Elsevier

NeuroImage

Volume 109, 1 April 2015, Pages 341-356
NeuroImage

Fiber estimation and tractography in diffusion MRI: Development of simulated brain images and comparison of multi-fiber analysis methods at clinical b-values

https://doi.org/10.1016/j.neuroimage.2014.12.060Get rights and content

Highlights

  • Development of simulated diffusion-weighted brain images based on in-vivo data.

  • Improvements in fiber estimation engendered more complete white-matter pathways.

  • Accurate fiber estimation essential to tractography through complex crossing-regions.

  • Non-negativity constrained super-resolved spherical deconvolution yielded best results on clinical diffusion-weighted data.

Abstract

Advances in diffusion-weighted magnetic resonance imaging (DW-MRI) have led to many alternative diffusion sampling strategies and analysis methodologies. A common objective among methods is estimation of white matter fiber orientations within each voxel, as doing so permits in-vivo fiber-tracking and the ability to study brain connectivity and networks.

Knowledge of how DW-MRI sampling schemes affect fiber estimation accuracy, tractography and the ability to recover complex white-matter pathways, differences between results due to choice of analysis method, and which method(s) perform optimally for specific data sets, all remain important problems, especially as tractography-based studies become common.

In this work, we begin to address these concerns by developing sets of simulated diffusion-weighted brain images which we then use to quantitatively evaluate the performance of six DW-MRI analysis methods in terms of estimated fiber orientation accuracy, false-positive (spurious) and false-negative (missing) fiber rates, and fiber-tracking. The analysis methods studied are: 1) a two-compartment “ball and stick” model (BSM) (Behrens et al., 2003); 2) a non-negativity constrained spherical deconvolution (CSD) approach (Tournier et al., 2007); 3) analytical q-ball imaging (QBI) (Descoteaux et al., 2007); 4) q-ball imaging with Funk–Radon and Cosine Transform (FRACT) (Haldar and Leahy, 2013); 5) q-ball imaging within constant solid angle (CSA) (Aganj et al., 2010); and 6) a generalized Fourier transform approach known as generalized q-sampling imaging (GQI) (Yeh et al., 2010). We investigate these methods using 20, 30, 40, 60, 90 and 120 evenly distributed q-space samples of a single shell, and focus on a signal-to-noise ratio (SNR = 18) and diffusion-weighting (b = 1000 s/mm2) common to clinical studies.

We found that the BSM and CSD methods consistently yielded the least fiber orientation error and simultaneously greatest detection rate of fibers. Fiber detection rate was found to be the most distinguishing characteristic between the methods, and a significant factor for complete recovery of tractography through complex white-matter pathways. For example, while all methods recovered similar tractography of prominent white matter pathways of limited fiber crossing, CSD (which had the highest fiber detection rate, especially for voxels containing three fibers) recovered the greatest number of fibers and largest fraction of correct tractography for complex three-fiber crossing regions.

The synthetic data sets, ground-truth, and tools for quantitative evaluation are publically available on the NITRC website as the project “Simulated DW-MRI Brain Data Sets for Quantitative Evaluation of Estimated Fiber Orientations” at http://www.nitrc.org/projects/sim_dwi_brain.

Introduction

Diffusion-weighted MRI (DW-MRI) (Beaulieu, 2002, LeBihan et al., 1986) is a unique imaging modality in which the diffusion of water molecules is used as a non-invasive probe of tissue microstructure. In this work, we are particularly interested in the utility of DW-MRI to infer the orientation of coherently oriented bundles of axons in the brain's white-matter. By application of fiber-tracking algorithms (Mori and van Zijl, 2002) the orientation information can be used to generate so-called tractograms, which are depictions of estimated white-matter connections between populations of neurons in gray-matter (Conturo et al., 1999, Mori et al., 1999).

In recent years tractography has found extensive application. A not exhaustive list includes neuroanatomical studies and atlases (e.g. Catani and Thiebaut de Schotten, 2008), neurosurgical planning (e.g. Golby et al., 2011) and post-surgery evaluation, and many aspects of assessment and study of neurological diseases such as multiple sclerosis (e.g. Mesaros et al., 2012), Alzheimer's disease (e.g. Morikawa et al., 2010) and schizophrenia (e.g. Voineskos et al., 2010). Tractography has also been instrumental in neurobehavioral modeling, where, for example, it contributed to an improved model of the limbic system (Catani et al., 2013). More recently tractography has been used to identify auditory pathways between the auditory thalamus/brainstem and different areas of auditory analysis in the cortex (Javad et al., 2014). Such non-invasive assessment of white-matter morphology could improve the prognosis of recovery of useful hearing following cochlear implantation, as the latter is influenced by the integrity of subcortical pathways (Vlastarakos et al., 2010). Last, white-matter tractography permits in-vivo graph theoretical analysis of structural brain networks (Bullmore and Sporns, 2009), and as such fulfills a fundamental role in mapping the human connectome (Toga et al., 2012).

