White matter fiber tractography: why we need to move beyond DTI

Clinical article

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Object

Diffusion-based MRI tractography is an imaging tool increasingly used in neurosurgical procedures to generate 3D maps of white matter pathways as an aid to identifying safe margins of resection. The majority of white matter fiber tractography software packages currently available to clinicians rely on a fundamentally flawed framework to generate fiber orientations from diffusion-weighted data, namely diffusion tensor imaging (DTI). This work provides the first extensive and systematic exploration of the practical limitations of DTI-based tractography and investigates whether the higher-order tractography model constrained spherical deconvolution provides a reasonable solution to these problems within a clinically feasible timeframe.

Methods

Comparison of tractography methodologies in visualizing the corticospinal tracts was made using the diffusion-weighted data sets from 45 healthy controls and 10 patients undergoing presurgical imaging assessment. Tensor-based and constrained spherical deconvolution–based tractography methodologies were applied to both patients and controls.

Results

Diffusion tensor imaging–based tractography methods (using both deterministic and probabilistic tractography algorithms) substantially underestimated the extent of tracks connecting to the sensorimotor cortex in all participants in the control group. In contrast, the constrained spherical deconvolution tractography method consistently produced the biologically expected fan-shaped configuration of tracks. In the clinical cases, in which tractography was performed to visualize the corticospinal pathways in patients with concomitant risk of neurological deficit following neurosurgical resection, the constrained spherical deconvolution–based and tensor-based tractography methodologies indicated very different apparent safe margins of resection; the constrained spherical deconvolution–based method identified corticospinal tracts extending to the entire sensorimotor cortex, while the tensor-based method only identified a narrow subset of tracts extending medially to the vertex.

Conclusions

This comprehensive study shows that the most widely used clinical tractography method (diffusion tensor imaging–based tractography) results in systematically unreliable and clinically misleading information. The higher-order tractography model, using the same diffusion-weighted data, clearly demonstrates fiber tracts more accurately, providing improved estimates of safety margins that may be useful in neurosurgical procedures. We therefore need to move beyond the diffusion tensor framework if we are to begin to provide neurosurgeons with biologically reliable tractography information.

Abbreviations used in this paper:AVM = arteriovenous malformation; CSD = constrained spherical deconvolution; DTI = diffusion tensor imaging; DWI = diffusion-weighted imaging; FA = fractional anisotropy; iPAT = integrated parallel acquisition technique; ROI = region of interest.

Abstract

Object

Diffusion-based MRI tractography is an imaging tool increasingly used in neurosurgical procedures to generate 3D maps of white matter pathways as an aid to identifying safe margins of resection. The majority of white matter fiber tractography software packages currently available to clinicians rely on a fundamentally flawed framework to generate fiber orientations from diffusion-weighted data, namely diffusion tensor imaging (DTI). This work provides the first extensive and systematic exploration of the practical limitations of DTI-based tractography and investigates whether the higher-order tractography model constrained spherical deconvolution provides a reasonable solution to these problems within a clinically feasible timeframe.

Methods

Comparison of tractography methodologies in visualizing the corticospinal tracts was made using the diffusion-weighted data sets from 45 healthy controls and 10 patients undergoing presurgical imaging assessment. Tensor-based and constrained spherical deconvolution–based tractography methodologies were applied to both patients and controls.

Results

Diffusion tensor imaging–based tractography methods (using both deterministic and probabilistic tractography algorithms) substantially underestimated the extent of tracks connecting to the sensorimotor cortex in all participants in the control group. In contrast, the constrained spherical deconvolution tractography method consistently produced the biologically expected fan-shaped configuration of tracks. In the clinical cases, in which tractography was performed to visualize the corticospinal pathways in patients with concomitant risk of neurological deficit following neurosurgical resection, the constrained spherical deconvolution–based and tensor-based tractography methodologies indicated very different apparent safe margins of resection; the constrained spherical deconvolution–based method identified corticospinal tracts extending to the entire sensorimotor cortex, while the tensor-based method only identified a narrow subset of tracts extending medially to the vertex.

Conclusions

This comprehensive study shows that the most widely used clinical tractography method (diffusion tensor imaging–based tractography) results in systematically unreliable and clinically misleading information. The higher-order tractography model, using the same diffusion-weighted data, clearly demonstrates fiber tracts more accurately, providing improved estimates of safety margins that may be useful in neurosurgical procedures. We therefore need to move beyond the diffusion tensor framework if we are to begin to provide neurosurgeons with biologically reliable tractography information.

The advent of clinically available white matter fiber tracking, a technique that maps white matter pathways from diffusion-weighted MRI data27 promises the ability to visualize a range of eloquent white matter tracts in individual patients.12,17,24,30,33 The potential power of this information in many clinical situations is such that 3D maps are already being integrated with neurosurgical navigation systems, often being relied upon for the purpose of presurgical planning and intraoperative navigation.10,23,33 Although the fundamental limitations of the most commonly used tractography method, namely DTI6-based tractography, are well described in the technical literature,39 DTI-based tractography remains the most widely used tractography method in the clinical setting. The current study is designed to systematically investigate the practical limitations of using tensor-based tractography for the purpose of clinical investigation and to determine whether using a method designed to address the problems that affect the tensor model provides an acceptable solution.

Diffusion MRI tractography requires 3 essential steps: the acquisition of appropriate DWI data; the correct estimation of fiber orientations; and finally the application of an appropriate tracking algorithm (Fig. 1A). The reliability of tractography results is dependent on all 3 steps, and these steps are interdependent—that is, data collection needs to be consistent with the intended data analysis method and vice versa.

Fig. 1.
Fig. 1.

A: Schematic showing the 3 key steps required to perform tractography, with the resulting fiber tracks illustrated by a coronal section from a “whole-brain” tractography data set. The color of the fiber tracks indicates the local fiber orientation (red: left-right, green: dorsal-ventral, blue: cranial-caudal; see colored arrows). B: Simulation data showing a detailed illustration of Step 2 of Panel A. Schematic images of voxels (i) containing white matter fibers (single fiber populations, left and middle; 2 fiber populations, right) are shown with illustrations corresponding to each of these voxels, showing the DWI signal (ii), diffusion tensor ellipsoids derived from the DWI signal within each voxel (iii), and fiber orientations derived using CSD (iv). Note that in the voxel containing 2 fiber populations, the DTI model not only fails to represent the number of fiber populations within each voxel, but also does not provide an orientation estimate that corresponds to either of the constituent fiber populations. The CSD-based method correctly identifies 2 appropriately oriented fiber populations in the third voxel (see i).

