Analysis of the pyramidal tract in tumor patients using diffusion tensor imaging

NeuroImage 50 (2010) 27–39

Contents lists available at ScienceDirect

NeuroImage j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / y n i m g

Analysis of the pyramidal tract in tumor patients using diffusion tensor imaging Rubén Cárdenes a,⁎, Emma Muñoz-Moreno a, Rosario Sarabia-Herrero b, Margarita Rodríguez-Velasco b, Juan José Fuertes-Alija b, Marcos Martin-Fernandez a a b

Laboratory of Image Processing, University of Valladolid, Spain Hospital Clínico Universitario de Valladolid, Spain

a r t i c l e

i n f o

Article history: Received 12 August 2009 Revised 4 December 2009 Accepted 5 December 2009 Available online 16 December 2009 Keywords: DTI DTMRI Tractography Fiber tracking Brain tumor Pyramidal tract DTI quantification

a b s t r a c t In this work, we propose to use fiber tracking in order to analyze and quantify the state of the pyramidal tracts in patients affected by tumors. We introduce a framework that includes an automatic method to obtain the fibers involved in the pyramidal tract of any subject, in order to compare robustly fiber bundles affected by tumors with healthy fiber tracts from control subjects and also to quantify the relative state of degeneration between the fiber tracts in the two hemispheres of the same patient. The comparative analyses proposed in our methodology are based on a new set of measures on the pyramidal tract, which take into account intrinsic properties of the fibers involved in the bundle as well as the similarity with the pyramidal tract of a standard healthy subject, modeled as the average of a set of controls. In order to perform better comparison studies and to take into account more information of the whole bundle, a mapping technique is used to represent the fiber tracts in 2D. Here, we show a set of experiments using 5 tumor patients and 10 control subjects, including pre- and post-operative studies in patients that have been treated with partial or total tumor resection. The results obtained indicate the usefulness of the method showing good overall performance. A reproducibility study using several acquisitions of the same patient is also presented to validate the techniques employed. © 2009 Elsevier Inc. All rights reserved.

Introduction Diffusion Tensor Magnetic Resonance Imaging (DTMRI) or Diffusion Tensor Imaging (DTI) has become a demanding modality in recent years, and many research efforts are being made to develop applications and algorithms dealing with this modality in order to visualize and analyze these data (Jiang et al., 2006). The main feature of this imaging modality is that it measures the diffusion of water molecules in tissues, and permits visualization of the fiber structure of the brain, since water diffusion is constrained mainly by axonal membranes as well as by the myelin covering of axons and other oriented micro-structures (Beaulieu, 2002; Von Meerwall and Fergusson, 1981). Therefore, it is possible to estimate the fiber trajectories by following the main diffusion direction at each voxel, which is known as fiber tracking or tractography (Basser et al., 2000; Gossl et al., 2002; Mori et al., 1999; Mori et al., 2000; Parker et al., 2002; Tench et al., 2002). Then, the visualization of these fiber paths provides to the specialist with a new insight about the white matter structure, and is also becoming a more employed technique for the quantification of lesions in the brain. Quantification of DTI data sets has become one key issue for the evaluation of neurological diseases (Smith et al., 2006), because it can

⁎ Corresponding author. E-mail address: [email protected] (R. Cárdenes). 1053-8119/$ – see front matter © 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.neuroimage.2009.12.032

take into account information that is not available with conventional MRI. The interest in using DTI has been reinforced due to the work developed by some authors, who provided evidence that changes in the structure of the brain white matter in specific areas could be directly related to some diseases such as multiple sclerosis (Audoin et al., 2007; Pagani et al., 2005; Roosendaal et al., 2009), epilepsy (Diehl et al., 2008; McDonald et al., 2008), or schizophrenia (Kubicki et al., 2005). In most of these cases, scalar measures such as the Fractional Anisotropy (FA) or the Mean Diffusivity (MD) (Pierpaoli and Basser, 1996) have been computed to look for significant differences between groups of subjects. However, recent works propose to search for those differences in relevant anatomical fiber tracts (Correia et al., 2008), or to analyze quantitatively the connectivity between brain regions (Hagmann et al., 2003; O’Donnell et al., 2002; Skudlarski et al., 2008). A major obstacle of fiber tract based measure techniques is that the same tract should be identified in every volume under study to make robust comparisons. For this reason, some atlas-based approaches have been proposed (Hagler et al., 2009; Hua et al., 2008; Lawes et al., 2008; Pagani et al., 2005) to avoid the variability introduced by manually generated fibers. There also exist some specific studies of brain tumors using DTI. For instance the works in Inoue et al. (2005>); Kinoshita et al. (2008); Price et al. (2003) explore tumor characteristics using FA and MD, but fiber tracking is not used. There exist however more recent works that use tractography to study brain tumors, quantifying along fiber tracts instead of using standard voxel based measures. That is the case of the

28

R. Cárdenes et al. / NeuroImage 50 (2010) 27–39

work proposed by Yu et al. (2005) who studied the pyramidal tract, corpus callosum and optic radiation for surgical planning and post operative evaluation. In that work they propose to classify the studied tracts with respect to tumors in three different groups: those whose fibers have been displaced by the tumor (simple displacement), those with disrupted fibers due to the tumor (single disrupted) and those whose fibers were displaced and also disrupted (displacement with disruption). As we will see later, the anatomical tracts are usually generated from some regions of interest or seeds. The location of these regions is studied in the work proposed by Schonberg et al. (2006) in the pyramidal tract and the superior longitudinal fasciculus of tumor patients, using functional information from functional Magnetic Resonance Imaging (fMRI) in order to obtain fibers with the same functional relationship. Despite the efforts already made to correctly quantify DTI data, there is still low agreement on what is the best methodology to compare different DTI data sets. Although quantification methods along fiber tracts have become important and have been shown to be reproducible (Partridge et al., 2005), the measures proposed up to date to quantify DTI data are limited to isolated standard tensor properties such as the anisotropy and the diffusivity. Therefore, a more global study that takes into account as much as possible, all the properties involved in the fiber tracts is still needed to better characterize bundles of interest. In this paper, we propose a method to analyze quantitatively the pyramidal tracts in tumor patients and to compare them with contralateral tracts, as well as with control subjects using an atlas based method to obtain the fibers automatically. The pyramidal tracts are analyzed using intrinsic properties of the fibers involved, and also using a mapping technique initially proposed in Cardenes et al. (2009) to generate 2D representations of them. This mapping is used to consider the transverse information or relation between fibers, and to compare tracts from patients with a 2D model built from a set of control subjects. A new metric is therefore proposed that measures the deviation of a given subject's pyramidal tract from an ideal one, considering how much anisotropy has been reduced with respect to that model. We show here the results on 5 tumor patients, where the quantification method proposed improves significantly the classic measures usually employed in the literature to quantify DTI data in this kind of patients. Methods Participants For the present study we have selected 5 patients aged from 41 to 73 years old, treated for brain tumor at the neurosurgical department of the Hospital Clínico Universitario in Valladolid (Spain). Selection criteria included adult patients that had been diagnosed of harboring a brain tumor affecting the pyramidal tract either cortically or subcortically for which they were subsequently operated upon. These patients were admitted to the hospital for further evaluation following a normal neurological examination for symptoms such as cephalea or new onset epileptic seizure with good recovery. In the following, we will refer to these 5 patients as P1 to P5. The pathological diagnosis of the patients' tumors corresponded to anaplastic astrocytoma located cortico-subcortically in the motor area in two cases, left in P3 (57 years), and right in P5 (73 years); one low grade astrocytoma located subcortically in the motor area of the right hemisphere in patient P4 (59 years); one multiform glioblastoma located in the left internal capsule and cerebral peduncle in P1 (44 years), and one cerebral breast metastasis located corticosubcortically in the left posterior frontal lobe in P2 (41 years). All these patients had a preoperative tractography as a complementary diagnostic tool to identify the distortion of the pyramidal tract induced by the tumor. All but one (P1) had a follow-up tractography

