Comparative validation of automated presurgical tractography based on constrained spherical deconvolution and diffusion tensor imaging with direct electrical stimulation.

OBJECTIVES: Accurate presurgical brain mapping enables preoperative risk assessment and intraoperative guidance. This cross-sectional study investigated whether constrained spherical deconvolution (CSD) methods were more accurate than diffusion tensor imaging (DTI)-based methods for presurgical white matter mapping using intraoperative direct electrical stimulation (DES) as the ground truth. METHODS: Five different tractography methods were compared (three DTI-based and two CSD-based) in 22 preoperative neurosurgical patients undergoing surgery with DES mapping. The corticospinal tract (CST, N = 20) and arcuate fasciculus (AF, N = 7) bundles were reconstructed, then minimum distances between tractograms and DES coordinates were compared between tractography methods. Receiver-operating characteristic (ROC) curves were used for both bundles. For the CST, binary agreement, linear modeling, and posthoc testing were used to compare tractography methods while correcting for relative lesion and bundle volumes. RESULTS: Distance measures between 154 positive (functional response, pDES) and negative (no response, nDES) coordinates, and 134 tractograms resulted in 860 data points. Higher agreement was found between pDES coordinates and CSD-based compared to DTI-based tractograms. ROC curves showed overall higher sensitivity at shorter distance cutoffs for CSD (8.5 mm) compared to DTI (14.5 mm). CSD-based CST tractograms showed significantly higher agreement with pDES, which was confirmed by linear modeling and posthoc tests (PFWE < .05). CONCLUSIONS: CSD-based CST tractograms were more accurate than DTI-based ones when validated using DES-based assessment of motor and sensory function. This demonstrates the potential benefits of structural mapping using CSD in clinical practice.

Tractographic and Microstructural Analysis of the Dentato-Rubro-Thalamo-Cortical Tracts in Children Using Diffusion MRI.

The dentato-rubro-thalamo-cortical tract (DRTC) is the main outflow pathway of the cerebellum, contributing to a finely balanced corticocerebellar loop involved in cognitive and sensorimotor functions. Damage to the DRTC has been implicated in cerebellar mutism syndrome seen in up to 25% of children after cerebellar tumor resection. Multi-shell diffusion MRI (dMRI) combined with quantitative constrained spherical deconvolution tractography and multi-compartment spherical mean technique modeling was used to explore the frontocerebellar connections and microstructural signature of the DRTC in 30 healthy children. The highest density of DRTC connections were to the precentral (M1) and superior frontal gyri (F1), and from cerebellar lobules I-IV and IX. The first evidence of a topographic organization of anterograde projections to the frontal cortex at the level of the superior cerebellar peduncle (SCP) is demonstrated, with streamlines terminating in F1 lying dorsomedially in the SCP compared to those terminating in M1. The orientation dispersion entropy of DRTC regions appears to exhibit greater contrast than that shown by fractional anisotropy. Analysis of a separate reproducibility cohort demonstrates good consistency in the dMRI metrics described. These novel anatomical insights into this well-studied pathway may prove to be of clinical relevance in the surgical resection of cerebellar tumors.

Brain connectomes in youth at risk for serious mental illness: an exploratory analysis.

BACKGROUND: Identifying early biomarkers of serious mental illness (SMI)-such as changes in brain structure and function-can aid in early diagnosis and treatment. Whole brain structural and functional connectomes were investigated in youth at risk for SMI. METHODS: Participants were classified as healthy controls (HC; n = 33), familial risk for serious mental illness (stage 0; n = 31), mild symptoms (stage 1a; n = 37), attenuated syndromes (stage 1b; n = 61), or discrete disorder (transition; n = 9) based on clinical assessments. Imaging data was collected from two sites. Graph-theory based analysis was performed on the connectivity matrix constructed from whole-brain white matter fibers derived from constrained spherical deconvolution of the diffusion tensor imaging (DTI) scans, and from the correlations between brain regions measured with resting state functional magnetic resonance imaging (fMRI) data. RESULTS: Linear mixed effects analysis and analysis of covariance revealed no significant differences between groups in global or nodal metrics after correction for multiple comparisons. A follow up machine learning analysis broadly supported the findings. Several non-overlapping frontal and temporal network differences were identified in the structural and functional connectomes before corrections. CONCLUSIONS: Results suggest significant brain connectome changes in youth at transdiagnostic risk may not be evident before illness onset.

