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00004728-200109000-0002300004728_2001_25_805_kochunov_normalization_5miscellaneous< 133_0_24_18 >Journal of Computer Assisted Tomography© 2001 Lippincott Williams & Wilkins, Inc.Volume 25(5)September/October 2001pp 805-816Regional Spatial Normalization: Toward an Optimal Target[IMAGE PROCESSING]Kochunov, Peter; Lancaster, Jack L.; Thompson, Paul; Woods, Roger; Mazziotta, John; Hardies, Jean; Fox, PeterFrom the Research Imaging Center, University of Texas Health Science Center at San Antonio, San Antonio, TX (P. Kochunov, J. L. Lancaster, J. Hardies, and P. Fox), and Brain Mapping Center, Department of Neurology, UCLA School of Medicine, Los Angeles, CA (P. Thompson, R. Woods, and J. Mazziotta), U.S.A.Address correspondence and reprint requests to Dr. J. L. Lancaster at Research Imaging Center, University of Texas Health Science Center at San Antonio, 7703 Floyd Curl Dr., San Antonio, TX 78284, U.S.A. E-mail: jlancaster@uthscsa.eduAbstractPurpose: The purpose of this work was to develop methods for defining, constructing, and evaluating a “minimal deformation target” (MDT) brain for multisubject studies based on analysis of the entire group. The goal is to provide a procedure that will create a standard, reproducible target brain image based on common features of a group of three-dimensional MR brain images.Method: The average deformation and dispersion distance, derived from discrete three-dimensional deformation fields (DFs), are used to identify the best individual target (BIT) brain. This brain is assumed to be the one with the minimal deformation bias within a group of MR brain images. The BIT brain is determined as the one with the minimal target quality score, our cost function based on the deformation displacement and dispersion distance. The BIT brain is then transformed to the MDT brain using an average DF to create an optimized target brain. This analysis requires the calculation of a large number of DFs. To overcome this limitation, we developed an analysis method (the fast method) that reduces the task from order N2 complexity to one of order N, a tremendous advantage for large-N studies.Results: Multiscale correlation analysis in a group of 20 subjects demonstrated the superiority of warping using the MDT target brain, made from the BIT brain, over several individual and MDT-transformed target brains also from the group.Conclusion: Analysis of three-dimensional DF provides a means to quickly create a reproducible MDT target brain for any set of subjects. Warping to the MDT target was shown by an independent multiscale correlation method to produce superior results.A fundamental problem for human brain-mapping studies, when it is necessary to integrate data from many different subjects, is that there are significant anatomic variations in the size, shape, and position of human brain structures. Spatial normalization is the image-processing tool used in brain-mapping research to reduce interindividual anatomic variance by matching homologous spatial features of a “source brain” to those of a “target brain.” Spatial normalization can be broadly classified as global or regional (1,2). Global normalization uses a parametric description of the whole brain (position, orientation, and dimensions) to perform affine transformations with up to 12 parameters in a 4 × 4 homogeneous coordinate transform matrix (3). Most forms of global normalization use only nine parameters (three each for rotation, translation, and scaling); however, these must be carefully selected (1,4). Manual global spatial normalization methods require identification of key landmarks, such as the anterior and posterior commissures, to perform appropriate translation, rotation, and scaling (5,6). Automated global spatial normalization methods, matching features such as the brain's convex hull surface, have also been reported (2,7,8). Although global spatial normalization methods remove global anatomic differences, they cannot correct for smaller regionalized differences.A deformation field (DF), a three-dimensional array with three-dimensional displacement vectors stored in each element, can accurately encode regional coordinate transformations (9–12). The three-dimensional displacement vectors in the DF provide a mapping from points in the source brain to corresponding points in the target's volume space or vice versa. Regional spatial normalization methods usually generate the DF using a coarse to fine, multiscale, iterative approach. Other methods such as spectral estimation (13,14) have been reported. At each processing step, the goal is to generate DF components for a given resolution controlled by the scale or effective size of the regions analyzed.Previously, we proposed a regional spatial normalization algorithm called octree spatial normalization (OSN) that reduces processing time from hours to minutes while approaching the accuracy of previous methods. The sources of improved performance and several key properties (continuity correction, global translations and scaling, management of nonhomologous features, and regional warping performance) were described and tested on three-dimensional models (11). Modifications of the OSN algorithm for use in human brain images were recently described and tested (12). The anatomic landmark-matching capability of OSN was evaluated with several major sulci, and it was shown that OSN significantly reduced intersubject anatomic variability relative to a global transform in every sulcus studied.With the advent of fast high-quality regional spatial normalization methods such as OSN, research efforts can begin to focus on appropriate target brains. Current methods spatially warp (spatially normalize) each subject's brain to either an average or an individual target brain. One example is the MNI-305 brain that was created by averaging MR images from 305 young, normal subjects (15) following global spatial normalization to a Talairach-like brain space (16). For global spatial normalization, where feature matching primarily involves the brain location, size, and orientation, such an average