performed one month after brain tumor surgical excision (total or subtotal). Also, a group of 40 control subjects in total have taken part in this work. These controls are divided into two groups, the first one consisting of 30 subjects, aged from 24 to 62 years old, with mean age of 32.4, was selected to build a DTI model. A second group that consists of 10 subjects, aged from 23 to 56 years old, with mean age of 32.9, was selected to perform comparison studies with the patients. All the controls that participated in this study were right handed healthy volunteers, without any known neurological disorder nor image artifacts encountered after scanning. The average age in the control groups is lower than in the patients group due to the difficulty to find volunteers over 40 years old. However, this difference is not a major issue in this work because, as we have seen in our experiments, the individual measures obtained for older patients (around 50 years old) in the control group do not differ significantly from the measures of younger controls (around 25 years old), meaning that age differences will not bias the results significantly. Data acquisition All the data sets used in this work have been acquired in a GE Signa 1. 5 T MR scanner. Two acquisition protocols have been used in this work, that we will call protocol I and II respectively. Protocol I is a long duration protocol that takes 20 min, performed only over the first group of 30 control subjects described in Section 2.1, and used to construct a DTI model that will be explained in Section 2.4. Protocol I is designed to obtain high quality images, at expense of time duration, and therefore it is not clinically suitable for patient scanning due to short time slot requirements at the MR scanner, patient movement, etc. For this reason, a different protocol, called protocol II, is used to scan patients, decreasing the scanning time up to 6 min, but maintaining a good image quality. In order to compare the data from patients with data from controls, the second group of 10 controls were also scanned with this second protocol. No single control has been acquired with both protocols, and the criteria to assign each control subject to protocol I or II was done randomly. The parameters used in protocol I are 15 gradient directions, one baseline volume, b = 1000 s/mm2, 1.015 × 1.015 × 3 mm of voxel size, TR = 10 s, TE = 80.90 ms, 128x128 matrix, NEX = 8, and spanning the entire brain in 41 slices. The parameters of protocol II are: 25 gradient directions, one baseline volume, b = 1000 s/mm2, 1.015 × 1.015 × 3 mm of voxel size, TR = 13 s, TE = 85. 5 ms, 128 × 128 matrix, NEX = 2, and also spanning the entire brain in 39 slices. Data pre-processing Before obtaining the pyramidal tracts by means of the tractography algorithms, some data processing techniques are performed over the original data for two main reasons. First, the original data are Diffusion Weighted Images (DWIs) acquired with different gradient directions (each DWI set acquired with a specific gradient direction will be referred to as a DWI channel). Therefore, the tensor at each voxel is not available and has to be estimated using an appropriate algorithm from the DWI channels. Second, the acquired data presents a high level of noise that can be reduced to improve the quality of the data and to obtain more accurate results. For that purpose, a Linear Minimum Mean Squared Error (LMMSE) method described in TristánVega and Aja-Fernández (2008) is applied to the DWIs in order to reduce noise preserving structures of interest. The LMMSE method uses classical linear functions and prior information about the noise distribution to improve the estimation of the signal. In the case of DWI data, the noise is known to have a Rician distribution. With the filter used, not only the information of all DWI channels, but also the

R. Cárdenes et al. / NeuroImage 50 (2010) 27–39

correlations between them are exploited to estimate the noise-free signals. After filtering the DWIs, another algorithm is executed to compute a mask, that will be applied over the data to remove the image background, as well as non brain structures, such as the skull. This is specially useful for subsequent operations that will take place only in the points inside the mask, saving computational time. This method is performed using the Otsu (Otsu, 1979) threshold method. Finally, the tensor at each voxel inside the mask is computed using the least squares method described in Salvador et al., (2005). Automated extraction of fiber tracts The proposed methodology allows quantitative analysis and comparison of fiber tracts in sets of DTI of different populations. The fiber tracking algorithm requires the selection of seed regions in the images in order to identify the fiber tracts of interest. The manual selection of these regions becomes a tedious task and results can be influenced by the variability on the choice of the seeds depending on the skills and expertise of the person labeling the image. For this reason, we propose an automatic method to obtain the specific fiber tracts that will be analyzed, that allows to straightforwardly generalize our proposal to other tracts or bigger populations. This automatic method is atlas-based, that is, a model of the brain where fiber tracts are identified should be built in order to obtain such fiber bundles in other data volumes. In order to build the atlas, the 30 control healthy subjects acquired with the protocol I described in Section 2.2 are normalized. One of the volumes is chosen as a reference volume, and the others are registered against it. The registration algorithm is a template matching algorithm driven by the DTB (Diffusion Type Based) similarity measure (MuñozMoreno and Martin-Fernandez, 2009), that has been proposed specifically for DTI, since it is based on the similarity between the diffusion direction described by the DT, as well as its shape (i.e., prolate, oblate or isotropic) and the amount of diffusion. Thus, all the control volumes are transformed1 so they are aligned and can be averaged in order to obtain a normalized model. The computation of the mean diffusion tensor is not a trivial issue, and in order to compute a tensor describing the mean diffusion in each voxel, a three-step procedure is employed: (1) A set of transformed DWI channels is computed from each of the aligned DTI, by means of the Stejskal–Tanner equation (Stejskal and Tanner, 1965). (2) The DWIs are averaged in the normalized space. (3) The mean DTI is estimated from the mean DWIs.

29

efficiency (Press et al., 1992). In order to obtain more reliable tracts, a brute force approach is followed: the fiber tracts for the whole brain are computed, stopping the tracking when the FA is lower than 0.15 as suggested by Stadlbauer et al. (2007) or the angular difference in the orientation of the fiber between consecutive points was greater than 90°. Each fiber tract so computed is assigned with an index value. Therefore, each voxel with a FA value greater than 0.15 will point to an array of indexes corresponding to the fibers that pass through it. Then, the fibers belonging to a given tract will be those passing through the voxels of the specified ROI. The fibers obtained with this method can include more fibers than those strictly belonging to the pyramidal tract, but using seeds placed at the PLIC we guarantee to get the maximum number of fibers belonging to the pyramidal tract in a more standardized way. Note that the methodology described in the previous paragraph of fiber tracts identification does not warp the fibers in the subject, so it allows to perform robust measures over the original fibers computed from each subject, and not over the warped fibers (as in (Hua et al., 2008)), or over a set of voxels in the skeleton (as in (Smith et al., 2006)). Of course, this methodology is not error free, and is affected by the accuracy of the tractography and the registration. Although both methods can be improved, the effect of registration errors has negative impact only in the case that the deformed regions do not cover completely the target regions in the subject data, because only the voxels with FA N 0.15 are finally considered. Also, more complex methods such as High Angular Resolution Diffusion Imaging (HARDI) (Tuch et al., 2002), Q-Ball Imaging (QBI) (Tuch, 2004) or Q-Space Imaging (QSI) (Callaghan et al., 1990) can be used to solve fiber crossings, but it will affect drastically the execution time and the acquisition requirements, making this method non-practical for clinical use. In what follows we propose some measures computed along the pyramidal tracts to robustly analyze and compare them. Fiber tracts quantification The main goal of this work is to obtain quantitative measures that allow to discriminate between normal and abnormal fiber bundles, using the automatic fiber clustering described above. It is important to highlight that due to the automatic method to extract them the user variability is removed from the process. We propose to use measures computed along the fiber paths obtained. In order to motivate this idea, Fig. 2 shows the average FA profiles obtained along the trajectory followed by two fiber bundles. They correspond to the right pyramidal tract of a healthy subject and

