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Fiber Tracking with DWI
Fiber Tracking with DWI J-D Tournier, Florey Neuroscience Institutes, Heidelberg West, VIC, Australia S Mori, Johns Hopkins University School of Medicine, Baltimore, MD, USA ã 2015 Elsevier Inc. All rights reserved.
DWI Diffusion-weighted image FACT Fiber assignment by continuous tracking HARDI High angular resolution diffusion imaging ODF Orientation density function
Abbreviations DEC Directionally encoded color DTI Diffusion tensor imaging DW Diffusion weighting
Diffusion MRI can provide information about the orientation of white matter pathways within each image voxel. While this information can be displayed as 2-D directionally encoded color (DEC) maps, this can only reveal a cross section of white matter tracts; it is difficult to appreciate their often convoluted 3-D trajectories from a slice-by-slice inspection. Computer-aided 3-D tract-tracing techniques (a.k.a. fiber tracking or tractography) can be very useful to delineate and visualize tract trajectories and appreciate their relationships with other white matter tracts and/or gray matter structures. Fiber-tracking techniques essentially work by using fiber orientation estimates (whether provided using diffusion tensor imaging (DTI) or more advanced higher-order models) to establish how one particular point in 3-D space might connect with other regions.
How Does Fiber Tracking Work? The Streamline Approach The simplest and most common approach to fiber tracking is the so-called streamline approach, also known as fiber assignment by continuous tracking (FACT) (Mori, Crain, Chacko, & van Zijl, 1999). The idea in this case is to consider 3-D space as continuous and simply to follow the local fiber orientation estimate in small incremental steps. Starting from a userspecified seed point, this process gradually delineates the path of the white matter fibers through the seed point, resulting in a 3-D curve or streamline that should in the ideal case correspond to the path of the white matter pathway of interest, as illustrated in Figure 1. In practice, streamline tractography is typically performed using a large number of seed points densely packed within a seed ROI. This provides a much richer representation of the tract, including any potential branching and ‘fanning’ of the tract. It also provides some resilience to errors introduced by inaccuracies in the location of the seed point, which might otherwise lead to the delineation of tracts of no interest that happen to run adjacent to the tract of interest at that point.
Other Approaches Voxel linking This approach is the earliest form of fiber tracking and is based on the concept of simply linking one of the adjacent
Brain Mapping: An Encyclopedic Reference
voxels (e.g., Jones, Simmons, Williams, & Horsfield, 1999; Koch, Norris, & Hund-Georgiadis, 2002; Parker, WheelerKingshott, & Barker, 2002): if the fiber orientation estimate in one voxel points toward the center of an adjacent voxel and this voxel’s orientation estimate likewise points toward the center of the first voxel, then it is likely that a white matter pathway connects through these two voxels (Figure 2). By starting from a user-specified ‘seed’ voxel, adjacent voxels can be identified that likely belong to the same structure. These new voxels can then be considered in turn, and voxels adjacent to them can be investigated. By using this type of ‘region-growing’ approach, the region in space that is likely to be connected with the seed point can be identified. This approach can be extended to provide a more fine-grained description of that connectivity, by assigning to each voxel an index of its ‘probability of connection,’ providing results that better reflect the uncertainty inherent in these approaches (Anwander, Tittgemeyer, von Cramon, Friederici, & Kno¨sche, 2007; Descoteaux, Deriche, Kno¨sche, & Anwander, 2009; Koch et al., 2002; Parker et al., 2002). An issue with these voxel-linking approaches is the poor angular resolution inherent in limiting propagation to directions joining voxel centers. Even if all 3 3 3 nearest neighbors are included, this only provides a total of 26 directions that can be followed, with an angular resolution of 45 . This inherently means that the results will be ‘blurred’ to some extent in the orientation domain and introduce more spread (and potentially bias) in the results than might have been obtained using other methods.
Global approaches More recently, advanced algorithms have been proposed to perform ‘global’ tractography (e.g., Fillard, Poupon, & Mangin, 2009; Kreher, Mader, & Kiselev, 2008). These methods attempt to simultaneously estimate the set of all pathways in the brain, using a process of optimization. The reason this might be advantageous is that this allows the algorithm to consider nonlocal effects, for example, the fact that a voxel has a fixed volume, and therefore, the reconstruction should not allow more tract volume to exist within each voxel than is physically possible. These approaches have the potential to provide more biologically plausible reconstructions but are currently limited by the typically enormous amount of computation involved in solving this type of problem.
http://dx.doi.org/10.1016/B978-0-12-397025-1.00294-3
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Figure 1 Fiber assignment by continuous tracking (FACT). Starting from the user-defined seed point (arrow), the algorithm traces out a path following the local estimate of the fiber orientation (black lines). The resulting streamline provides an estimate of the path of the white matter pathway.