brain target has the advantage because it avoids spatial biases that can arise when using an individual brain (2,4). For high-resolution regional spatial normalization, such an average target brain derived using global spatial normalization is not adequate, because feature matching must be extended to the limiting resolution of brain images. To overcome this problem, Collins and colleagues (9) developed and tested a high-resolution brain volume template based on a single high-resolution MR brain volume. Under optimal conditions (both target and source brains fully homologous), a DF can provide a comprehensive map of local transformations from target to source brain volumes. However, selection of an individual brain as a target for spatial normalization inevitably leads to a bias in the quality of regional spatial normalization, with good matching for some brains (similar to the target) and poor matching for others. We propose methods for defining, constructing, and evaluating a “minimal deformation target” (MDT) brain for multisubject studies to minimize this target selection bias. In this article, we introduce a procedure to create a standard, reproducible target brain from a group of individual brain images based on deformation properties common to the group.DEVELOPMENT BACKGROUNDAn analysis of average deformation and dispersion distances, derived from DFs, is used to identify the best individual target (BIT) brain. This analysis is done using each brain as a candidate best target. The selected BIT brain is then transformed to the MDT (i.e., optimized target brain) using an average DF.DF Analysis for Determining BIT and MDT BrainsWe define the MDT brain as the target brain that minimizes deformation among all the brains in a study. The need for minimal deformation is based on the fact that a DF is limited by continuity constraints in the amount of deformation that it can store (12). Warping individual brains to a target brain that requires the least amount of deformation for the group should therefore provide better feature matching. A similar method was proposed by Grenander and Miller (17) based on the empirical assumption that the best target brain will minimize deformation energy.The initial processing step for a set of MR images is the transformation of each to a standardized brain space (1,4) using the automated global spatial normalization method: the convex hull (2). This software is freely available from http://ric.uthscsa.edu/projects/chsn/chsn . html. After global spatial normalization, one brain (test brain) from the set is selected as the target and transformed to all brains in the set, creating a unique DF for each transform. Each DF contains deformation vectors (one per voxel) that point from target brain voxels to corresponding locations in a source brain (Fig. 1). The set of deformation vectors, pointing from a single voxel in the target brain to corresponding locations in the set of brains, mathematically describe the transformation of a target brain voxel into a collective brain space. An optimal target site is proposed as the geometric centroid of the set of corresponding locations for each voxel. Averaging the set of DFs (by averaging deformations for each target brain voxel) results in a DF that can be used to directly transform the test brain into the MDT brain for the set (Fig. 1, bold vector). Thus, regional spatial normalization to the MDT brain for a given set of brains will result in the total deformation magnitude of the brain set being minimized.FIG. 1. A set of deformation vectors, pointing from a single voxel in the target brain to corresponding locations in a set of brains, is shown. An average displacement vector S (bold vector) can be used to directly transform this voxel into its central (minimal deformation target) location, and dispersion vector D (dotted vector) can be used to estimate the variability of the deformation vectors about this optimal site.Ideally, an identical MDT brain should be obtained regardless of which test brain from the set is used as the basis for construction (17). However, noticeable anatomic differences are seen among MDT brains constructed from different test brains (Fig. 2, bottom row). These differences arise from natural differences between individual brain images and image-processing characteristics that adversely impact warping (poor anatomic homology, gross anatomic differences, poor image quality, segmentation errors, etc.). To resolve this issue, a scoring scheme was developed and evaluated to select the brain from a group that is best suited for constructing the MDT brain (i.e., the BIT brain). Two measures of quality were considered for the scoring scheme. The first was the mean distance from sites in the test brain to their optimal sites in MDT brain made from the test brain (Fig. 1, bold vector; see S in Eq. 1). The second measure of quality was the variability in the distance of brains from the optimal site (i.e., the dispersion of vectors in Fig. 1 about the bold vector/dotted vector; see D in Eq. 1). This second measure was assessed using the dispersion distance from the MDT brain site to corresponding locations in the brain set and averaged across the brain. The goal was to minimize both of these measures: one relating to the deformation effort to create the MDT brain (S) and the other to the deformation effort for warping individual brains in the group to the MDT brain (D).FIG. 2. Top row: Sagittal slices at x = +10 mm (Talairach coordinate) for best individual target (BIT) (brain no. 9), intermediate target quality score (TQS) (no. 5), and worst TQS (no. 11) brains following global spatial normalization; colored outlines represent BIT brain tissue borders. Middle row: Same brains with colored outlines representing tissue borders of the minimal deformation target (MDT)-transformed BIT brain (left, bottom brain). Bottom row: MDT-transformed brains with colored outlines representing tissue borders of the MDT-transformed BIT brain (brain no. 9).Equation 1In this work, the BIT brain is the one with the minimum cost function or target quality score (TQS). The TQS was