Introduction. NeuroImage 31 (2006)

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1 NeuroImage 31 (2006) Discriminative analysis of relapsing neuromyelitis optica and relapsing remitting multiple sclerosis based on two-dimensional histogram from diffusion tensor imaging Fuchun Lin, a,1 Chunshui Yu, b,1 Tianzi Jiang, a, * Kuncheng Li, b Chaozhe Zhu, c Wanlin Zhu, a Wen Qin, b Yunyun Duan, b Yun Xuan, b Hong Sun, d and Piu Chan d a National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing , PR China b Department of Radiology, Xuanwu Hospital of Capital University of Medical Sciences, Beijing , PR China c National Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing , PR China d Department of Neurology, Xuanwu Hospital of Capital University of Medical Sciences, Beijing , PR China Received 12 October 2005; revised 14 December 2005; accepted 30 December 2005 Available online 2 March 2006 It is difficult to completely differentiate patients with relapsing neuromyelitis optica (RNMO) from relapsing remitting multiple sclerosis (RRMS) for their similarities in clinical manifestation. In this study, we proposed a novel approach, using two-dimensional histogram of apparent diffusion coefficient (ADC) and fractional anisotropy (FA) of the brain derived from diffusion tensor imaging (DTI) as classification feature, to discriminate patients with RNMO from RRMS. In this approach, two-dimensional principal component analysis (2D-PCA) was used to extract feature and reduce dimensionality of matrix-formed data efficiently. Then linear discriminant analysis (LDA) was performed on these extracted features to find the best projection direction to separate patients with RNMO from RRMS. Finally, a minimum distance classifier was generated on the basis of projection scores. The correct recognition rate of our method reached 85.7%, validated by the leave-one-out method. This result was much higher than that using feature of ADC or FA separately (59.5% for ADC, 76.2% for FA). In conclusion, the proposed method on the basis of combined features is more effective for classification than those merely using the features separately, and it may be helpful in differentiating RNMO from RRMS patients. D 2006 Elsevier Inc. All rights reserved. Keywords: Discriminative analysis; Two-dimensional PCA; Diffusion tensor imaging; Relapsing neuromyelitis optica; Relapsing remitting multiple sclerosis * Corresponding author. Fax: address: jiangtz@nlpr.ia.ac.cn (T. Jiang). 1 These authors contributed equally to this work. Available online on ScienceDirect ( Introduction Both relapsing neuromyelitis optica (RNMO) and relapsing remitting multiple sclerosis (RRMS) are recurrent demyelinating diseases. RNMO is an idiopathic inflammatory demyelinating disease with generally poor prognosis that selectively involves spinal cord and optic nerves (Lennon et al., 2004; Weinshenker, 2003; Wingerchuk et al., 1999; Wingerchuk and Weinshenker, 2003). Most of RNMO patients have no lesions on brain MRI; however, a minority of these patients has punctate lesions that occur in the parenchyma or brain stem late in the disease course (Filippi et al., 1999; Mandler et al., 1993; Wingerchuk et al., 1999). RNMO is a severe demyelinating disease. Within 5 years, 50% of RNMO patients lose functional vision in at least one eye or are unable to walk independently (Lennon et al., 2004). RRMS is an inflammatory disease of the central nervous system characterized by demyelinating lesions disseminated in both space and time. Most of patients with RRMS show focal brain tissue abnormalities and have focal or diffuse lesions in spinal cord (Grossman and McGowan, 1998; Lycklama et al., 2003; Nijeholt et al., 1998). A few RRMS patients have normal brain MRI, but in whom spinal MRI was abnormal (Lycklama et al., 2003; Nijeholt et al., 1998). Herein, some patients with RNMO are misdiagnosed as RRMS, particularly at the early stage of onset, for some overlap features in clinical and imaging manifestations. Moreover, RNMO and RRMS differ in the prognosis and optimum treatment (Goodin et al., 2002; Keegan et al., 2002; Mandler et al., 1998). Therefore, it is very important to discriminate patients with RNMO from RRMS before progression and fulfillment of all clinical diagnostic criteria. Discriminative analysis or multivariate classifiers using neuroimaging information from brain have been playing an increasingly important role in brain disease studies (Dehmeshki /$ - see front matter D 2006 Elsevier Inc. All rights reserved. doi: /j.neuroimage

