On non-linear characterization of tissue abnormality by constructing disease manifolds

Transcription

1 On non-linear characterization of tissue abnormality by constructing disease manifolds Nematollah Batmanghelich Ragini Verma Section of Biomedical Image Analysis, Department of Radiology, University of Pennsylvania {nematollah.batmanghelich, Abstract Tissue deterioration as induced by disease can be viewed as a continuous change of tissue from healthy to diseased and hence can be modeled as a non-linear manifold with completely healthy tissue at one end of the spectrum and fully abnormal tissue such as lesions, being on the other end. The ability to quantify this tissue deterioration as a continuous score of tissue abnormality will help determine the degree of disease progression and treatment effects. We propose a semi-supervised method for determining such an abnormality manifold, using multi-parametric magnetic resonance features incorporated into a support vector machine framework in combination with manifold regularization. The position of a tissue voxel on this spatially and temporally smooth manifold, determines its degree of abnormality. We apply the framework towards the characterization of tissue abnormality in brains of multiple sclerosis patients followed longitudinally, to obtain a voxel-wise score of abnormality called the tissue abnormality map, thereby obtaining a voxel-wise measure of disease progression. 1. Introduction Tissue abnormality characterization has gained importance as a research area owing to the need for identifying tissue regions that are progressively becoming more abnormal owing to disease induced pathology, with the research being especially pertinent with respect to longitudinal studies, where this can be used for treatment planning. However traditionally tissue characterization has been limited to the identification of gross tissue abnormality such as lesions, tumors etc. However research has shown that the tissue outside of the gross tissue abnormality region may also be affected by disease and is progressing to a higher degree of abnormality with the onset of pathology [3]. Such tissue is referred to as normal appearing brain tissue (NABT) and is of great importance in the study of diseases such as multiple sclerosis (MS) where healthy tissue converts to lesions over time. Further, studies have shown that different magnetic resonance (MR) protocols convey different information about the tissue abnormality and combining them into a multi-parametric profile should provide better tissue characterization [19, 1]. Not only has it helped researchers identify the diseased tissue more accurately, but it is expected that it may also help them to quantify the deviation of tissue from healthiness that is, the degree of abnormality [14]. In this work, we use several MR protocols. to create a multi-parametric feature for the tissue which is then incorporated into a SVM-based manifold regularization framework that models the manifold of tissue abnormality from healthy to diseased (see Figure 1). Each tissue voxel (qualified by its multi-parametric feature) based on its position on the manifold is associated with a continuous score that quantifies its degree of abnormality ranging from 0 (healthy) to 1 (completely diseased). Voxel-wise application of this produces a tissue abnormality map for the whole brain. The tissue abnormality maps are expected to be an indicator of such a conversion, aiding in early detection of disease progression and damage, with prevention possibilities. Most of the work on tissue characterization has concentrated on tissue segmentation [19, 1, 13, 10] or classification which assigns a class label to each tissue voxel such as diseased or healthy tissue, mainly by learning their patterns from expert-defined samples collected from these tissue types [4]. Standard classification techniques such as Support Vector Machines (SVM) [8, 4], Bayesian [6], or Neural networks [11], that are traditionally used for classification and segmentation, are not sufficient to characterize intermediate tissue as they assign a discrete label to each voxel. Thus these methods provide a voxel-wise label of healthy or diseased tissue, but they do not characterize the degree of abnormality in the white matter outside of the lesions that is also deteriorating as part of the progression of /08/$ IEEE