The majority of studies in the field use the diffusion tensor model (DTI)6 to estimate white matter fiber orientations from DWI data. It is, however, increasingly recognized that DTI-based tractography methods are fundamentally limited, in that a single tensor can only resolve a single fiber direction within an imaging voxel (see Fig. 1B, i and iii).1,15,38,41 This limitation has important ramifications for the application of tractography in particular, as the proportion of white matter voxels in the brain that contain multiple fibers has been demonstrated to be at least 90%.20 Given that diffusion-weighted data acquired on clinical scanners are typically limited to a spatial resolution of 2–3 mm, the scale of this problem is not unexpected.

Over the past decade, many higher-order models have been developed specifically to address the limitation of the DTI framework—that is, the so-called “crossing fiber problem”2,3,14,19,31,38,41,43 (see Tournier et al.39 for recent review). However, these developments have not yet translated into improvements in clinical practice. Over 98% of the 160 neurosurgical tractography studies published to date were reported to use the DTI framework to generate fiber orientation estimations. Software availability, technical expertise, and in some cases clinically impractical scan times14 are just a few reasons why higher-order models have not yet been readily adopted in the clinical setting. In this work, constrained spherical deconvolution (CSD),37,38 a higher-order model shown in phantom studies to be robust to crossing fiber effects,40 is used to explore the practical advantage of applying a more sophisticated framework to diffusion data acquired in clinically feasible time frames.

In short, CSD is an approach that uses high angular resolution diffusion-weighted imaging (HARDI)42 data to generate estimates of the fiber orientation distribution within each imaging voxel, with no prior knowledge required regarding the number of fibers in any given voxel.37 The simulation data presented in Fig. 1B illustrate the advantage of using this robust fiber orientation estimation method in the presence of multiple fiber populations. Note that the CSD method correctly identifies 2 appropriately oriented fiber populations in a voxel containing 2 fiber populations (Fig. 1B, i and iv), whereas the DTI-based method not only fails to represent the number of fiber populations within each voxel, but also does not provide an orientation estimate that corresponds to either of the constituent fiber populations (Fig. 1B, i and iii). As mentioned above, such voxels are widespread within the brain.

This study investigates the limitations of the most widely used tractography model (DTI)6 in visualizing the corticospinal tracts, and the advantages of using a higher-order method designed specifically to address the problems that affect the tensor model (namely, CSD37). Our aims are to investigate how these tractography methods perform in real clinical scenarios and to determine whether any of these methods provide a biologically realistic solution.

Methods

Study Participants

Forty-five healthy volunteers (24 male, 21 female) with a mean age of 28.17 years (SD 6.88 years, range 19–53 years) participated in this study. A consecutive series of 10 patients (3 male, 7 female) referred for presurgical imaging assessment to the Brain Research Institute, Melbourne, Australia, were also recruited. The patients' mean age was 32.89 years (SD 17.46 years, range 13.58–67.58 years) (Table 1). All participants provided informed written consent prior to taking part in this study in accordance with ethical approval from the local human research ethics committee (Austin Health).

TABLE 1:

Demographic and lesion characteristics in 10 cases*

CaseAge (yrs), SexLesion
A49, Flarge left-sided temporoparietal AVM
B24, Ffocal cortical dysplasia (2.5 cm) in right posterior frontal lobe
C17, M2-cm cavernoma involving right sensory motor cortex
D36, Fright inferior frontal neoplasm, not fully characterized glioma, DNET
E36, Fleft-sided neoplasm located posterior to central gyrus, likely DNET
F47, Fcomplex left posterior frontal AVM
G21, Mleft-sided AVM extending from left frontal sulcus to left insula
H18, Fbottom-of-sulcus dysplasia in region of left precuneus
I68, Msmall nonenhancing lesion in region of left temporoparietooccipital junction
J14, F2 small bottom-of-sulcus dysplasias in low central & mid centroparietal regions

* DNET = dysembryoplastic neuroepithelial tumor.

Data Acquisition

Magnetic resonance imaging data were acquired on a 3-T Siemens TIM Trio MRI system with a 12-channel receive-only head coil. Axial diffusion-weighted data (b value 3000 sec/mm2) were obtained for all patients and healthy volunteers using a twice-refocused single-shot echo-planar imaging sequence, with 60 diffusion-weighted directions equally spaced over a hemisphere in a scan time of 9.5 minutes (44 × 5 mm slices acquired interleaved, FOV 240 × 240 mm, matrix size 96 × 96, voxel size 2.5 × 2.5 × 2.5 mm; b value 3000 sec/mm2, TE 110 msec, TR 8400 msec, GRAPPA acceleration factor [iPAT] 2). In a subset of 12 healthy volunteers, additional DWI acquisition strategies were also used: a) 12 DW directions with b value 1000 sec/mm2, b) 60 DW directions with b value 1000 sec/mm2, and c) 30 DW directions with b value 2000 sec/mm2.

For all participants, additional 3D high-resolution magnetization prepared rapid gradient echo (MPRAGE) T1-weighted data and axial or coronal T2-weighted images were also acquired for anatomical reference. The 3D T1-weighted data for each individual were realigned to the individual's FA map, using the rigid body co-registration function provided in SPM8 (http://www.fil.ion.ucl.ac.uk/spm/) to allow fiber-tracking results to be displayed overlaid on the high-resolution image for improved anatomical visualization.

Control Subject Data: Data Processing

To perform comparable tractography analysis within each individual's native space independent of user subjectivity, normal control subject images were first normalized to common template space to enable common seed and target regions to be created for every individual, using the following steps. Step 1: DWI data were processed using the MRtrix software package36 (http://www.brain.org.au/software/) to produce an FA map.5 A custom FA map template, derived from 10 randomly selected healthy volunteers (control subjects), was generated using the ANTS registration software (http://picsl.upenn.edu/ANTS/). Step 2: Individual FA maps were registered to the resulting FA template using the symmetric normalization (SyN) algorithm4 to generate a set of diffeomorphisms (nonlinear mappings) and inverse diffeomorphisms for each individual. Step 3: Target and seed regions for fiber tracking were manually generated in the sensorimotor cortex and brainstem in template space, as shown in Fig. 2. A midline exclusion region of interest was also defined at the level of the corpus callosum to constrain tractography results to within each hemisphere. Step 4: The inverse diffeomorphisms for each individual were then used to map these template-space ROIs into each individual subject space, so that fiber tracking could be performed in native space while ensuring that seed/target regions were consistent between subjects. (Note: The FA map is inherently in the same space as the DWI data used for tractography, since the FA is derived from the DW images.)

Fig. 2.
Fig. 2.