2 544 F. Lin et al. / NeuroImage 31 (2006) et al., 2002; Fan et al., 2005; Golland et al., 2001; Kontos et al., 2004; Lao et al., 2004; Liu et al., 2004; Stoeckel et al., 2004; Zhu et al., 2005). Dehmeshki et al. (2002) distinguished patients with MS from healthy subjects based on one-dimensional magnetization transfer ratio (MTR) histogram information; however, they failed to separate different MS subtypes. A reason may be that the classification information from onedimensional MTR histogram is not enough for accurate discrimination different MS subtypes. We suppose that the more information is used, the higher correct recognition rate can be reached. Thus, in this study, we employed information from the two-dimensional histogram of apparent diffusion coefficient (ADC) and fractional anisotropy (FA) of the brain derived from diffusion tensor imaging (DTI), as classification feature to discriminate patients with RNMO from RRMS. DTI is a useful imaging technique, which can give information about the orientation and shape of brain tissues at a microscopic level (Basser et al., 1994a). Some rotationally invariant indices, such as ADC and FA, which are derived from DTI, can provide information of the magnitude and directionality of water diffusion in brain tissues. ADC reflects average diffusivity of water molecular motion and FA measures the degree of directionality of water diffusion (Basser and Pierpaoli, 1996). Therefore, two-dimensional histogram of ADC and FA, considering more information of water molecular motion, may be superior to one-dimensional ADC or FA histogram in distinguishing RNMO from RRMS patients. In order to extract feature and reduce dimensionality of matrixformed data efficiently, two-dimensional principal component analysis (2D-PCA) was used. 2D-PCA keeps the two-dimensional structure of image by considering it as a matrix so that it is not necessary to reshape the two-dimensional matrices into vectors (Yang et al., 2004). On these extracted features, linear discriminative analysis (LDA) was performed to find the optimal projection vector, and a minimum classifier was generated. Materials Subjects In this study, 20 patients (19 women and 1 man) with a relapsing course satisfied the diagnosis criteria for NMO (Wingerchuk et al., 1999). They satisfied all absolute criteria and at least one major supportive criterion or two minor supportive criteria. Sixteen of these RNMO patients had normal brain MRIs and four of them had brain lesions. Their mean age was 35.5 T 11.4 years (range = years). Their mean Expanded Disability Status Scale (EDSS) score (Kurtzke, 1983) was 3.5 T 1.3 (range = ), and the mean disease duration was 5.1 T 4.2 years (range = years). Twenty-two MS patients (15 women and 7 man; mean age = 34.7 T 8.6 years, range = years; mean EDSS scores = 3.0 T 1.4, range = ; mean disease duration = 4.4 T 3.6 years, range = years), satisfying the proposed diagnostic criteria for RRMS (Lublin and Reingold, 1996) were selected. Twenty of these patients had typical lesions on brain MRI and two of them had normal brain MRIs. Local Ethical Committee approval and written informed consent from all the subjects were obtained before study initiation. MR data acquisition All MR imaging was performed on a 1.5 T MR scanner (Sonata; Siemens, Erlangen, Germany). All slices were positioned to parallel to a line that joins the most inferoanterior and inferoposterior parts of the corpus callosum (Miller et al., 1991). The following sequences with the identical slice position, number of slices (30), slice thickness (4 mm), and inter-slice gap (0.4 mm) were obtained: (1) Turbo spin-echo (TSE) T2-weighted imaging (TR = 5500 ms, TE = 94 ms, number of excitation (NEX) = 3, echo train length = 11, matrix = , field of view (FOV) = mm); (2) T1- weighted spin-echo imaging (TR = 650 ms, TE = 6ms, NEX = 3, matrix = , FOV = mm); (3) A spin-echo single shot echo-planar pulse (EPI) sequence (TR = 5000 ms, TE = 100 ms, NEX = 10, matrix = , FOV = mm). The diffusion sensitizing gradients were applied along six non-collinear directions ([1 0 1], [1 0 1], [0 1 1], [0 1 1], [1 1 0], [1 1 0]) with a b value of 1000 s/mm 2, together with an acquisition without diffusion weighting (b = 0). Methods Two-dimensional histogram of ADC and FA The diffusion tensor of each voxel was first calculated according to the linear least-square fitting algorithm (Basser et al., 1994b). ADC, measuring the average diffusivity of water molecular diffusion, and FA, measuring the directionality of water molecular diffusion, were derived for each voxel according to the equations in (Basser and Pierpaoli, 1996). After the ADC and FA images were derived, the diffusion-unweighted images of DTI (b = 0) were coregistered with TSE T2-weighted images based on normalized mutual information by using SPM2 (Wellcome Department of Imaging Neuroscience, London). The same transformation parameters were then applied to coregister ADC and FA images. Voxels containing extra-cerebral tissue were removed from T2- weighted images using a semi-automated technique provided by MRIcro (a free software download from: Then the corresponding voxels were removed from ADC and FA images. The two-dimensional histogram of ADC and FA was calculated to make full use of ADC and FA information for classification. A matrix containing elements characterized two-dimensional