Tractography uses diffusion-weighted magnetic resonance imaging ( diffusion MRI ) data to identify specific white matter fascicles as well as the connections these fascicles make between cortical regions 1–6 ., Specifying the pattern of connections between brain regions ( “connectome” ) is a fundamental goal of neuroscience 7–9 ., One of the major goals of tractography is to establish a model of the complete collections of white matter tracts and connections ( “structural connectome” , also referred as “tractogram” ) in the human brain ., Hereafter , we refer to structural connectomes estimated using tractography as “connectomes” or “connectome models” ., A variety of tractography algorithms are in wide use 10–18 ( see “Related literature” in Discussion ) ., These algorithms calculate streamlines ( also called “estimated fascicles” ) through the white matter using somewhat different principles ., Some tractography methods ( local tractography ) calculate streamlines by tracking the orientation of diffusion signal locally and step-wise based on deterministic 10 , 19–21 or probabilistic selection methods 11 , 12 ., Other tractography methods ( global tractography ) reconstruct the trajectory of streamlines based on goodness-of-fit to diffusion signals 16 , 22–31 ., Each algorithm offers some advantages and disadvantages ., For any tractography method , investigators must set parameter values ., Key tractography parameters include maximum and minimum streamline length , seed selection , and stopping criteria for terminating a streamline , and the minimum radius of curvature allowed for building each streamline ., Differences in parameter values yield differences in streamlines 32–39 ., The parameter dependency of tractography has been observed in both local and global tractography algorithms 34 ., In common practice , investigators choose an algorithm and set fixed parameter values in the hope of optimizing streamlines for general use ., However , recent studies 40 , 41 demonstrated that no algorithm or parameter values are optimal across all conditions ., Specifically , Chamberland and colleagues 41 show that the best choice depends on a variety of factors such as the specific region of white matter or the specific tract being studied ., For example , Fig 1 compares two tracts and shows how the best parameter value differs ., Tracts between nearby regions on the cortical surface have short association fibers with relatively high curvature ( U-fiber; left panels in Fig 1 ) ., To identify U-fibers investigators must set parameters that allow tracts with high curvature ( top panels in Fig 1 ) ., In contrast , the major fascicles of the brain , such as the Inferior Longitudinal Fasciculus ( ILF ) or the Superior Longitudinal Fasciculus ( SLF ) , have relatively long and straight cores ., Better estimates of the core of these tracts are obtained by sampling streamlines with relatively low curvature ( middle panels in Fig 1 ) ., Additional factors affecting the optimal parameter choice for streamline generation may include diffusion MRI acquisition parameters ( e . g . , b-value , voxel size and angular resolution ) ., In general , no single parameter value may capture the full range of streamlines globally in every brain ., In the machine learning and statistical classification literature , it has been shown that for large and heterogeneous data sets combining multiple types of classifiers improves performance over single classifier methods ( Ensemble methods 42–44 , see 45 for a review ) ., The human white matter provides similar challenges , because it contains large sets of heterogeneous fascicles different in length , volume and curvature ., Given the complexity of human white matter , ensemble methods incorporating a range of tractography algorithms and parameters may be a valuable approach for improving tractography performance ., The idea of incorporating tracts from multiple sources in the initial construction of a connectome has been suggested in earlier publications 27 , 31 ., We describe an ensemble method , which we call Ensemble Tractography ( ET ) , to reduce problems arising from single algorithm and parameter selection ., We illustrate the method with an example that addresses the parameter selection problem ., First , we create a set of connectomes , each generated using a different parameter setting ., These are called single parameter connectomes ( SPCs ) ., We then combine streamlines from multiple SPCs into a new candidate connectome , and we use Linear Fascicle Evaluation ( LiFE 46 ) to optimize this connectome and eliminate redundant streamlines ., We call the result the Ensemble Tractography Connectome ( ETC ) ., Fig 2 shows a flow diagram of the ET algorithm ., We report two key findings ., ETCs ( 1 ) include streamlines that span a wider range of curvatures as compared to any of the SPCs , including both short- and long-range fibers ( bottom panel in Fig 1 ) , and ( 2 ) ETCs predict the diffusion signal more accurately than any SPC ., To support reproducible research , the algorithm implementation and example data sets are made available at an open website ( http://purl . stanford . edu/qw092zb0881 ) ., We now return to the example in Fig 1 ., All connectomes in Fig 1 were optimized using LiFE ., The left-panels show U-fibers connecting two adjacent cortical regions , V3A/B and V3d ( see Materials and Methods and S1 Fig ) ., The SPCs with high ( 1/0 . 