knowledge about the trajectory of the tract of interest. In its simplest form, tract editing is done simply by supplying another, distinct region that the tract of interest is expected to run through; such an ROI is commonly referred to as a waypoint, inclusion, or AND ROI. The idea is that if the fibertracking algorithm deviates from the real path, it is very unlikely to come back to it by chance and enter this second ROI. Streamlines that do not run through both ROIs are therefore discarded. It is also possible to reject streamlines when they enter regions that they are not expected to run through; such an ROI is commonly referred to as an exclusion or NOT ROI. Similarly, though less commonly used, streamlines can be included based on their entering one of a set of regions, using an OR operation. In this way, users can combine multiple ROIs to impose as much anatomical prior information as is deemed reasonable. What constitutes ‘reasonable’ in this context is a subjective judgment; it is possible, for instance, to outline the entire pathway of interest as an inclusion ROI and the rest of the brain as an exclusion ROI, in which case fiber tracking would be somewhat redundant. In general, fiber tracking is most informative when the results match the expectation with minimal use of prior information. When imposing too much prior information, the algorithm can only provide what is essentially already known. When imposing little prior information and the results do not match the expectation, there is a good chance the results might be due to an artifact of the fiber-tracking method, rather than genuine biology; it can however be very difficult to distinguish between the two, making the results ambiguous.
Challenges in Fiber Tracking Crossing Fibers and Partial Volume Averaging
Figure 2 Illustration of fiber tracking by voxel linking. The idea is essentially to establish whether two adjacent voxels are ‘connected,’ based on simple rules. In this case, the rule is that the center of one voxel must be within a certain angle of the direction of the other voxel, and vice versa. Starting from the seed voxel (colored red), adjacent voxels that satisfy the criterion are included (colored gray). In the next iteration, the neighbors of these newly included voxels are considered, until no further voxels can be found.
Adding Prior Anatomical Information: Tract Editing Fiber tracking is subject to a number or problems (described in the succeeding text) that will introduce errors. The fibertracking algorithm however has no way of assessing which results are real and which are artifact (i.e., false-positives). One of the most effective ways of dealing with such errors is the so-called tract-editing or multi-ROI approach, illustrated in Figure 3. This technique can be considered as a way of removing false-positives based on the user’s prior anatomical
Fiber tracking relies on accurate estimates of fiber orientations. Most implementations simply use the direction of the major eigenvector of the diffusion tensor as the fiber orientation estimate. Unfortunately, the diffusion tensor model can only characterize one fiber orientation per voxel; when multiple fiber bundles with distinct orientations are colocated within an individual voxel, the orientation estimated will in general not correspond to either fiber orientations present. While this problem was initially thought to affect only a few areas of brain white matter, it is now clear that the problem is endemic to diffusion imaging, with serious implications for DTI-based fiber tracking (Jeurissen, Leemans, Tournier, Jones, & Sijbers, 2013). Thankfully, there are now many approaches that can estimate multiple fiber orientations per voxel, typically based on high angular resolution diffusion imaging (HARDI) data (Tournier, Mori, & Leemans, 2011). While there are many potential ways that this multifiber information could be used for fiber tracking, in practice, the simplest and most widely used consists of simply extending the original streamline algorithm to use one of the orientations identified at each spatial location. When multiple orientations are present, most algorithms will simply pick the orientation closest to the incoming direction of tracking (Behrens, Berg, Jbabdi, Rushworth, & Woolrich, 2007; Berman et al., 2008; Haroon, Morris, Embleton, Alexander, & Parker, 2009; Jeurissen, Leemans, Jones, Tournier, & Sijbers, 2011; Parker & Alexander, 2005; Wedeen et al., 2008), as illustrated in
INTRODUCTION TO METHODS AND MODELING | Fiber Tracking with DWI
(a)
Exclusion (NOT) region
Inclusion (AND) region
Seed region
(b)
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(c)
Figure 3 Illustration of tract editing using regions of interest. (a) Using a large seed region leads to the delineation of a number of different branches. (b) The tract of interest is known to run through the green region; placing an inclusion ROI there removes the most obvious false-positives. (c) If the tract of interest is known not to project to the red region, an exclusion ROI can be used to remove any spurious trajectories through it.
Figure 4 The FACT algorithm can easily be extended to handle crossing fiber information. The algorithm starts from the user-defined seed point (arrow) and proceeds in small steps, as for the standard FACT approach. However, at each step, the algorithm may be faced with a number of possible orientations to follow. The simplest approach is to select the orientation that is most closely aligned with the current direction of the streamline; this is equivalent to choosing the path of least curvature. In the absence of any other information, this is the most sensible approach since the path of least curvature must be the most likely path.
Figure 4. Alternatively, a number of methods also explicitly track along all possible orientations, assigning an index of probability to each branch based on the turning angle, to produce a more distributed model of connectivity (Chao et al., 2008). In some probabilistic approaches, any fiber orientation within a certain turning angle of the incoming direction is considered suitable candidates for sampling (see later text for a description of probabilistic approaches); these will therefore preferentially track through crossing fiber regions while still allowing for changes in direction that would not be permitted using most methods mentioned previously (Tournier, Calamante, & Connelly, 2012).