calculated as the mean voxel-wise product (averaged over the brain) of the average distance (S) and dispersion distance (D) as described above:EQUATION (1) where S is average distance, D is dispersion distance for target volume element i located at (xi, yi, zi) within the brain volume, and N is the number of voxels in the brain. S and D are calculated from the set of DFs that transform each test brain to all brains in the group. The TQS cost function was selected, based on preliminary testing, to reward low S, low D, or both. The square root in Eq. 1 is used to express TQS in units of distance. It has been shown (12) that the bulk of white matter (82%) is matched by the global spatial normalization, whereas a significant fraction (35%) of cortical gray matter is left mismatched. To make TQS ranking sensitive to gray matter mismatch, the TQS was calculated only for gray matter-classified voxels using the following:EQUATION (2) Equation 2We propose that the BIT brain is the best one for constructing an optimal MDT brain for a group.Fast Method for Determination of BIT Brain for a SetAn array of N ×N DFs is needed to determine a TQS for every brain in a set of size N. This array is described using matrix notation in Eq. 3 where each row contains the set of DFs needed to calculate the TQS for one test brain in the set:EQUATION (3) Equation 3Here Aij is the DF that transforms test (or target) brain i to brain j. All diagonal elements in A are null DFs because they represent test-to-test brain transformations. Also, Aij is not necessarily equal to Aji because regions with poor matching (i.e., nonhomology or methodology limitations) can lead to different forward and inverse estimates of deformations. It follows that N (N − 1) DFs must be calculated to completely define the N ×N A matrix so that a TQS can be determined for each test brain. This leads to a very large number of warps (380) for a set of just 20 brains. Even with fast high-quality warping methods (12), 30 min/warp, this processing would require 190 h. Additionally, >9 Gbytes of disk space is needed to store the 1283 floating point DFs commonly used for 2563 brain volumes (approximately 1 mm voxels). Although it would be desirable to create an MDT brain from a large set of brain image volumes (approximately 1,000), the processing time increases by about 2,600 times (exceeding 50 years), discouraging researchers from attempting such a feat.To overcome this processing limitation, a highly efficient method was developed to estimate the array of DFs needed to identify the BIT brain and to construct the optimal MDT brain. This new method reduces the number of direct DF calculations to 2(N − 1), an N/2 reduction in processing effort. This method is based on the assumption that most of the DFs in the A matrix can be estimated by concatenation of two known DFs (Appendix) rather than by direct calculation. The result of concatenation of Aij and Ajk DFs yields the Aik DF:EQUATION (4) Equation 4where ∧ denotes concatenation. Note that the row-column index (ik) of the concatenated DF is derived from the row index of one DF and the column index of the other. Therefore, matrix A can be completely calculated using only directly calculated DFs from row 1 (with a full set of column indexes) and column 1 (with a full set of row indexes). This method was used for calculation of the A matrix and will be called the fast method as opposed to the direct method.MATERIALS AND METHODSSubject Selection and PreprocessingTwenty T1-weighted anatomical three-dimensional MR brain images were selected from images of a group of healthy volunteers (8 men, 12 women) in the ICBM project (18). Subjects ranged in age from 19 to 31 years. All brain images were globally spatially normalized to the Talairach atlas template and resliced to 0.85 × 0.85 × 0.85 mm voxels using an automated global spatial normalization procedure (convex hull software). Deformable anatomic templates (12) were created for each MR brain volume using an automated brain tissue segmentation procedure that defines regions of white matter, gray matter, and CSF (19,20). Each subject's anatomic template is therefore a three-dimensional volume image, where white matter, gray matter, CSF, and empty space are encoded as 512, 256, 128, and 0, respectively, to uniquely identify them.Evaluation of Fast Method for Determination of BIT BrainA 20 × 20 matrix of DFs was constructed for the 20 three-dimensional brain images by direct calculation (i.e., with OSN) of the first row and first column of matrix A (Eq. 3) and by estimating the remainder of the matrix elements (DFs) using the fast method (i.e., concatenation). To improve processing time, nearest neighbor interpolation was used during concatenation. DF analysis was performed along the rows of the A matrix using Eq. 2 to determine the TQS for each test brain in the set. The test brain with the lowest TQS was selected for development of the optimal MDT brain for the set.A five-brain subset of the 20 brain images was used to compare direct calculation of the matrix A with the fast method. The set of five brains included brains with the best and worst fast method TQS values from the group of 20 brains. The other three brains were selected with intermediate TQS values, two of which differed from each other by <1%. For the five brain images, a complete 5 × 5 A matrix was directly calculated. Five fast method versions of the A matrix were also calculated, each with a different brain used as the basis brain (i.e., the one selected for the direct calculation of row 1 and column 1 of the A matrix). TQS scores for each row of the fast 5 × 5 matrices and the single directly calculated 5 × 5 matrix were ordered and compared. They were also compared with TQS values from the fast 20 × 20 matrix.Evaluation of Individual and MDT BrainsThree measures of target brain quality (mean displacement, average dispersion distance, and TQS) were calculated for each individual brain in the five-brain subset. An MDT brain was also constructed for each individual brain, and quality measurements were repeated. These data were analyzed to see if there