: coronal T1-weighted, transaxial Proton Density (PD), and transaxial T2-weighted MRIs respectively.

The T1-weighted 3D coronal scan was made using a gradient-echo (SPGR) sequence with TR=24ms, TE=Sms, Flip Angle=45", Field of View=24x24cm2, 124 slices, Slice Thickness=l.Smm, and 0.86x0.86 mm2 in-plane resolution. The PD and TZweighted MRIs were acquired using a turbo spin echo (TSE) with TR=45ms, TEl=14ms, TE2=85ms, 51 slices, Slice thickness=3mm, and 1 .Ox 1 .0mm2 in-plane resolution.

C. Brain Segmentation The brain was segmented from the background of RGB postmortem images by selectively thresholding the RGB intensity values as shown Fig. 1, then stored in gray scale. For segmenting the brain out of a reference 3D MRI, the Brain Surface Extraction (BSE) Algorithm developed by Sander and Leahy [3], which extracts brain regions using a morphological algorithm, was used to strip off the skull and scalp in the MR images. In addition, the regions of pons and cerebrum were removed manually by inspecting each slice, since these regions were absent in the postmortem slices. The optimal segmentation parameters for BSE were selected when the segmented brain had minimal loss on the contours of the gray matter visually.

Figure 1: A digitized (left) and segmented (Right) brain slice.

D. Image Registration The purpose of this work is to relate MR signal characteristics (TI, T2, and PD) derived from transaxial or coronal images to corresponding lesions or regions of interest (ROI) in the postmortem images by matching a postmortem slice to a MRI section lying within the MRI volume. Since only a few slices of postmortem images contain regions of interest for lesions, this approach is cost effective. Also better sensitivity in

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matching images can be obtained because only a slice of image is considered at a time. Due to the higher resolution of MRI, a set of coronal T1-weighted MR images was used to form the reference volume.

Image warping for registration from 2D to 3D was incorporated by a polynomial transformation using modified general nth-order polynomials as given below [7]:

u = a. + alx + a2y + a3x2 + a 4 q + a5y2 + ... v = bo + blx + b2y + b3x2 + b 4 q + bsy2 + ... w =cg + CIX + c2y + c3x2 + c 4 q + c,y2 + ...

where x and y are indices of 2D image, u,v, and w are coordinates of pixels in the 3D reference volume image, and a,, b, and c, are the coefficients of image transformation.

This polynomial transformation translates the coordinates of pixels in a 2D postmortem slice to voxels in the 3D MRI volume. Therefore a slice of MRI, representing a warped 2D section lying within the 3D volume, is derived at every iteration until a matching MR slice to a postmortem slice is found. The best matching MR image to a postmortem image is found by minimizing the error between the recursively sliced and warped MR image and a given postmortem image.

The registration algorithm is designed to take an initial guess image that produces the minimum error, then transformation parameters are estimated using a quasi-Newton- based multidimensional optimization algorithm [4]. To produce an image at transformed voxel coordinates, linear or cubic 3D interpolation methods [4] are used.

To define the registration error between a postmortem slice and a registered MRI, we have investigated two different cost criteria. Based on our registration work in functional MRI [5] and its proven effectiveness in AIR [2], first we derived a cost function from a ratio of variance over mean of voxel intensity ratio between two images. However our initial studies using AIR and the use of variancelmean cost suggest that these methods do not work well due to extreme distortions and nonuniform pixel intensity distribution between postmortem images and MR images. In this study, we utilize the mean-squared error (MSE) as a minimizing cost for best registration between postmortem and MR images. Thus our objective is to estimate the optimal parameters ai, bi,and ci. The objective function to minimize becomes:

where i is the index of polynomial coefficients, xj and yj a~ the voxel intensity with index j .

111. RESULTS AND DISCUSSION

A. Computer Simulation Studies To validate the registration procedure numerically, we have conducted computer simulation studies. First a 2D slice was selected from a reference MRI volume with pre-specified slicing parameters. The image is shown in Fig. 2(a). Then the resliced image was warped using 4"'- order polynomials with

randomly selected 2D warping coefficients to simulate a postmortem slice (Fig. 2(b)). Finally registration was performed using the 2"d-order polynomial to find a matching slice to the postmortem slice. Fig. 2 (c) shows the registered MRI where distortions were compensated with the Td-order polynomials.

(a) (b) cci Figure 2: Simulation results of 2"d-~rder registration. (a) shows the resliced image without any distortion. (b) shows the warped image using the 4'"order polynomials and (c) the registered image using the 2"d-order polynomials.

B. Experimental Studies: Second order registration Fig. 3 (a) shows a typical postmortem image. Severe

structural deformation is visible in the ventricles. The registration algorithm was initialized with a MR image shown in Fig. 3 (b) since minimum mean-squared error was obtained initially with this image. Fig. 3 (c) was obtained at convergence (convergence threshold is typically set to be 1 .OE- 6 ) as the registered MR image to the postmortem image of Fig. 3 (a). Fig. 3 (d) shows the edges of the postmortem in white and registered MR image in gray. It is clear that outer edges of the brain regions and gyri match closely, although there is a mismatch in the shapes of ventricles.Fig. 4 shows the convergence plot of a typical postmortem image to its matching MRI. The mean-squared error between postmortem images and MRIs decreased quite rapidly and no significant drop in the error was found after 1000 iterations.

Figure 3: Results of coronal image registration using the 2nd-~rder polynomial registration. (a) A postmortem image (b) Initialized MRI for iterative registration (c) Registered MRI (d) Edges of (a) i n white compared to those of (c) in gray.

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Figure 4: Convergence plot of the 2"d-~rder registration.

C. Third order Registration To further account for differences in cross-sectional orientation and structural deformation in postmortem images (e.g., shrinkage artifacts and ventricle collapse), we increased the order of polynomials up to the 3'd-order. This increases the number of polynomial coefficients (i.e., 18 coefficients in the 2"d-order model vs. 30 in the 3d-order) and adds complications to the estimation procedure. The third order transformation however is expected to improve the co-registration for those cases with more severe distortions in postmortem slices.

Fig. 5 shows a represehtative result using the 3d-0rder polynomial transformation. Improved registration is noticed in several gyri, and collapsed ventricles are better matched in the registered MR image. The mean-squared error at convergence using the 2"d-order registration was 1.28E5, and 3.3E4 using the 3Corder.

Figure 5 : Comparison of 2nd-order and 3fd-~rder registration. A postmortem slice is shown in (a), the registered MR slice using the 2"d-~rder transformation in (b) and the registered MR slice using the 31d-order polynomials in (c).

D. Identification of Anatomical Landmarks To verify that the registered MRIs do contain the same anatomical structures originally found in the postmortem slices, we inspected some pre-specified anatomical landmarks in both images. Fig. 6 shows a representative postmortem image and its corresponding registered MRI. The optic chiasm and a marked perivascular space (indicated by arrows) are clearly co-registered in these images.

Iv. CONCLUSION

The results suggest the feasibility of registering postmortem images to in-vivo MRI. With this approach, MR characteristics of a disease can be correlated to the pathology of disease. Our approach in this study is efficient and cost- effective, and can be applied automatically with minimum human intervention.

Figure 6: Identification of the same anatomical landmarks. The contrast-enhanced postmortem slice (Left) shows optic chiasm and perivascular space from left to right with different arrows. The same structures are clearly visible in the registered MRI (Right).

V. ACKNOWLEDGMENT This work is supported in part by grants NIA-NIH lPOl

AG 12453 and NIA-NIH P50 AG05142.

VI. REFERENCES

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