Uncertainty: Noise and Limited Angular Resolution Diffusion imaging is inherently a noisy technique, and this introduces uncertainty into the results. Imaging noise will translate into noisy orientation estimates, and this will cause
streamlines to deviate from their true trajectory. In general, any measurement will be contaminated by noise to some extent, and diffusion imaging is no exception. However, the effect of noise on fiber-tracking results is altogether different, and its impact can be profound. This is due to the way streamlines propagate through the data, visiting many different voxels and therefore accumulating errors from each noisy orientation estimate as tracking proceeds. This accumulation effect is compounded by the fact that streamlines that deviate into adjacent structures may then delineate a completely different path; given the size of most white matter structures, even a relatively small deviation of a few millimeters could therefore have a dramatic effect on the results. Another source of uncertainty is the intrinsic angular resolution of the DW signal, as illustrated in Figure 5. The signal varies smoothly as a function of orientation, and this means that we can only obtain ‘blurred’ estimates of fiber orientations. This is particularly relevant for higher-order models that aim to characterize the fiber orientation distribution. Most implementations simply extract the peak(s) of this blurred distribution, which not only provides much tighter estimates but also imposes the assumption that fibers from the same bundle are completely straight and parallel within a voxel. This may be a good approximation in many regions of the white matter, but there will undoubtedly be regions where this assumption does not hold. A number of methods have been proposed to deal with uncertainty in fiber tracking. In general, the idea is to provide an estimate of all the paths originating from the seed point(s) that are plausible given the data and its uncertainty, rather than a single ‘best-guess’ path. This is akin to providing the confidence interval of a measurement, in addition to its actual estimate. In general, a measurement is not informative without an idea of its confidence interval, since we cannot otherwise assess whether an observed difference in the measurement is significant or relevant. This is also true of tractography, with the additional problem that a confidence interval on a trajectory is quite difficult to envisage: there is no simple scalar estimate of the ‘standard deviation’ or ‘confidence interval’ of a path. The way this uncertainty is typically represented in fiber tracking is by generating an estimate of the distribution of possible paths, approximated by a set of representative trajectories. This is akin to approximating a normal distribution as a set of representative samples drawn from the distribution, as illustrated in Figure 6. This nonparametric approach is in fact much more general than using parametric measures such as the
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INTRODUCTION TO METHODS AND MODELING | Fiber Tracking with DWI
Fiber configuration
DW signal
Fiber ODF
Figure 5 The intrinsic angular resolution of the DW signal itself introduces uncertainty as to the exact fiber configuration. The three configurations on the left are all predominantly aligned left–right, and consequently, the DW signal intensity is smallest along that axis (middle). The DW signal is inherently broad, and this essentially blurs the signal. This means that the DW signal for the three configurations shown will be essentially identical, and consequently, the estimated diffusion or fiber orientation density function (ODF) will be the same in all three cases. The practice of using the peak orientation of the fiber or diffusion ODF as the ‘best’ fiber orientation estimate is appealing as it provides much ‘tighter’ results, but this is only valid for one of the three configurations shown. It is clear that some ambiguity remains as to what the true fiber orientations are, and this source of uncertainty should be included in probabilistic algorithms.
Figure 6 Any distribution can be approximated using a set of representative samples. A Gaussian distribution (left) can be represented by a set of values drawn at random from its probability density function (PDF); any property of the distribution can then be computed in a straightforward manner from these samples (mean, standard deviation, etc.). While this is needlessly complex for a Gaussian distribution, this approach can be used to represent much more complex, multimodal distributions for which no simple model exists, such as the distribution of streamline trajectories from a given seed point, as shown on the right. The most likely path (blue), as might be obtained using deterministic approaches, can be viewed as being the ‘mean’ of the distribution. As shown in this illustration, this most likely path may be very different from some of the other possible paths. This information is not available using deterministic approaches, yet knowledge of these other likely paths may significantly influence interpretation and/or the decision-making process.
standard deviation, since it can be applied to any type of data, regardless of whether or not they can be approximated by a normal distribution. This approach is therefore much more suitable for fiber tracking, since streamlines clearly cannot be assumed to originate from a Gaussian distribution. The most common approach to estimating uncertainty in fiber tracking is the concept of probabilistic streamlines. These extend the simple deterministic streamline approach by following a random orientation sample from within the range of possible orientations, rather than a single ‘peak’ orientation, as illustrated in Figure 7. This means that each successive streamline will take a slightly different path through the data that nonetheless remain consistent with the estimated orientations and their associated uncertainty. These methods therefore rely on the availability of an estimate of the uncertainty around each fiber orientation. Various methods exist for this step, including bootstrap approaches (Berman et al., 2008; Haroon et al., 2009;
Figure 7 The streamline algorithm can also be extended to take the various sources of uncertainty into account. As before, tracking is initiated from the user-defined seed point (arrow) and proceeds by taking small steps along the local fiber orientation estimate. In this case, however, the fiber orientation estimate used is taken from the range of likely possible orientations at this location, by drawing a random sample from the probability density function (PDF) of the fiber orientation. This generally incorporates a curvature constraint by ensuring that the fiber orientation sample is taken from within a ‘cone of uncertainty’ (Jones, 2003) about the current direction of tracking. By generating a large number of such streamlines, an approximation to the distribution of possible paths is produced.
