Estimation of fiber orientation and spin density distribution by diffusion deconvolution

Reduced structural integrity and functional lateralization of the dorsal language pathway correlate with hallucinations in schizophrenia: a combined diffusion spectrum imaging and functional magnetic resonance imaging study

Recent studies suggest that structural and functional alterations of the language network are associated with auditory verbal hallucinations (AVHs) in schizophrenia. However, the ways in which the underlying structure and function of the network are altered and how these alterations are related to each other remain unclear. To elucidate this, we used diffusion spectrum imaging (DSI) to reconstruct the dorsal and ventral pathways and employed functional magnetic resonance imaging (fMRI) in a semantic task to obtain information about the functional activation in the corresponding regions in 18 patients with schizophrenia and 18 matched controls. The results demonstrated decreased structural integrity in the left ventral, right ventral and right dorsal tracts, and decreased functional lateralization of the dorsal pathway in schizophrenia. There was a positive correlation between the microstructural integrity of the right dorsal pathway and the functional lateralization of the dorsal pathway in patients with schizophrenia. Additionally, both functional lateralization of the dorsal pathway and microstructural integrity of the right dorsal pathway were negatively correlated with the scores of the delusion/hallucination symptom dimension. Our results suggest that impaired structural integrity of the right dorsal pathway is related to the reduction of functional lateralization of the dorsal pathway, and these alterations may aggravate AVHs in schizophrenia.

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

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/mm(2)) 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.

Advanced diffusion MRI fiber tracking in neurosurgical and neurodegenerative disorders and neuroanatomical studies: A review

Diffusion MRI enabled in vivo microstructural imaging of the fiber tracts in the brain resulting in its application in a wide range of settings, including in neurological and neurosurgical disorders. Conventional approaches such as diffusion tensor imaging (DTI) have been shown to have limited applications due to the crossing fiber problem and the susceptibility of their quantitative indices to partial volume effects. To overcome these limitations, the recent focus has shifted to the advanced acquisition methods and their related analytical approaches. Advanced white matter imaging techniques provide superior qualitative data in terms of demonstration of multiple crossing fibers in their spatial orientation in a three dimensional manner in the brain. In this review paper, we discuss the advancements in diffusion MRI and introduce their roles. Using examples, we demonstrate the role of advanced diffusion MRI-based fiber tracking in neuroanatomical studies. Results from its preliminary application in the evaluation of intracranial space occupying lesions, including with respect to future directions for prognostication, are also presented. Building upon the previous DTI studies assessing white matter disease in Huntington's disease and Amyotrophic lateral sclerosis; we also discuss approaches which have led to encouraging preliminary results towards developing an imaging biomarker for these conditions.

Investigating the tradeoffs between spatial resolution and diffusion sampling for brain mapping with diffusion tractography: time well spent?

Interest in mapping white matter pathways in the brain has peaked with the recognition that altered brain connectivity may contribute to a variety of neurologic and psychiatric diseases. Diffusion tractography has emerged as a popular method for postmortem brain mapping initiatives, including the ex-vivo component of the human connectome project, yet it remains unclear to what extent computer-generated tracks fully reflect the actual underlying anatomy. Of particular concern is the fact that diffusion tractography results vary widely depending on the choice of acquisition protocol. The two major acquisition variables that consume scan time, spatial resolution, and diffusion sampling, can each have profound effects on the resulting tractography. In this analysis, we determined the effects of the temporal tradeoff between spatial resolution and diffusion sampling on tractography in the ex-vivo rhesus macaque brain, a close primate model for the human brain. We used the wealth of autoradiography-based connectivity data available for the rhesus macaque brain to assess the anatomic accuracy of six time-matched diffusion acquisition protocols with varying balance between spatial and diffusion sampling. We show that tractography results vary greatly, even when the subject and the total acquisition time are held constant. Further, we found that focusing on either spatial resolution or diffusion sampling at the expense of the other is counterproductive. A balanced consideration of both sampling domains produces the most anatomically accurate and consistent results.