were significant differences in target quality measures among individual target brains, among optimized target brains, and between individual and optimized target brains.Assessment of Target Brain Matching Using Multiscale Cross-Correlation AnalysisDuring the OSN feature-matching process (12), a target dominant feature (TDF) is identified as either white matter, gray matter, CSF, or empty space in each octant. The cross-correlation coefficient (R) between TDFs in regionally transformed and target brains was calculated to assess the quality of match. This coefficient is an indicator of geometric/anatomic similarity (R ≈ 1) or difference (low R) between transformed and target brains. The coefficient provides an independent (i.e., not determined from the DF) assessment of fit quality. R was calculated at varying scales from large octants (1283) at step 1 to small octants (23) at step 7 for the multiscale regional spatial transformation of OSN.The cross-correlation analysis method was used to measure similarity to target brains for the group of 20 subject brains following global (convex hull) and regional (OSN) spatial normalization. Individual brains with best and worst TQS and MDT brains were used as reference targets. Multiscale maps of individual R values were analyzed to determine mean and standard deviation of R for each target brain and transform method. Correlation coefficient maps at the limiting resolution (23) were averaged to obtain the volumetric distribution of octants with low correlation.RESULTSEvaluation of Fast Method for Determination of BIT BrainTable 1, shows TQS values computed using the fast method (DF concatenation) for a group of 20 brains. The subset selected for detailed analysis consisted of brain 9 (best TQS = 4.54), brain 11 (worst TQS = 5.54), brain 4 (TQS = 4.71), brain 5 (TQS = 4.72), and brain 2 (TQS = 5.18). The TQS values for this subset of brains, obtained from the direct method, are shown in Table 2. The TQS rank order for this 5 brain subset was the same as for the 20 brain set. The difference between the best and worst TQS scores was also similar (1.0 for fast method versus 0.9 for direct method).TABLE 1. Target quality score (TQS) for 20 brainsTABLE 2. Target quality score (TQS) calculated directly for five brain setTable 3 shows TQS, average deformation, and average dispersion distance values obtained for the five possible fast methods for determination of the BIT brain, each based on a different basis brain. Regardless of the brain used as a basis for the fast method, brain 9 maintained the best TQS. The order among all but two brains remained unchanged. Brain 5 exchanged positions with brain 4, when brain 4 was used as the basis brain, and brain 5 had the worst TQS score.TABLE 3. Target quality score (TQS), average displacement (S), and average dispersion distance ( D ) for five 5 × 5 matricesa Brain used as the basis for reconstruction.Evaluation of Individual and MDT BrainsFigure 3 shows that the TQS, average displacement, and dispersion distance values for individual target brains were consistently poorer (i.e., larger) than for their corresponding MDT-transformed brains. The least difference in TQS between the individual and MDT-transformed brains was seen for the BIT brain (lowest TQS value, brain 9; leftmost point, Fig. 3), and the largest difference was seen for the brain with the worst TQS value (brain 11; rightmost point, Fig. 3).FIG. 3. Average displacement (S), target quality score, and average dispersion distance (D) calculated directly for original (diamond) and minimal deformation target-transformed (square) brains (nos. 9, 4, 5, 2, and 11).The results presented graphically in Fig. 3 are illustrated in Fig. 2 using sagittal slices at x = +10 mm (Talairach coordinate) for best TQS (brain 9), intermediate TQS (brain 5), and worst TQS (brain 11) brains. The upper images are individual brains following global spatial normalization only. Color overlays, made from the best individual target brain (brain 9, upper left), are provided in all upper images to aid visual comparisons. White arrows highlight areas of large differences between the BIT brain and the other two brains (middle and right). These areas relate to the upper graph data of Fig. 3, where target quality values are different between individual brains. These images illustrate the differences between target brains when individual images are not MDT transformed.The middle images in Fig. 2 were obtained using the MDT transform of the BIT brain as the target for transformation of all brain images. Several gross differences, seen in the upper row of images, are reduced by using this optimal target brain. This illustration indicates that less effort is needed to match brains to the MDT version of the BIT brain (middle row) than directly to the BIT brain (upper row).The lower row images in Fig. 2 are MDT brains created from each individual brain (upper row). Note the improvement in similarity among these images (white arrows). Also note the general improvement in similarity throughout the brain when compared with the upper row images. These images relate to the lower data in Fig. 3, where target quality values are more similar. They illustrate the reduction of anatomic differences in target brains when individual images are all MDT transformed.Assessment of Target Brain Matching Using Multiscale Cross-Correlation AnalysisMultiscale plots of transformed to target brain image average cross-correlation coefficients for a group of 20 brains following global (convex hull;Fig. 4E and F) and regional spatial normalization (OSN;Fig. 4A–D) are shown. All curves have a similar trend:R is close to 1 at the first step (octant size = 1283) and gradually decreases with smallest values at step 7 (octant size = 23). Geometric/anatomic similarity (R ≈ 1) is indicated for large octants for all evaluations. As octant size decreases, a rapid drop in R is seen for global spatial normalization (curves E and F). However, for regional spatial normalization (curves A–D), R declines gradually, with values exceeding 0.9 through step 5 (8 mm octants) for curves A and B.FIG. 