histogram. Its value at the coordinate (S ADC, S FA ) was the number of corresponding voxel pairs having S ADC in the ADC image and S FA in the FA image. One-dimensional ADC and FA histograms containing 1000 bins were derived in a similar way. To compensate for variability of brain size, each histogram was normalized by the total number of voxels contributing to the calculation of histogram. Two-dimensional principal component analysis In this study, the two-dimensional histogram of ADC and FA derived from DTI was used as original classification feature. We should extract feature and reduce dimensionality of these data before classification. Generally, principal component analysis (PCA) can do these for it is an efficient feature extraction and data representation technique widely used in the areas of pattern recognition and computer vision. However, in a traditional

3 F. Lin et al. / NeuroImage 31 (2006) PCA-based technique, two-dimensional matrices must be reshaped into vectors since only features in vector form can be analyzed. One issue arises when doing this, especially in the small sample size case, the dimensionality of the feature vectors is too high to accurately estimate the covariance matrix and reliably perform the spectral decomposition of covariance matrix. To solve the problems, Yang et al. proposed twodimensional PCA (2D-PCA), which keeps the two-dimensional structure of an image by considering it as a matrix, and therefore, it is not necessary to reshape the two-dimensional matrices into vectors (Yang et al., 2004). Therefore, 2D-PCA was used to extract feature and reduce dimensionality of these matrix formed data in this study. The aim of 2D-PCA is to find the optimal projection vector, P opt, such that the sample structure is preserved, that is, P opt ¼ arg max P X M traceðs P Þ ¼ P T 1 M i ¼ 1 ç P T G t P! T!! H i H H i H P where, H i a R m n ði ¼ 1; N ; MÞ are two-dimensional histograms, M is the number of samples. H is the mean two-dimensional histogram of all samples. Obviously, the optimal projection vector P opt is the eigenvector with the largest eigenvalue of G t. In practice, one projection vector is not enough to extract sufficient features. Therefore, a set of orthogonal vectors should be used to maximize the criterion (Eq. (1)). Usually, these projection vectors can be selected as the k eigenvectors corresponding to the first k k largest eigenvalues of G t. Suppose { P i } i = 1 are the optimal projection directions, then all the projections of each twodimensional histogram H i in the k directions make up an mkdimensional vector h i defined by: h T i ¼ P1 T H i T ; N ; Pk T H i T Linear discriminant analysis Linear discriminant analysis (LDA) is a well-known scheme for feature extraction and dimensionality reduction in pattern recognition. The aim of LDA is to find the optimal projection so that the ð1þ ð2þ ratio of the variance of the between-class and the within-class of the projected samples reaches its maximum (Duda et al., 2001), that is, w opt ¼ arg max w w T S b w w T S w w where S b and S w are the between-class scatter and within-class scatter matrices, having the following expressions, S b ¼ XC i ¼ 1 S w ¼ XC n i h i h X ni i ¼ 1 j ¼ 1 h j h h i h T ð3þ T hj h ð4þ where h j is the sample transformed by 2D-PCA using (2), h i is average vector of the ith class, h is the average vector of total samples; n i and C are the number of the ith class and number of classes. Theoretically, in two classes problem, the optimal projection vector w opt can be determined by: w opt ¼ Sw 1 S b ¼ Sw 1 h 1 h 2 ð5þ Because of n 1 +n 2 << mk in our study, this will result in an ill-posed problem of computing inverse matrix of S w and an unreliable result by using classical LDA. To solve this problem, we used the pseudo-inverse of S w to substitute the inverse of S w (Raudys and Duin, 1998). Firstly, complete PCA is applied on samples, h i, transformed by 2D-PCA to find a linear subspace, R D ðd ¼ n 1 þ n 2 1Þ, spanned by all the eigenvectors D {a i } i =1,corresponding to the non-zero eigenvalues (Yang and Yang, 2003). Projecting these samples h i a R mk, onto the PCA subspace would result in a low-dimensional vector, h i a R D. Then, Eq. (5) can be used in this PCA subspace to find the optimal projection vector w opt a R D. After projecting each sample h i a R D onto w opt, a discriminative score, z i, can be obtained for each two-dimensional histogram, H i, by z i ¼ w T h opt i. Classifier and validation After the discriminative scores were obtained, then a minimum distance classifier was used for classification. If mean value l i is Fig. 1. Mean one-dimensional histogram of RNMO and RRMS patients. (A) Mean ADC (10 3 mm 2 /s) histogram of these two groups of patients; (B) mean FA histogram of these two groups of patients. ADC = apparent diffusion coefficient; FA = fractional anisotropy; RNMO = relapsing Neuromyelitis Optica; RRMS = relapsing remitting multiple sclerosis.