A set of regions of interest (ROI) is defined in the DTI model related to different anatomical fiber bundles. The ROIs involved in the definition of the pyramidal tract, that is the one analyzed in this paper, are located at the posterior limb of the internal capsule (PLIC) of the right and left hemispheres (Mori et al., 2005). These regions are shown in Fig. 1 superimposed over a slice of the FA volume of the model, and the same slice in a control subject. To automatically obtain the tracts of a given subject, the ROIs defined in the model are deformed to fit the subject data. This deformation is a nonlinear transformation, that is obtained by means of a multi-resolution template matching registration (Collins and Evans, 1997) between the model FA and the subject FA volumes. In this step the FA volumes are used instead of the DTI volumes in order to speed up the registration procedure. Then, a tractography method is executed using the voxels in the deformed ROIs as seeds. In this work a fourth order Runge–Kutta method is employed due to its 1 The geometrical warping of DTIs involves also the warping of the DT at each voxel in order to be consistent with the underlying fiber structures. In this implementation, the Finite Strain strategy proposed in(Alexander et al., 2001) has been used.

Fig. 1. FA slices of the model (a) and of a control subject (b), with the ROIs used as seeds for the tracking algorithm superimposed. Red for the left PLIC ROI, and violet for the right PLIC ROI.

30

R. Cárdenes et al. / NeuroImage 50 (2010) 27–39

whose high values are associated to loss of myelin as stated by Song et al. (Song et al., 2003). It can be stated then that FA and Drad are good descriptors to characterize the inherent properties of the fibers, and can be used to define an integrity measure for a given tract. Bearing these properties in mind, a fiber tract will present more integrity when its amount of anisotropy is high, and the diffusion along the perpendicular direction of the fibers is low, and the integrity measure can be defined as the total amount of FA computed at the points involved in the fiber paths, divided by the total amount of radial diffusion, or equivalently the relation between the average FA and the average Drad: I=

Fig. 2. Average FA profiles in the right pyramidal tract of a control subject (dashed line) and of a patient with a tumor in the right hemisphere (solid line). Fiber length represented in the x axis ranges from inferior (PLIC) to superior (cortex) as shown by the tags.

of a tumor patient with a tumor in the right hemisphere. Notice that the profile corresponding to the tumor patient presents a clear reduction in the FA, differing notably from the tract profile of a normal subject. Standard measures such as the FA or MD can therefore be used, but we show next that more complex measures are needed in order to obtain a robust quantification method. Tract integrity measure The first measure proposed here is the integrity of the fiber tracts, and is defined using two intrinsic features of the tensors fibers: the FA and the radial diffusivity. The first quantity is an anisotropy measure, limited between zero and one, which increases with the directionality of the tensors involved in the fiber tract. A high FA value means that the diffusion is produced in a predominant direction, due to axonal membranes, myelin covering of axons and other oriented micro-structures (Beaulieu, 2002), meaning that a high number of axons are aligned in that predominant direction. Consequently, low FA values can be associated to loss of myelin or a low number of axons involved. On the other hand, diffusivity is a measure of the magnitude of the diffusion produced at each voxel. MD is the average diffusivity produced in a voxel, i.e. in all directions and is the diffusivity magnitude often used in the literature (Audoin et al., 2007; McDonald et al., 2008; Pagani et al., 2005). Diffusivity can be divided into more useful values which are, diffusion in the direction parallel to the fibers, called parallel or axial diffusivity Dax, and in the direction perpendicular to the fibers: perpendicular or radial diffusivity Drad. These quantities are computed using the tensor eigenvalues as: MD =

1 ðλ + λ2 + λ3 Þ 3 1

Dax = λ1 Drad =

1 ðλ + λ3 Þ 2 2

ð1Þ ð2Þ ð3Þ

Where λ1, λ2 and λ3 are the tensor eigenvalues ordered in descending order. Therefore, a high value of Dax is related to a high diffusion along the fiber, and a high value of Drad is related to a high diffusion in the perpendicular direction to the fiber. The relation between these quantities is already included in the FA, so only one of them is going to be used in our integrity measure. For this reason we will only use Drad,

FA Drad

ð4Þ

This index is able to reflect the impact of axonal damage produced by brain tumors, as well as the impact due to other biological effects. For instance, brain ischaemia produces axonal swelling effects, that are responsible for anisotropy reduction, as seen in chronic ischaemia observations (Beaulieu, 2002). In addition, although myelin axonal covering is not the primary source of anisotropy, it is partially responsible of it, and therefore demyelination processes produced in diseases such as multiple sclerosis are directly associated to reduction of anisotropy, as well as to an increase of perpendicular diffusivity (Gulani et al., 2001). Consequently, the integrity index proposed here would decrease in the fiber tracts affected by ischaemia or demyelinating diseases, with respect to healthy fiber tracts, although the degree of reduction should be further evaluated in these cases. 2D tract mapping The defined measures are longitudinal in the sense that they are computed along a given fiber trajectory and do not use the transverse direction or information between neighboring fibers. Hence, we propose to introduce information about this transverse direction using a 2D tract mapping method to visualize and obtain additional measures from the fibers profiles in a two-dimensional way. This consists in projecting the fiber tracts in a plane. Starting from the seeds, the FA along the fibers are stored in a 2D matrix where the columns represent the longitudinal dimension and the rows represent the transverse dimension. The implementation of this mapping is easy in the pyramidal tract, because the fibers can be ordered from anterior to posterior direction, and the longitudinal dimension is ordered from inferior to superior. Then, the 2D mapping is done by representing the fibers points in a 2D image, as if the fibers were individually transformed into straight lines, and placed one beside the other in an anterior to posterior ordering. Notice that all fibers points are represented in the map, and only transverse spatial relations of such points are altered to fit into a 2D image. For this reason, spatial relationship between neighbors could be slightly affected. In order to show the relationship preservation between neighbor fibers, we show in Fig. 3 (left) the order of them, from anterior to posterior in the pyramidal tracts of two control subjects using a color coding. This color coding shows from red to blue fibers placed from anterior to posterior. The 2D maps obtained using this procedure are illustrated in Fig. 3 (right), where from left to right of each map is represented the anterior to posterior direction, and from top to bottom of each map is represented the superior to inferior direction of the fibers. In this figure, anatomical tags (A, P, I, S) are shown to illustrate the anatomical orientation of the mapped tract, but in the following figures these tags will be omitted. The representation of the FA using this procedure simplifies the analysis of the tracts and provides a useful visual information of the global state of the pyramidal tracts. It is possible for instance, to observe regions with a particular low FA, and to analyze the shape and size of affected

R. Cárdenes et al. / NeuroImage 50 (2010) 27–39

31

Fig. 3. Left: 3D rendering of the pyramidal tracts of two control subjects, showing the order preservation. Color code shows from red to blue, the fibers ordered from anterior to posterior. Right: corresponding 2D maps of the pyramidal tracts of these subjects, for the left and right hemispheres, color code shows the FA values from red (0.2) to blue (0.8).