Coronal template FA image overlaid with seed and target regions defined in the right and left sensorimotor motor cortices (red and blue, respectively) and brainstem (yellow). These regions were warped back into each control participant's native space to perform all fiber tracking in native space (see Methods: Tractography).

Control Subject Data: Tractography Analysis

Diffusion-weighted imaging data sets were processed using the MRtrix software package36 (http://www.brain.org.au/software/) to first generate DTI6 and CSD37,38 fiber orientation estimates. These fiber orientation estimates were combined with appropriate tractography algorithms to generate results from the following tractography approaches: 1) DTI combined with a deterministic streamlines algorithm,26 2) DTI combined with a probabilistic “bootstrap” algorithm,21 and 3) CSD combined with a probabilistic streamlines algorithm.7,32 In each case, tracks were initiated to perform fiber tracking from seed to target ROIs in each individual's own space and tracking was performed both from the brainstem to sensorimotor cortex and vice versa. Fiber tracking results included only tracks that reached the target ROIs, and the tracking process was terminated when 10,000 tracks had successfully reached the target region or when 100,000 tracks in total had been initiated.

Control Subject Data: Quantification

Fiber tracking results for control subject data were mapped back into template space using each individual's diffeomorphism generated using the abovementioned ANTS registration software. For the results from each tractography method, frequency maps were generated using the MRtrix software package36 as follows. First, for each subject a binary map was generated by identifying those voxels containing more than 10 tracks; a threshold of 10 was used to exclude unlikely connections. Next, these maps were summed across all subjects to generate the frequency map, with the value within each voxel indicating the number of subjects with tractography results that passed through that location.16,28

Patient Data: Data Processing and Tractography Analysis

To avoid imperfections in co-registration due to the presence of pathology, patient data were not normalized to a common template space; instead, seed and target regions were generated directly in each individual's native space. Fiber tracking from the sensorimotor cortex to the brainstem using manually defined ROIs, similar to those used for the control subjects, was performed using 1) DTI combined with a deterministic streamlines algorithm26 and 2) CSD combined with a probabilistic streamlines algorithm7,32 using the MRtrix software package.36 As described above for the control subject data, fiber tracking results included only tracks that reached the target ROIs, and the tracking process was terminated when 10,000 tracks had successfully reached the target region or when 100,000 tracks in total had been initiated.

To allow improved visualization of fiber tracking results and patient pathology, 3D contour segmentation was performed to delineate the lesion from each patient's 3D T1-weighted data set using the ITK-SNAP software package45 (www.itksnap.org). Fiber-tracking results and segmented pathology volumes were then overlaid on the high-resolution image using FSL software (http://www.fmrib.ox.ac.uk).

Results

Control Subject Data

Diffusion tensor imaging–based tractography methods (both deterministic and probabilistic) produced only a narrow subset of tracks to the medial part of the sensorimotor cortex in all subjects, as demonstrated in both the individual control subject data and the group quantification data (Fig. 3). The CSD-based method, combined with a probabilistic tractography algorithm, consistently produced the fan-shaped configuration of tracks expected from known anatomy, with fibers extending to the lateral aspects of the sensorimotor cortex (Fig. 3). These findings were consistent across a series of DWI data sets with a range of b values and number of directions (Fig. 3B) and were independent of whether tracking was performed from the brainstem to sensorimotor cortex or vice versa (Fig. 3A).

Fig. 3.
Fig. 3.

Comparison of control data tractography results obtained using seed and target ROIs identified in the brainstem and sensorimotor cortex, as shown in Fig. 2. For the individual subject data, the color of the fiber tracks indicates the local fiber orientation (with red indicating left-right, green indicating dorsal-ventral, and blue indicating cranial-caudal). A: Tractography results for DTI combined with a deterministic algorithm, DTI combined with a probabilistic algorithm, and CSD combined with a probabilistic algorithm. All data were acquired using 60 diffusion-weighted directions with b = 3000 sec/mm2. In each case, tracking was performed both from superior to inferior (left group of 6 images, labeled “motor to brain stem”) and from inferior to superior (right group of 6 images, labeled “brain stem to motor”). The upper row shows coronal T1-weighted images overlaid with tractography results from a representative normal control subject. The bottom row shows coronal FA template image overlaid with frequency maps representing the number of subjects from the 45 control subjects in which tracks were identified in any given voxel (range = 0–45). B: Tractography results using DTI combined with a deterministic algorithm and CSD combined with a probabilistic algorithm, across a range of acquisition protocols that differed in the number of diffusion directions and b-value used, as indicated in the figure. Panel B(i) shows coronal T1-weighted images overlaid with tractography results using DTI (left column) and CSD (right column) from a representative normal control subject. Panel B(ii) shows a coronal FA template image overlaid with frequency maps representing the number of subjects (out of 12 control subjects) in whom tracks were identified in any given voxel, using DTI (left column) and CSD (right column) (range 0–12).

In all cases, further examination of the individual voxels confirmed the presence of many voxels containing multiple fiber orientations using CSD in regions where the DTI-based tractography method failed to produce any tracks (see representative data set in Fig. 4, magnified regions).

Fig. 4.
Fig. 4.

Coronal FA images overlaid with fiber tracking results using CSD (left) and DTI (right) from a representative healthy control subject. The magnified regions in the orange boxes show the fiber orientation estimates within individual voxels. The CSD fiber orientation estimates (upper left image) confirm the presence of many voxels containing multiple fiber orientations, within individual voxels. The tensor-derived orientation in equivalent voxels (upper right image) does not represent any of the constituent fiber populations in regions where the DTI-based tractography method failed to produce tracks.

Summary of Patient Tractography Results

In all patients, the DTI-based method produced only a narrow subset of tracks descending from the medial periphery of the sensorimotor cortex to the brainstem (see Fig. 5A, i and ii; Fig. 5Bi and ii; and Fig. 6, all panels labeled i), despite the seed region encompassing the whole of the sensorimotor cortex. In contrast, the CSD-based method successfully reconstructed tracks descending from the sensorimotor cortex in both the affected and contralateral hemisphere (see Fig. 5A, iii and iv; Fig. 5B iii and iv; and Fig. 6C, all panels labeled ii). Safe margins of resection clearly appeared to be greater using DTI-based tractography compared with the CSD-based approach in all cases except for Case E, in which the lesion was located close to the midline. Two representative cases are described in further detail below.

Fig. 5.
Fig. 5.