Jeurissen et al., 2011; Jones, 2008; Whitcher, Tuch, Wisco, Sorensen, & Wang, 2008) and various modeling approaches including Markov chain Monte Carlo (MCMC) (Behrens, Johansen-Berg, et al., 2003; Behrens, Woolrich, et al., 2003; Behrens et al., 2007; Hosey, Harding, Carpenter, Ansorge, & Williams, 2008; Hosey, Williams, & Ansorge, 2005).
Conclusion Diffusion MRI fiber tracking is clearly a very exciting technology, being the only method that can be used to delineate white
INTRODUCTION TO METHODS AND MODELING | Fiber Tracking with DWI matter pathways in the human brain in vivo. It is also a very efficient method, since the same dataset can be used to delineate any white matter pathway (within the limitations of the data quality and reconstruction approach used), in contrast to tracer studies that can typically only be used to trace one pathway at a time. For this reason, it has very rapidly been adopted by neuroscientists and clinicians. However, it is also clear that fiber tracking is not without its limitations and idiosyncrasies, and this unfortunately makes it very easy for inexperienced users to come to the wrong conclusions. It is therefore essential that scientists and clinicians become well acquainted with the methods and particularly with their limitations before applying them in practice.
See also: INTRODUCTION TO ACQUISITION METHODS: Diffusion MRI; INTRODUCTION TO METHODS AND MODELING: Diffusion Tensor Imaging; Probability Distribution Functions in Diffusion MRI; Q-Space Modeling in DiffusionWeighted MRI.
References Anwander, A., Tittgemeyer, M., von Cramon, D. Y., Friederici, A. D., & Kno¨sche, T. R. (2007). Connectivity-based parcellation of Broca’s area. Cerebral Cortex, 17, 816–825. Behrens, T. E.J, Berg, H. J., Jbabdi, S., Rushworth, M. F. S., & Woolrich, M. W. (2007). Probabilistic diffusion tractography with multiple fibre orientations: What can we gain? NeuroImage, 34, 144–155. Behrens, T. E. J., Johansen-Berg, H., Woolrich, M. W., Smith, S. M., Wheeler-Kingshott, C. A.M, Boulby, P. A., et al. (2003). Non-invasive mapping of connections between human thalamus and cortex using diffusion imaging. Nature Neuroscience, 6, 750–757. Behrens, T. E. J., Woolrich, M. W., Jenkinson, M., Johansen-Berg, H., Nunes, R. G., Clare, S., et al. (2003). Characterization and propagation of uncertainty in diffusionweighted MR imaging. Magnetic Resonance in Medicine, 50, 1077–1088. Berman, J. I., Chung, S., Mukherjee, P., Hess, C. P., Han, E. T., & Henry, R. G. (2008). Probabilistic streamline q-ball tractography using the residual bootstrap. NeuroImage, 39, 215–222. Chao, Y.-P., Chen, J.-H., Cho, K.-H., Yeh, C.-H., Chou, K.-H., & Lin, C.-P. (2008). A multiple streamline approach to high angular resolution diffusion tractography. Medical Engineering & Physics, 30, 989–996. Descoteaux, M., Deriche, R., Kno¨sche, T. R., & Anwander, A. (2009). Deterministic and probabilistic tractography based on complex fibre orientation distributions. IEEE Transactions on Medical Imaging, 28, 269–286. Fillard, P., Poupon, C., & Mangin, J.-F. (2009). A novel global tractography algorithm based on an adaptive spin glass model. Medical Image Computing and ComputerAssisted Intervention, 12, 927–934.