Isotropic non-white matter partial volume effects in constrained spherical deconvolution

Diffusion-weighted (DW) magnetic resonance imaging (MRI) is a non-invasive imaging method, which can be used to investigate neural tracts in the white matter (WM) of the brain. Significant partial volume effects (PVEs) are present in the DW signal due to relatively large voxel sizes. These PVEs can be caused by both non-WM tissue, such as gray matter (GM) and cerebrospinal fluid (CSF), and by multiple non-parallel WM fiber populations. High angular resolution diffusion imaging (HARDI) methods have been developed to correctly characterize complex WM fiber configurations, but to date, many of the HARDI methods do not account for non-WM PVEs. In this work, we investigated the isotropic PVEs caused by non-WM tissue in WM voxels on fiber orientations extracted with constrained spherical deconvolution (CSD). Experiments were performed on simulated and real DW-MRI data. In particular, simulations were performed to demonstrate the effects of varying the diffusion weightings, signal-to-noise ratios (SNRs), fiber configurations, and tissue fractions. Our results show that the presence of non-WM tissue signal causes a decrease in the precision of the detected fiber orientations and an increase in the detection of false peaks in CSD. We estimated 35-50% of WM voxels to be affected by non-WM PVEs. For HARDI sequences, which typically have a relatively high degree of diffusion weighting, these adverse effects are most pronounced in voxels with GM PVEs. The non-WM PVEs become severe with 50% GM volume for maximum spherical harmonics orders of 8 and below, and already with 25% GM volume for higher orders. In addition, a low diffusion weighting or SNR increases the effects. The non-WM PVEs may cause problems in connectomics, where reliable fiber tracking at the WM-GM interface is especially important. We suggest acquiring data with high diffusion-weighting 2500-3000 s/mm(2), reasonable SNR (~30) and using lower SH orders in GM contaminated regions to minimize the non-WM PVEs in CSD.

Sparse solution of fiber orientation distribution function by diffusion decomposition

Fiber orientation is the key information in diffusion tractography. Several deconvolution methods have been proposed to obtain fiber orientations by estimating a fiber orientation distribution function (ODF). However, the L₂ regularization used in deconvolution often leads to false fibers that compromise the specificity of the results. To address this problem, we propose a method called diffusion decomposition, which obtains a sparse solution of fiber ODF by decomposing the diffusion ODF obtained from q-ball imaging (QBI), diffusion spectrum imaging (DSI), or generalized q-sampling imaging (GQI). A simulation study, a phantom study, and an in-vivo study were conducted to examine the performance of diffusion decomposition. The simulation study showed that diffusion decomposition was more accurate than both constrained spherical deconvolution and ball-and-sticks model. The phantom study showed that the angular error of diffusion decomposition was significantly lower than those of constrained spherical deconvolution at 30° crossing and ball-and-sticks model at 60° crossing. The in-vivo study showed that diffusion decomposition can be applied to QBI, DSI, or GQI, and the resolved fiber orientations were consistent regardless of the diffusion sampling schemes and diffusion reconstruction methods. The performance of diffusion decomposition was further demonstrated by resolving crossing fibers on a 30-direction QBI dataset and a 40-direction DSI dataset. In conclusion, diffusion decomposition can improve angular resolution and resolve crossing fibers in datasets with low SNR and substantially reduced number of diffusion encoding directions. These advantages may be valuable for human connectome studies and clinical research.

Differences Between Generalized Q-Sampling Imaging and Diffusion Tensor Imaging in the Preoperative Visualization of the Nerve Fiber Tracts Within Peritumoral Edema in Brain

BACKGROUND:

Diffusion tensor imaging (DTI) tractography enables the in vivo visualization of white matter tracts inside normal brain tissue, which provides the neurosurgeon important information to plan tumor resections. However, DTI is associated with restrictions in the resolution of crossing fibers in the vicinity of the tumor or in edema. We find that generalized q-sampling imaging (GQI) can overcome these difficulties and is advantageous over DTI for the tractography of the fiber bundle in peritumoral edema.

OBJECTIVE:

To demonstrate the differences between GQI and DTI in the preoperative mapping of fiber tractography in peritumoral edema of cerebral tumors, and discuss the clinical application of GQI in neurosurgical planning.

METHODS:

Five patients with brain tumors underwent 3-T magnetic resonance imaging scans, and the data were reconstructed by DTI and GQI. We adjusted the parameters and compared the differences between DTI and GQI in visualizing the fiber tracts in the peritumoral edema of cerebral tumors.

RESULTS:

GQI and DTI showed substantial differences in displaying the nerve fibers in the edema surrounding the tumor. The GQI tractography method could fully display existing intact fibers in the edema, whereas the fiber tracts in edema displayed by DTI tractography were incomplete, missing, or ruptured.

CONCLUSION:

GQI can visualize the tracts in the peritumoral edema of cerebral tumors better than DTI. Although GQI has many limitations, its future in the preoperative guidance of brain tumor lesions is promising.