25 mm ) and low ( 1/2 mm ) curvature parameters return very different results ., The high curvature parameter SPC includes many streamlines , and the low curvature SPC has very few streamlines ., The right-panels show estimates of the relatively long-range projections that make up the inferior longitudinal fasciculus ( ILF ) ., In this case the situation is reversed: the high curvature SPC has many fewer streamlines than the low curvature SPC ., Moreover , the terminations of these streamlines do not show the same branching pattern and do not extend into the occipital lobe ., The images in the bottom panels of Fig 1 show the streamlines in the optimized ETC ., The ETC model includes many U-fiber streamlines , similar to the 0 . 25 mm SPC ., The estimated ILF contains the same branching pattern that extends into the occipital lobe as the 2 mm SPC ., The color of the individual ETC streamlines indicates its SPC origin ., The ETC estimates of the U-fibers include streamlines mainly from SPC that permit high curvature ( 0 . 25 mm ) ., The optimized ILF includes streamlines mainly from SPCs with lower curvature ( 1 to 4 mm ) ., The ETC includes streamlines from all of the SPCs ., Nominally , the curvature parameter is a bound—one should not have higher curvature than the specified level 18 ., In practice , however , we find that the bound impacts many properties of the candidate connectome ., We illustrate the effect of the curvature threshold on each SPC in the occipital white matter of the 10 hemispheres in STN96 dataset ( Fig 3; see Materials and Methods; S2 Fig depicts white matter regions used for the analysis ) ., For each of the bounds we tested , the candidate and optimized connectome curvatures form compact , single-peaked distributions; the peak increases monotonically as the minimum radius of curvature increases ( see S3 Fig for distribution in candidate connectomes ) ., When the curvature bound is high ( small radius of curvature ) , the candidate connectome streamlines tend to have a relatively high mean curvature ., When the curvature bound is low ( high radius of curvature ) , the candidate connectome tends to have a relatively low mean curvature ., Thus , the curvature parameter is not simply a threshold; it influences the distribution of streamline curvatures in the optimized and candidate connectomes ., For this reason , setting a lenient bound on the curvature ( i . e . , a low value of the minimum radius of curvature ) does not yield a good representation of long-straight fascicles ( Fig 1 ) ., Conversely , setting a strict bound on the curvature ( i . e . , a high value of minimum radius of curvature ) eliminates U-fibers from the candidate connectome ., We confirmed that the lenient bound on the curvature does not produce many straight streamlines using other tractography algorithm implemented in a different software package ( PICo 11; S4 Fig , S1 Text , Section 1 ) ., To reduce the curvature bias present in each SPC , the candidate connectome for the ETC combines samples from multiple SPCs whose parameters span a significant curvature range ( thick orange line; Fig 3 ) ., Hence , the ETC strategy is effective in the sense that ETCs include streamlines with a broader range of curvatures ., The optimized ETC includes more streamlines than any of the optimized SPCs ( Fig 4a ) ., Importantly , nearly twice as many streamlines from the candidate ETC survive the LiFE process and contribute to the diffusion signal predictions ., Typically streamlines generated using whole brain tractography do not pass through all of the voxels in the white matter ., For very simple algorithms , such as deterministic tracking based on diffusion tensors 10 , as many as 17% of the white matter voxels contain no streamlines ( see S8c Fig ) ., We show that ETC streamlines pass through a larger percentage of white matter voxels than any of the individual SPCs ( Fig 4b ) ., The streamlines in SPCs ( based on CSD and probabilistic tractography methods 18 ) cover up to 95% of the white matter , whereas streamlines in the ETC cover up to 98% of the white matter ., Because in reality the entire white matter volume contains streamlines , this result suggests that ET recovers more information from the diffusion data ., The failure to find streamlines in about 2% of the voxels shows that we continue to miss some fascicles ., While the number of ETC streamlines is nearly twice the number in any SPC , the white matter coverage is only about 3 percent greater ., It follows that the number of streamlines per white matter voxel in the ETC is larger than the number in any of the SPCs ., Whereas the mean number of streamlines per voxel in the SPCs is around 13 , the mean in the ETC is nearly 18 ., Fig 4c shows a histogram that counts the number of streamlines in each voxel , comparing the 2 mm SPC and the ETC ., Notice that many of the voxels ( 77 . 