4. Multiscale correlation analysis curves. [A]: Following octree spatial normalization (OSN) transformation using the minimal deformation target (MDT)-transformed best individual target (BIT) brain as a target; [B]: following OSN transformation using the BIT brain as a target; [C]: following OSN transformation using the MDT-transformed worst target quality score (TQS) brain as a target; [D]: following OSN transformation using the worst TQS brain as a target; [E]: following global spatial normalization to Talairach template, using the BIT brain as a reference for correlation analysis; [F]: following global spatial normalization to Talairach template, using the worst TQS brain as a reference for correlation analysis.The highest R values (Fig. 4, curve A) were seen for regional spatial normalization using the MDT-transformed BIT brain as the target brain (brain 9; best TQS). Curve B, obtained using the BIT brain as the target, fell slightly below curve A. The MDT transformation provided a larger incremental improvement in R values for the worst TQS brain (brain 11, curve D to C) than for the best TQS brain (brain 9, curve B to A).A value of R < 0.71 was used as an indicator of brain octants with poor correlation between target and transformed brains following spatial normalization. The analysis was applied at the 23 octant level (Fig. 4, step 7), and the threshold R value was selected as the p = 0.05 point for a correlation data set of size 8. Resulting average R values for regional spatial normalization (curves A–D, step 7) all exceeded 0.71. However, R values for global spatial normalization (curves E and F) all fell bellow 0.71.The volumetric distribution of uncorrelated octants at step 7 (23) for each reference target was calculated by intersubject averaging of three-dimensional images of correlation coefficients. The average brain volume for octants falling below 0.71 (Table 4) showed a trend similar to Fig. 4. Following global spatial normalization, the volume of uncorrelated tissue is large (about 1,000 cm3) and is diffusely distributed (Fig. 5, left). This was true regardless of which brain (worst or best TQS) was used as the target brain. The volume of uncorrelated tissue, after regional spatial normalization, is reduced by almost an order of magnitude (to about 100 cm3) when compared with global spatial normalization. Residual uncorrelated regions for individual target brains are mostly distributed about sulci (Fig. 5, middle). The extent of uncorrelated regions is further reduced when using optimized brains as targets (Fig. 5, right). The best overall fit seen visually was for the target brain with the best TQS following the MDT optimization (Fig. 5, top right).TABLE 4. Volume of uncorrelated brain tissue following global SN (convex hull) and regional SN (OSN)MDT-transformed and individual BIT brain (no. 9) and worst TQS (no. 11) were used as references to calculate correlation coefficients. SN, spatial normalization; OSN, octree spatial normalization; MDT, minimal deformation target; BIT, best individual target; TQS, total quality score.FIG. 5. Distribution of estimated uncorrelated tissue along brain surface. Top row: Following global spatial normalization (SN) using best individual target (BIT) as a reference (left), octree spatial normalization (OSN) transformation to the BIT brain (middle), and OSN transformation to minimal deformation target (MDT)-transformed BIT brain (right). Bottom row: Following global SN using worst target quality score (TQS) brain as a reference (left), OSN transformation to the worst TQS brain (middle), and OSN transformation to MDT-transformed worst TQS brain (right).DISCUSSIONSelecting the BIT Brain Using TQSIdeally, an identical MDT-transformed brain should be obtained regardless of which test brain from the set is used as the basis for construction (17). However, differences that arise from the natural anatomic variability among individual brain images adversely impact warping (poor anatomic homology, gross anatomic differences, poor image quality, segmentation errors, etc.), and these differences lead to a different set of locations for corresponding sites for different test brains. In this article, we have presented an empirical cost function, the TQS, to select the BIT brain. The BIT brain was defined as the one that has a minimal voxel-wise average product of the displacement and dispersion distance: the minimal TQS. The BIT brain was then transformed using the MDT transformation to construct an optimal target brain for a given set. Although the TQS function was selected empirically, the following considerations lead us to this choice. Ideally, the best prospective MDT brain should have the minimal values for both displacement and dispersion distance for each voxel, but realistically a minimum of either of them is plausible. A zero displacement vector for a given voxel indicates that this voxel is already in the central location, and a zero dispersion distance indicates that the MDT transformation will easily move this voxel to its central location owing to good agreement among brain images in this anatomic region. We showed that for OSN regional spatial normalization, correlation between source and target brains was highest across all scales when the BIT brain, that is, one with the lowest TQS, was used as the target for spatial normalization. This correlation was further improved by using the BIT brain optimized using the MDT transformation as the target for spatial normalization.Evaluation of Fast Method for Determination of BIT BrainTables 1 and 2 show that the rank order of TQS values, using the fast method in 20 brains, did not change when compared with the direct method with the subset of five brains. Even brains with <1% difference in their TQS scores (brains 4 and 5) remained in the same order. The TQS values and their standard deviations were similar in range and slightly smaller for the five-brain subset. This finding in this single five-brain subset is not proof that the same ranking will be found for any five-brain subset, but rather an indication that it is possible to maintain the ranking