Diffusion MRI connectometry automatically reveals affected fiber pathways in individuals with chronic stroke

Building a human connectome database has recently attracted the attention of many researchers, although its application to individual subjects has yet to be explored. In this study, we acquired diffusion spectrum imaging of 90 subjects and showed that this dataset can be used as a norm to examine pathways with deviant connectivity in individuals. This analytical approach, termed diffusion MRI connectometry, was realized by reconstructing patient data to a common stereotaxic space and calculating the percentile rank of the diffusion quantities with respect to those of the norm. The affected tracks were constructed with deterministic tractography using the local tract orientations with substantially low percentile ranks as seeds. To demonstrate the performance of the connectometry, we applied it to 7 patients with chronic stroke and compared the results with lesions shown on T₂-weighted images, apparent diffusion coefficient (ADC) maps, and fractional anisotropy (FA) maps, as well as clinical manifestations. The results showed that the affected tracks revealed by the connectometry corresponded well with the stroke lesions shown on T₂-weighted images. Moreover, while the T₂-weighted images, as well as the ADC and FA maps, showed only the stroke lesions, connectometry revealed entire affected tracks, a feature that is potentially useful for diagnostic or prognostic evaluation. This unique capability may provide personalized information regarding the structural connectivity underlying brain development, plasticity, or disease in each individual subject.

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Diffusion MRI connectometry can identify tracks with decreased connectivity.

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T₂-weighted images, and ADC, and FA maps show only the stroke lesions.

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Diffusion MRI connectometry reveals the entire affected pathways.

Mean apparent propagator (MAP) MRI: a novel diffusion imaging method for mapping tissue microstructure

Diffusion-weighted magnetic resonance (MR) signals reflect information about underlying tissue microstructure and cytoarchitecture. We propose a quantitative, efficient, and robust mathematical and physical framework for representing diffusion-weighted MR imaging (MRI) data obtained in "q-space," and the corresponding "mean apparent propagator (MAP)" describing molecular displacements in "r-space." We also define and map novel quantitative descriptors of diffusion that can be computed robustly using this MAP-MRI framework. We describe efficient analytical representation of the three-dimensional q-space MR signal in a series expansion of basis functions that accurately describes diffusion in many complex geometries. The lowest order term in this expansion contains a diffusion tensor that characterizes the Gaussian displacement distribution, equivalent to diffusion tensor MRI (DTI). Inclusion of higher order terms enables the reconstruction of the true average propagator whose projection onto the unit "displacement" sphere provides an orientational distribution function (ODF) that contains only the orientational dependence of the diffusion process. The representation characterizes novel features of diffusion anisotropy and the non-Gaussian character of the three-dimensional diffusion process. Other important measures this representation provides include the return-to-the-origin probability (RTOP), and its variants for diffusion in one- and two-dimensions-the return-to-the-plane probability (RTPP), and the return-to-the-axis probability (RTAP), respectively. These zero net displacement probabilities measure the mean compartment (pore) volume and cross-sectional area in distributions of isolated pores irrespective of the pore shape. MAP-MRI represents a new comprehensive framework to model the three-dimensional q-space signal and transform it into diffusion propagators. Experiments on an excised marmoset brain specimen demonstrate that MAP-MRI provides several novel, quantifiable parameters that capture previously obscured intrinsic features of nervous tissue microstructure. This should prove helpful for investigating the functional organization of normal and pathologic nervous tissue.

Linear transforms for Fourier data on the sphere: application to high angular resolution diffusion MRI of the brain

This paper presents a novel family of linear transforms that can be applied to data collected from the surface of a 2-sphere in three-dimensional Fourier space. This family of transforms generalizes the previously-proposed Funk-Radon Transform (FRT), which was originally developed for estimating the orientations of white matter fibers in the central nervous system from diffusion magnetic resonance imaging data. The new family of transforms is characterized theoretically, and efficient numerical implementations of the transforms are presented for the case when the measured data is represented in a basis of spherical harmonics. After these general discussions, attention is focused on a particular new transform from this family that we name the Funk-Radon and Cosine Transform (FRACT). Based on theoretical arguments, it is expected that FRACT-based analysis should yield significantly better orientation information (e.g., improved accuracy and higher angular resolution) than FRT-based analysis, while maintaining the strong characterizability and computational efficiency of the FRT. Simulations are used to confirm these theoretical characteristics, and the practical significance of the proposed approach is illustrated with real diffusion weighted MRI brain data. These experiments demonstrate that, in addition to having strong theoretical characteristics, the proposed approach can outperform existing state-of-the-art orientation estimation methods with respect to measures such as angular resolution and robustness to noise and modeling errors.