4 546 F. Lin et al. / NeuroImage 31 (2006) Fig. 2. Mean two-dimensional histogram of RNMO and RRMS patients. (A) Mean two-dimensional histogram of RNMO patients; (B) mean two-dimensional histogram of RRMS patients. considered as the prototype of jth class and sample z satisfies dz;l ð k Þ ¼ min j ¼ 1; N ;c d z; l j, then z belongs to class k. Where, d(i,i) denotes Euclidean distance. In order to test the predictive ability of our classifier, leave-oneout (LOO) cross validation method was performed in this study. First, in each LOO validation experiment, one subject was selected as testing sample, and the remaining subjects were used as training samples to construct the classifier. Then, the classification result on the testing sample was compared with the testing subject using the ground-truth class label, to evaluate the predictive power of our method. Correct recognition rate from all the LOO experiments was obtained by repeatedly leaving each subject out as testing sample. Classification results The proposed method based on two-dimensional histogram of ADC and FA of the brain derived from DTI was used to discriminate patients with RNMO from RRMS. Classification results, validated by the LOO cross-validation method using twodimensional histogram of ADC and FA, were listed in the top row of Table 1, from which the correct predictive rates performed on RNMO and RRMS patients were 85.0% and 86.4%, respectively. The total correct predictive rate reached 85.7%. The distribution map of discriminative scores based on twodimensional histogram of ADC and FA as classification feature of both the training and predicting samples in a 42-round LOO test were shown in Fig. 3, where white circles and squares Results Group mean histograms Mean one-dimensional histograms of RNMO and RRMS patients are presented in Fig. 1. Difference in peak height and location can be seen in mean ADC and FA histograms for these two groups. Mean two-dimensional histograms of ADC and FA for RNMO and RRMS patients are shown in Fig. 2. Twodimensional histogram makes use of all information from ADC and FA, which may be useful to discriminate RNMO from RRMS patients. Table 1 Classification results based on different features Classification LOO test correct recognition rate feature RNMO (%) RRMS (%) Total (%) Two-dimensional histogram of ADC and FA ADC histogram FA histogram Note. The correct recognition rate based on two-dimensional histogram of ADC and FA is much higher than that of using features of ADC or FA separately. It indicates that the proposed method on the basis of combined feature is more effective for classification than those merely using the features separately. Fig. 3. Distribution map of discriminative scores based on the twodimensional histogram of ADC and FA. White circles: mean discriminative score of patients with RRMS in LOO test; White squares: mean discriminative score of patients with RNMO in LOO test. Black circles: discriminative score of patients with RRMS sample in LOO test; Black squares: discriminative score of patients with RNMO sample in LOO test. Black crosses: the classification thresholds determined by averaging mean discriminative scores from RRMS and RNMO patients. This figure indicates that there are only three testing RRMS patients and RNMO patients located on the wrong sides of the classification boundary by using two-dimensional histogram.