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Haroon, H. A., Morris, D. M., Embleton, K. V., Alexander, D. C., & Parker, G. J. M. (2009). Using the model-based residual bootstrap to quantify uncertainty in fiber orientations from Q-ball analysis. IEEE Transactions on Medical Imaging, 28, 535–550. Hosey, T. P., Harding, S. G., Carpenter, T. A., Ansorge, R. E., & Williams, G. B. (2008). Application of a probabilistic double-fibre structure model to diffusion-weighted MR images of the human brain. Magnetic Resonance Imaging, 26, 236–245. Hosey, T., Williams, G., & Ansorge, R. (2005). Inference of multiple fiber orientations in high angular resolution diffusion imaging. Magnetic Resonance in Medicine, 54, 1480–1489. Jeurissen, B., Leemans, A., Jones, D. K., Tournier, J.-D., & Sijbers, J. (2011). Probabilistic fiber tracking using the residual bootstrap with constrained spherical deconvolution. Human Brain Mapping, 32, 461–479. Jeurissen, B., Leemans, A., Tournier, J.-D., Jones, D. K., & Sijbers, J. (2013). Investigating the prevalence of complex fiber configurations in white matter tissue with diffusion magnetic resonance imaging. Human Brain Mapping, 34, 2747–2766. Jones, D. K. (2003). Determining and visualizing uncertainty in estimates of fiber orientation from diffusion tensor MRI. Magnetic Resonance in Medicine, 49, 7–12. Jones, D. K. (2008). Tractography gone wild: Probabilistic fibre tracking using the wild bootstrap with diffusion tensor MRI. IEEE Transactions on Medical Imaging, 27, 1268–1274. Jones, D. K., Simmons, A., Williams, S. C., & Horsfield, M. A. (1999). Non-invasive assessment of axonal fiber connectivity in the human brain via diffusion tensor MRI. Magnetic Resonance in Medicine, 42, 37–41. Koch, M. A., Norris, D. G., & Hund-Georgiadis, M. (2002). An investigation of functional and anatomical connectivity using magnetic resonance imaging. NeuroImage, 16, 241–250. Kreher, B. W., Mader, I., & Kiselev, V. G. (2008). Gibbs tracking: A novel approach for the reconstruction of neuronal pathways. Magnetic Resonance in Medicine, 60, 953–963. Mori, S., Crain, B., Chacko, V., & van Zijl, P. (1999). Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging. Annals of Neurology, 45, 265–269. Parker, G., & Alexander, D. (2005). Probabilistic anatomical connectivity derived from the microscopic persistent angular structure of cerebral tissue. Philosophical Transactions of the Royal Society of London, Series B: Biological Sciences, 360, 893–902. 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. IEEE Transactions on Medical Imaging, 21, 505–512. Tournier, J., Calamante, F., & Connelly, A. (2012). MRtrix: Diffusion tractography in crossing fiber regions. International Journal of Imaging Systems and Technology, 22, 53–66. Tournier, J.-D., Mori, S., & Leemans, A. (2011). Diffusion tensor imaging and beyond. Magnetic Resonance in Medicine, 65, 1532–1556. Wedeen, V. J., Wang, R. P., Schmahmann, J. D., Benner, T., Tseng, W. Y.I, Dai, G., et al. (2008). Diffusion spectrum magnetic resonance imaging (DSI) tractography of crossing fibers. NeuroImage, 41, 1267–1277. Whitcher, B., Tuch, D. S., Wisco, J. J., Sorensen, A. G., & Wang, L. (2008). Using the wild bootstrap to quantify uncertainty in diffusion tensor imaging. Human Brain Mapping, 29, 346–362.
DWI Diffusion-weighted image FACT Fiber assignment by continuous tracking HARDI High angular resolution diffusion imaging ODF Orientation density function
Abbreviations DEC Directionally encoded color DTI Diffusion tensor imaging DW Diffusion weighting
Diffusion MRI can provide information about the orientation of white matter pathways within each image voxel. While this information can be displayed as 2-D directionally encoded color (DEC) maps, this can only reveal a cross section of white matter tracts; it is difficult to appreciate their often convoluted 3-D trajectories from a slice-by-slice inspection. Computer-aided 3-D tract-tracing techniques (a.k.a. fiber tracking or tractography) can be very useful to delineate and visualize tract trajectories and appreciate their relationships with other white matter tracts and/or gray matter structures. Fiber-tracking techniques essentially work by using fiber orientation estimates (whether provided using diffusion tensor imaging (DTI) or more advanced higher-order models) to establish how one particular point in 3-D space might connect with other regions.
How Does Fiber Tracking Work? The Streamline Approach The simplest and most common approach to fiber tracking is the so-called streamline approach, also known as fiber assignment by continuous tracking (FACT) (Mori, Crain, Chacko, & van Zijl, 1999). The idea in this case is to consider 3-D space as continuous and simply to follow the local fiber orientation estimate in small incremental steps. Starting from a userspecified seed point, this process gradually delineates the path of the white matter fibers through the seed point, resulting in a 3-D curve or streamline that should in the ideal case correspond to the path of the white matter pathway of interest, as illustrated in Figure 1. In practice, streamline tractography is typically performed using a large number of seed points densely packed within a seed ROI. This provides a much richer representation of the tract, including any potential branching and ‘fanning’ of the tract. It also provides some resilience to errors introduced by inaccuracies in the location of the seed point, which might otherwise lead to the delineation of tracts of no interest that happen to run adjacent to the tract of interest at that point.