Estimation of fiber orientation by filtered q-ball imaging*

We proposed a filtered q-ball imaging (fQBI) method for the reconstruction of fiber orientation distribution function (ODF) together with the quantitative comparison to unfiltered QBI. The filter kernel increases the high angular frequency content that is beneficial for the angular resolution in resolving crossing fibers. Through a series of simulations using Monte-Carlo model, the angular resolution of fQBI was demonstrated better than traditional QBI but the deviation of fiber orientation estimate also becomes larger. The improvement of the angular resolution can also reduce the underestimation of separation angles as well as the bias of fiber orientation estimations. In conclusion, fQBI was demonstrated to improve the angular resolution of QBI in resolving crossing fibers. This improvement will be helpful to precisely reconstruct fiber tract and brain network in applications by QBI.

Structural human brain networks: hot topics in diffusion tractography

PURPOSE OF REVIEW

After more than 10 years of methodological developments and clinical applications, diffusion imaging tractography has reached a crossroad. Although the method is still in its infancy, the time has come to address some important questions. Can tractography reproduce reliably known anatomy or describe new anatomical pathways? Are interindividual differences, for example in tract lateralization, important to understand heterogeneity of clinical manifestations? Do novel tractography algorithms provide a real advantage over previous methods? Here we focus on some of the most exciting recent advancements in diffusion tractography and critically highlight their advantages and limitations.

RECENT FINDINGS

A flourishing of diffusion methods and models are bringing new solutions to the well known limitations of classical tractography based on the tensor model. However, these methods pose also new challenges and require the convergence and integration of different disciplines before they can replace what is currently widely available.

SUMMARY

Rigorous postmortem validation, clinical optimization and experimental confirmation are obligatory steps before advanced diffusion technologies can translate into clear benefits for neurological patients.

Diffusion spectrum MRI using body-centered-cubic and half-sphere sampling schemes

The optimum sequence parameters of diffusion spectrum MRI (DSI) on clinical scanners were investigated previously. However, the scan time of approximately 30 min is still too long for patient studies. Additionally, relatively large sampling interval in the diffusion-encoding space may cause aliasing artifact in the probability density function when Fourier transform is undertaken, leading to estimation error in fiber orientations. Therefore, this study proposed a non-Cartesian sampling scheme, body-centered-cubic (BCC), to avoid the aliasing artifact as compared to the conventional Cartesian grid sampling scheme (GRID). Furthermore, the accuracy of DSI with the use of half-sphere sampling schemes, i.e. GRID102 and BCC91, was investigated by comparing to their full-sphere sampling schemes, GRID203 and BCC181, respectively. In results, smaller deviation angle and lower angular dispersion were obtained by using the BCC sampling scheme. The half-sphere sampling schemes yielded angular precision and accuracy comparable to the full-sphere sampling schemes. The optimum b(max) was approximately 4750 s/mm(2) for GRID and 4500 s/mm(2) for BCC. In conclusion, the BCC sampling scheme could be implemented as a useful alternative to the GRID sampling scheme. Combination of BCC and half-sphere sampling schemes, that is BCC91, may potentially reduce the scan time of DSI from 30 min to approximately 14 min while maintaining its precision and accuracy.

White matter reorganization and functional response after focal cerebral ischemia in the rat

After stroke, the brain has shown to be able to achieve spontaneous functional recovery despite severe cerebral damage. This phenomenon is poorly understood. To address this issue, focal transient ischemia was induced by 60 min middle cerebral artery occlusion in Wistar rats. The evolution of stroke was followed using two magnetic resonance imaging modalities: diffusion spectrum imaging (acquired before, one and four weeks after stroke) and functional magnetic resonance imaging (acquired before and five weeks after stroke). To confirm the imaging observations, immunohistochemical staining for myelin, astrocytes and macrophages/microglia was added. At four weeks after stroke, a focal alteration of the diffusion anisotropy was observed between the ipsilesional ventricle and the lesion area. Using tractography this perturbation was identified as reorganization of the ipsilesional internal capsule. Functional imaging at five weeks after ischemia demonstrated activation of the primary sensorimotor cortex in both hemispheres in all rats except one animal lacking a functional response in the ipsilesional cortex. Furthermore, fiber tracking showed a transhemispheric fiber connection through the corpus callosum, which-in the rat without functional recovery-was lost. Our study shows the influence of the internal capsule reorganization, combined with inter-hemispheric connections though the corpus callosum, on the functional activation of the brain from stroke. In conclusion, tractography opens a new door to non-invasively investigate the structural correlates of lack of functional recovery after stroke.