9% voxels on average ) have more streamlines in the ETC ., The larger number of streamlines within each voxel implies that the ETC streamlines can predict more complex diffusion orientation distribution functions ., S5 Fig describes the example crossing fascicle voxel in which ETC predicts diffusion signal significantly better than SPC ., This is because each streamline can point in a slightly different direction and thus potentially predict diffusion in more directions ., Coupled with the greater coverage across white matter voxels , the ETC should be able to provide a better prediction of the diffusion signal ., Next , we compare SPC and ETC connectome accuracy ( Fig 5 ) ., Accuracy is evaluated as the ratio of root mean square error between model and data to the test-retest reliability ( Rrmse 46–48; see Eq 3 in Materials and Methods ) ., Fig 5a shows a two-dimensional histogram comparing the accuracy of the ETC and the 2 mm SPC in a single , typical subject ., For large portions of the white matter ( 62 . 4% voxels in Fig 5a ) , accuracy is higher ( Rrmse lower ) for the ETC than the SPC ., Fig 5b describes the median Rrmse of the 6 connectome models ( SPC; 0 . 25 , 0 . 5 , 1 , 2 and 4 mm and ETC ) across all ten occipital lobes ., The median ETC accuracy is significantly higher than any of the SPCs ., S6 Fig compares the prediction accuracy of ETC and SPC ( 2 mm ) and tests whether increasing the size of the candidate SPC reduces the primacy of the ETC over the SPC ( see S1 Text , Section 2 ) ., In this comparison , we matched the size of candidate SPC to that of ETC ( 800 , 000 streamlines; BigSPC model; see S1 Text , Section 2 ) ., The optimized BigSPC supports as many streamlines as the ETC ( S6b Fig ) but the ETC covers a larger portion of the total white matter volume ( S6c Fig ) ., Importantly , the prediction accuracy of ETC is consistently higher than BigSPC ( S6d Fig; see S6e Fig for comparison in individual hemispheres ) ., Fig 6 compares connectome model accuracy between different white matter pathways ( U-fiber and the ILF , as shown in Fig 1 ) ., We compared the accuracy of six connectome models in the voxels defined by the best U-fiber ( Fig 6a , left , ETC U-fiber ) and ILF ( Fig 6b , left , ETC ILF ) within the same hemisphere of the same subject ., In all SPC models , 0 . 25 mm curvature threshold produces the best performance as compared with other thresholds in the U-fiber voxels , whereas the 4 mm SPC performs better than others in the ILF voxels ( Fig 6b ) ., This shows that the best SPC differs between white matter pathways and brain volumes ., In both U-fiber and the ILF , ETC model performs similarly or better than the best SPC model ( Fig 6 ) ., Testing the ETC performance in the total white matter volume is computationally demanding , because of the increase of the matrix size in LiFE with ET ( see the recent paper 49 for computational load of LiFE ) ., For example , if we combine five whole-brain SPCs including 2 million streamlines , the candidate ETC size is 10 million streamlines ., In order to generate whole-brain ETC model , we used the ETC-preselection method ( see S1 Text , Section 5 ) ., Briefly , we selected streamlines from each SPC with highest weight ( best contributing to predicting the diffusion signal ) to build the candidate ETC ., This ETC-preselection method reduces the size of the candidate ETC , but produces better prediction accuracy as compared with any SPC ( S10 Fig ) ., Using ETC-preselection method , we optimized the whole-brain ETCs in five brains ( Fig 7 ) ., We compared properties of preselected ETC with those of the SPCs ., Consistent with results in occipital white matter ( Figs 4 and 5 ) , the whole-brain ETC supports a larger number of streamlines ( Fig 7a ) , covers larger portion of white matter ( Fig 7b ) and predicts the diffusion signal better than any of the SPCs ( Fig 7c ) ., Fig 7d shows maps of measured ( Data 1 and 2 ) and predicted diffusion signal for a single diffusion direction using two connectome models ( SPC 0 . 25 mm and ETC with preselection ) ., The result suggests that the ET approach is also effective for whole-brain connectome analysis ., We evaluated ET also using data from the Human Connectome Project ( HCP90 50; see Materials and Methods ) ., Consistent with results obtained on the STN96 data set , ET included a wider range of curvatures ( S7b Fig ) , increased streamline count and white matter coverage ( S7a and S7c Fig ) , and higher accuracy for predicting diffusion signal ( S7d Fig ) ., ETC on HCP90 dataset also supports example short- and long-range fascicles , U-fiber and the ILF ( S7e Fig ) , as identified on the STN96 data ., Thus , the properties of ET are consistent between these different datasets ., In addition to the ET method described above , we also used the ET