5 F. Lin et al. / NeuroImage 31 (2006) Fig. 4. Distribution maps of discriminative scores based on the one-dimensional histogram. (A) Distribution of discriminative scores based on ADC histogram; (B) distribution of discriminative scores based on FA histogram. White circles: mean discriminative score of patients with RRMS in LOO test; White squares: mean discriminative score of patients with RNMO in LOO test. Black circles: discriminative score of patients with RRMS sample in LOO test; Black squares: discriminative score of patients with RNMO sample in LOO test. Black crosses: the classification thresholds determined by averaging mean discriminative scores from RRMS and RNMO patients. This figure indicates that correct recognition rate based on one-dimensional histogram is lower than that based on twodimensional histogram. represented average discriminative score of patients with RRMS and RNMO in the training set of LOO test, respectively, and black circles and squares represented discriminative score of the RRMS and RNMO patients for predicting sample, respectively. The crosses represented the corresponding classification thresholds determined by the average of mean discriminative scores from RRMS and RNMO patients. As in Fig. 3, there were only three testing RRMS patients and three RNMO patients located on the wrong sides of the classification boundary by our method. To compare the discriminative ability of two-dimensional histogram of ADC and FA with that of one-dimensional histogram, ADC and FA were also used as classification features to discriminate RNMO from RRMS patients. The classification results were listed in the middle and bottom rows of Table 1. The distribution maps of discriminative scores based on only ADC or FA classification features of both the training and predicting samples in a 42-round LOO test were shown in Fig. 4. From Table Table 2 Classification results according to patient s disease duration Patients with LOO test correct recognition rate disease duration RNMO RRMS Total (%) 3 years 8/9 10/ years 11/11 10/ years 11/12 12/ years 14/15 13/ years 14/16 16/ years 16/19 17/ All patients 17/20 19/ Note. The lowest and highest LOO test correct recognition rates according to the disease duration, based on two-dimensional histogram of ADC and FA, are 82.5% and 85.7%, respectively. The LOO test correct recognition rates indicate that our classification method is very robust and be influenced little by the disease duration. 1, we could see that the correct recognition rate of our method (85.7%) on the basis of combined FA and ADC feature from twodimensional histogram was much higher that that using only one classification feature from one-dimensional histogram, either ADC (59.5%) or FA (76.2%). In order to evaluate the influence of the disease duration on our classification method, we also discriminated RNMO from RRMS patients according to their disease durations. The LOO test correct recognition rates based on classification information from the twodimensional histogram of ADC and FA were listed in Table 2. The lowest and highest LOO test correct recognition rates according to disease duration were 82.5% and 85.7%, respectively, which indicate that our classification method is very robust. Discussion In this study, we used two-dimensional histogram of ADC and FA of the brain derived from DTI, which was capable of quantifying microstructural brain tissue changes not visible on conventional MRI, to discriminate patients with RNMO and RRMS. Our method based on two-dimensional histogram performs better in distinguishing patients with RNMO from RRMS than one-dimensional histogram. Although two-dimensional histogram contains more information for classification, it is more difficult to extract feature than one-dimensional case because two-dimensional histogram has a huge dimensionality if it is directly reshaped into vector (in our study, the dimensionality was 250,000). To solve this problem, 2D-PCA was used to extract features directly from these two-dimensional histograms. The two-dimensional structure characteristic of the two-dimensional histogram is kept for regarding it as a matrix. Moreover, it is not necessary to reshape twodimensional histograms into vectors (Yang et al., 2004). LDA is a widely used scheme for discriminative analysis in pattern cognition and computer vision; however, the result is not reliable by using classical LDA in a small sample size problem, like in our

6 548 F. Lin et al. / NeuroImage 31 (2006) study. Herein, PCA analysis is used to reduce dimensionality further before LDA. Moreover, all the eigenvectors responding to the positive eigenvalues should be kept in order to keep all the useful classification information (Yang and Yang, 2003). The predictive ability based on classification information from two-dimensional histogram was 85.7%, which was much higher than that of merely using one classification feature from onedimensional histogram, either ADC (59.5%) or FA (76.2%). The results support our hypothesis that a two-dimensional histogram is superior to a one-dimensional case for classification. The classification results also indicate that ADC and FA might provide complementary information for distinguishing RNMO from RRMS patients. ADC and FA are widely used rotationally invariant indices in many brain disease studies and in monitoring their treatment (Sotak, 2002; Sundgren et al., 2004). ADC, measuring the