Other Approaches Voxel linking This approach is the earliest form of fiber tracking and is based on the concept of simply linking one of the adjacent
Brain Mapping: An Encyclopedic Reference
voxels (e.g., Jones, Simmons, Williams, & Horsfield, 1999; Koch, Norris, & Hund-Georgiadis, 2002; Parker, WheelerKingshott, & Barker, 2002): if the fiber orientation estimate in one voxel points toward the center of an adjacent voxel and this voxel’s orientation estimate likewise points toward the center of the first voxel, then it is likely that a white matter pathway connects through these two voxels (Figure 2). By starting from a user-specified ‘seed’ voxel, adjacent voxels can be identified that likely belong to the same structure. These new voxels can then be considered in turn, and voxels adjacent to them can be investigated. By using this type of ‘region-growing’ approach, the region in space that is likely to be connected with the seed point can be identified. This approach can be extended to provide a more fine-grained description of that connectivity, by assigning to each voxel an index of its ‘probability of connection,’ providing results that better reflect the uncertainty inherent in these approaches (Anwander, Tittgemeyer, von Cramon, Friederici, & Kno¨sche, 2007; Descoteaux, Deriche, Kno¨sche, & Anwander, 2009; Koch et al., 2002; Parker et al., 2002). An issue with these voxel-linking approaches is the poor angular resolution inherent in limiting propagation to directions joining voxel centers. Even if all 3 3 3 nearest neighbors are included, this only provides a total of 26 directions that can be followed, with an angular resolution of 45 . This inherently means that the results will be ‘blurred’ to some extent in the orientation domain and introduce more spread (and potentially bias) in the results than might have been obtained using other methods.
Global approaches More recently, advanced algorithms have been proposed to perform ‘global’ tractography (e.g., Fillard, Poupon, & Mangin, 2009; Kreher, Mader, & Kiselev, 2008). These methods attempt to simultaneously estimate the set of all pathways in the brain, using a process of optimization. The reason this might be advantageous is that this allows the algorithm to consider nonlocal effects, for example, the fact that a voxel has a fixed volume, and therefore, the reconstruction should not allow more tract volume to exist within each voxel than is physically possible. These approaches have the potential to provide more biologically plausible reconstructions but are currently limited by the typically enormous amount of computation involved in solving this type of problem.
http://dx.doi.org/10.1016/B978-0-12-397025-1.00294-3
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Figure 1 Fiber assignment by continuous tracking (FACT). Starting from the user-defined seed point (arrow), the algorithm traces out a path following the local estimate of the fiber orientation (black lines). The resulting streamline provides an estimate of the path of the white matter pathway.
knowledge about the trajectory of the tract of interest. In its simplest form, tract editing is done simply by supplying another, distinct region that the tract of interest is expected to run through; such an ROI is commonly referred to as a waypoint, inclusion, or AND ROI. The idea is that if the fibertracking algorithm deviates from the real path, it is very unlikely to come back to it by chance and enter this second ROI. Streamlines that do not run through both ROIs are therefore discarded. It is also possible to reject streamlines when they enter regions that they are not expected to run through; such an ROI is commonly referred to as an exclusion or NOT ROI. Similarly, though less commonly used, streamlines can be included based on their entering one of a set of regions, using an OR operation. In this way, users can combine multiple ROIs to impose as much anatomical prior information as is deemed reasonable. What constitutes ‘reasonable’ in this context is a subjective judgment; it is possible, for instance, to outline the entire pathway of interest as an inclusion ROI and the rest of the brain as an exclusion ROI, in which case fiber tracking would be somewhat redundant. In general, fiber tracking is most informative when the results match the expectation with minimal use of prior information. When imposing too much prior information, the algorithm can only provide what is essentially already known. When imposing little prior information and the results do not match the expectation, there is a good chance the results might be due to an artifact of the fiber-tracking method, rather than genuine biology; it can however be very difficult to distinguish between the two, making the results ambiguous.
Challenges in Fiber Tracking Crossing Fibers and Partial Volume Averaging
Figure 2 Illustration of fiber tracking by voxel linking. The idea is essentially to establish whether two adjacent voxels are ‘connected,’ based on simple rules. In this case, the rule is that the center of one voxel must be within a certain angle of the direction of the other voxel, and vice versa. Starting from the seed voxel (colored red), adjacent voxels that satisfy the criterion are included (colored gray). In the next iteration, the neighbors of these newly included voxels are considered, until no further voxels can be found.