regions. For this reason, the information provided by these maps is extremely useful to make quantitative analysis of the pyramidal tracts. In order to perform robust measures based on these maps, a new measure is defined. The idea is to compare the map of an individual subject with the map of a standard healthy subject, and to compute how different those maps are. To do this, first healthy standard maps have to be constructed, one for each hemisphere2. We will call them model maps. In this work, each model map is built by averaging all the maps in a group of 10 healthy subjects acquired with the protocol II described in Section 2.2. The alignment of the maps should be done with care in order to compare the same regions in each subject, although it is impossible to find a perfect correspondence due to intersubjects variations in anatomy, shape, length, etc. To align all the maps in the IS direction an anatomical axial plane placed at the PLIC is chosen as a reference, and all the maps are built starting at that plane. With respect to the anterior–posterior location of the fibers, the reference is chosen at the midcoronal plane, centering all the maps at that reference plane. Then, all the maps are scaled to the same size, chosen as the average size of the control group, and using cubic interpolation in the resampling. The model maps obtained for the control group are shown in Fig. 4. Using these models we can measure the deviation of a given subject map from the standard map, by 2 Notice that although the studies carried out in this work distinguishes between left and right hemispheres, a more robust division should be done between non dominant and dominant handsides. However, as all the participants are right handed, in the following we will refer to left and right hemispheres that can be regarded as non dominant and dominant hand sides respectively.

computing the average difference of the subject maps points that are bellow the FA value in the model map, as follows: PL Em =

ðM − Xi ÞuðMi − Xi Þ ; PL i i = 1 uðMi − Xi Þ

i = 1

ð5Þ

where Mi are the values of the model map, Xi the values of the subject map, u(x) is the Heaviside step function, and L is the total number of pixels in the map. Notice that using u(Mi − Xi) only the points with FA values lower than the model are considered because higher FA values indicate a normal behavior of the fiber, or compression of fibers displaced by the tumor (Schonberg et al., 2006). These higher values compared to the model are not considered as they are likely to occur outside of the lesion produced by the tumor, and also because accounting for them would increase the overall anisotropy values in the case of compressed fibers, reducing the effect produced by the tumor lesion in this measure, and decreasing its sensitivity. We will refer to this measure as the deviation from the model. In order to compare images with the same size, the model map is resized to the subject map size using again cubic interpolation. Also, in order to reduce the effect of noise, and to emphasize neighbor relationships, an average filtering with a 5 × 5 window size is applied over the 2D map before the computation of Em. Examples of the maps used to obtain this measure are shown in Fig. 5, where the original maps of control subjects are presented, as well as the filtered maps and the error maps obtained subtracting the filtered map of the subject from the resized model map, and setting to zero the negative values.

32

R. Cárdenes et al. / NeuroImage 50 (2010) 27–39

of FA in the right pyramidal tract, especially in the posterior area, which is more affected by the tumor, and the increase in the diffusivity in that area. The 2D maps corresponding to these pyramidal tracts are also shown in Fig. 7, as well as the filtered maps and the error map obtained from them. The deviation from the model shown in the error map of the affected pyramidal tract (right) is clearly seen in this figure.

Fig. 4. FA model maps corresponding to the average along the 10 control subjects.

Fig. 6 shows the pyramidal tracts of patient P3, affected by a tumor in the right hemisphere. The tracts are colored using the FA values between 0.2 and 0.7 (top row) and using the diffusivity between 0.065 and 0.125 (bottom row). This figure shows clearly the reduction

Tract connectivity measure Due to the intrinsic nature of fibers, which are neuronal connexions, the most natural and important measure related to these structures is connectivity. A connectivity measure should be therefore a way to measure the degree of connexion between two or more regions of the brain. In the present work we propose a definition of connectivity based on three main contributions or terms, one of them corresponding to the global intrinsic properties of the fiber tract, a second one derived from the deviation with respect to the standard fiber tract or model, that will be based on the Em model based measure and a third one based on the number of fibers contained in the bundle. We illustrate the definition of the connectivity measure using experiment with a set of phantoms, shown in Fig. 8 and named from

Fig. 5. FA maps corresponding to the pyramidal tracts of two control subjects. Left pyramidal tracts (a) and (c) and right pyramidal tracts (b) and (d).

R. Cárdenes et al. / NeuroImage 50 (2010) 27–39

33

Fig. 6. Pyramidal tracts of patient P3 affected by a tumor in the right hemisphere. Left column: sagittal view of the right pyramidal tract. Right column: 3D view of both tracts along with a T2 axial slice showing the tumor. Fibers are colored using the FA, between 0.2 and 0.7, in the first row and colored using MD between 0.065 and 0.125 in the second row.

Fig. 7. 2D FA maps corresponding to the pyramidal tracts of patient P3, affected by a tumor in the right hemisphere, filtered maps and error maps obtained subtracting the filtered map from the resized model. Left (a) and right (b).

34

R. Cárdenes et al. / NeuroImage 50 (2010) 27–39

Fig. 8. Synthetic 2D fiber phantoms: model phantom (a), phantom with lower number of fibers (b), phantom with lower anisotropy (c), phantom with higher diffusivity (d), and phantom with an artifact of reduced anisotropy in a zone of the bundle (e).

Pa to Pe. The phantoms used here are constructed computationally, and they represent fiber tracts aligned vertically, connecting the bottom and top regions of the image. As tensors can be represented by semi-definite positive matrices, it is also possible to represent them visually using ellipsoids. For the sake of simplicity, the phantom used here is built in a 2D domain image, using ellipses instead of ellipsoids. The fibers derived from the phantoms are those obtained following the trajectory defined by the major eigenvector of the tensor at each position, or equivalently following the major semi-axis of each ellipse. For clearness, the fiber paths are not represented in the images. The first phantom shown in Fig. 8a represents an ideal tract or model, and is built using λ1 = 2 and λ2 = 0.6. The rest of phantoms are obtained changing properties of this model phantom. For instance, the second phantom shown in Fig. 8b has been created by removing one fiber from the ideal phantom in order to show the effect of fiber reduction. Notice that in this case, the average FA and average Drad are the same as in the ideal case. The third phantom, shown in Fig. 8c, is constructed by reducing the anisotropy of the tensors of the model phantom (using λ1 = 1.6 and λ2 = 0.6), in order to show the effect of a global reduction of anisotropy. The fourth phantom in Fig. 8d is a simulation of what happens when diffusivity is increased. In this case both eigenvalues and therefore both radial and axial diffusivity are increased at the same proportion to maintain the same average FA as in the model phantom, (λ1 = 1.2×1.6 and λ2 = 1.2×0.6). For the fifth phantom, shown in Fig. 8e, an artifact is simulated in the tract by decreasing the anisotropy in a region, but increasing the anisotropy of the rest of tensors, in order to keep the same average FA and average radial diffusivity (λ1 = 1.497 and λ2 = 1.197 for the more isotropic tensors and λ1 = 2.694 and λ2 = 0.401 for the rest of tensors). Using this phantom the usefulness of the deviation from the model measure as a contribution to the connectivity is shown. In this latter case, looking at the standard deviation of the FA will give us a good measure to discriminate between phantom Pe from the ideal phantom Pa. However, this only applies when the FA values falls in a narrow range as in this ideal case, but it does not happen in a real case where the FA values of the pyramidal tract have a higher variability. From the phantom experiment just shown before, we define the connectivity measure as the sum of the three contributions aforementioned. The first one can be intuitively deduced from phantoms Pc and Pd, where a decrease of the anisotropy or an increase of the diffusivity affects negatively the connectivity. The behavior of these intrinsic properties of the tensors involved in the fiber bundle is considered in the integrity measure previously defined, so the integrity will be the first term of this measure. The second contribution to the connectivity measure is related to how well the

fiber tract adapts to a model, as represented in phantom Pe, and which can be measured by using the deviation from the model Em, expounded before. Thus, a magnitude derived from Em will be the second term to include in the connectivity measure. And finally it is reasonable to think that another contribution to connectivity is the number of fibers present in the bundle N, because as shown in phantom Pb, it seems clear that if the number of fibers connecting two regions is reduced, the connectivity measure will be reduced consequently. Therefore, N has to be taken into consideration as a third term in the connectivity measure. Including this last term, we can express the three contributions of the connectivity measure numerically as: C = I + α 1 ð1 − β  Em Þ + α 2 N

