Multivariate Voxel Based Morphometry for Diagnosing Schizophrenia Sampath Kumar* and Dr. M. Sukumar **, *N. M. A. M. Institute of Technology/ E&C Dept., Nitte, INDIA ** Sri Jayachamarajendra college of Engineering/ IT Dept., Mysore, INDIA
[email protected],
[email protected] Abstract There is no laboratory test or diagnostic tool is available for diagnosing schizophrenia. In schizophrenics significant structural changes are observed in certain parts of the brain. Voxel-based analysis based on the stereotactic coordinates provides a wholebrain and unbiased technique for characterizing regional cerebral functions and structure. The multivariate linear model (MLM) has been proposed to characterize the functional brain response as a global pattern in the brain. Application of the MLM to voxelbased morphometry (VBM) enables to capture and explain the interrelationship between the voxel-wise MRI data and a set of predictors in the spatial pattern of tissue distribution. Thus, this procedure is applied to differentiate schizophrenia patients from healthy subjects. This process is achieved using a multivariate tool box (MM2) implemented in old version of statistical parametric mapping (SPM2). The scripts in MM2 are upgraded to make it compatible with new version SPM5 so that more accurate and efficient method of classification can be obtained.
I. INTRODUCTION Current operational diagnostic systems for major psychiatric disorders such as schizophrenia are based solely on clinical manifestations and associated psycho-social impairments [2], [3]. Converging evidence has revealed that subtle but significant structural changes are observed principally in fronto- temporolimbic- paralimbic regions in schizophrenia [4], [5]. Because the anatomy of the brain is stable relative to clinical manifestations and functional brain measures, structural neuroimaging is a useful tool for the clinical diagnosis of schizophrenia [6]. Another study showed that a combination of 10 anatomical variables on MRI scans enabled reliable classification of 76% of male schizophrenia patients and 79% of healthy people [7]. One of the previous MRI study with discriminant function analysis using 14 anatomical measures has showed correct classification of 80% of the male and 78% of the female schizophrenia patients, and 80% of the healthy males and 86% of the healthy females [8]. These results suggest clinical applicability of structural neuroimaging data to a future diagnostic system for schizophrenia. Voxel-based analysis based on the stereotactic coordinates provides a whole-brain and unbiased technique for characterizing regional cerebral functions and structure. The multivariate linear model (MLM) has recently been proposed to characterize the functional brain response as a global pattern in the brain [9], [10]. The MLM takes into account the spatial covariance between the voxels and provides a formal test of the number of components based on Gaussian
random field theory. MLM analysis, similar to the discriminant function analysis [11], can identify the models of variation (i.e., eigenimage) that best represent inter-subject variability. An eigenimage and subject scores are obtained by MLM analysis of certain original data. Because the eigenimage can be used as a predictor within the separate test data for a replication, prospective classification is made based on the subject scores of test data [12]. Application of the MLM to voxel-based morphometry (VBM) [13] enables to capture and explain the interrelationship between the voxel-wise MRI data and a set of predictors in the spatial pattern of tissue distribution. This leads to the development of an accurate and efficient diagnostic tool for schizophrenia [1]. The structural MRI of the brain is preprocessed using statistical parametric mapping (SPM). Images are realigned, spatially normalized into a standard space, and smoothed. Parametric statistical models are assumed at each voxel, using the General Linear Model (GLM) to describe the data in terms of experimental and confounding effects, and residual variability. Classical statistical inference is used to test hypotheses that are expressed in terms of GLM parameters. This uses an image whose voxel values are statistics, a Statistic Image, or Statistical Parametric Map (SPM {t}, SPM {Z}, SPM {F}). For such classical inferences, the multiple comparisons problem is addressed using continuous random field theory (RFT), assuming the statistic image to be a good lattice representation of an underlying continuous stationary random field. This results in inference based on corrected pvalues. It also calculates the contrast, which tells SPM how to subtract the means, to look at the particular comparisons that one is interested in. Thus SPM analysis will provide a first apriori model and the corresponding estimated parameters and residual sum of square images. Six schizophrenic patients and six healthy people’s brain MRI images are preprocessed using SPM. Output of this procedure is segmented gray matter images. Multivariate Linear Modeling (MLM) procedure is used to classify these images in to two classes. Given image files and a contrast of a general linear model, this procedure performs PCA analysis on the projected data in the sub-space defined by the contrast. Orthogonal projections allow studying the residual part of a model. The gray level intensity of gray matter voxel in schizophrenics is less and observed in patches, where as the healthy people have continuous gray matter with more gray level intensity. This parameter is used to differentiate schizophrenics from healthy people.