Rethinking the role of the middle longitudinal fascicle in language and auditory pathways

The middle longitudinal fascicle (MdLF) was originally described in the monkey brain as a pathway that interconnects the superior temporal and angular gyri. Only recently have diffusion tensor imaging studies provided some evidence of its existence in humans, with a connectivity pattern similar to that in monkeys and a potential role in the language system. In this study, we combine high-angular-resolution fiber tractography and fiber microdissection techniques to determine the trajectory, cortical connectivity, and a quantitative analysis of the MdLF. Here, we analyze diffusion spectrum imaging (DSI) studies in 6 subjects (subject-specific approach) and in a template of 90 DSI studies (NTU-90 Atlas). Our tractography and microdissection results show that the human MdLF differs significantly from the monkey. Indeed, the human MdLF interconnects the superior temporal gyrus with the superior parietal lobule and parietooccipital region, and has only minor connections with the angular gyrus. On the basis of the roles of these interconnected cortical regions, we hypothesize that, rather than a language-related tract, the MdLF may contribute to the dorsal "where" pathway of the auditory system.

Connectivity of thalamo-cortical pathway in rat brain: combined diffusion spectrum imaging and functional MRI at 11.7 T

Fiber tracking in combination with functional MRI has recently attracted strong interest, as it may help to elucidate the structural basis for functional connectivities and may be selective in the determination of the fiber bundles responsible for a particular circuit. Diffusion spectrum imaging provides a more complex analysis of fiber circuits than the commonly used diffusion tensor imaging approach, also allowing the discrimination of crossing fibers in the brain. For the understanding of pathophysiological alterations during brain lesion and recovery, such studies need to be extended to small-animal models. In this article, we present the first study combining functional MRI with high-resolution diffusion spectrum imaging in vivo. We have chosen the well-characterized electrical forepaw stimulation paradigm in the rat to examine the thalamo-cortical pathway. Using the functionally activated areas in both thalamus and somatosensory cortex as seed and target regions for fiber tracking, we are able to characterize the fibers responsible for this stimulation pathway. Moreover, we show that the selection of the thalamic nucleus and primary somatosensory cortex on the basis of anatomical description results in a larger fiber bundle, probably encompassing connectivities between the thalamus and other areas of the somatosensory cortex, such as the hindpaw and large barrel field cortex.

High-Definition Fiber Tractography of the Human Brain

BACKGROUND:

High-definition fiber tracking (HDFT) is a novel combination of processing, reconstruction, and tractography methods that can track white matter fibers from cortex, through complex fiber crossings, to cortical and subcortical targets with subvoxel resolution.

OBJECTIVE:

To perform neuroanatomical validation of HDFT and to investigate its neurosurgical applications.

METHODS:

Six neurologically healthy adults and 36 patients with brain lesions were studied. Diffusion spectrum imaging data were reconstructed with a Generalized Q-Ball Imaging approach. Fiber dissection studies were performed in 20 human brains, and selected dissection results were compared with tractography.

RESULTS:

HDFT provides accurate replication of known neuroanatomical features such as the gyral and sulcal folding patterns, the characteristic shape of the claustrum, the segmentation of the thalamic nuclei, the decussation of the superior cerebellar peduncle, the multiple fiber crossing at the centrum semiovale, the complex angulation of the optic radiations, the terminal arborization of the arcuate tract, and the cortical segmentation of the dorsal Broca area. From a clinical perspective, we show that HDFT provides accurate structural connectivity studies in patients with intracerebral lesions, allowing qualitative and quantitative white matter damage assessment, aiding in understanding lesional patterns of white matter structural injury, and facilitating innovative neurosurgical applications. High-grade gliomas produce significant disruption of fibers, and low-grade gliomas cause fiber displacement. Cavernomas cause both displacement and disruption of fibers.

CONCLUSION:

Our HDFT approach provides an accurate reconstruction of white matter fiber tracts with unprecedented detail in both the normal and pathological human brain. Further studies to validate the clinical findings are needed.