method to create candidate connectomes that include streamlines from different algorithms ( Tensor deterministic , CSD deterministic and CSD probabilistic in MRtrix 18; see S1 Text , Section 3 ) ., The optimized connectomes from the ensemble of these algorithms had better prediction accuracy , and both increased streamline count and white matter coverage ( S8 Fig ) ., We also observed that the ETC generated using an ensemble of Fiber Orientation Distribution ( FOD ) amplitude cutoff parameters had better prediction accuracy as compared with SPCs ( S9 Fig; S1 Text , Section 4 ) ., Hence , we find substantial evidence across different diffusion datasets , tractography methods and parameters sets that ET improves the connectome model ., There is an enormous space of possible methods for creating candidate ETCs ., The method for creating ensembles will need to evolve over many experiments from different laboratories ., This paper presents one simple ET architecture that we found to be effective and efficient; just adding all streamlines from each parameter setting and optimize the ETC ., One of the disadvantages of the ETC method presented in this paper is the computational demand required in building large candidate sets ., In the following we discuss alternative architectures that we considered ., S1 Text ( Section 5 ) proposes one alternative ET method; ETC-preselection ., In this method , we chose 20% of streamlines contributing diffusion signal prediction from each of the individually optimized SPCs to build a new candidate ETC ., The advantage of this method is that the resulting size of new candidate ETC becomes equal to that of original candidate SPCs ., The disadvantage of this method is that we must evaluate ( using LiFE ) individually each SPC and also the ETC ., Our results show that ETC-preselection performs significantly better than SPCs , and only slightly worse than ETC without preselections ( S10 Fig ) ., Preselection is particularly useful for whole-brain models including large streamline sets ( Fig 7 ) , but not necessarily the best for connectome models with smaller size ., As it is impossible to evaluate all possible ET algorithms in an initial paper , we describe the method and provide an open-source implementation ( francopestilli . github . io/life/; github . com/brain-life/life/ ) to the community for exploration of the many possible options ., Several groups have analyzed tractography limitations , including parameter and algorithm dependence 32–40 ., Bastiani and colleagues 34 analyzed how parameter and tractography algorithms influence connectomes and network properties ., Their paper and others motivates the need for a means of deciding which solutions are best supported by the data 46 , 51–55 ( see also 56 ) ., Several other groups also noted that the best parameter differs between different white matter pathways 40 , 41 ., BlueMatter 27 used streamlines generated by three different algorithms ( STT 20 , TEND 21 , ConTrack 16 ) to create a candidate connectome ., An important difference is that the BlueMatter algorithm could only be run on a supercomputer ( BlueGene/L , a 2048-processor supercomputer with 0 . 5 TB of memory ) , while the current ET algorithm using LiFE runs on a personal computer 49 ., This advance enables investigators to systematically combine streamlines from many different parameters and algorithms and adopt ensemble tractography into their daily work flow ., This paper is the first systematic exploration to sweep out several key parameters ( curvature , stopping criterion ) in tractography and demonstrate the advantage of ensemble methods in terms of anatomy ( Fig 1 ) and prediction accuracy for diffusion signal ( Figs 5 and 7 ) ., A number of groups compared tractography with an independent measurement , such as invasive tract tracing or manganese enhanced MRI in macaques or mice 39 , 40 , 57–60 ., For example , Thomas et al . 22 collected a diffusion data set in one macaque and compared the results of several single parameter connectomes with tracer measurements from a different macaque ., This comparison has several limitations ., First , the tracer measurements depend upon factors including the tracer type ( e . g . , anterograde or retrograde ) and the selection of planes and injection sites; hence , they can differ substantially ( e . g . 61 , 62 ) ., When the methods disagree , it is often best to assemble a conclusion from multiple studies ., Second , comparisons in a particular data set do not guarantee validation in a different experiment ., For example , we cannot use high-resolution human adult brain fMRI data acquired in 7T scanner to support conclusions made from lower resolution fMRI data in children acquired using a 1 . 