even when differences in TQS are small for some brains.The fast method produced different TQS values depending on the basis brain. More importantly, TQS rank order varied slightly (Table 3). In all cases, brain 9 remained the BIT brain (i.e., best TQS score). This was expected as the directly calculated TQS for brain 9 was about 11% smaller than the next larger score (Table 2). A change in rank order of other brains by one or more positions was seen. The only fast method sort order that exactly matched the direct method was when the brain with the best TQS score (brain 9) was selected as the basis brain. When brains 4 or 5 were used for the basis brains, they moved lower in the ranking. Brains 2 and 11 remained in their same rank order when they were used as basis brains. These results indicate that the brain selected for the basis brain will either remain fixed or move to a lower rank order.Based on these observations, we propose an algorithm that will find the same BIT brain with the fast method and direct methods. First, a brain is selected at random to be the basis brain and TQS rankings determined. Next, the brain at the top of the rank (lowest TQS) is picked and the processing repeated using it as the basis brain. If it remains at the top of the rank, it is selected as the BIT brain. If it drops from the top rank, the process is repeated until a basis brain that stays at the top of the rank is found.Evaluation of Individual and MDT-Transformed BrainsOptimizing an individual brain, by transforming each volume element to its estimated central location among the set, reduces average displacement. Ideally, any individual brain from a set can be transformed to the MDT brain with an equal success. This was indicated in the lower data points of Fig. 3, where the quality scores were similar among MDT brains. Though quality scores were similar among the group of MDT-transformed target brains, they show that a finite mean difference (about 2 mm) still exists. The regional nature of these differences is seen in the middle brain images in Fig. 2. The mean residual TQS difference is approximately the same as the smallest dimension of the processing method (smallest octants approximately 2 mm). We have not studied this relationship carefully but speculate that higher-resolution MR images and smaller octants can decrease this difference to <1 mm.Significant regional large-scale spatial differences are seen between individual brains and a target brain even for the best individual target brain (best TQS) (Fig. 2, top row). These differences are smaller for the MDT-transformed version of the best individual brain as the target (Fig. 2, middle row), because it attempts to average spatial difference across all brains in the group. The differences between brains can be reduced even more by MDT transforming each brain in the group (Fig. 2, bottom row). The MDT transform regionally warps each brain to its group estimate of a minimal deformation or group optimal deformation brain, thereby decreasing spatial differences among the transformed brains. The current regional spatial normalization processing strategy was to select a single optimized brain as the target. A better strategy might be to calculate optimized target brains for every brain as a preprocessing step before proceeding with regional spatial normalization. As seen in the bottom row of Fig. 2, the starting difference between brains is less for this alternative processing strategy. The preprocessing needed for this alternative method can be done with little additional effort because it requires only calculation of the average displacement for each row in Eq. 3. An indication of the quality of this alternative processing strategy is shown in Fig. 6, where multiscale correlation analysis was performed for original brains (Fig. 2, middle row) and MDT-transformed brains (Fig. 2, bottom row). The MDT-transformed brain curves showed higher correlation coefficients at each scale, indicating a definite improvement in similarity among these optimized brains.FIG. 6. Multiscale correlation analysis curves for minimal deformation target-transformed (top) and original (bottom) brains (nos. 4, 5, 2, and 11) were octree spatial normalization matched to the target obtained by optimization of the best target quality score brain.Another promising processing strategy is recursive calculation of optimized brains until some predetermined measure of similarity is achieved. This latter processing strategy is attractive because a target brain does not have to be selected; rather, each brain evolves to a group-determined similarity brain. However, much additional processing will be required, and even with our fast method, this processing strategy presents a major challenge for current computers and processing methods.Assessment of Target Brain Matching Using Multiscale Cross-Correlation AnalysisAt the largest scale analyzed (octant size = 1283), all brains are expected to be anatomically similar, and this was seen with the average correlation coefficient (R) approaching unity. At smaller scale, regional anatomic differences among brains should lead to reduced correlation between transformed and target brains when only global spatial normalization is used. A monotonic decrease in R values was seen for all evaluations, with the lowest R approaching 0.5 at the smallest scale (octant size = 23).Multiscale correlation analysis independently confirmed the superiority of the MDT-transformed BIT brain when it is used as a target for regional spatial normalization. Using this brain as a target gave the highest multiscale correlation coefficient and lowest volume of uncorrelated tissue.The correlation analysis was done between target dominant tissue types (white matter, gray matter, CSF, or nonbrain) and is therefore not an anatomic correlation. Nevertheless, it appears to be a very powerful tool when used for tissue-type correlation.Further DevelopmentIn this study, we used the analysis of average deformation and dispersion distance, derived from DFs, to identify an individual target brain with minimum deformation bias within a group of MR