Results of DTI-based tractography (blue) and CSD-based tractography (red) (derived from the same DWI data set) with segmented pathology volumes (green) overlaid on coronal T1-weighted images for Case A (A) and Case B (B). Case A involved a 49-year-old woman with a large left-sided temporoparietal AVM. See MR images in Panel A(v). Case B involved a 24-year-old woman with a right focal cortical dysplasia situated in the right posterior frontal lobe. See MR images in Panel B(v). The DTI-based tractography results in Case A suggest a clear margin surrounding the lesion (i and ii), whereas the CSD-based tractography results indicate that lateral projections of the corticospinal pathway may be at risk (iii and iv). The DTI-based tractography results in Case B suggest that only the medial aspect of the lesion impinges on the corticospinal tracts (i and ii), whereas the CSD-based tractography results suggest that the lesion is enveloped by medial and lateral projections of corticospinal fibers (iii and iv).

Fig. 6.
Fig. 6.

Results of DTI-based tractography (i) and CSD-based tractography (ii) for Cases C–J with segmented pathology volumes (green) overlaid on coronal T1-weighted images. The panel labels correspond to the cases listed in Table 1. Note: The difference in apparent safe margins of resection is substantially greater using the DTI-based tractography method (blue) compared with the CSD-based tractography method (red).

Illustrative Cases

Case A

This 49-year-old woman presented with a 10-day history of severe left-sided headache with associated nausea and vomiting. Conventional MRI confirmed the presence of a large left posterior temporoparietal AVM supplied by feeding vessels in the posterior-parietal and angular branches of the right middle cerebral artery, the occipital temporal artery, and the posterior temporal branches of the left posterior cerebral artery, with drainage mainly to the superior sagittal sinus (Fig. 5A, v). Evaluation of corticospinal tractography results indicated that apparent safe margins of resection surrounding this lesion were clearly greater using DTI-based tractography than with the CSD-based approach: DTI-based tractography results suggested a clear margin surrounding the lesion (Fig. 5A, i and ii), whereas the CSD-based tractography results (derived from the same DWI data set) indicated that lateral projections of the corticospinal pathway might be at risk (Fig. 5A, iii and iv).

Case B

This 23-year-old woman presented with refractory complex partial seizures largely involving her left leg, arm, and eyelid and the left side of her face. Conventional MRI demonstrated a 2 × 2 × 3-cm region of focal dysplasia in the right precentral gyrus consistent with the abnormal right centroparietal electroencephalographic activity (Fig. 5B, v). Evaluation of corticospinal tractography results indicated that apparent safe margins of resection surrounding this lesion were clearly greater using DTI-based tractography than with the CSD-based approach: DTI-based tractography suggested that only the medial aspect of the lesion impinged on the corticospinal tracts (Fig. 5B, i and ii); however, the CSD-based tractography results (derived from the same DWI data set) suggested that the lesion was enveloped by medial and lateral projections of corticospinal fibers (Fig. 5B, iii and iv). In this case, available intraoperative electrocorticography and monitoring of the left hand function demonstrated good correlation with CSD-based tractography results.

Discussion

Neurosurgical intervention requires biologically accurate mapping of white matter pathways that support eloquent cortical regions to provide optimal lesion excision with minimal damage to the patient's neurological function.25,34 In this study, we systematically explored the practical limitations of DTI-based tractography as well as the advantage of using CSD-based tractography to delineate the fiber pathways of neurosurgical interest, in both cases using the example of the corticospinal tracts. It is clear from the data from the 45 healthy control subjects that DTI-based tractography methods consistently fail to identify well-known corticospinal connections extending to the majority of the sensorimotor cortex (Fig. 3). In contrast, the CSD-based tractography method consistently produced the expected fan-shaped configuration of corticospinal fiber pathways extending throughout the sensorimotor cortex (Fig. 3) that much more closely resembles the known anatomy in this region (Fig. 7). These results emphasize that the method used to generate fiber orientation estimations from diffusion MRI data has important practical ramifications.

Fig. 7.
Fig. 7.

Dorsal views of the right pyramidal tract. A: Coronal plane [sketch] depicting the pyramidal tract of the right hemisphere (dorsal view) and its landmarks (1 = wall of the lateral ventricle, 2 = upper circular [periinsular] sulcus, 3 = the cingular sulcus). B: Specimen of the right pyramidal tract (dorsal view) and its landmarks (lateral wall of the lateral ventricle, superior circular sulcus). C: Tractography results using CSD and a probabilistic algorithm. D: Tractography results using DTI and a deterministic algorithm. Panels A and B are reprinted from Ebeling U, Reulen HJ: Subcortical topography and proportions of the pyramidal tract. Acta Neurochir (Wien) 118:164–171, 1992 (Figs. 1 and 5), with kind permission from Springer Science and Business Media.

The clinical importance of applying an appropriate fiber orientation estimation method (for example, DTI vs higher-order models) to DWI data is clearly illustrated in the patient cohort of this study, where tractography was performed to visualize the corticospinal pathways in patients at risk for neurological deficit following neurosurgical resection (see Table 1). In all cases, the CSD-based method identified the corticospinal tracts extending to the entire sensorimotor cortex, whereas the DTI-based method only identified a narrow subset of tracts extending, in the majority of cases, medially to the vertex (see Figs. 5 and 6). It should be emphasized that the tractography results presented from these real clinical scenarios are entirely consistent with the results in healthy controls. In 3 cases (Cases F, G, and H; Fig. 6) the DTI-based method produced a few tracks in the vicinity of the lateral aspect of the sensorimotor cortex; however, it is important to note that these fiber pathways were not represented across subjects, or even in the same subject on the contralateral side, and hence are likely to be unreliable.

The limited delineation of the corticospinal tracts found in the patient cohort in the present study using tensor-based tractography is completely consistent with the DTI tractography literature to date.8,9,12,18,23,25,30,44 Although many of these studies suggest that their findings show great promise for the use of DTI-based tractography as a pre- or intraoperative tool, they commonly visualize only the medial portion of the corticospinal tracts. The results from the present study demonstrate that such a limited extent of tract delineation using DTI-based tractography is actually inherent to the tensor model and hence is likely to result in very unreliable and misleading clinical information that is clearly insufficient for safe neurosurgical navigation. This may provide an explanation for the undesirable functional consequences reported in previous neurosurgical tractography studies23,29 that used DTI-based fiber tractography information to guide safe margins of resection. Even in carefully performed studies that have tested reproducibility of tracking results,29 the resulting corticospinal tract visualization shows only the medial part of the tract: the underlying problem is a systematic error that cannot be addressed using a test-retest approach. Demonstrating reproducibility in the presence of a systematic error (the incorrect estimation of fiber orientations in voxels containing multiple fiber populations) merely shows that the same erroneous outcome is obtained each time.