5 T scanner ., Each methodology requires means for stating both the conclusions and the strength of the support for those conclusions ., It is best to integrate fully justified findings derived by a variety of methods rather than discarding one method or another ., Others have proposed to evaluate tractography by defining ground truth using synthetic phantoms 31 , 63–66 ., Some investigators have pointed out the logical limitations of this approach 5 ., We agree that there are limitations to using phantoms for testing tractography but that in some cases synthetic phantoms can be valuable for analyzing computational methods ., Unfortunately , for our current work none of the currently available phantoms can be used ., This is because most phantoms have been generated using either single tractography parameters 67 or simple fiber configurations 63 ., Close and colleagues 68 provide software for generating numerical phantoms that can simulate complex fiber organization ., However , their method was not proposed to evaluate tractography performance by comparison with ground truth ., This fact makes it impossible for us to use the current phantoms to test the superiority of multiple tractography approaches such as ET to resolving multiple types of fiber configurations simultaneously ., The potential value of creating connectomes from a collection of tractography methods was mentioned by both Sherbondy et al . 27 and Lemkaddem et al . 31 ., Here , we provide a specific , open-source , implementation , and we begin a systematic analysis of this methodology ., The analyses show that ET based on sweeping out the curvature parameter has the specific benefit of creating connectomes with both short- and long-range fascicles ., In addition , the ET method produces more fascicles , larger coverage , and a better cross-validated prediction error ., In this paper , we described the advantage of combining multiple tractography parameters and algorithms in order to improve the accuracy of connectome models ., We use several example parameters and algorithms as a target for ET applications , and there are likely to be other beneficial combinations of algorithms and parameters which will be tested in future work ., For example , we could combine connectomes by sweeping out two different parameters , or combine connectomes generated by different software packages that implement different algorithms , or combine connectome generated by using different seeding strategy tested in the literature 38 , 65 , 69 ., Although it is impossible to test every pattern of combinations in this paper , we made LiFE software open ( http://francopestilli . github . io/life/; https://github . com/brain-life/life/ ) to help other researchers test different ET architectures ., Future studies by multiple research groups will clarify the optimal ET architecture in both model accuracy and computational efficiency ., ET will be generally applicable for many different proposed tractography algorithms ., Several groups proposed generating streamlines based on the goodness-of-fit on the local diffusion signals ( global tractography; 16 , 22–31 , 53 ) ., While global tractography has advantages compared with local tractography 70 , it too requires the user to set the parameters and this produces a parameter-selection dependency 34 ., The ET approach will be effective in supporting both local and global tractography ., Current tractography uses a fixed set of parameters to generate each streamline ., However , several fascicles , such as many within the optic radiation , include both curving and straight sections 71–74 ., When this is known a priori , it may be more accurate to change the tractography parameter along one fascicles , allowing high and low curvature in the relevant portions of the tract ., LiFE and ET will provide the opportunity to evaluate the model accuracy of new tractography tools in terms of the prediction accuracy on diffusion signal ., It is widely agreed that diffusion MRI contributes useful information about the large and long-range fasciculi in the human brain 75–78 ., Meanwhile , the existence of U-fiber system has been supported 79 , 80 , but not extensively studied in the literature presumably because of the limitations in tractography parameter selections ., The optimized ETCs extend tractography to include both long- and short-range fascicles in a single connectome , improving on the optimized SPCs which include one or the other ., The higher model-accuracy and the inclusion of both short- and long-range fibers is a validation that the optimized ETC improves on any SPC ., The preliminary ET results are encouraging , but they will surely benefit from further optimization ., Tracer studies are not well-suited to identifying long-range pathways in the human brain ., Even in animal models , with more than a century of history , recent tracer measurements challenge conventional thinking about long-range pathways ., Reports describing many new found projections demonstrate that the field is active and evolving 62 , 81 , 82 ., The progress in human tractography complements the strengths of tracer studies in animal models ., Ultimately , combining insights from these technologies will provide a more complete view of human brain anatomy and function ., We used two magnetic resonance diffusion imaging datasets ., The STN96 dataset was acquired at the Stanford Center for Neurobiological Imaging ( CNI ) ; the HCP90 dataset was acquired by the Human Connectome Consortium 50 ., We identified several tracts within each optimized connectome to compare how different connectome represents anatomical features of the white-matter fascicles ., All figures of brain anatomy and fascicles were made using Matlab Brain Anatomy ( www . github . com/francopestilli/mba ) ., We evaluated model accuracy for whole-brain connectomes ., To do so , we generated five 2-million streamlines candidate SPCs by using different curvature thresholds ( from 0 . 