ð6Þ

where I is the integrity measure, Em is the deviation from the model, and the parameters α1 and α2 and β are weight factors used to sum comparable magnitudes. In the experiments performed in this work the values used are 5, 0.01 and 10 respectively. The reason to choose a low value for α2 with respect to α1 is because N has a high variability, near 20% in the control group, and therefore its contribution has to be limited with respect to the others in order to avoid a high bias in the results. The contribution of the second term can be even negative, when Em is over 0.1, meaning a clear pathological case, and reducing the connectivity value. The connectivity measure defined here increases with the anisotropy FA and the number of fibers N, and decreases with the radial diffusivity Drad and the deviation from the model Em. The numerical quantities obtained for the phantoms are summarized in Table 1. In this case α1 and α2 are equal to one, and β has been set to 20, in order to obtain comparable magnitudes in the three terms considered in the connectivity measure. Notice that average FA, average MD, average radial diffusivity, or the number of fibers are not enough to characterize the fiber tracts, presenting similar values, even though the tracts have quite different behaviors. For instance,

Table 1 Phantom measures.

Pa Pb Pc Pd Pe

FA

Drad

MD

N

I

Em

C

0.6705 0.6705 0.5852 0.6705 0.6705

0.600 0.600 0.600 0.720 0.600

1.30 1.30 1.10 1.56 1.49

3 2 3 3 3

1.117 1.117 0.975 0.931 1.117

0.0 0.0 0.0073 0.0 0.0661

5.117 4.117 4.830 4.931 3.795

R. Cárdenes et al. / NeuroImage 50 (2010) 27–39

phantoms Pa, Pd and Pe have the same FA values and the same number of fibers, and phantoms Pa, Pb and Pe present the same average Drad value, and also the same FA. This example shows clearly that more features need to be taken into account to characterize numerically the behavior of fiber tracts. Integrity and deviation from the model are not enough to discriminate between tracts, see for instance phantoms Pa, Pb and Pe with the same I, and phantoms Pa, Pb and Pd with the same Em. Here, the connectivity measure is the only measure considering all the factors involved. It is shown that different connectivity values are obtained for each phantom, being the model phantom the one with higher connectivity. The magnitude of the connectivity measure and the order obtained with this measure are not particularly relevant in this experiment, for instance, the difference obtained between phantoms Pc and Pd seems to be quite small compared to the difference obtained for phantoms Pe and Pc. These differences depend on the election of the parameters α1, α2 and β. However, from this experiment it is clear that all the effects described in the design of the connectivity measure are taken into account and therefore it can be used as a final descriptor to analyze the tract state, which is the main contribution of this work. With respect to the parameters selection, they have to be chosen appropriately for the real case under study. For instance, in the pyramidal tract case we will use different parameters because N is much higher and Drad is significantly lower than in the phantom case. From the experiments carried out here, we can say that the parameters chosen can be safely used for the pyramidal tract, and they should be changed if the typical number of fibers change as can be the case in other fiber tracts, and also if the average eigenvalues magnitude change, as can be the case of other tissues. Experiments In this section several experiments are presented to show the performance of our quantification method. The data have been acquired with the parameters of the protocol II, described in Section 2.2. First, the measures proposed here have been computed for the pyramidal tracts of 10 controls subjects, aged from 23 to 56 years old, with mean 32.9 and standard deviation (std) of 9.5 years, and the same measures are obtained for the patient data using the same procedures. Damaged vs. healthy hemispheres analysis The measures computed here have been carried out in five different patients selected as described in Section 2.1, previous to the intervention. Table 2 shows the values obtained for each of the measures proposed here: integrity I, deviation form the model Em, connectivity C, as well as the classic similarity measures for comparisons: average FA, average radial diffusivity Drad, and number of fibers N. For comparisons, the mean and std obtained for the control group are also shown in the table. These values are summarized graphically in Fig. 10, separating the control group from two group of patients: PL which are patients with the left hemisphere affected (P1, P2 and P5) and PR, patients with the right hemisphere affected (P3 and P4). The results obtained are clearly different for the hemispheres in patients P1, P2, P3 and P5 but small differences are encountered in patient P4. In this particular case, these lower differences are due to the small pyramidal tract zone affected by the tumor. The comparison between the control and patients group is also illustrated in Fig. 9, where the integrity I, deviation from the model Em, and connectivity values C, of the control and patients are shown graphically. It is clear how the pyramidal tracts are affected by the tumor, compared to the controls and also compared to the contralateral hemisphere, especially for patients P1, P2, P3 and P5 in the Em and C measures. It is clear from this figure that the control

35

Table 2 Pyramidal tract measures in the group of tumor patients previous to tumor resection, and mean and std of the control group. In bold are the values of the patients corresponding to the side of the tumor. I

Em

C

Right

Left

Right

Left

Right

Left

P1 P2 P3 P4 P5

7.590 8.141 5.215 7.523 7.261

5.209 6.659 9.564 8.298 6.348

0.0615 0.0560 0.1152 0.0508 0.0708

0.1690 0.0942 0.0339 0.0649 0.1433

13.053 13.659 6.844 12.541 13.049

3.350 8.388 15.017 12.850 7.514

C. Mean

9.088

9.539

0.0577

0.0527

14.2610

15.005

C. std C. std (%)

0.687 7.56

0.708 7.42

0.0086 14.87

0.0092 17.47

1.0838 7.60

1.264 8.43

FA

MD

N

Right

Left

Right

Left

Right

Left

P1 P2 P3 P4 P5

0.450 0.464 0.386 0.456 0.439

0.351 0.407 0.504 0.471 0.421

0.0813 0.0795 0.0941 0.0831 0.0822

0.0842 0.0804 0.0769 0.0798 0.0885

354 332 239 256 433

159 144 215 280 333

C. Mean

0.470

0.480

0.0730

0.0720

305.9

310.4

C. std C. std (%)

0.025 5.30

0.022 4.51

0.004 5.26

0.003 4.03

64.757 21.17

59.850 19.28

group presents very similar values between both hemispheres in all the measures proposed, and also similar values among different subjects. It is also clear from Fig. 10 that I and C measures present higher average values (lower average values for Em) and lower std values in the control group than in the pathological groups (PL left and PR right). A statistical study has been also performed in these data. A set of t-tests have been performed to explore the mean differences of the I, Em, C, FA, MD and N measures between the patient groups in the two hemispheres (PL right, PL left, PR right and PR left) with respect to the corresponding hemisphere sides in the controls. Therefore, the same sides are always being compared. The p-values obtained in these tests are shown in the Table 3, showing in bold the statistically significant ones (p b 0.05). It is clear from this table that the mean differences obtained for I, C, and MD are statistically significant in the pathological groups, and for FA and specially for N there are no significant differences in both groups. Due to the low number of cases considered here, the results of these tests are just exploratory, and should be considered as a first validation approach. For instance results in PR groups have to be considered more carefully because they consist of only 2 patients. It is also important to highlight that the connectivity measures obtained have a variability in the control group which is comparable or even lower than the other measures, and at the same time is more discriminant than integrity in the patient group, which makes the connectivity measure proposed here a quite useful measure to characterize the pyramidal tracts. Pre- and post-operative data analysis A comparative study between pre and post operative data has been also carried out. The post-operative data have been acquired 1 month after the tumor resection. Post-operative data from P1 are not available, and therefore this study is performed for patients P2 to P5, whose values are shown in Table 4. They show a positive progression in patients P2, P3 and P5, for all the measures in the affected hemisphere. At the same time, a slight negative evolution in the contralateral hemisphere is also observed for those patients.