2 Diseased Healthy Diseased Figure 1. Distribution of samples that vary on a smooth manifold encompassing the normal tissue at one end to the diseased tissue at the other. disease. There has been some attempt in the MS literature, such as [7], to characterize tissue that is not fully diseased but is progressing towards it. Comprehensive characterization of such tissue is difficult as there are no training samples available for such tissue and hence no ground truth. In addition, characterization of intermediate tissue requires smoothing on the abnormality manifold as well as the incorporation of information from neighboring voxels, both of which are not handled in traditional classification methods. Multi-modality medical images have been used for tissue characterization [15, 19], but did not assign continuous abnormality score to each voxel. Soltanian-Zadeh et al. [16] proposed the use of eigen images to detect abnormality in regions around a cerebral tumor. Corso et al. [5] proposed a hierarchical method for segmentation of tumor and edema from healthy tissue in the brain. Their method is based on SWA (Segmentation by Weighted Aggravation) which is implemented within a Bayesian framework with hierarchical weight assignment. Taskar et al. [18] incorporate SVM and MRF and proposed Maximum Margin Markov (M 3 ) network which can handle multi-dimensional features and interdependency between samples simultaneously. Song et al. [17] suggested semi-automated tissue segmentation using a Gaussian process. In [21], graph models were used for segmentation of tumour tissue, based on user identified tumor regions. In all these cases, segmentation or in other words, separation of two classes was the main interest, but not a continuous characterization of abnormality as we provide in our framework. The main drawback of these methods is that each pixel or voxel is treated as an independent sample. To consider the correlation between neighboring voxel features, usually intensities of neighboring voxels are concatenated into a big feature vector. However, this violates the underlying assumption of classification methods which consider that the samples are independent and identically distributed (i.i.d). Our aim in this paper is to combine multi-parametric information to learn the manifold of disease abnormality and characterize each voxel by mapping it to this manifold. As there is no ground truth available, we have to utilize the cues from the diseased and healthy tissue samples that have been delineated by the expert. We have used a technique called Laplacian RLS (regularized least squares) to construct a smooth manifold of tissue abnormality (which incorporates the neighborhood information in the form of spatial constraints). The value of a pixel on this manifold provides it with a continuous score of abnormality, which has been validated against healthy and lesion tissue identified by the expert. These voxel-wise tissue abnormality maps can then be used in clinical studies to correlate with clinical measures of tissue abnormality, in order to determine treatment options and disease progression. 2. Methods In this paper, we have designed a method of tissue abnormality characterization that treats tissue abnormality as a gradual change from healthy to diseased lying on an abnormality manifold and tissue in the process of becoming fully diseased will have intermediate characteristics between the healthy and diseased tissue (see Figure 1). We use expert labeled samples of diseased and healthy tissue to create the disease manifold using a technique called Laplacian RLS (regularized least squares) framework. This is a manifold regularization framework that in addition to creating the manifold imposes spatial smoothness in the feature space by incorporating neighborhood information, as well as smoothness along the manifold. The overview of the method can be found in Figure 2. We assume that there is a smooth manifold encompassing healthy and diseased (such as, lesion) tissue with normal appearing abnormal tissue lying on this manifold. Furthermore, abnormality score should be continuous and smooth on the abnormality manifold and spatially on the image. However, there are some issues to be addressed: first, conventional regression methods like Support Vector Regression (SVR) does not provide leverage to control the smoothness on the unlabeled samples; second, tissue abnormality in the absence of consistent ground truth may be easier to be characterized using combination of MR protocols rather than a single one. Also, as we are interested in tissue abnormality characterization, assigning discrete numbers (class labels), as in traditional classification schemes is not sufficient because it is not depictive of the gradual transition of tissue from diseased to healthy. We have some samples from healthy brain and some samples from lesion part of diseased brain as labeled training samples. Voxels of the brain which are to be tested are considered as unlabeled samples. Taking advantage of Laplacian Regularized Least Square (LapRLS) [2] formulation as a semisupervised regression method, we associate a continuous abnormality score pertaining to each voxel of the brain im- 2