25 mm to 4 mm ) ., We then used LiFE to assign a weight to each streamline ., Next , we selected the top 400 , 000 streamlines with highest weight from each SPC ( preselection method; see S1 Text , Section 5 ) ., This resulted in an ETC connectome containing 2 million streamlines ., Finally , we optimized this ETC using LiFE ., The processing of one whole-brain connectome model with 2 million streamlines requires 28 . 4 hours on a computer with 16 processing cores and 32GB Random Access Memory ., The ILF extends outside the occipital white matter region used for the main analysis ( S2 Fig ) ., In order to evaluate the connectome model along these fascicles , we selectively fitted LiFE to white matter voxels containing these tracts ., To do so , we ( 1 ) identified the ILF from candidate connectome in all connectome models using the identification method described above , ( 2 ) concatenated all streamlines identified as ILF across multiple connectome models , ( 3 ) extracted the voxels in which any of streamlines are passing through ., Finally we obtained a white matter region covering the ILF ., LiFE analysis on the ILF is limited to these portions of white matter in all connectome models tested .
Tractography uses diffusion MRI to estimate the trajectory and cortical projection zones of white matter fascicles in the living human brain ., There are many different tractography algorithms and each requires the user to set several parameters , such as curvature threshold ., Choosing a single algorithm with specific parameters poses two challenges ., First , different algorithms and parameter values produce different results ., Second , the optimal choice of algorithm and parameter value may differ between different white matter regions or different fascicles , subjects , and acquisition parameters ., We propose using ensemble methods to reduce algorithm and parameter dependencies ., To do so we separate the processes of fascicle generation and evaluation ., Specifically , we analyze the value of creating optimized connectomes by systematically combining candidate streamlines from an ensemble of algorithms ( deterministic and probabilistic ) and systematically varying parameters ( curvature and stopping criterion ) ., The ensemble approach leads to optimized connectomes that provide better cross-validated prediction error of the diffusion MRI data than optimized connectomes generated using a single-algorithm or parameter set ., Furthermore , the ensemble approach produces connectomes that contain both short- and long-range fascicles , whereas single-parameter connectomes are biased towards one or the other ., In summary , a systematic ensemble tractography approach can produce connectomes that are superior to standard single parameter estimates both for predicting the diffusion measurements and estimating white matter fascicles .
Diffusion MRI and tractography opened a new avenue for studying white matter fascicles and their tissue properties in the living human brain ., There are many different tractography methods , and each requires the user to set several parameters ., A limitation of tractography is that the results depend on the selection of algorithms and parameters ., Here , we analyze an ensemble method , Ensemble Tractography ( ET ) , that reduces the effect of algorithm and parameter selection ., ET creates a large set of candidate streamlines using an ensemble of algorithms and parameter values and then selects the streamlines with strong support from the data using a global fascicle evaluation method ., Compared to single parameter connectomes , ET connectomes predict diffusion MRI signals better and cover a wider range of white matter volume ., Importantly , ET connectomes include both short- and long-association fascicles , which are not typically found together in single-parameter connectomes .
medicine and health sciences, diagnostic radiology, tractography, nervous system, applied mathematics, brain, neuroscience, cerebral hemispheres, occipital lobe, magnetic resonance imaging, algorithms, simulation and modeling, left hemisphere, brain morphometry, mathematics, brain mapping, neuroimaging, research and analysis methods, diffusion magnetic resonance imaging, imaging techniques, connectomics, radiology and imaging, diagnostic medicine, neuroanatomy, diffusion tensor imaging, anatomy, central nervous system, biology and life sciences, physical sciences, cerebral cortex