[Fiber direction estimation using constrained spherical deconvolution based on multi-model response function].

Constrained spherical deconvolution can quantify white matter fiber orientation distribution information from diffusion magnetic resonance imaging data. But this method is only applicable to single shell diffusion magnetic resonance imaging data and will provide wrong fiber orientation information in white matter tissue which contains isotropic diffusion signals. To solve these problems, this paper proposes a constrained spherical deconvolution method based on multi-model response function. Multi-shell data can improve the stability of fiber orientation, and multi-model response function can attenuate isotropic diffusion signals in white matter, providing more accurate fiber orientation information. Synthetic data and real brain data from public database were used to verify the effectiveness of this algorithm. The results demonstrate that the proposed algorithm can attenuate isotropic diffusion signals in white matter and overcome the influence of partial volume effect on fiber direction estimation, thus estimate fiber direction more accurately. The reconstructed fiber direction distribution is stable, the false peaks are less, and the recognition ability of cross fiber is stronger, which lays a foundation for the further research of fiber bundle tracking technology.

Multi-tissue spherical deconvolution of tensor-valued diffusion MRI.

Multi-tissue constrained spherical deconvolution (MT-CSD) leverages the characteristic b-value dependency of each tissue type to estimate both the apparent tissue densities and the white matter fiber orientation distribution function from diffusion MRI data. In this work, we generalize MT-CSD to tensor-valued diffusion encoding with arbitrary b-tensor shapes. This enables the use of data encoded with mixed b-tensors, rather than being limited to the subset of linear (conventional) b-tensors. Using the complete set of data, including all b-tensor shapes, provides a categorical improvement in the estimation of apparent tissue densities, fiber ODF, and resulting tractography. Furthermore, we demonstrate that including multiple b-tensor shapes in the analysis provides improved contrast between tissue types, in particular between gray matter and white matter. We also show that our approach provides high-quality apparent tissue density maps and high-quality fiber tracking from data, even with sparse sampling across b-tensors that yield whole-brain coverage at 2 mm isotropic resolution in approximately 5:15 min.

The effect of gradient nonlinearities on fiber orientation estimates from spherical deconvolution of diffusion magnetic resonance imaging data.

Gradient nonlinearities in magnetic resonance imaging (MRI) cause spatially varying mismatches between the imposed and the effective gradients and can cause significant biases in rotationally invariant diffusion MRI measures derived from, for example, diffusion tensor imaging. The estimation of the orientational organization of fibrous tissue, which is nowadays frequently performed with spherical deconvolution techniques ideally using higher diffusion weightings, can likewise be biased by gradient nonlinearities. We explore the sensitivity of two established spherical deconvolution approaches to gradient nonlinearities, namely constrained spherical deconvolution (CSD) and damped Richardson-Lucy (dRL). Additionally, we propose an extension of dRL to take into account gradient imperfections, without the need of data interpolation. Simulations show that using the effective b-matrix can improve dRL fiber orientation estimation and reduces angular deviations, while CSD can be more robust to gradient nonlinearity depending on the implementation. Angular errors depend on a complex interplay of many factors, including the direction and magnitude of gradient deviations, underlying microstructure, SNR, anisotropy of the effective response function, and diffusion weighting. Notably, angular deviations can also be observed at lower b-values in contrast to the perhaps common assumption that only high b-value data are affected. In in vivo Human Connectome Project data and acquisitions from an ultrastrong gradient (300 mT/m) scanner, angular differences are observed between applying and not applying the effective gradients in dRL estimation. As even small angular differences can lead to error propagation during tractography and as such impact connectivity analyses, incorporating gradient deviations into the estimation of fiber orientations should make such analyses more reliable.

Constrained spherical deconvolution of nonspherically sampled diffusion MRI data.

Constrained spherical deconvolution (CSD) of diffusion-weighted MRI (DW-MRI) is a popular analysis method that extracts the full white matter (WM) fiber orientation density function (fODF) in the living human brain, noninvasively. It assumes that the DW-MRI signal on the sphere can be represented as the spherical convolution of a single-fiber response function (RF) and the fODF, and recovers the fODF through the inverse operation. CSD approaches typically require that the DW-MRI data is sampled shell-wise, and estimate the RF in a purely spherical manner using spherical basis functions, such as spherical harmonics (SH), disregarding any radial dependencies. This precludes analysis of data acquired with nonspherical sampling schemes, for example, Cartesian sampling. Additionally, nonspherical sampling can also arise due to technical issues, for example, gradient nonlinearities, resulting in a spatially dependent bias of the apparent tissue densities and connectivity information. Here, we adopt a compact model for the RFs that also describes their radial dependency. We demonstrate that the proposed model can accurately predict the tissue response for a wide range of b-values. On shell-wise data, our approach provides fODFs and tissue densities indistinguishable from those estimated using SH. On Cartesian data, fODF estimates and apparent tissue densities are on par with those obtained from shell-wise data, significantly broadening the range of data sets that can be analyzed using CSD. In addition, gradient nonlinearities can be accounted for using the proposed model, resulting in much more accurate apparent tissue densities and connectivity metrics.