3 k M uu k, k M Unlabeled voxels uu k k uu k, k 1, k +1 k 1 k+ 1 uu + k, k M k+m + S Positive Class (labeled) j lu jk lu ik Negative Class (labeled) S p ll pq q i L 11 L 21 L = L 12 T 21 L L p p 2 ( x i xj ) ( ) + 2 2σ [ L22] ij : = η[ L22] ij + (1 η) e Figure 2. Schematic of our framework which shows all the steps from defining samples to create the graph Laplacian, which in turn produces the tissue abnormality map Figure 3. Graph Laplacian created from the labeled (healthy (S ) and diseased (S + )) and unlabeled (samples to be categorized and assigned a number) plemented as an embedding graph consisting of labeled and unlabeled voxels. Training samples (obtained from expert labeled samples of healthy and diseased tissue) and unlabeled voxels set up vertices of an embedding graph (as seen in (Fig.3)). Associations between neighborhood voxels are taken care of using a proper edge weighting scheme between vertices of embedding graph. This addresses the scenario that if two voxels of an image are close together spatially, they should be associated with a similar abnormality value. For example, this is the place that SVR can not be applied because there is no notion of spatial smoothness (smoothness on unlabeled samples). However, LapRLS is able to produce spatially smooth function on the graph based on weighting scheme which will be described in the following sections. Employing LapRLS, we propose a method which can handle both the criteria (spatial feature and manifold smoothness) in one framework, so that a continuous abnormality score is obtained. The detailed framework can be seen in Figure 2. The framework is applied to multiparametric data acquired on MS patients with the idea of characterizing white matter (WM) that is progressing to abnormality based on the stage of the disease. We will now explain in detail, how we construct the manifold and impose the smoothness constraints on it. This will be followed by an explanation of how to obtain the tissue abnormality map for the brain Creation of multi-parametric features We define a multi-parametric feature for each voxel in the brain, by combining all the MR protocols that have been acquired. Suppose we have N protocols, with each denoted by I i, i = 1, N. Then any voxel x i will be represented by the feature (I i1,, I in ), where I ij represents the intensity of the i-th voxel in the j-th MR protocol. For example for the MS data we have several MR protocols, namely, T1, T2, mprage, Magnetic transfer, mprage (pre and post GAD) and Diffusion Tensor Imaging (DTI). Each voxel is then assigned a multi-dimensional feature vector, with each component corresponding to the intensity of that voxel in a particular modality. This will be discussed in greater detail in the results section Creation of the disease manifold Given a set of labeled examples (x i, y i ), i = 1,..., l, where x i s are voxels with multi-parametric intensities that have been labeled (y i ) as diseased (+1) or healthy (-1), our 3

4 aim is to find a function, referred to as the abnormality function f, which satisfies similarity criterion between voxels, based on their proximity to diseased or healthy tissue as well as smoothness which models gradual and continuous transition of the abnormality score. This is modeled mathematically as the function: f 1 l = arg min C(x i, y i, f)+λ R f 2 K +λ M f 2 M f H K l i=1 (1) where l is the number of labeled samples. The first term, C(x i, y i, f), penalizes the error between the labels, y i, and the samples x i and is a measure of similarity in the feature space, that is, how close voxels are in terms of tissue abnormality. We model it as the square loss function C(x i, y i, f) = (y i f(x i )) 2, although alternate similarity measures can be used. The second and third term, λ R f 2 K, and λ M f 2 M, together impose different smoothness conditions on the abnormality function f. Broadly, the second term imposes smoothness in the feature space as it is in ordinary SVR. The third term takes care of spatial smoothness (in the sense that if two voxels are close to each other, corresponding abnormality function value f should also be close) and manifold smoothness (in the sense that if a sample has the tissue profile which looks like a sample which has a high abnormality value f, this should also have a high f value). f is abnormality score derived from minimization of eq.1 in which f > 0 is considered abnormal and f < 0 is considered normal. As described in [2], the last term f 2 M,can be approximated by graph Laplacian which is constructed based on labeled (denoted by features l) and unlabeled samples (denoted by features u) (see Figure 3). Unlike traditional transductive SVM method like [12] in which feature similarity between labeled and unlabeled samples are used for categorizing them to be closer or further from a tissue type, manifold-based methods incorporate similarity with the neighborhood information. In fact, prior knowledge could be incorporated in terms of weights between samples, such as in You et al. [20] and Geng et al. [9]. Since the main goal of this paper is not classification or lesion segmentation, but aims at tissue characterization, we design a weighting scheme for the graph Laplacian that can reveal underlying abnormality coded by various MR modalities. As is mentioned earlier, we have