An important step towards further clinical application of tractography is a broader understanding of how the data acquisition, analysis method and fiber-tracking algorithm each affect track reconstruction. Also, it is beneficial to know which analysis method yields the most complete and accurate tractography when applied to DW data acquired with a particular set of parameters. While tractography is strongly dependent on the fiber-tracking algorithm itself, results are fundamentally determined by the DW-MRI analysis methods' ability to resolve crossing fibers and provide accurate estimates of their orientations. Development of appropriate synthetic DW-MRI data sets with ground-truth and quantitative metrics for evaluating the fiber estimation performance of multi-fiber analysis methods, and an examination of how results impact tractography, is the focus of this paper.

The most common approach to DW-MRI analysis is diffusion tensor imaging (DTI) (Basser et al., 1994a, Basser et al., 1994b, Basser and Pierpaoli, 1996), which models the diffusion of water molecules by a single rank-2 tensor (a 3 × 3 symmetric matrix). The method is popular because considerable quantitative information, such as fractional anisotropy (FA), mean diffusivity (MD) and white-matter fiber orientation, can be obtained robustly from relatively small data sets (Jones, 2004). However, DTI is limited to modeling a single-fiber orientation per voxel and is therefore incapable of resolving complex intra-voxel geometry such as crossing-fibers (Alexander et al., 2002, Frank, 2001, Tuch et al., 2002), which are thought to occur in at least one-third of voxels in white-matter (Behrens et al., 2007). To overcome this problem, many alternative multi-fiber analysis methods have been proposed.

The alternatives include high-angular resolution diffusion imaging (HARDI) methods such as a family of q-ball imaging (Canales‐Rodríguez et al., 2009, Descoteaux et al., 2007, Hess et al., 2006, Michailovich and Rathi, 2010, Tuch, 2004) and many other variants of the methods listed here, spherical deconvolution approaches (Dell'Acqua et al., 2010, Tournier et al., 2004, Tournier et al., 2007) which sample single or multiple shells in q-space, and methods based on Cartesian sampling schemes of q-space such as diffusion spectrum imaging (DSI) (Tuch et al., 2003, Wedeen et al., 2005, Wedeen et al., 2008), DSI with partial sampling schemes (Kuo et al., 2013, Yeh et al., 2008), and related variant (Canales-Rodríguez et al., 2010). This list is not exhaustive and a great many other model and non-model based methods exist; see e.g. Assemlal et al. (2011) and Haldar and Leahy (2013) for a more comprehensive list and theoretical differences.

As multi-fiber analysis is a relatively young field, much of the initial work has focused on development of new methods, which are often presented with simulation studies for comparison against a few alternatives. However, differences in signal models, simulation parameters and/or evaluation metrics usually prevent a broader comparison of similar work. Combined with variations in data sets (e.g. number and magnitude of diffusion-weighting directions, or SNR), often it remains unclear whether new methods are improvements over existing approaches, and if so, under what conditions.

Many diffusion phantoms have been developed for validation of DW-MRI analysis methods, such as biological phantoms constructed from a rat's spinal cord (Campbell et al., 2005), spherical (Moussavi‐Biugui et al., 2011) or straight (Pullens et al., 2010) crossings of polyester fibers, and planar phantoms of various materials including water-filled plastic capillaries (Tournier et al., 2008), permeable Rayon fibers (Perrin et al., 2005), solid acrylic fibers (Poupon et al., 2008), polyethylene fibers (Farrher et al., 2012), and many more. These phantoms have generally consisted of simple geometries (e.g. a single crossing-fiber region) for basic DW-MRI validation purposes, and as such have not been used for detailed characterization and comparison of analysis methods.

The “Fiber Cup” phantom (Fillard et al., 2011, Poupon et al., 2010) and contest (MICCAI 2009 conference, http://www.lnao.fr/spip.php?rubrique79) was purposely developed to address the lack of a publicly available diffusion-weighted data set including tractography ground-truth and evaluation tools to aid comparison of analysis methods. The Fiber Cup is a planar phantom with fiber configurations modeled from a coronal cross-section of the brain. Overall it consists of seven fiber branches having three fiber crossings, one merging/diverging region, and one fiber splitting region. As Fiber Cup data is publicly available it has been frequently used for both qualitative and quantitative evaluation of DW-MRI analysis methods and tractography. In addition, an online tool “Tractometer” (Côté et al., 2013; http://tractometer.org) is available for connectivity-based evaluation of reconstructed Fiber Cup tracks, permitting extensive comparison of data analysis methods and tractography algorithms.