The reliability and reproducibility of tractography results have generated much discussion in the literature.11,16 Tractography results are reported to be dependent on the particular placement of ROIs and on the quality of acquired data.29,30 Therefore, it is important to emphasize that our study was designed to ensure that all control data results were independent of user subjectivity. The same template-generated ROIs were transformed into each individual's native space to ensure that the results for each of the tractography methodologies were comparable across all subjects. In addition, the results obtained using a range of b values and diffusion direction schemes (specifically including data commonly believed to be optimal for both DTI- and CSD-based methods22,35) indicate that failure of the DTI-based tractography method to delineate tracks extending to the lateral aspect of the cortex across all subjects occurs irrespective of the DWI acquisition scheme (see Fig. 3B). In contrast, the CSD-based tractography performed well and identified the expected fan-shaped configuration of tracks extending throughout the sensorimotor cortex across the same range of DWI data sets. However, it is important to note that the configuration of tracks identified by the CSD-based method appear on visual inspection to be more organized and exhibited fewer spurious tracks with higher b-value DWI data acquired using a higher number of diffusion directions, as demonstrated in Fig. 3B. This is consistent with our previous experimental finding that diffusion acquisition schemes with a minimum of 45 directions and a b value of 3000 sec/mm2,35 are recommended for robust estimations of fiber orientations using models such as CSD.37

A common misconception in the clinical setting is that the problems experienced using DTI-based tractography methods can be addressed by the application of more complex fiber tracking algorithms to fiber orientations estimated using the tensor model. In the present study, direct comparison of tensor-based data analyzed using a deterministic algorithm26 versus a probabilistic algorithm21 emphasizes that, while there remain some advantages to using probabilistic algorithms, the application of such an algorithm cannot compensate for fundamental limitations of the fiber orientation estimates obtained using the tensor model. This is evident in the data presented in Fig. 3A, where the extent of the fiber connections generated by the probabilistic DTI-based method closely matches those generated using the deterministic DTI-based tractography method. This indicates that probabilistic tractography remains limited by the poor-quality fiber orientation information provided by the diffusion tensor model and does not alone provide an acceptable clinical solution.

The implications of the results presented here are of clinical concern because neurosurgeons are increasingly using tractography software to localize major white matter fiber tracts (in particular, the corticospinal tracts) in patients who may be at risk for neurological deficit following resection. The majority of tractography software packages available to clinicians rely on the DTI framework to generate fiber orientations from DWI data. It is commonly argued that the inability of the tensor model to represent multiple fiber orientations is not a problem when dealing with the larger tracts in the brain, since a large tract in the presence of a small tract will result in a tensor with the orientation of the so-called “dominant” tract, with tracking results thought to be minimally affected. However, it is clear from the present data that even large fiber bundles, such as the corticospinal tract, cannot be adequately described by DTI-based tractography methods in regions where the tract crosses other major fiber bundles, such as the corpus callosum or the longitudinal fasciculus. These data confirm that many voxels along the corticospinal tract contain substantial contributions from 2 or more fiber populations, and in such cases the tensor-derived direction does not represent any of the constituent fiber populations (as illustrated in Fig. 1 and in vivo in Fig. 4). It should be emphasized that the scale of this problem cannot be overstated, given that recent work in the field demonstrates that more than 90% of imaging voxels in the white matter contain multiple fiber populations.20 While the present work is confined to demonstrating these limitations in the delineation of corticospinal pathways, it is highly likely that the results shown in the present study will apply to most major fiber tracts, given that such tracts will inevitably traverse voxels containing substantial contributions from 2 or more fibers at some point along their path.

Conclusions

This comprehensive study shows that the most widely used clinical tractography method (DTI-based tractography) results in systematically unreliable and clinically misleading information. The higher-order tractography model, using the same diffusion-weighted data, clearly demonstrates fiber tracts more accurately, providing improved estimates of safety margins that may be useful in neurosurgical procedures. We therefore need to move beyond the diffusion tensor framework if we are to begin to provide neurosurgeons with biologically reliable tractography information.

Disclosure

The authors do not report any conflicts of interest concerning the materials or methods used in this study or in the findings specified in this paper. This work was supported by the National Health and Medical Research Council of Australia and the Victorian government's Operational Infrastructure Support Program.

Author contributions to the study and manuscript preparation include the following. Conception and design: Farquharson, Tournier, Connelly. Acquisition of data: Farquharson, Fabinyi, Jackson, Connelly. Analysis and interpretation of data: Farquharson, Tournier, Jackson, Connelly. Drafting the article: all authors. Critically revising the article: all authors. Reviewed submitted version of manuscript: all authors. Approved the final version of the manuscript on behalf of all authors: Farquharson. Administrative/technical/material support: Farquharson. Study supervision: Schneider-Kolsky, Jackson, Connelly.

Acknowledgements

The authors thank A. Gottschalk for assistance with manuscript preparation and the radiographers at the Melbourne Brain Centre, R. Mineo, S. Ansari, and M. Macmillan, who scanned the participants in this study.

This article contains some figures that are displayed in color online but in black-and-white in the print edition.

Portions of this work were presented in abstract form at the 18th Annual Meeting of the Section of Magnetic Resonance Technologists, Honolulu, Hawaii, April 18, 2009.

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    Behrens TEBerg HJJbabdi SRushworth MFWoolrich MW: Probabilistic diffusion tractography with multiple fibre orientations: what can we gain?. Neuroimage 34:1441552007

  • 8

    Berman JIBerger MSChung SNagarajan SSHenry RG: Accuracy of diffusion tensor magnetic resonance imaging tractography assessed using intraoperative subcortical stimulation mapping and magnetic source imaging. J Neurosurg Pediatr 107:4884942007

  • 9

    Berman JIBerger MSMukherjee PHenry RG: Diffusiontensor imaging-guided tracking of fibers of the pyramidal tract combined with intraoperative cortical stimulation mapping in patients with gliomas. J Neurosurg 101:66722004

  • 10

    Bozzao ARomano AAngelini AD'Andrea GCalabria LFCoppola V: Identification of the pyramidal tract by neuronavigation based on intraoperative magnetic resonance tractography: correlation with subcortical stimulation. Eur Radiol 20:247524812010

  • 11

    Ciccarelli OParker GJMToosy ATWheeler-Kingshott CAMBarker GJBoulby PA: From diffusion tractography to quantitative white matter tract measures: a reproducibility study. Neuroimage 18:3483592003

  • 12

    Clark CABarrick TRMurphy MMBell BA: White matter fiber tracking in patients with space-occupying lesions of the brain: a new technique for neurosurgical planning?. Neuroimage 20:160116082003

  • 13

    Ebeling UReulen HJ: Subcortical topography and proportions of the pyramidal tract. Acta Neurochir (Wien) 118:1641711992