assumed that abnormal tissue samples lie between normal and lesion clusters on the sample manifold. In addition, voxels which are spatially close should supposedly possess similar abnormality scores. Taking into account these two facts, we propose a weighting scheme that imposes spatial (manifold) and features space smoothness (between samples), simultaneously. After building the graph which consists of labeled and unlabeled sample (Fig. 3), and assigning weights to the edges of the graph, we can make a slight change in the Laplacian of graph in order to consider spatial information. The Laplacian of the graph is a matrix which is created based on weights assigned to the edges of the graph, which are edge weights between the nodes. The Laplacian of the matrix can be decomposed into four blocks as follows: [ ] L11 L L = 12 L 21 L + (2) 22 L 12 = L T 21 L + 22 : [l+ 22 ] ij = η[l 22 ] ij + (1 η)e ( (x p i xp j )2 2σ 2 ) in which L 11, L 12, L 21 and L 22 are ordinary weights, e.g. binary nearest neighbor weights or heat kernel or any other method, which is solely derived from features, in our case multi-parametric intensity features. L 11 in a block matrix represents the graph Laplacian between labeled samples and L 21 and L 21 respectively shows the graph Laplacian between labeled-unlabeled and unlabeled-labeled samples respectively, and L 22 corresponds to unlabeled-unlabeled graph Laplacian. We have modified original graph Laplacian for L 22 by adding extra term in order to consider spatial smoothness. x p i and xp j are positions vectors of i th and j th voxels in space respectively. Equation (2) says that if there is any relationship, say nearest neighbor, between samples of labeled instances, it should be kept intact; for unlabeled voxels, Eq.2 combines weights derived from features embedded in L 22 and their location with each other with arbitrary ratio η to derive new block, L In fact, η and σ could be seen as leverages to control spatial smoothness. Using these weights and constraints, as shown in [2], the function to be optimized can be written as: f 1 l = arg min C(x i, y i, f)+λ R f 2 K + λ M f H K l (u + l) 2 f T Lf i=1 (3) where matrix L is the graph Laplacian matrix described above that incorporates edge weights of embedding graph. Mathematical details about how to derive Eq. 3can be found in [2]. As is shown in [2], the decision function would be in the form of f(x) = u+l i=1 α ik(x i, x). In this study, we have used the RBF kernel, although we propose to investigate alternate kernels in the future. On optimizing the above function, we obtain an optimal solution for α i and hence an abnormality score for the corresponding voxel. The schematic of the entire process can be seen in Figure Tissue Abnormality Profile On applying the above framework to each tissue voxel in brain, for which multi-parametric features have been defined, the optimization of the abnormality function f pro- 4

5 B0 FA FLAIR Post-gad pre-gad MTR T2 Trace (a) (b) (c) Figure 4. (a),(b): Tissue abnormality map depicting the effect of manifold and spatial feature smoothing. The figures on the left are the color-coded voxel-wise outcome of the abnormality function. The figures on the right are obtained by thresholding the tissue abnormality map to determine the regions of high abnormality (or lesions). (a) Less weight for manifold smoothing (last term two terms in Eq.1) terms lead to less smooth decision function and noisier labeling as indicated by the patchy color map and high false positives, as seen by the red patches in the right hand image. (b) shows smoother color map, prominent abnormality region in red and removal of false positives in the lesion map on the right. This shows that both manifold(λ M) and spatial feature smoothing (η) are important for obtaining a smooth tissue characterization (and hence a smoother tissue abnormality map). The more reddish, the more abnormal tissue would be and the more bluish, the healthier tissue is. duces an abnormality value at each voxel that forms a voxelwise smooth measure of abnormality for a brain, which is referred to as the Tissue Abnormality Profile. This is color coded to visualize the level of abnormality. Red indicates high abnormality and blue indicates healthy. These tissue abnormality maps can be segmented (using a threshold) to obtain maps of diseased tissue, that is, lesions in the case of the images chosen. These regions are depicted in red in Fig.4 (a),(b). In all color maps, minimum and maximum of abnormality score values are normalized to zero and one, respectively, with all levels of abnormality lying in between. Figure 5. Row 1 shows a representative slice from each of the modalities from a single patient. These have all been spatially normalized to the FLAIR image of the baseline scan (time point 1). Row 2 shows examples of training samples (a) slice from a FLAIR image (b) lesion region marked in red is the training sample for lesion tissue (c) tissue in green is sample for healthy tissue identified on the brain of a healthy control. 