Adding Prior Anatomical Information: Tract Editing Fiber tracking is subject to a number or problems (described in the succeeding text) that will introduce errors. The fibertracking algorithm however has no way of assessing which results are real and which are artifact (i.e., false-positives). One of the most effective ways of dealing with such errors is the so-called tract-editing or multi-ROI approach, illustrated in Figure 3. This technique can be considered as a way of removing false-positives based on the user’s prior anatomical
Fiber tracking relies on accurate estimates of fiber orientations. Most implementations simply use the direction of the major eigenvector of the diffusion tensor as the fiber orientation estimate. Unfortunately, the diffusion tensor model can only characterize one fiber orientation per voxel; when multiple fiber bundles with distinct orientations are colocated within an individual voxel, the orientation estimated will in general not correspond to either fiber orientations present. While this problem was initially thought to affect only a few areas of brain white matter, it is now clear that the problem is endemic to diffusion imaging, with serious implications for DTI-based fiber tracking (Jeurissen, Leemans, Tournier, Jones, & Sijbers, 2013). Thankfully, there are now many approaches that can estimate multiple fiber orientations per voxel, typically based on high angular resolution diffusion imaging (HARDI) data (Tournier, Mori, & Leemans, 2011). While there are many potential ways that this multifiber information could be used for fiber tracking, in practice, the simplest and most widely used consists of simply extending the original streamline algorithm to use one of the orientations identified at each spatial location. When multiple orientations are present, most algorithms will simply pick the orientation closest to the incoming direction of tracking (Behrens, Berg, Jbabdi, Rushworth, & Woolrich, 2007; Berman et al., 2008; Haroon, Morris, Embleton, Alexander, & Parker, 2009; Jeurissen, Leemans, Jones, Tournier, & Sijbers, 2011; Parker & Alexander, 2005; Wedeen et al., 2008), as illustrated in
INTRODUCTION TO METHODS AND MODELING | Fiber Tracking with DWI
(a)
Exclusion (NOT) region
Inclusion (AND) region
Seed region
(b)
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(c)
Figure 3 Illustration of tract editing using regions of interest. (a) Using a large seed region leads to the delineation of a number of different branches. (b) The tract of interest is known to run through the green region; placing an inclusion ROI there removes the most obvious false-positives. (c) If the tract of interest is known not to project to the red region, an exclusion ROI can be used to remove any spurious trajectories through it.
Figure 4 The FACT algorithm can easily be extended to handle crossing fiber information. The algorithm starts from the user-defined seed point (arrow) and proceeds in small steps, as for the standard FACT approach. However, at each step, the algorithm may be faced with a number of possible orientations to follow. The simplest approach is to select the orientation that is most closely aligned with the current direction of the streamline; this is equivalent to choosing the path of least curvature. In the absence of any other information, this is the most sensible approach since the path of least curvature must be the most likely path.
Figure 4. Alternatively, a number of methods also explicitly track along all possible orientations, assigning an index of probability to each branch based on the turning angle, to produce a more distributed model of connectivity (Chao et al., 2008). In some probabilistic approaches, any fiber orientation within a certain turning angle of the incoming direction is considered suitable candidates for sampling (see later text for a description of probabilistic approaches); these will therefore preferentially track through crossing fiber regions while still allowing for changes in direction that would not be permitted using most methods mentioned previously (Tournier, Calamante, & Connelly, 2012).
Uncertainty: Noise and Limited Angular Resolution Diffusion imaging is inherently a noisy technique, and this introduces uncertainty into the results. Imaging noise will translate into noisy orientation estimates, and this will cause
streamlines to deviate from their true trajectory. In general, any measurement will be contaminated by noise to some extent, and diffusion imaging is no exception. However, the effect of noise on fiber-tracking results is altogether different, and its impact can be profound. This is due to the way streamlines propagate through the data, visiting many different voxels and therefore accumulating errors from each noisy orientation estimate as tracking proceeds. This accumulation effect is compounded by the fact that streamlines that deviate into adjacent structures may then delineate a completely different path; given the size of most white matter structures, even a relatively small deviation of a few millimeters could therefore have a dramatic effect on the results. Another source of uncertainty is the intrinsic angular resolution of the DW signal, as illustrated in Figure 5. The signal varies smoothly as a function of orientation, and this means that we can only obtain ‘blurred’ estimates of fiber orientations. This is particularly relevant for higher-order models that aim to characterize the fiber orientation distribution. Most implementations simply extract the peak(s) of this blurred distribution, which not only provides much tighter estimates but also imposes the assumption that fibers from the same bundle are completely straight and parallel within a voxel. This may be a good approximation in many regions of the white matter, but there will undoubtedly be regions where this assumption does not hold. A number of methods have been proposed to deal with uncertainty in fiber tracking. In general, the idea is to provide an estimate of all the paths originating from the seed point(s) that are plausible given the data and its uncertainty, rather than a single ‘best-guess’ path. This is akin to providing the confidence interval of a measurement, in addition to its actual estimate. In general, a measurement is not informative without an idea of its confidence interval, since we cannot otherwise assess whether an observed difference in the measurement is significant or relevant. This is also true of tractography, with the additional problem that a confidence interval on a trajectory is quite difficult to envisage: there is no simple scalar estimate of the ‘standard deviation’ or ‘confidence interval’ of a path. The way this uncertainty is typically represented in fiber tracking is by generating an estimate of the distribution of possible paths, approximated by a set of representative trajectories. This is akin to approximating a normal distribution as a set of representative samples drawn from the distribution, as illustrated in Figure 6. This nonparametric approach is in fact much more general than using parametric measures such as the
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INTRODUCTION TO METHODS AND MODELING | Fiber Tracking with DWI
Fiber configuration
DW signal
Fiber ODF
Figure 5 The intrinsic angular resolution of the DW signal itself introduces uncertainty as to the exact fiber configuration. The three configurations on the left are all predominantly aligned left–right, and consequently, the DW signal intensity is smallest along that axis (middle). The DW signal is inherently broad, and this essentially blurs the signal. This means that the DW signal for the three configurations shown will be essentially identical, and consequently, the estimated diffusion or fiber orientation density function (ODF) will be the same in all three cases. The practice of using the peak orientation of the fiber or diffusion ODF as the ‘best’ fiber orientation estimate is appealing as it provides much ‘tighter’ results, but this is only valid for one of the three configurations shown. It is clear that some ambiguity remains as to what the true fiber orientations are, and this source of uncertainty should be included in probabilistic algorithms.