Quantification of increased cellularity during inflammatory demyelination

Multiple sclerosis is characterized by inflammatory demyelination and irreversible axonal injury leading to permanent neurological disabilities. Diffusion tensor imaging demonstrates an improved capability over standard magnetic resonance imaging to differentiate axon from myelin pathologies. However, the increased cellularity and vasogenic oedema associated with inflammation cannot be detected or separated from axon/myelin injury by diffusion tensor imaging, limiting its clinical applications. A novel diffusion basis spectrum imaging, capable of characterizing water diffusion properties associated with axon/myelin injury and inflammation, was developed to quantitatively reveal white matter pathologies in central nervous system disorders. Tissue phantoms made of normal fixed mouse trigeminal nerves juxtaposed with and without gel were employed to demonstrate the feasibility of diffusion basis spectrum imaging to quantify baseline cellularity in the absence and presence of vasogenic oedema. Following the phantom studies, in vivo diffusion basis spectrum imaging and diffusion tensor imaging with immunohistochemistry validation were performed on the corpus callosum of cuprizone treated mice. Results demonstrate that in vivo diffusion basis spectrum imaging can effectively separate the confounding effects of increased cellularity and/or grey matter contamination, allowing successful detection of immunohistochemistry confirmed axonal injury and/or demyelination in middle and rostral corpus callosum that were missed by diffusion tensor imaging. In addition, diffusion basis spectrum imaging-derived cellularity strongly correlated with numbers of cell nuclei determined using immunohistochemistry. Our findings suggest that diffusion basis spectrum imaging has great potential to provide non-invasive biomarkers for neuroinflammation, axonal injury and demyelination coexisting in multiple sclerosis.

Nonparametric Bayesian inference of the fiber orientation distribution from diffusion-weighted MR images

Diffusion MR imaging provides a unique tool to probe the microgeometry of nervous tissue and to explore the wiring diagram of the neural connections noninvasively. Generally, a forward model is established to map the intra-voxel fiber architecture onto the observable diffusion signals, which is reformulated in this article by adopting a measure-theoretic approach. However, the inverse problem, i.e., the spherical deconvolution of the fiber orientation density from noisy MR measurements, is ill-posed. We propose a nonparametric representation of the tangential distribution of the nerve fibers in terms of a Dirichlet process mixture. Given a second-order approximation of the impulse response of a fiber segment, the specified problem is solved by Bayesian statistics under a Rician noise model, using an adaptive reversible jump Markov chain Monte Carlo sampler. The density estimation framework is demonstrated by various experiments with a diffusion MR dataset featuring high angular resolution, uncovering the fiber orientation field in the cerebral white matter of the living human brain.

Ball and rackets: Inferring fiber fanning from diffusion-weighted MRI

A number of methods have been proposed for resolving crossing fibers from diffusion-weighted (DW) MRI. However, other complex fiber geometries have drawn minimal attention. In this study, we focus on fiber orientation dispersion induced by within-voxel fanning. We use a multi-compartment, model-based approach to estimate fiber dispersion. Bingham distributions are employed to represent continuous distributions of fiber orientations, centered around a main orientation, and capturing anisotropic dispersion. We evaluate the accuracy of the model for different simulated fanning geometries, under different acquisition protocols and we illustrate the high SNR and angular resolution needs. We also perform a qualitative comparison between our parametric approach and five popular non-parametric techniques that are based on orientation distribution functions (ODFs). This comparison illustrates how the same underlying geometry can be depicted by different methods. We apply the proposed model on high-quality, post-mortem macaque data and present whole-brain maps of fiber dispersion, as well as exquisite details on the local anatomy of fiber distributions in various white matter regions.

Tractography: where do we go from here?

Diffusion tractography offers enormous potential for the study of human brain anatomy. However, as a method to study brain connectivity, tractography suffers from limitations, as it is indirect, inaccurate, and difficult to quantify. Despite these limitations, appropriate use of tractography can be a powerful means to address certain questions. In addition, while some of tractography's limitations are fundamental, others could be alleviated by methodological and technological advances. This article provides an overview of diffusion magnetic resonance tractography methods with a focus on how future advances might address challenges in measuring brain connectivity. Parts of this review are somewhat provocative, in the hope that they may trigger discussions possibly lacking in a field where the apparent simplicity of the methods (compared to their functional magnetic resonance imaging counterparts) can hide some fundamental issues that ultimately hinder the interpretation of findings, and cast doubt as to what tractography can really teach us about human brain anatomy.