3. Experimental Design and Results Dataset: We have applied our framework to a dataset of patients with multiple sclerosis (MS). We have 11 patients and 4 controls. The same patient is scanned every 3 months. Therefore, we have 3-4 time points for each patient. The aim is to be able to characterize the abnormality in Normal Appearing Brain Tissue (NABT) in the patients, using samples identified in the lesions in the patients and the healthy tissue in the controls. In each case several MR protocols were acquired. Namely, FLAIR, T1, T2, Magnetization Transfer (MT), and diffusion tensor imaging(dti). In order to create the intensity-based multi-parametric features, we combine information across different modalities. However, a direct comparison between successively scanned images is usually not possible, even within the same patient, since patient position is never identical, acquisition parameters may drift between scans, and a variety of complex global and local deformations of anatomical structure may occur. Thus feature creation requires pre-processing the im- 5

6 ages so that they are spatially normalized and comparable across scans, of the same patients over time. We refer to the first scan of the patient as time-point 0 or the baseline scan. The subsequent scans are referred to as time-points 1, 3 and so on, or as follow-ups 1, 2 etc. For each patient, for every time-point, we use the Magnetization Transfer-on and -off images to create the Magnetization Transfer Ratio (MTR) image. We also reconstruct the DTI data into 6 dimensional tensor data and create two scalar maps of Fractional Anisotropy (FA) (a measure of the anisotropy of the tissue) and Trace (equivalent to ADC or MD) (a measure of the diffusivity within the tissue). We also use the B0 image (image acquired with no gradient direction as part of the DTI acquisition which emulate T2* contrast) as a separate modality. We pre-process the images by first applying inhomogeneity correction to account for day-to-day scanner changes. We then apply histogram matching to make intensities across patients of the same protocol comparable. With the aim of creating intensity features by combining all the modalities on a voxel-wise basis, we first rigidly register all the modalities for a patient at a given time point to the FLAIR image. The FLAIR image is deformably registered to a template. By concatenating the vector fields, we have registered all the modalities of each subject (at all time points) to the template. Fig. 5 (row 1) shows snapshots of a representative slice from each of the modalities that have been pre-processed, that is, inhomogeneity corrected, histogram matched and spatially normalized to the FLAIR image of the baseline. These images are Gaussian smoothed with standard deviation 1, prior to their being used to create feature vectors. Multi-parametric intensity features are defined at each voxel, by concatenating the intensity value at that voxel from each protocol into a vector, as described in section 2.1. For training samples for healthy tissue, various parts of the brains of the 4 healthy controls were outlined which should include gray and white matter in addition to CSF. Lesion tissue was identified by experts on brains of 11 patients. Only 2000 voxels were chosen randomly out of this big ensemble to create labeled voxels. Figure 5 (row 2) provides some examples of the training samples. Since FLAIR was used to obtain the lesion and healthy tissue ground truth (and GAD was not acquired on the controls), these were not used as channels in the feature vector. Multi-parametric features are defined at each training voxel. Effect of Manifold and Feature Smoothing: Fig.4 (a),(b) shows that decreasing the effect of the manifold terms, lower values for λ R and λ M, (second and third terms in Eq.1), results in a noisier voxel-wise tissue labeling (right) and abnormality map (left) in Fig.4 (a). The tissue abnormality maps (left) are created by the voxel-wise scores obtained by solving the tissue abnormality function in f. These maps are thresholded at 0.9 to obtain the lesion segmentation maps on the right (this threshold is empirically chosen by comparing with expert chosen samples of lesions). The combined effect of the parameters yields a smoother result in the tissue abnormality maps in Fig.4 (b) indicating the need for both spatial and manifold smoothness. The patchiness in the lesion segmentation maps on the right in (a) indicate a greater false positives (in comparison to the outlining by the expert) as compared to (b), further establishing the need for both feature smoothing as well as manifold smoothing. Progression of Abnormality: In order to demonstrate that our method can capture abnormality, we will study the behavior of abnormality over time (Fig.6) using the Tissue Abnormality maps. Fig.6(a) shows how normal appearing brain tissue that is progressing to abnormal