36

R. Cárdenes et al. / NeuroImage 50 (2010) 27–39

Fig. 9. Measures computed in the pyramidal tract in two groups: controls and tumor patients.

Patient P5 is the one with a more clear progression looking at the connectivity measure. Finally, P4 shows a slightly negative evolution in the affected hemisphere, which correlates well with the clinical evolution of the patient, who even experimented a slightly negative evolution after tumor resection. However, due to the small difference in the values obtained before and after the operation, we cannot conclude that the evolution of this patient is directly explained by the

Fig. 10. Mean and std of the I, Em and C measures for the left and right pyramidal tracts of the control group: C, the patient group with the left hemisphere affected: PL, and the patient group with the right hemisphere affected: PR.

R. Cárdenes et al. / NeuroImage 50 (2010) 27–39

values obtained in the pyramidal tract. In conclusion, the accordance between the values obtained with the clinical state of the patients studied here allows us to point out that our quantification method has a good behavior. In Fig. 11 the pyramidal tracts of patient P3 before and after tumor resection, colored using FA and MD, are shown. From this figure the evolution followed by the patient, achieving almost normal values in the affected hemisphere in both FA and MD values, is also clear as illustrated using the color coding. Reproducibility study The reproducibility has been studied using three different data sets from the same control subject, acquired with different parameters. The first volume was acquired with the parameters of the protocol I described in Section 2.2. For the second data set, the same parameters were used but changing to NEX = 2, and in the third data set, the parameters are the same used in the first volume but changing the matrix size to 192 × 192. Table 5 shows the mean and std of the measures obtained in the pyramidal tract. Notice that the std values obtained in this experiment are significantly lower than the std obtained for the control group, shown in Table 2. For instance, the std in % of the connectivity measures is reduced from 7.60% and 8.43% to 1.20% and 3.69% in the right and left hemispheres respectively. These results show that the variability is strongly reduced in intra patient data, acquired with different parameters, compared to inter patient data acquired with the same parameters, meaning that the quantification method is more sensitive to structural changes than to changes due to acquisition protocols, and therefore the method proposed is reproducible. Conclusions We have shown that our proposed methodology is determinant to effectively characterize the pyramidal tracts in tumor patients, allowing to compare them to healthy tracts, such as those obtained in control subjects or the contralateral fiber bundles of the same patient. The quantification methodology expounded here is based on key features extracted from the fiber tracts, such as inherent features obtained from the tensors involved in fibers, and other features such as the number of fibers involved in the tract, and the difference between the patient's tract and the healthy tracts of a set of control subjects. The intrinsic properties extracted from the fibers (anisotropy and radial diffusivity) have been gathered in a measure called tract integrity, which is one of the contributions presented in this work. We have shown that the combination of the FA and Drad as in Eq. (4) provides values that discriminate between pathologic and healthy fiber tracts better than single FA or single MD. In order to develop an easy way to compare between the tracts of an individual subject and the fiber tracts of a control population, a

Table 3 p-Values of the t-test performed over the tumor groups with respect to the control group. Patients are divided into two groups, those with tumor in the left (PL) and right (PR) hemispheres. In bold we highlight the statistically significant p-values (p b 0.05), showing the groups statistically different from the control group, for each measure. PL right I Em C FA MD N

PL left −3

6.72 × 10 3.77 × 10− 1 1.21 × 10− 1 2.48 × 10− 1 5.64 × 10− 3 2.49 × 10− 1

PR right −5

1.49 × 10 2.59 × 10− 5 6.15 × 10− 6 2.76 × 10− 1 1.41 × 10− 4 5.68 × 10− 2

PR left −3

1.76 × 10 7.65 × 10− 2 4.83 × 10− 3 5.11 × 10− 2 1.03 × 10− 3 2.49 × 10− 1

3.07 × 10− 1 7.09 × 10− 1 3.10 × 10− 1 6.64 × 10− 1 2.16 × 10− 2 5.68 × 10− 2

37

Table 4 Pyramidal tract measures in the group of tumor patients: pre and post operative data of 4 patients. In bold are the values corresponding to the side of the tumor. I

P2 P2 P3 P3 P4 P4 P5 P5

(pre) (post) (pre) (post) (pre) (post) (pre) (post)

Em

C

Right

Left

Right

Left

Right

Left

8.141 8.246 5.215 5.582 7.523 6.385 7.261 6.754

6.659 8.082 9.564 9.101 8.298 7.813 6.348 6.595

0.05604 0.06080 0.115226 0.111988 0.05083 0.06612 0.0708 0.0984

0.09422 0.09113 0.033947 0.055826 0.06495 0.05768 0.1433 0.1085

13.659 12.766 6.844 7.313 12.541 11.099 13.049 11.713

8.388 9.716 15.017 13.870 12.850 13.259 7.514 9.978

mapping algorithm has been developed to normalize the pyramidal tract to a standard space in which measures can be done easily. This mapping procedure has allowed us to construct a 2D model or average 2D map of the control population, which has been used to make easy comparisons with the pyramidal tract of any patient. The measure derived from these maps, called deviation from the model Em, provides useful information about the state of the tracts, and the difference between their values in tracts affected by a tumor and healthy tracts are statistically significant in the PL group (left hemisphere). Moreover, this measure provides lower p-values in that group than classic measures such as average FA, average MD or number of fibers as shown in the experiments. Therefore, the Em measure derived from this mapping method can be used to perform more robust fiber tract quantification than other classic methods. This 2D mapping of the pyramidal tract has also clear advantages for visual inspection of tracts, obtaining a new insight of the state of the fiber tract, providing information about the global state of the fibers, and local abnormalities such as holes or bands placed at particularly important anatomical regions. The new integrity measure proposed here, together with the deviation from the model measure and the number of fibers of the bundle are finally considered to define a connectivity measure which gives an aggregate measure about the degree of connection of the pyramidal tract. This quantity does not measure the connection between different regions of the brain. However, it is a connectivity measure because its values are increased as they approach to the ideal pyramidal tract provided by the model, when the number of fibers increase, and when the axons in the fibers are strongly aligned in the fibers directions. All these situations are related to a stronger connection between the principal motor areas in the cortex and the starting seed ROI considered (the PLIC), provided by the pyramidal tract. Finally, the mean differences of the values obtained with the connectivity measure are shown to be statistically significant, when comparing healthy and pathological bundles, obtaining lower pvalues than in average FA, average MD (in the PL group, left hemisphere) or in the number of fibers. The connectivity defined here also correlates well with the clinical state of the patients considered in this work, even in the case of negative evolution of patient P4 after tumor resection. The experiments carried out here have shown that this methodology is valid to quantify correctly the pyramidal tracts of tumor patients, in the sense that our measures distinguish clearly healthy pyramidal tracts from affected ones. Three main comparison experiments have been carried out in this work. First, a comparison between hemispheres of the same patient shows clear differences between the healthy and the affected side of the same patient as shown in Table 2. Second, comparison with controls is shown to be useful to detect affected tracts, which are related to reduced connectivity values, as shown in the significance study of Table 3. Finally a study made before and after tumor resection has been performed, proving that our method can be employed successfully to evaluate the evolution of patients, see Table 4.