images of the brain. To overcome this computationally prohibitive process, we developed the fast method to calculate DFs. The fast method reduces the task from an order of N2 complexity to one of order N, making it realistic to create an MDT brain for populations as large as 7,000 subjects (number of normal subjects projected for the ICBM project).Currently, the most widely accepted brain atlas for human brain-mapping studies is the atlas of Talairach and Tournoux (16). It is an atlas of an individual brain, with associated anatomic biases toward this individual. We propose that an optimized brain, based on a large population of normal subjects, constructed using the methods presented here, would have minimal anatomic biases while retaining the anatomic detail needed to define labels in such an atlas.Population-specific optimized target brains offer a new method to detect and analyze anatomic differences among populations. Thompson and co-workers (21,22) were the first to build disease-specific brain atlases to analyze anatomic changes in brains in a disease state. The Thompson method was based on brain surface tracings and did not account for volumetric changes. We believe that the MDT-transformed BIT target brain (i.e., our optimal target brain) will represent the common anatomic features of a population better than any individual brain. By comparing optimal target brains from two populations, we propose that significant differences between the populations will be readily identified without target selection bias. Work is underway to determine whether analysis of corresponding DFs can be used to provide additional insight into the significance of these findings. This could support a hypothesis-free method for detection of differences in anatomy due to disease states when compared with normal values.Acknowledgment: Research support was provided by the Human Brain Mapping Project, which is jointly funded by NIMH and NIDA (P20 MH/DA52176).APPENDIXConcatenation of Deformation FieldsDeformation fields (DFs) used for spatial normalization are three-dimensional vector fields, with one vector for each x-y-z node in the field. The DFs are three-dimensional arrays with indexes that address corresponding x-y-z locations in the three-dimensional arrays containing brain images. The displacement vectors encode regional transformations for each indexed location in these three-dimensional images (9,11). The displacement vectors in DF Aij map points in brain image (i) to the corresponding points in the brain image (j), providing the means to regionally deform brain (i) to match brain (j). Likewise, DF Ajk maps points from brain (j) to brain (k). Calculation of DFs Aik was done directly or by concatenation of two known DFs (Aij and Ajk) (Eq. 4). Concatenation is much more efficient than direct calculation. Concatenation of two vector fields is accomplished by head-to-tail summing of serial displacement vectors, one from each vector field (Fig. 7). The following algorithm is used for the concatenation process:FIG. 7. Concatenation of displacement field vectors: head-to-tail summing of serial displacement vectors, one from each vector field. Using location x,y,z and the displacement vector D (x,y,z) from DF Aij, determine the location x `, y `, z ` in brain image (j) pointed to from brain image (i):EQUATIONEquation U1 Using this calculated location x `, y `, z ` and the displacement vector D (x `, y `, z `) from DF Ajk, determine the location x ", y ", z " in brain image (k) pointed to from brain image (j):EQUATION Equation U2 Sum the components of the two displacement vectors to get net displacement vector components that point from brain image (i) to brain image (k) and assign this to location x,y,z:EQUATION Equation U3 Repeat for all x,y,z in brain (i), inserting DD (x,y,z) into the concatenated DF Aik.Deformation vectors calculated directly by spatial normalization software are recorded as floating point values. The displacements calculated in steps 1 and 2 above usually point to sites that fall between the discrete locations in three-dimensional brain images or three-dimensional DFs. Some form of three-dimensional interpolation is therefore needed to estimate values for these intermediate locations. We used nearest neighbor interpolation to reduce processing time. The concatenated DF was filtered using three passes of a three point uniform average to reduce the discreteness of the final DF. The concatenation of two 1283 DFs takes <5 min on a Sun Microsystems SPARCstation (250 MHz; Spec95fp = 11.4).REFERENCES1. Fox P. Spatial normalization origins: objectives, applications, and alternatives. Hum Brain Map 1995; 3:161–4. [Context Link]2. Lancaster J, Fox P, Downs H, et al. Global spatial normalization of the human brain using convex hulls. J Nucl Med 1999; 40:942–55. [Medline Link] [Context Link]3. Foley J, van Dam A, Feiner S, et al. Computer Graphics: Principles and Practice. 2nd Ed. Reading, MA: Addison-Wesley, 1990:201–20. [Context Link]4. Woods R. Correlation of brain structure and function. In: Toga A, Mazziotta J, eds. Brain Mapping: The Methods. San Diego: Academic Press, 1996:313–42. [Context Link]5. Fox P, Perlmutter J, Raichle M. A stereotactic method of anatomic localization for positron emission tomography. J Comput Assist Tomogr 1985; 9:141–53. [CrossRef] [Full Text] [Medline Link] [Context Link]6. Lancaster JL, Glass TG, Lankipalli BR, et al. A modality-independent approach to spatial normalization of tomographic images of the human brain. Hum Brain Map 1995; 3:209–23. [Context Link]7. Minoshima S, Koeppe RA, Mintum M, et al. Automated detection of the intercommissural line for stereotaxric localization of functional brain images. J Nucl Med 1993; 34:322–9. [Medline Link] [Context Link]8. Roland PE, Graufelds CJ, Wahlin J, et al. Human brain atlas: for high-resolution functional and anatomic mapping. Hum Brain Map 1994; 1:127–84. [Context Link]9. Collins D, Holmes C, Peters T, et al. Automatic three-dimensional model-based neuroanatomic segmentation. Hum Brain Map 1995; 3:190–208. [Context Link]10. Collins D, Holmes C, Peters T, et al. ANIMAL: automated nonlinear image matching and anatomical labeling. In: Toga A, ed. Brain Warping. San Diego: Academic Press, 1999:133–42. [Context Link]11. Kochunov P, Lancaster J, Fox P. Accurate high-speed spatial normalization using an octree method. Neuroimage 1999; 10:724–37. [CrossRef] [Medline Link] [Context Link]12. Kochunov P, Lancaster J, Thompson P, et al. Evaluation of octree regional spatial normalization method for regional anatomical matching. Hum Brain Map 2000; 11:193–206. [Context Link]13. Miller M, Christensen G, Amit Y, et al. Mathematical textbook of deformable neuroanatomies. Proc Natl Acad Sci 1993; 90:11944–8. [CrossRef] [Medline Link] [Context Link]14. Ashburner J, Friston KJ. Nonlinear spatial normalization using basis functions. Hum Brain Map 1999; 7:254–66. [Context Link]15. Evans A, Collins D, Holmes C. Computational approaches to quantifying human neuroanatomic variability. In: Toga A, Mazziotta J, eds. Brain Mapping: The Methods. New York: Academic Press, 1996:343–61. [Context Link]16. Talairach J, Tournoux P. Co-Planar Stereotaxic Atlas of the Human Brain. New York: Thieme Medical, 1988. [Context Link]17. Grenander U, Miller M. Computational anatomy: an emerging discipline. Q J Appl Math 1998; 56:617–94. [Context Link]18. Mazziotta JC, Toga AW, Evans A, et al. A probabilistic atlas of the human brain: theory and rationale for its development. Neuroimage 1995; 2:89–101. [CrossRef] [Medline Link] [Context Link]19. Herndon C, Lancaster J, Toga A, et al. Quantification of white matter and gray matter volumes from T1 parametric images using fuzzy classifiers. J Magn Res Imag 1996; 6:425–35. [CrossRef] [Medline Link] [Context Link]20. Herndon C, Lancaster J, Giedd J, et al. Quantification of white matter and gray matter volumes from three-dimensional magnetic resonance volume studies using fuzzy classifiers. J Magn Reson Imaging 1998; 8:1097–105. [CrossRef] [Medline Link] [Context Link]21. Thompson P, Woods R, Mega M, et al. Mathematical/computational challenges in creating deformable and probabilistic atlases of the human brain. Hum Brain Map 2000; 9:81–92. [Context Link]22. Thompson P, Schwartz C, Lin R, et al. Three-dimensional statistical analysis of sulcal variability in the human brain. J Neurosci 1996; 16:4261–74. [Medline Link] [Context Link]Index Terms: Spatial normalization; Brain imaging; Brain atlasovid.com:/bib/ovftdb/00004728-200109000-0002300005105_1999_40_942_lancaster_normalization_|00004728-200109000-00023#xpointer(id(R2-23))|11065405||ovftdb|SL0000510519994094211065405P92[Medline Link]10452309ovid.com:/bib/ovftdb/00004728-200109000-0002300004728_1985_9_141_fox_stereotactic_|00004728-200109000-00023#xpointer(id(R5-23))|11065213||ovftdb|00004728-198501000-00025SL000047281985914111065213P95[CrossRef]10.1097%2F00004728-198501000-00025ovid.com:/bib/ovftdb/00004728-200109000-0002300004728_1985_9_141_fox_stereotactic_|00004728-200109000-00023#xpointer(id(R5-23))|11065404||ovftdb|00004728-198501000-00025SL000047281985914111065404P95[Full Text]00004728-198501000-00025ovid.com:/bib/ovftdb/00004728-200109000-0002300004728_1985_9_141_fox_stereotactic_|00004728-200109000-00023#xpointer(id(R5-23))|11065405||ovftdb|00004728-198501000-00025SL000047281985914111065405P95[Medline Link]3881487ovid.com:/bib/ovftdb/00004728-200109000-0002300005105_1993_34_322_minoshima_intercommissural_|00004728-200109000-00023#xpointer(id(R7-23))|11065405||ovftdb|SL0000510519933432211065405P97[Medline Link]8429356ovid.com:/bib/ovftdb/00004728-200109000-0002300042393_1999_10_724_kochunov_normalization_|00004728-200109000-00023#xpointer(id(R11-23))|11065213||ovftdb|SL0004239319991072411065213P101[CrossRef]10.1006%2Fnimg.1999.0509ovid.com:/bib/ovftdb/00004728-200109000-0002300042393_1999_10_724_kochunov_normalization_|00004728-200109000-00023#xpointer(id(R11-23))|11065405||ovftdb|SL0004239319991072411065405P101[Medline Link]10600418ovid.com:/bib/ovftdb/00004728-200109000-0002300006702_1993_90_11944_miller_neuroanatomies_|00004728-200109000-00023#xpointer(id(R13-23))|11065213||ovftdb|SL000067021993901194411065213P103[CrossRef]10.1073%2Fpnas.90.24.11944ovid.com:/bib/ovftdb/00004728-200109000-0002300006702_1993_90_11944_miller_neuroanatomies_|00004728-200109000-00023#xpointer(id(R13-23))|11065405||ovftdb|SL000067021993901194411065405P103[Medline Link]8265653ovid.com:/bib/ovftdb/00004728-200109000-0002300042393_1995_2_89_mazziotta_probabilistic_|00004728-200109000-00023#xpointer(id(R18-23))|11065213||ovftdb|SL00042393199528911065213P108[CrossRef]10.1006%2Fnimg.1995.1012ovid.com:/bib/ovftdb/00004728-200109000-0002300042393_1995_2_89_mazziotta_probabilistic_|00004728-200109000-00023#xpointer(id(R18-23))|11065405||ovftdb|SL00042393199528911065405P108[Medline Link]9343592ovid.com:/bib/ovftdb/00004728-200109000-0002300002516_1996_6_425_herndon_quantification_|00004728-200109000-00023#xpointer(id(R19-23))|11065213||ovftdb|SL000025161996642511065213P109[CrossRef]10.1002%2Fjmri.1880060303ovid.com:/bib/ovftdb/00004728-200109000-0002300002516_1996_6_425_herndon_quantification_|00004728-200109000-00023#xpointer(id(R19-23))|11065405||ovftdb|SL000025161996642511065405P109[Medline Link]8724407ovid.com:/bib/ovftdb/00004728-200109000-0002300002516_1998_8_1097_herndon_quantification_|00004728-200109000-00023#xpointer(id(R20-23))|11065213||ovftdb|SL0000251619988109711065213P110[CrossRef]10.1002%2Fjmri.1880080515ovid.com:/bib/ovftdb/00004728-200109000-0002300002516_1998_8_1097_herndon_quantification_|00004728-200109000-00023#xpointer(id(R20-23))|11065405||ovftdb|SL0000251619988109711065405P110[Medline Link]9786148ovid.com:/bib/ovftdb/00004728-200109000-0002300005095_1996_16_4261_thompson_dimensional_|00004728-200109000-00023#xpointer(id(R22-23))|11065405||ovftdb|SL00005095199616426111065405P112[Medline Link]8753887Regional Spatial Normalization: Toward an Optimal TargetKochunov, Peter; Lancaster, Jack L.; Thompson, Paul; Woods, Roger; Mazziotta, John; Hardies, Jean; Fox, PeterImage Processing525

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Journal of Computer Assisted Tomography25(5):805-816, September/October 2001.

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