evolves over time and converts to purely lesion tissue. The time interval between successive scans are about three months. However, MS lesions may appear and disappear in the intervening period; in other words, it is possible that a part of tissue that appears purely healthy in the first scan progressively converts to abnormal and eventually to lesion. As it can be seen in Fig.6(a), although a very diffuse white area is evident in the peri-ventricular region in the first time point (T0), with no high intensity lesion, however our tissue abnormality map is able to pick it up as abnormal in the color map (red and yellow colored values). This region progressively becomes higher intensity in the FLAIR modality which is characteristic of MS lesion and eventually, it becomes a full-fledged lesion at time point T4. This shows that the more abnormal the tissue is initially, the more likely it is to convert to lesion over time. It also demonstrates that the tissue abnormality map is able to identify diseased tissue several months ahead of time and hence help in determining treatment options to prevent a future lesion, thereby changing the course of the disease. Validation: As there is no ground truth available for NABT, we have validated the results of this framework by comparing its classification accuracy of the healthy and lesion tissue with that of standard SVM (support vector machine) method [4]. We classified healthy and lesion tissue identified by experts, in a leave-one-subject-out paradigm, using our method and SVM-based method and obtained the same accuracy of 93%. Thus the manifold regularization method is better because it classifies tissue with same accuracy as SVM. But instead of producing discrete class labels for each tissue voxel classifying it as lesion or healthy, our method produces a continuous score of tissue abnormality. In addition, we measured the ability of our method to quantify abnormality (Fig. 6(b)). In order to do that, we conduct the fol- 6

7 %ever been lesion time f<0 t=0 T1 T2 T3 T4 Lesion appears gradually in FLAIR Lesion appears T0 Figure 6. Progression of tissue abnormality. (a): shows the result of the tissue abnormality score in time point 0. This shows high abnormality, indicated by redness in the tissue abnormality map. It is also seen that while the lesion is not evident in the first time point it appears gradually as time progresses (time points T1 to T4) as shown by it becoming a high intense area in the FLAIR modality which is the manifestation of MS lesion. Eventually, it becomes a full-fledged lesion. This shows that the abnormality score is indicative of tissue progression, even when modalities like FLAIR are unable to capture it. It shows that the portion of tissue with high abnormality value (f) becomes lesion over time rather than those which posses lower abnormality value. b: 3D histogram which illustrates how f score of tissue voxels in the baseline can be used to predict its becoming a lesion in the follow ups (subsequent time points). For more description, please refer to the Validation section. lowing test: intuitively, if f actually estimates the extent of abnormality, we expect that voxels which appear healthy in the baseline (t = T 0) should have less likelihood of becoming a lesion in the following time point versus tissue which looks more lesion-like. In order to quantify it, we concentrate on tissue which are classified as non-lesion, namely f < 0. In fact f = 0 is the border between lesion (f > 0) and non-lesion (f < 0). Presumably, we expect that lower the f, lower is the chance of it becoming a lesion in the subsequent time points. To assess this hypothesis, we quantized f < 0 into several bins (X-axis in Fig.6(b)). Abnormality score of each non-lesion voxel in the first time point, f, associates with one of these bins. In the other words, each non-lesion voxel falls into one of these bins. Given that, we counted the number of voxels which cross the border, f = 0, as time (Y-axis in Fig.6(b)) goes by and normalize it with total number of voxels in that bin (Z-axis in Fig.6(b) shows normalized values). Therefore, we get the 3D histogram shown in Fig.6(b). As is shown and expected, the healthier the tissue is, the more negative f, the less chance it has of becoming a lesion. 4. Discussion and Conclusion In this paper we have proposed a framework for characterizing the tissue abnormality by constructing a manifold of pathology-induced change that encompasses the entire range of tissue change from healthy tissue to its gradual transition to pathology affected tissue, by modeling this as a non-linear manifold. Our framework incorporates manifold regularization to classify voxels with multi-parametric features. Manifold regularization induced by the technique of LapRLS helps incorporate tissue features, neighborhood information as well as positioning on the abnormality manifold. The outcome of application to real data is to obtain a gradually varying abnormality value (that is, a smoother color map visualization as well as lower false positives) when compared to expert defined labeled voxels of healthy and diseased tissue. Although many have applied SVM or 7