38

R. Cárdenes et al. / NeuroImage 50 (2010) 27–39

Fig. 11. Pyramidal tracts of patient P2 before tumor resection (top row) and after tumor resection (bottom row). Color code is based on FA from 0.2 to 0.7 (left column) and based on MD from 0.065 to 0.125 (right column). Red arrows show the location of fibers affected by the tumor.

Table 5 Measure values obtained for 3 different DTI data sets acquired from the same volunteer. I

R1 R2 R3 Mean Std Std (%)

R1 R2 R3 Mean Std Std (%)

Em

C

Right

Left

Right

Left

Right

Left

9.803 9.826 10.029 9.886 0.124 1.26 FA

10.903 10.614 10.053 10.524 0.432 4.11

0.046439 0.051874 0.051416 0.049910 0.003014 6.04 MD

0.044265 0.050171 0.055196 0.049877 0.005472 10.97

15.301 15.213 15.568 15.361 0.185 1.20 N

16.460 16.126 15.314 15.966 0.590 3.69

Right

Left

Right

Left

Right

Left

282 298 311 297.0 14.526 4.89

277 302 302 293.7 14.434 4.91

0.493 0.492 0.502 0.496 0.006 1.16

0.515 0.508 0.499 0.507 0.008 1.63

0.0723 0.0724 0.0737 0.0728 0.001 1.07

0.0704 0.0706 0.0727 0.0712 0.001 2.53

Needless to say, this methodology can be used to study other neurological disorders affecting the pyramidal tract, as is the case of multiple sclerosis (Pagani et al., 2005), taking advantage of the simplicity of the procedure. Also, the measures proposed in this work, can be extended to other main fiber bundles such as the corpus callosum, the superior longitudinal fasciculus or the inferior longitudinal fasciculus. Some of these fiber bundles are easy to map into 2D. For instance, the corpus callosum, with its characteristic U-shape, can be unfolded and mapped to a plane ordering the fibers in the midsagittal plane, and the inferior longitudinal fasciculus present long parallel fibers from anterior to posterior direction, and thus, can be easily mapped to a plane ordering the fibers in a mid-coronal plane. Using this mappings, the measures proposed here are straightforward to compute. Nevertheless, care has to be taken in the mapping of new structures in order to preserve the spatial relationships among neighboring fibers as much as possible. The validity of the quantification methodology proposed has been shown with a reproducibility study, obtaining successful results numerically. However, further analyses have to be done using other tractography techniques, to try to deal with fiber crossings, and other acquisition parameters have to be analyzed to verify the validity of the method in a more general way.

R. Cárdenes et al. / NeuroImage 50 (2010) 27–39

Acknowledgments This work has been funded by the National Spanish grant TEC2007-67073, and the data sets have been acquired at Centro de Diagnóstico Recoletas, Valladolid. References Alexander, D., Pierpaoli, C., Basser, P., Gee, J., 2001. Spatial transformations of diffusion tensor magnetic resonance images. IEEE Trans. Med. Imaging 20 (11), 1131–1139 Nov. Audoin, B., Guye, M., Reuter, F., Duong, M.-V. A., Confort-Gouny, S., Malikova, I., Soulier, E., Viout, P., ChÈrif, A.A., Cozzone, P.J., Pelletier, J., Ranjeva, J.-P., 2007. Structure of WM bundles constituting the working memory system in early multiple sclerosis: a quantitative DTI tractography study. NeuroImage 36, 1324–1330. Basser, P.J., Pajevic, S., Pierpaoli, C., Duda, J., Aldroubi, A., 2000. In vivo fiber tractography using DT-MRI data. Magn. Reson. Med. 44, 625–632. Beaulieu, C., 2002. The basis of anisotropic water diffusion in the nervous system–a technical review. NMR Biomed. 15, 435–455. Callaghan, P.T., MacGowan, D., Packer, K.J., Zelaya, F.O., 1990. High resolution Q-space imaging in porous structures. J. Magn. Reson. 90, 177–182. Cardenes, R., Argibay-Quiñones, D., Muñoz-Moreno, E., Martin-Fernandez, M., 2009. Characterization of anatomic fiber bundles for diffusion tensor image analysis. Medical Image Computing and Computer-Assisted Intervention (MICCAI). Springer-Verlag, London, UK, pp. 903–910. Collins, D.L., Evans, A.C., 1997. Animal: validation and applications of nonlinear registration-based segmentation. Int. J. Pattern Recogn. Artif. Intell. 11 (8), 1271–1294. Correia, S., Lee, S.Y., Voorn, T., Tate, D.F., Paul, R.H., Zhang, S., Salloway, S.P., Malloy, P.F., Laidlaw, D.H., 2008. Quantitative tractography metrics of white matter integrity in diffusion-tensor MRI. NeuroImage 42, 568–581. Diehl, B., Busch, R.M., Duncan, J.S., Piao, Z., Tkach, J., Luders, H.O., 2008. Abnormalities in diffusion tensor imaging of the uncinate fasciculus relate to reduced memory in temporal lobe epilepsy. Epilepsia 49 (8), 1409–1418. Gossl, C., Fahrmeir, L., Putz, B., Auer, L.M., Auer, D.P., 2002. Fiber tracking from dti using linear state space models: detectability of the pyramidal tract. NeuroImage 16, 378–388. Gulani, V., Webb, A.G., Duncan, I.D., Lauterbur, P.C., 2001. Apparent diffusion tensor measurements in myelin-deficient rat spinal cords. Magn. Reson. Med. 45, 191–195. Hagler, D.J.J., Ahmadi, M.E., Kuperman, J., Holland, D., McDonald, C.R., Halgren, E., Dale, A. M., 2009. Automated white matter tractography using a probabilistic diffusion tensor atlas: application to temporal lobe epilepsy. Hum. Brain Mapp. 30 (5), 1535–1547. Hagmann, P., Thiran, J.-P., Jonasson, L., Vandergheynst, P., Clarke, S., Maeder, P., Meulib, R., 2003. DTI mapping of human brain connectivity: statistical fibre tracking and virtual dissection. NeuroImage 19, 545–554. Hua, K., Zhang, J., Wakana, S., Jiang, H., Li, X., Reich, D.S., Calabresi, P.A., Pekar, J.J., va Zijl, P.C.M., Mori, S., 2008. Tract probability maps in stereotaxic spaces: analyses of white matter anatomy and tract-specific quantification. NeuroImage 39, 336–347. Inoue, T., Ogasawara, K., Beppu, T., Ogawa, A., Kabasawa, H., 2005. Diffusion tensor imaging for preoperative evaluation of tumor grade in gliomas. Clin. Neurol. Neurosurg. 107, 174–180. Jiang, H., van Zijl, P.C.M., Kim, J., Pearlson, G.D., Mori, S., 2006. DtiStudio: resource program for diffusion tensor computation and fiber bundle tracking. Comp. Methods Prog. Biomed. 81, 106–116. Kinoshita, M., Hashimoto, N., Goto, T., Kagawa, N., Kishima, H., Izumoto, S., Tanaka, H., Fujita, N., Yoshimine, T., 2008. Fractional anisotropy and tumor cell density of the tumor core show positive correlation in diffusion tensor magnetic resonance imaging of malignant brain tumors. NeuroImage 43, 29–35. Kubicki, M., Park, H., Westin, C.F., Nestor, P.G., Mulkern, R.V., Maier, S.E., Niznikiewicz, M., Connor, E.E., Levitt, J.J., Frumin, M., Kikinis, R., Jolesz, F.A., McCarley, R.W., Shenton, M.E., 2005. DTI and MTR abnormalities in schizophrenia: analysis of white matter integrity. NeuroImage 26, 1109–1118. Lawes, I.N.C., Barrick, T.R., Murugam, V., Spierings, N., Evans, D.R., Song, M., Clark, C.A., 2008. Atlas-based segmentation of white matter tracts of the human brain using diffusion tensor tractography and comparison with classical dissection. NeuroImage 39, 62–79. McDonald, C.R., Ahmadi, M.E., Hagler, D.J., Tecoma, E.S., Iragui, V.J., Gharapetian, L., Dale, A.M., Halgren, E., 2008. Diffusion tensor imaging correlates of memory and language impairments in temporal lobe epilepsy. Neurology 71, 1869–1876. Mori, S., Crain, B.J., Chacko, V.P., van Zijl, P.C., 1999. Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging. Ann. Neurol. 45, 265–269.