Figure 6 Any distribution can be approximated using a set of representative samples. A Gaussian distribution (left) can be represented by a set of values drawn at random from its probability density function (PDF); any property of the distribution can then be computed in a straightforward manner from these samples (mean, standard deviation, etc.). While this is needlessly complex for a Gaussian distribution, this approach can be used to represent much more complex, multimodal distributions for which no simple model exists, such as the distribution of streamline trajectories from a given seed point, as shown on the right. The most likely path (blue), as might be obtained using deterministic approaches, can be viewed as being the ‘mean’ of the distribution. As shown in this illustration, this most likely path may be very different from some of the other possible paths. This information is not available using deterministic approaches, yet knowledge of these other likely paths may significantly influence interpretation and/or the decision-making process.
standard deviation, since it can be applied to any type of data, regardless of whether or not they can be approximated by a normal distribution. This approach is therefore much more suitable for fiber tracking, since streamlines clearly cannot be assumed to originate from a Gaussian distribution. The most common approach to estimating uncertainty in fiber tracking is the concept of probabilistic streamlines. These extend the simple deterministic streamline approach by following a random orientation sample from within the range of possible orientations, rather than a single ‘peak’ orientation, as illustrated in Figure 7. This means that each successive streamline will take a slightly different path through the data that nonetheless remain consistent with the estimated orientations and their associated uncertainty. These methods therefore rely on the availability of an estimate of the uncertainty around each fiber orientation. Various methods exist for this step, including bootstrap approaches (Berman et al., 2008; Haroon et al., 2009;
Figure 7 The streamline algorithm can also be extended to take the various sources of uncertainty into account. As before, tracking is initiated from the user-defined seed point (arrow) and proceeds by taking small steps along the local fiber orientation estimate. In this case, however, the fiber orientation estimate used is taken from the range of likely possible orientations at this location, by drawing a random sample from the probability density function (PDF) of the fiber orientation. This generally incorporates a curvature constraint by ensuring that the fiber orientation sample is taken from within a ‘cone of uncertainty’ (Jones, 2003) about the current direction of tracking. By generating a large number of such streamlines, an approximation to the distribution of possible paths is produced.
Jeurissen et al., 2011; Jones, 2008; Whitcher, Tuch, Wisco, Sorensen, & Wang, 2008) and various modeling approaches including Markov chain Monte Carlo (MCMC) (Behrens, Johansen-Berg, et al., 2003; Behrens, Woolrich, et al., 2003; Behrens et al., 2007; Hosey, Harding, Carpenter, Ansorge, & Williams, 2008; Hosey, Williams, & Ansorge, 2005).
Conclusion Diffusion MRI fiber tracking is clearly a very exciting technology, being the only method that can be used to delineate white
INTRODUCTION TO METHODS AND MODELING | Fiber Tracking with DWI matter pathways in the human brain in vivo. It is also a very efficient method, since the same dataset can be used to delineate any white matter pathway (within the limitations of the data quality and reconstruction approach used), in contrast to tracer studies that can typically only be used to trace one pathway at a time. For this reason, it has very rapidly been adopted by neuroscientists and clinicians. However, it is also clear that fiber tracking is not without its limitations and idiosyncrasies, and this unfortunately makes it very easy for inexperienced users to come to the wrong conclusions. It is therefore essential that scientists and clinicians become well acquainted with the methods and particularly with their limitations before applying them in practice.
See also: INTRODUCTION TO ACQUISITION METHODS: Diffusion MRI; INTRODUCTION TO METHODS AND MODELING: Diffusion Tensor Imaging; Probability Distribution Functions in Diffusion MRI; Q-Space Modeling in DiffusionWeighted MRI.
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