8 other classification techniques to classify each voxel individually and independently, our method takes into account the spatial position of samples in feature space and their arrangement on abnormality manifold simultaneously. Therefore, as is expected, it yields results which are smoother and consequently smoothness removes some false positives. Through the process of employing manifold regularization, we are able to capture smooth transition from the normal, to normal-appearing and finally to fully diseased tissue. The framework is particularly applicable to high dimensional multi-parametric data (obtained by a combination of several MR protocols) which is difficult to regularize in general, and obtain a framework for tissue abnormality characterization. The application of the manifold regularization methods to the multi-parametric MS datasets, produces a voxel-wise decision map of abnormality that can be used to investigate tissue that is progressively becoming abnormal. We expect that such a novel characterization of tissue abnormality will help determine tissue that is in various stages of deterioration and thereby help in prognosis and determining the course of disease progression and treatment, especially in longitudinal studies. In the future, we propose to correlate these abnormality values with clinical scores obtained for each patient. In addition, we hope to address several challenging mathematical aspects of the problem, that is, choice of kernel and better regularization parameters. We propose to investigate parallelization options in order to speeden up the computation, as the process is computationally intensive at the moment, so that it can be applied to several datasets at a time. References [1] P. Anbeek, K. L. Vincken, and et al. Automatic segmentation of different-sized white matter lesions by voxel probability estimation. Med. Imag. Anal., 8(3): , [2] M. Belkin, P. Niyogi, and V. Sindhwani. On manifold regularization. In Workshop on AISTAT 05, [3] C. Bjartmar and et al. Axonal loss in normal-appearing white matter in a patient with acute ms. Neurology, 57: , [4] C. J. C. Burges. A tutorial on support vector machines for pattern recognition. data mining and knowledge discovery. Data Mining and Knowledge Discovery, 2:121167, [5] J. J. Corso, E. Sharon, and et al. Multilevel segmentation and integrated bayesggytian model classification with an application to brain tumor segmentation. In MICCAI 06, volume 2, pages , [6] G. D.-Phocion, M. Gonzalez, and et al. Hierarchical segmentation of multiple sclerosis lesions in multi-sequence mri. In ISBI 04, pages , [7] H. V. et al. Altered diffusion tensor in multiple sclerosis normal-appearing brain tissue: Cortical diffusion changes seem related to clinical deterioration. J Magn Reson Imaging, 23(5):628 36, [8] R. J. Ferrari, X. Wei, and et al. Segmentation of multiple sclerosis lesions using support vector machines. In SPIE 03, volume 5032, pages 16 26, [9] X. Geng and et al. Supervised nonlinear dimensionality reduction for visualization and classification. IEEE Trans. on Sys., Man, and Cyber-Part B:Cyber., 35(6): , [10] G. Gerig and et al. Exploring the discrimination power of the time domain for segmentation and characterization of active lesions in serial mr data. Medical Image Analysis, 4(1):31 42, [11] A. Hadjiprocopis and P. Tofts. An automatic lesion segmentation method for fast spin echo magnetic resonance images using an ensemble of neural networks. In IEEE Workshop on Neur. Net. for Sig. Proc., NNSP 03, pages , [12] T. Joachims. Transductive inference for text classification using support vector machines. ICML, pages , [13] K. V. Leemput and et al. Automated segmentation of multiple sclerosis lesions by model outlier detection. TMI, 20:677688, [14] D. S. Meier and C. Guttmann. Time-series analysis of mri intensity patterns in multiple sclerosis. NeuroImage, 20(2): , [15] M.W.Vannier, R. Butterfield, and et al. Multispectral analysis of magnetic resonance images. Radiology, 154: , [16] H. Soltanian-Zadeh and et al. Brain tumor segmentation and characterization by pattern analysis of multispectral nmr images. NMR in Biomedicine, 11(5): , [17] Y. Song and et al. A discriminative method for semiautomated tumorous tissue segmentation of mr brain images. In CVPR 06, pages 79 86, [18] B. Taskar and et al. Max-margin markov networks. In NIPS 04, volume 16, [19] Y. Wu, S. K. Warfield, and et al. Automated segmentation of multiple sclerosis lesion subtypes with multichannel mri. NeuroImage, 32(3): , [20] Q. You and et al. Neighborhood discriminant projection for face recognition. In ICPR 06, volume 2, pages , [21] X. Zhu, Z. Ghahramani, and et al. Semi-supervised learning using gaussian fields and harmonic functions. In ICML 03, volume 20,