  • 14

    Fernandez-Miranda JCPathak SEngh JJarbo KVerstynen TYeh FC: High-definition fiber tractography of the human brain: neuroanatomical validation and neurosurgical applications. Neurosurgery 71:4304532012

  • 15

    Frank LR: Characterization of anisotropy in high angular resolution diffusion-weighted MRI. Magn Reson Med 47:108310992002

  • 16

    Heiervang EBehrens TEJMackay CERobson MDJohansen-Berg H: Between session reproducibility and between subject variability of diffusion MR and tractography measures. Neuroimage 33:8678772006

  • 17

    Holodny AIOllenschleger MDLiu WCSchulder MKalnin AJ: Identification of the corticospinal tracts achieved using blood-oxygen-level-dependent and diffusion functional MR imaging in patients with brain tumors. AJNR Am J Neuroradiol 22:83882001

  • 18

    Itoh DAoki SMaruyama KMasutani YMori HMasumoto T: Corticospinal tracts by diffusion tensor tractography in patients with arteriovenous malformations. J Comput Assist Tomogr 30:6186232006

  • 19

    Jansons KMAlexander DC: Persistent angular structure: new insights from diffusion magnetic resonance imaging data. Inf Process Med Imaging 18:6726832003

  • 20

    Jeurissen BLeemans ATournier JDJones DKSijbers J: Investigating the prevalence of complex fiber configurations in white matter tissue with diffusion magnetic resonance imaging. Hum Brain Mapp 2012

  • 21

    Jones DK: Tractography gone wild: probabilistic fibre tracking using the wild bootstrap with diffusion tensor MRI. IEEE Trans Med Imaging 27:126812742008

  • 22

    Jones DKHorsfield MASimmons A: Optimal strategies for measuring diffusion in anisotropic systems by magnetic resonance imaging. Magn Reson Med 42:5155251999

  • 23

    Kinoshita MYamada KHashimoto NKato AIzumoto SBaba T: Fiber-tracking does not accurately estimate size of fiber bundle in pathological condition: initial neurosurgical experience using neuronavigation and subcortical white matter stimulation. Neuroimage 25:4244292005

  • 24

    Maruyama KKamada KShin MItoh DMasutani YIno K: Optic radiation tractography integrated into simulated treatment planning for Gamma Knife surgery. J Neurosurg 107:7217262007

  • 25

    Mikuni NOkada TEnatsu RMiki YHanakawa TUrayama S: Clinical impact of integrated functional neuronavigation and subcortical electrical stimulation to preserve motor function during resection of brain tumors. J Neurosurg 106:5935982007

  • 26

    Mori SCrain BJChacko VPvan Zijl PC: Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging. Ann Neurol 45:2652691999

  • 27

    Mori Svan Zijl PCM: Fiber tracking: principles and strategies— a technical review. NMR Biomed 15:4684802002

  • 28

    Newton JMWard NSParker GJMDeichmann RAlexander DCFriston KJ: Non-invasive mapping of corticofugal fibres from multiple motor areas—relevance to stroke recovery. Brain 129:184418582006

  • 29

    Nimsky CGanslandt OFahlbusch R: Implementation of fiber tract navigation. Neurosurgery 58:4 Suppl 2ONS292ONS3042006

  • 30

    Okada TMiki YKikuta KMikuni NUrayama SFushimi Y: Diffusion tensor fiber tractography for arteriovenous malformations: quantitative analyses to evaluate the corticospinal tract and optic radiation. AJNR Am J Neuroradiol 28:110711132007

  • 31

    Özarslan EMareci TH: Generalized diffusion tensor imaging and analytical relationships between diffusion tensor imaging and high angular resolution diffusion imaging. Magn Reson Med 50:9559652003

  • 32

    Parker GJMHaroon HAWheeler-Kingshott CAM: A framework for a streamline-based probabilistic index of connectivity (PICo) using a structural interpretation of MRI diffusion measurements. J Magn Reson Imaging 18:2422542003

  • 33

    Romano AD'Andrea GMinniti GMastronardi LFerrante LFantozzi LM: Pre-surgical planning and MR-tractography utility in brain tumour resection. Eur Radiol 19:279828082009

  • 34

    Sanai NBerger MS: Glioma extent of resection and its impact on patient outcome. Neurosurgery 62:7537642008

  • 35

    Tournier JDCalamante FConnelly A: How many diffusion gradient directions are required for HARDI?. Proc Intl Soc Mag Reson Med 17:3582009. (Abstract)

  • 36

    Tournier JDCalamante FConnelly A: MRtrix: diffusion tractography in crossing fibre regions. Int J Imaging Syst Technol 22:53662012

  • 37

    Tournier JDCalamante FConnelly A: Robust determination of the fibre orientation distribution in diffusion MRI: nonnegativity constrained super-resolved spherical deconvolution. Neuroimage 35:145914722007

  • 38

    Tournier JDCalamante FGadian DGConnelly A: Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution. Neuroimage 23:117611852004

  • 39

    Tournier JDMori SLeemans A: Diffusion tensor imaging and beyond. Magn Reson Med 65:153215562011

  • 40

    Tournier JDYeh CHCalamante FCho KHConnelly ALin CP: Resolving crossing fibres using constrained spherical deconvolution: validation using diffusion-weighted imaging phantom data. Neuroimage 42:6176252008

  • 41

    Tuch DS: Q-ball imaging. Magn Reson Med 52:135813722004

  • 42

    Tuch DSReese TGWiegell MRMakris NBelliveau JWWedeen VJ: High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. Magn Reson Med 48:5775822002

  • 43

    Wedeen VJHagmann PTseng WYReese TGWeisskoff RM: Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging. Magn Reson Med 54:137713862005

  • 44

    Yamada KKizu OIto HNishimura T: Tractography for an arteriovenous malformation. Neurology 62:6692004

  • 45

    Yushkevich PAPiven JHazlett HCSmith RGHo SGee JC: User-guided 3D active contour segmentation of anatomical structures: significantly improved efficiency and reliability. Neuroimage 31:111611282006

Article Information

Address correspondence to: Shawna Farquharson, M.Sc., Melbourne Brain Centre, 245 Burgundy Street, Melbourne 3084, Australia. email: s.farquharson@brain.org.au.

Please include this information when citing this paper: published online March 29, 2013; DOI: 10.3171/2013.2.JNS121294.

© AANS, except where prohibited by US copyright law.