39

Mori, S., Kaufmann, W.E., Pearlson, G.D., Crain, B.J., Stieltjes, B., Solaiyappan, M., van Zijl, P.C., 2000. In vivo visualization of human neural pathway by magnetic resonance imaging. Ann. Neurol. 47 (3), 412–414. Mori, S., Wakana, S., Nagae-Poetscher, L., van Zijl, P.C.M., 2005. MRI Atlas of Human Whitte Matter. Elsevier. Muñoz-Moreno, E., Martin-Fernandez, M., 2009. Characterization of the similarity between diffusion tensors for image registration. Comput. Biol. Med. 39 (3), 251–265. O’Donnell, L., Haker, S., Westin, C.F., 2002. New approaches to estimation of white matter connectivity in diffusion tensor MRI: Elliptic PDEs and geodesics in a tensorwarped space. Medical Image Computing and Computer-Assisted Intervention (MICCAI). Springer-Verlag, Tokyo, Japan, pp. 459–466. September. Otsu, N., 1979. A threshold selection method from gray-level histograms. IEEE Trans. Syst., Man Cybern. 9 (1), 62–66 Jan. Pagani, E., Filippi, M., Rocca, M.A., Horsfield, M.A., 2005. A method for obtaining tractspecific diffusion tensor MRI measurements in the presence of disease: application to patients with clinically isolated syndromes suggestive of multiple sclerosis. NeuroImage 26, 258–265. Parker, G.J.M., Wheeler-Kingshott, C.A.M., Barker, G.J., 2002. Estimating distributed anatomical connectivity using fast marching methods and diffusion tensor imaging. Trans. Med. Imaging 21 (5), 505–512. Partridge, S.C., Mukherjee, P.M., Berman, J.I., Henry, R.G., Miller, S.P., Lu, Y., Glenn, O.A., Ferriero, D.M., Barkovich, A.J., Vigneron, D.B., 2005. Tractography-based quantitation of diffusion tensor imaging parameters in white matter tracts of preterm newborns. J. Magn. Reson. Imaging 22, 467–474. Pierpaoli, C., Basser, P.J., 1996. Toward a quantitative assessment of diffusion anisotropy. Magn. Reson. Med. 36, 893–906. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P., 1992. Numerical Recipes in C. Cambridge University Press. Price, S.J., Burnet, N.G., Donovan, T., Green, H.A.L., PeÒa, A., Antoun, N.M., Pickard, J.D., Carpenter, T.A., Gillard, J.H., 2003. Diffusion tensor imaging of brain tumors at 3 T: A potential tool for assessing white matter tract invasion? Clin. Radiol. 58, 455–462. Roosendaal, S.D., Geurts, J.J.G., Vrenken, H., Hulst, H.E., Cover, K.S., Castelijns, J.A., Pouwels, P.J.W., Barkhof, F., 2009. Regional DTI differences in multiple sclerosis patients. NeuroImage 44, 1397–1403. Salvador, R., PeÒa, A., Menon, D.K., Carpenter, T.A., Pickard, J.D., Bullmore, E.T., 2005. Formal characterization and extension of the linearized diffusion tensor model. Hum. Brain Mapp. 24, 144–155. Schonberg, T., Pianka, P., Hendler, T., Pasternak, O., Assaf, Y., 2006. Characterization of displaced white matter by brain tumors using combined DTI and fMRI. NeuroImage 30, 1100–1111. Skudlarski, P., Jagannathan, K., Calhoun, V.D., Hampson, M., Skudlarska, B.A., Pearlson, G., 2008. Measuring brain connectivity: diffusion tensor imaging validates resting state temporal correlations. NeuroImage 43, 554–561. Smith, S.M., Jenkinson, M., Johansen-Berg, H., Rueckert, D., Nichols, T.E., Mackay, C.E., Watkins, K.E., Ciccarelli, O., Cader, M.Z., Matthews, P.M., Behrens, T.E.J., 2006. Tract-based spatial statistics: voxelwise analysis of multi-subject diffusion data. NeuroImage 31, 1487–1505. Song, S.K., Sun, S.W., Ju, W.K., Lin, S.J., Cross, A.H., Neufeld, A.H., 2003. Diffusion tensor imaging detects and differentiates axon and myelin degeneration in mouse optic nerve after retinal ischemia. NeuroImage 20, 1714–1722. Stadlbauer, A., Nimsky, C., Buslei, R., Salomonowitz, E., Hammen, T., Buchfelder, M., Moser, E., Ernst-Stecken, A., Ganslandt, O., 2007. Diffusion tensor imaging and optimized fiber tracking in glioma patients: histopathologic evaluation of tumor-invaded white matter structures. NeuroImage 34, 949–956. Stejskal, E.O., Tanner, J.E., 1965. Spin diffusion measurements: spin-echoes in the presence of time-dependent field gradient. J. Chem. Phys. 42, 288–292. Tench, C.R., Morgan, P.S., Blumhardt, L.D., Constantinescu, C., 2002. Improved white matter fiber tracking using stochastic labeling. Magn. Reson. Med. 48, 677–683. Tristán-Vega, A., Aja-Fernández, S., 2008. Joint LMMSE estimation of DWI data for DTI processing. Medical Image Computing and Computer-Assisted Intervention (MICCAI). Springer-Verlag, New York, NY, USA, pp. 27–34. September. Tuch, D.S., 2004. Q-Ball Imaging. Magn. Reson. Med. 52, 1358–1372. Tuch, D.S., Reese, T.G., Wiegell, M.R., Makris, N., Belliveau, J.W., Wedeen, V.J., 2002. High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. Magn. Reson. Med. 48, 577–582. Von Meerwall, E., Fergusson, R.D., 1981. Interpreting pulsed-gradient spin-echo diffusion experiments with permeable membranes. J. Chem. Phys. 74, 6956–6959. Yu, C.S., Li, K.C., Xuan, Y., Ji, X.M., Qin, W., 2005. Diffusion tensor tractography in patients with cerebral tumors: a helpful technique for neurosurgical planning and postoperative assessment. Eur. J. Radiol. 56, 197–204.