average diffusivity of water molecular diffusion motion, is affected by cell size and integrity. FA, measuring the degree of directionality of diffusion, indicates the structural integrity and degree of structural alignment within fiber tracts. These two measurements provide different information about water molecular diffusion motion at different view, and can give information about the size, shape, orientation, and geometry of brain tissues (Basser and Pierpaoli, 1996). Therefore, two-dimensional histogram of ADC and FA makes full use of information of water molecular diffusion motion, and is more effective for discrimination of patients with RNMO from RRMS than using them separately, either ADC or FA. In this study, in order to assess the influence from the disease duration, we also applied the proposed classification method to discriminate RNMO from RRMS patients according to their disease durations. The lowest and highest correct recognition rates, validated by the LOO method, were 82.5% and 85.7%, respectively (Table 2), which indicate that our classification method may be influenced little by the disease duration. These results also indicate that our classification method may be expected to find similar results in patients with disease duration less then 3 years. Thus, our proposed classification method may be helpful in early diagnosing RNMO from RRMS patients, particularly before progression and fulfillment of all clinical diagnostic criteria. In order to reduce the effect of noise, the images of DTI were scanned with 10 averages; as a consequence, the signal to noise increased about 3 times. In our method, the classification results were carried out from whole brain rather than normal-appearing brain tissue (NABT) or normal-appearing white matter (NAWM) like in many histogram-based analysis in MS. There are several reasons for this. First of all, both the LOO test correct recognition rates based on two-dimensional histogram from NABT and NAWM are 85.0% for RNMO patients, 86.4% for RRMS patients and 85.7% for the total patients. The results are similar with those based on the whole brain, which indicate that CSF and brain lesions may influence little the final classification results. This observation is also described by Dehmeshki et al. (2001). Second, brain lesions are often extracted manually, which is time-consuming and not very reliable, particularly for punctate lesions in RNMO and RRMS patients. Moreover, there is no very robust brain tissue segmentation algorithm especially for clinical brain MRI data. Therefore, we derived histograms from whole brain rather than NABT or NAWM as original classification features in our study. NMO is a severe inflammatory demyelinating disease that selectively targets optic nerve and spinal cord, typically sparse in the brain, and generally follows a relapsing course. About onethird of RNMO patients have severe cervical myelitis causing respiratory failure, and the mortality rate of these patients is 32% (Wingerchuk, 2001). Therefore, early diagnosis and treatment are very important to reduce the mortality of RNMO. Furthermore, some RNMO patients are commonly misdiagnosed as RRMS for many similarities in clinical features, especially at the course of onset, but the optimum treatments for these two diseases are different (Goodin et al., 2002; Keegan et al., 2002; Mandler et al., 1998). Therefore, it is very important to discriminate patients with RNMO from RRMS. Our classification method may be helpful in diagnosing these two groups of patients in clinical application. Conclusion In this paper, a novel method discriminating patients with RNMO from RRMS based on the two-dimensional histogram of ADC and FA derived from DTI has been proposed. Compared with the approach based on classification information from onedimensional histogram, our method achieved much better classification performance. This implies that two-dimensional histogram may be more suitable for classification than one-dimensional histogram. Our proposed classification method on the basis of neuroimaging information is influenced little by the disease duration, which may be helpful in early diagnosing RNMO from RRMS patients, particularly before progression and fulfillment of all clinical diagnostic criteria. Although our method is promising, evaluation of the proposed method with larger sample size and multi-center imaging data sets deserves further investigation. Moreover, functional imaging information will be taken into account to raise the correct recognition rate in the feature research. Acknowledgments The authors are highly grateful to the anonymous reviewers for their significant and constructive comments and suggestions, which greatly improve the article. This work was partially supported by the Natural Science Foundation of China, Grant Nos , , and , and the National Key Basic Research and Development Program (973), Grant No. 2004CB and Beijing Natural Science Foundation, Grant No References Basser, P.J., Pierpaoli, C., Microstructural and physiological features of tissues elucidated by quantitative diffusion tensor MRI. J. Magn. Reson., B 111, Basser, P.J., Mattiello, J., LeBihan, D., 1994a. MR diffusion tensor spectroscopy and imaging. Biophys. J. 66, Basser, P.J., Mattiello, J., LeBihan, D., 1994b. Estimation of the effective self-diffusion tensor from the NMR spin echo. J. Magn. 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