Headings

Figures

  • View in gallery

    A: Schematic showing the 3 key steps required to perform tractography, with the resulting fiber tracks illustrated by a coronal section from a “whole-brain” tractography data set. The color of the fiber tracks indicates the local fiber orientation (red: left-right, green: dorsal-ventral, blue: cranial-caudal; see colored arrows). B: Simulation data showing a detailed illustration of Step 2 of Panel A. Schematic images of voxels (i) containing white matter fibers (single fiber populations, left and middle; 2 fiber populations, right) are shown with illustrations corresponding to each of these voxels, showing the DWI signal (ii), diffusion tensor ellipsoids derived from the DWI signal within each voxel (iii), and fiber orientations derived using CSD (iv). Note that in the voxel containing 2 fiber populations, the DTI model not only fails to represent the number of fiber populations within each voxel, but also does not provide an orientation estimate that corresponds to either of the constituent fiber populations. The CSD-based method correctly identifies 2 appropriately oriented fiber populations in the third voxel (see i).

  • View in gallery

    Coronal template FA image overlaid with seed and target regions defined in the right and left sensorimotor motor cortices (red and blue, respectively) and brainstem (yellow). These regions were warped back into each control participant's native space to perform all fiber tracking in native space (see Methods: Tractography).

  • View in gallery

    Comparison of control data tractography results obtained using seed and target ROIs identified in the brainstem and sensorimotor cortex, as shown in Fig. 2. For the individual subject data, the color of the fiber tracks indicates the local fiber orientation (with red indicating left-right, green indicating dorsal-ventral, and blue indicating cranial-caudal). A: Tractography results for DTI combined with a deterministic algorithm, DTI combined with a probabilistic algorithm, and CSD combined with a probabilistic algorithm. All data were acquired using 60 diffusion-weighted directions with b = 3000 sec/mm2. In each case, tracking was performed both from superior to inferior (left group of 6 images, labeled “motor to brain stem”) and from inferior to superior (right group of 6 images, labeled “brain stem to motor”). The upper row shows coronal T1-weighted images overlaid with tractography results from a representative normal control subject. The bottom row shows coronal FA template image overlaid with frequency maps representing the number of subjects from the 45 control subjects in which tracks were identified in any given voxel (range = 0–45). B: Tractography results using DTI combined with a deterministic algorithm and CSD combined with a probabilistic algorithm, across a range of acquisition protocols that differed in the number of diffusion directions and b-value used, as indicated in the figure. Panel B(i) shows coronal T1-weighted images overlaid with tractography results using DTI (left column) and CSD (right column) from a representative normal control subject. Panel B(ii) shows a coronal FA template image overlaid with frequency maps representing the number of subjects (out of 12 control subjects) in whom tracks were identified in any given voxel, using DTI (left column) and CSD (right column) (range 0–12).

  • View in gallery

    Coronal FA images overlaid with fiber tracking results using CSD (left) and DTI (right) from a representative healthy control subject. The magnified regions in the orange boxes show the fiber orientation estimates within individual voxels. The CSD fiber orientation estimates (upper left image) confirm the presence of many voxels containing multiple fiber orientations, within individual voxels. The tensor-derived orientation in equivalent voxels (upper right image) does not represent any of the constituent fiber populations in regions where the DTI-based tractography method failed to produce tracks.

  • View in gallery

    Results of DTI-based tractography (blue) and CSD-based tractography (red) (derived from the same DWI data set) with segmented pathology volumes (green) overlaid on coronal T1-weighted images for Case A (A) and Case B (B). Case A involved a 49-year-old woman with a large left-sided temporoparietal AVM. See MR images in Panel A(v). Case B involved a 24-year-old woman with a right focal cortical dysplasia situated in the right posterior frontal lobe. See MR images in Panel B(v). The DTI-based tractography results in Case A suggest a clear margin surrounding the lesion (i and ii), whereas the CSD-based tractography results indicate that lateral projections of the corticospinal pathway may be at risk (iii and iv). The DTI-based tractography results in Case B suggest that only the medial aspect of the lesion impinges on the corticospinal tracts (i and ii), whereas the CSD-based tractography results suggest that the lesion is enveloped by medial and lateral projections of corticospinal fibers (iii and iv).

  • View in gallery

    Results of DTI-based tractography (i) and CSD-based tractography (ii) for Cases C–J with segmented pathology volumes (green) overlaid on coronal T1-weighted images. The panel labels correspond to the cases listed in Table 1. Note: The difference in apparent safe margins of resection is substantially greater using the DTI-based tractography method (blue) compared with the CSD-based tractography method (red).

  • View in gallery

    Dorsal views of the right pyramidal tract. A: Coronal plane [sketch] depicting the pyramidal tract of the right hemisphere (dorsal view) and its landmarks (1 = wall of the lateral ventricle, 2 = upper circular [periinsular] sulcus, 3 = the cingular sulcus). B: Specimen of the right pyramidal tract (dorsal view) and its landmarks (lateral wall of the lateral ventricle, superior circular sulcus). C: Tractography results using CSD and a probabilistic algorithm. D: Tractography results using DTI and a deterministic algorithm. Panels A and B are reprinted from Ebeling U, Reulen HJ: Subcortical topography and proportions of the pyramidal tract. Acta Neurochir (Wien) 118:164–171, 1992 (Figs. 1 and 5), with kind permission from Springer Science and Business Media.

References

1

Alexander ALHasan KMLazar MTsuruda JSParker DL: Analysis of partial volume effects in diffusion-tensor MRI. Magn Reson Med 45:7707802001

2

Anderson AW: Measurement of fiber orientation distributions using high angular resolution diffusion imaging. Magn Reson Med 54:119412062005

3

Assaf YFreidlin RZRohde GKBasser PJ: New modeling and experimental framework to characterize hindered and restricted water diffusion in brain white matter. Magn Reson Med 52:9659782004

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Avants BBEpstein CLGrossman MGee JC: Symmetric diffeomorphic image registration with cross-correlation: evaluating automated labeling of elderly and neurodegenerative brain. Med Image Anal 12:26412008

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Basser PJ: Inferring microstructural features and the physiological state of tissues from diffusion-weighted images. NMR Biomed 8:3333441995

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Basser PJMattiello JLeBihan D: MR diffusion tensor spectroscopy and imaging. Biophys J 66:2592671994

7

Behrens TEBerg HJJbabdi SRushworth MFWoolrich MW: Probabilistic diffusion tractography with multiple fibre orientations: what can we gain?. Neuroimage 34:1441552007

8

Berman JIBerger MSChung SNagarajan SSHenry RG: Accuracy of diffusion tensor magnetic resonance imaging tractography assessed using intraoperative subcortical stimulation mapping and magnetic source imaging. J Neurosurg Pediatr 107:4884942007

9

Berman JIBerger MSMukherjee PHenry RG: Diffusiontensor imaging-guided tracking of fibers of the pyramidal tract combined with intraoperative cortical stimulation mapping in patients with gliomas. J Neurosurg 101:66722004