This is implemented in MATLAB 5.3 using SPM99 and MM toolbox. The newer versions of SPM [14] and MM [15] toolboxes are available. SPM2 with better segmentation algorithm and MM2 toolbox is used for classification in MATLAB 6.1. Then much newer version SPM5 with improved statistical methods and image processing algorithms is used for segmentation in MATLAB 7.1. The MM2 toolbox is re-engineered to work in SPM5. Since these toolboxes are implemented in MALAB 7.1, the newer version, the procedure is much faster, accurate and very much efficient. II. PREPROCESSING The structural brain MRI images (T1 type) of size 157x189x156 with voxel size 3 mm3 are used in this analysis. Image analysis is performed with Statistical Parametric Mapping (SPM5) software implemented in MATLAB 7.1. Voxel Based Morphometry (VBM) method is used for segmenting brain image in to gray matter image, white matter image and cerebrospinal fluid images. MM2 tool box, upgraded to work in SPM5 and MATLAB 7.1, is used for differentiating schizophrenics from healthier ones. The input images were a subset of images that were already preprocessed using optimized VBM & reported in a previous study [13] [14]. A. Spatial normalization First all the images are registered to the customized template image. The optimum 12 parameter Affine transformation is used for registering images from different subjects. A non linear registration is also used for correcting gross differences in the head shapes that can not be accounted for by the Affine transformation alone. The non linear warps are modeled by the linear combination of smooth discrete cosine transform basis functions. Most of the nonlinear spatial variability between images is automatically corrected using Taylor’s theorem and the separable nature of the basis functions. This procedure spatially normalizes the structural brain MRI images of different people to a common stereotactic space. B. Segmentation The spatially normalized images were re-sliced to a final voxel size of 1 mm × 1 mm × 1 mm. These images are then typically partitioned into different tissue classes (gray matter, white matter and cerebrospinal fluid) using the segmentation technique known as Voxel Based Morphometry (VBM). Modulated segments of gray matter were smoothed with a 12mm full-width at half maximum (FWHM) isotropic Gaussian kernel. Each voxel in the smoothed image contains the average concentration of gray matter from around the voxel (i.e., gray matter concentration). According to the central limit theorem, the smoothing procedure has the advantage of rendering the data more normally distributed and of increasing the validity of parametric voxel by voxel statistical analysis.
Fig. 1. VBM output image: Segmented, smoothed gray matter image
III. STATISTICAL ANALYSIS USING SPM AND MLM A group containing of six schizophrenia patients (patient’s) and another group with six healthy people (normal’s) are used in this study. After preprocessing and segmentation using VBM procedure, only gray matter images are used in the statistical analysis. The statistical evaluation comparing schizophrenia patients and healthy controls was performed by a two sample t - test. The two sample t- test modeled in general linear model tests the null hypothesis that the mean of one group of observations is identical to the mean of a second group of observations. The design matrix is initialized with six normal’s images and six patient’s images. A contrast weight matrix [-1 1] is used as contrast. A two sample t - test is performed on this design matrix using SPM5 implemented in MATLAB 7.1. This analysis using SPM5 will provide a first a priori model and the corresponding estimated parameters and residual sum of square images. The gray matter voxel intensities of healthy people are continuous and brighter compared to schizophrenics. A contrast weight matrix [-1 1] is used, which specifies that the
values can be used to differentiate schizophrenics from healthier ones. IV. RE-ENGINEERING SPM AND MM TOOL BOXES The currently available MM tool box (MM2) is meant for SPM2. These tool boxes (SPM2 and MM2) can only be implemented in MATLAB 6.1 and not in higher versions. SPM5 is the latest version in statistical parametric mapping and has improved statistical procedures and image processing algorithms. MM2 if re-engineered can be used with SPM5. The modified MM2 implemented with SPM5 in MATLAB 7.1 will make the procedure much faster, accurate and very much
Fig. 2. Two sample t-test results for contrast matrix [-1 1] voxel intensity of the healthy controls have to be subtracted from the mean where as that of schizophrenia patients to be added to the mean. The patterns of gray matter distribution that differed most between the patients and healthy people in these groups were extracted with MLM software. The MLM method is based on singular value decomposition of the matrix Z, where Y are the data, X is the linear model, and Σ represents the temporal covariance matrix of the data
Fig. 3. MLM analysis showing negative global values for normal’s and positive for schizophrenic patients
Z = (X`ΣX) -1/2 X`Y efficient. As there is no temporal covariance for VBM data, the matrix of present method is in fact an orthonormalized PLS in which Σ is identity. Therefore the matrix X`ΣX is simplified to X`X. By this method a normalized correlation between the data and a set of regressors that were contained in the design matrix is computed. This correlation matrix is then decomposed in an “eigen image” that best represents the variance in the correlation. Since the MLM operates on voxel-by-voxel correlation matrices, the extracted eigen image reflects the patterns of correlated gray matter concentration. The method provides an assessment of the variance explained by a given pattern, as well as a test of significance based on the MLM. The test for a global effect is performed using two sample t test with same contrast weight matrix. The resultant patterns for each voxel had a positive or negative value depending on how much the gray matter concentration of this voxel contributed to the given pattern. The expression of the pattern (i.e., inner product) for every given scan was calculated as a scalar with a positive or negative coefficient. This global value is found to be negative for normal’s and positive for schizophrenic patients. These
The MLM procedure is derived from PLS or CVA methods and permits to study the normalized correlation structure between the model and the data. The original aim of this method is to determine a new set of predictors (contrast), linear combinations of the original ones. This contrast represents the "best contrast" in the sense that it maximises in a multivariate manner the results. In other words, this contrast gives globally the best correlation between the linear combination of the regressors defined by it and the data. MLM is performed on a space of interest, such that the contrast that is chosen to define this space is usually a sub-space of the space of interest. V. CONCLUSION The re-engineered tool boxes along with a suitable classification algorithm can be used as a diagnostic method for Schizophrenia. Even functional images like fMRI, PET and SPECT images can be processed and analyzed using the method used here. These computations are very much useful in understanding human brain functions as well as in diagnosis of many brain disorders like epilepsy, Alzheimer’s disease etc.
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