Fiber Cup is geared towards tractography evaluation however, and as such is not suited to detailed characterization of fiber estimation performance — the phantom has few crossing angles, and without a ground-truth of orientations it is impossible to quantify the accuracy of estimated fibers. Furthermore, one cannot distinguish between estimated fibers that are representative of the ground-truth, or are artifacts of the analysis method. A more recent “HARDI reconstruction challenge” (ISBI 2012 conference, http://hardi.epfl.ch/static/events/2012_ISBI; Daducci et al., in press) attends to these issues by the use of simulated DW phantoms which offer considerable versatility (e.g. choice of signal model, diffusion sampling schemes, signal to noise ratio, and known fiber ground-truth) over physical phantoms, albeit over-simplifying the real diffusion process and MR signal. In comparison to Fiber Cup, the HARDI challenge focuses exclusively on intra-voxel multi-fiber estimation.

The contributions of this work are two-fold. First is the development of synthetic brain-like diffusion-weighted data sets based on a ground-truth of fiber orientations estimated from in-vivo data, in conjunction with quantitative measures associated with fiber detection accuracy (false-positives, false-negatives, and individual fiber orientation error) and tractography. Second is application of synthetic data resembling a typical clinical acquisition to compare six well-known DW-MRI analysis methods.

Developing the ground-truth from in-vivo data has the advantage of preserving realistic crossing-fiber configurations, and ability to observe the implications of fiber estimation accuracy on tractography, which is of crucial importance to brain network and human connectome studies (Bastiani et al., 2012, Cheng et al., 2012, Gigandet et al., 2013). Furthermore, both Fiber Cup and HARDI reconstruction challenge data sets contain large fiber tracks (at least 3 voxels in width) with adjacent slices having identical structure. This means each voxel is surrounded by a neighborhood of similar or identical voxels which is unrealistic of real white-matter configurations and could bias analysis methods that make use of neighborhood information. We avoid this problem and preserve realistic neighborhood information by deriving the ground-truth from in-vivo data.

While several aspects of our work are similar to those of the HARDI reconstruction challenge (Daducci et al., in press), such as the choice of fiber estimation metrics, there are important differences between the simulation models and the overall goals. Specifically, we include a free diffusion compartment in the signal model to accommodate sources of isotropic diffusion, as well as T2-weighting MR signal decay, which both impact fiber estimation accuracy, even in the simple case of single fiber estimation. Overall, our goal is to determine which analysis method is optimal for clinically acquired data, whereas in Daducci et al. (in press) each method is evaluated with a custom (optimal) data set, meaning the outcomes reflect the best possible result for each analysis method.

A previous simulation study (Ramirez-Manzanares et al., 2011) evaluated several HARDI-based methods using model and non-model based techniques for synthesizing clinical-like DW-MRI data at different SNR, however the compartment sizes for individual fibers were fixed to few discrete values and did not accommodate free diffusion, fiber crossing angles were limited to ≥ 30° for voxels with 2 fibers and fixed to 90° for voxels with 3 fibers, and no T2-weighting of the MR signal was present. By developing our simulation from in-vivo data we were able to avoid such constraints, leading to more comprehensive evaluation.

After generating the synthetic data we compare the following six multiple-fiber diffusion analysis methods: 1) a two-compartment “ball and stick” model (BSM) (Behrens et al., 2003); 2) a non-negativity constrained spherical deconvolution (CSD) approach (Tournier et al., 2007); 3) analytical q-ball imaging (QBI) (Descoteaux et al., 2007); 4) q-ball imaging with Funk–Radon and Cosine Transform (FRACT) (Haldar and Leahy, 2013); 5) q-ball imaging within constant solid angle (CSA) (Aganj et al., 2010); and 6) a generalized Fourier transform approach known as generalized q-sampling imaging (GQI) (Yeh et al., 2010). To investigate the effect of diffusion sampling each method is evaluated using 20, 30, 40, 60, 90 and 120 evenly distributed q-space samples of a single shell, at an SNR = 18 and diffusion-weighting (1000 s/mm2) common to clinical studies.

Section snippets

Material and methods

In this section we establish the ground-truth, define the data synthesis model, and present the quantitative metrics for comparison of results.

Results and discussion

In this section we define parameters used for the data synthesis and analysis, provide a brief qualitative comparison of results obtained from processing in-vivo and corresponding synthetic data as an example of the data being generated and processed in this study, and finally present a detailed discussion of the quantitative findings of our study.

Conclusion

Diffusion-weighted MRI uniquely has the potential to reveal the human brain's white-matter connectivity in-vivo, and as such it is being enthusiastically applied to a broad range of problems in neuroscience and clinical research. As the field has matured, advances in diffusion signal modeling and analysis have led to many alternative diffusion sampling strategies and analysis methodologies. For the researcher, it can be difficult to choose the optimal method for analyzing their data from the

Acknowledgments

We thank Richard Leahy and Justin Halder for their significant advice on methodology and support during the early stage of this work. Constrained spherical deconvolution, ball and stick modeling, and QBI within constant solid angle were performed using MRtrix (http://www.brain.org.au/software), FSL (http://www.fmrib.ox.ac.uk/fsl), and code by Iman Aganj, respectively. We additionally thank Iman for generous assistance with the CSA method. Illustrations of tractography were prepared using

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