10

Bozzao ARomano AAngelini AD'Andrea GCalabria LFCoppola V: Identification of the pyramidal tract by neuronavigation based on intraoperative magnetic resonance tractography: correlation with subcortical stimulation. Eur Radiol 20:247524812010

11

Ciccarelli OParker GJMToosy ATWheeler-Kingshott CAMBarker GJBoulby PA: From diffusion tractography to quantitative white matter tract measures: a reproducibility study. Neuroimage 18:3483592003

12

Clark CABarrick TRMurphy MMBell BA: White matter fiber tracking in patients with space-occupying lesions of the brain: a new technique for neurosurgical planning?. Neuroimage 20:160116082003

13

Ebeling UReulen HJ: Subcortical topography and proportions of the pyramidal tract. Acta Neurochir (Wien) 118:1641711992

14

Fernandez-Miranda JCPathak SEngh JJarbo KVerstynen TYeh FC: High-definition fiber tractography of the human brain: neuroanatomical validation and neurosurgical applications. Neurosurgery 71:4304532012

15

Frank LR: Characterization of anisotropy in high angular resolution diffusion-weighted MRI. Magn Reson Med 47:108310992002

16

Heiervang EBehrens TEJMackay CERobson MDJohansen-Berg H: Between session reproducibility and between subject variability of diffusion MR and tractography measures. Neuroimage 33:8678772006

17

Holodny AIOllenschleger MDLiu WCSchulder MKalnin AJ: Identification of the corticospinal tracts achieved using blood-oxygen-level-dependent and diffusion functional MR imaging in patients with brain tumors. AJNR Am J Neuroradiol 22:83882001

18

Itoh DAoki SMaruyama KMasutani YMori HMasumoto T: Corticospinal tracts by diffusion tensor tractography in patients with arteriovenous malformations. J Comput Assist Tomogr 30:6186232006

19

Jansons KMAlexander DC: Persistent angular structure: new insights from diffusion magnetic resonance imaging data. Inf Process Med Imaging 18:6726832003

20

Jeurissen BLeemans ATournier JDJones DKSijbers J: Investigating the prevalence of complex fiber configurations in white matter tissue with diffusion magnetic resonance imaging. Hum Brain Mapp 2012

21

Jones DK: Tractography gone wild: probabilistic fibre tracking using the wild bootstrap with diffusion tensor MRI. IEEE Trans Med Imaging 27:126812742008

22

Jones DKHorsfield MASimmons A: Optimal strategies for measuring diffusion in anisotropic systems by magnetic resonance imaging. Magn Reson Med 42:5155251999

23

Kinoshita MYamada KHashimoto NKato AIzumoto SBaba T: Fiber-tracking does not accurately estimate size of fiber bundle in pathological condition: initial neurosurgical experience using neuronavigation and subcortical white matter stimulation. Neuroimage 25:4244292005

24

Maruyama KKamada KShin MItoh DMasutani YIno K: Optic radiation tractography integrated into simulated treatment planning for Gamma Knife surgery. J Neurosurg 107:7217262007

25

Mikuni NOkada TEnatsu RMiki YHanakawa TUrayama S: Clinical impact of integrated functional neuronavigation and subcortical electrical stimulation to preserve motor function during resection of brain tumors. J Neurosurg 106:5935982007

26

Mori SCrain BJChacko VPvan Zijl PC: Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging. Ann Neurol 45:2652691999

27

Mori Svan Zijl PCM: Fiber tracking: principles and strategies— a technical review. NMR Biomed 15:4684802002

28

Newton JMWard NSParker GJMDeichmann RAlexander DCFriston KJ: Non-invasive mapping of corticofugal fibres from multiple motor areas—relevance to stroke recovery. Brain 129:184418582006

29

Nimsky CGanslandt OFahlbusch R: Implementation of fiber tract navigation. Neurosurgery 58:4 Suppl 2ONS292ONS3042006

30

Okada TMiki YKikuta KMikuni NUrayama SFushimi Y: Diffusion tensor fiber tractography for arteriovenous malformations: quantitative analyses to evaluate the corticospinal tract and optic radiation. AJNR Am J Neuroradiol 28:110711132007

31

Özarslan EMareci TH: Generalized diffusion tensor imaging and analytical relationships between diffusion tensor imaging and high angular resolution diffusion imaging. Magn Reson Med 50:9559652003

32

Parker GJMHaroon HAWheeler-Kingshott CAM: A framework for a streamline-based probabilistic index of connectivity (PICo) using a structural interpretation of MRI diffusion measurements. J Magn Reson Imaging 18:2422542003

33

Romano AD'Andrea GMinniti GMastronardi LFerrante LFantozzi LM: Pre-surgical planning and MR-tractography utility in brain tumour resection. Eur Radiol 19:279828082009

34

Sanai NBerger MS: Glioma extent of resection and its impact on patient outcome. Neurosurgery 62:7537642008

35

Tournier JDCalamante FConnelly A: How many diffusion gradient directions are required for HARDI?. Proc Intl Soc Mag Reson Med 17:3582009. (Abstract)

36

Tournier JDCalamante FConnelly A: MRtrix: diffusion tractography in crossing fibre regions. Int J Imaging Syst Technol 22:53662012

37

Tournier JDCalamante FConnelly A: Robust determination of the fibre orientation distribution in diffusion MRI: nonnegativity constrained super-resolved spherical deconvolution. Neuroimage 35:145914722007

38

Tournier JDCalamante FGadian DGConnelly A: Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution. Neuroimage 23:117611852004

39

Tournier JDMori SLeemans A: Diffusion tensor imaging and beyond. Magn Reson Med 65:153215562011

40

Tournier JDYeh CHCalamante FCho KHConnelly ALin CP: Resolving crossing fibres using constrained spherical deconvolution: validation using diffusion-weighted imaging phantom data. Neuroimage 42:6176252008

41

Tuch DS: Q-ball imaging. Magn Reson Med 52:135813722004

42

Tuch DSReese TGWiegell MRMakris NBelliveau JWWedeen VJ: High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. Magn Reson Med 48:5775822002

43

Wedeen VJHagmann PTseng WYReese TGWeisskoff RM: Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging. Magn Reson Med 54:137713862005

44

Yamada KKizu OIto HNishimura T: Tractography for an arteriovenous malformation. Neurology 62:6692004

45

Yushkevich PAPiven JHazlett HCSmith RGHo SGee JC: User-guided 3D active contour segmentation of anatomical structures: significantly improved efficiency and reliability. Neuroimage 31:111611282006

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