Optimized rectification of fiber orientation density function.

PURPOSE: To demonstrate an optimized rectification strategy for fiber orientation density functions (fODFs). THEORY AND METHODS: In white matter, fODFs can be estimated with diffusion MRI. However, because of signal noise, imaging artifacts and other factors, experimentally determined fODFs may take on unphysical negative values in some directions. Here, we show how to rectify such fODFs to eliminate all negative values while minimizing the mean square difference between the original and rectified fODFs. The method is demonstrated for a mathematical model and for fODFs estimated from experimental human data using both constrained spherical deconvolution and fiber ball imaging. Comparison with an alternative nonoptimized rectification approach is also provided. RESULTS: For the mathematical model, it is found that the optimized rectification procedure removes negative fODF values while at the same time reducing the mean square error. Relative to the alternative rectification approach, the optimized fODFs are substantially more accurate. For the experimental data, the optimized fODFs have a lower average fractional anisotropy axonal and often fewer small peaks than the original, unrectified fODFs. The calculation of optimized fODFs is straightforward where the main step is the finding of the root to an equation in one variable, as may be efficiently accomplished with the bisection method. CONCLUSION: Unphysical negative fODF values can be easily eliminated in a manner that minimizes the mean square difference between the original and rectified fODFs. Optimized fODF rectification may be useful in applications for which negative values are problematic.

Measurement of white matter fiber-bundle cross-section in multiple sclerosis using diffusion-weighted imaging.

BACKGROUND: When investigating white matter (WM) microstructure, the axonal fiber orientation should be considered. Constrained spherical deconvolution (CSD) is a diffusion-weighted imaging (DWI) method that estimates distribution of fibers within each imaging voxel. OBJECTIVE: To study fiber-bundle cross-section (FC) as measured by CSD in multiple sclerosis (MS) patients versus healthy controls (HCs). METHODS: DWI and three-dimensional (3D) T1-weighted magnetic resonance imaging (MRI) were obtained from 45 MS patients and 45 HCs. We applied fixel-based morphometry analysis to assess differences of FC in MS against HCs and voxel-based analysis of fractional anisotropy (FA). RESULTS: We found a significant widespread reduction of WM FC in MS compared to HCs. The decrease in FA was less extensive, mainly located in regions with high lesion occurrence such as the periventricular WM and the corpus callosum. Progressive MS patients showed a significant FC reduction in the right anterior cingulum, bilateral cerebellum, and in several mesencephalic and diencephalic regions compared to relapsing-remitting MS patients. CONCLUSION: The CSD method can be applied in MS for a fiber-specific study of WM microstructure and quantification of FC. Fixel-based findings offered greater anatomical specificity and biological interpretability by identifying tract-specific differences and allowed substantial abnormalities to be detected.

Generalized Richardson-Lucy (GRL) for analyzing multi-shell diffusion MRI data.

Spherical deconvolution is a widely used approach to quantify the fiber orientation distribution (FOD) from diffusion MRI data of the brain. The damped Richardson-Lucy (dRL) is an algorithm developed to perform robust spherical deconvolution on single-shell diffusion MRI data while suppressing spurious FOD peaks due to noise or partial volume effects. Due to recent progress in acquisition hardware and scanning protocols, it is becoming increasingly common to acquire multi-shell diffusion MRI data, which allows for the modelling of multiple tissue types beyond white matter. While the dRL algorithm could, in theory, be directly applied to multi-shell data, it is not optimised to exploit its information content to model the signal from multiple tissue types. In this work, we introduce a new framework based on dRL - dubbed generalized Richardson-Lucy (GRL) - that uses multi-shell data in combination with user-chosen tissue models to disentangle partial volume effects and increase the accuracy in FOD estimation. Further, GRL estimates signal fraction maps associated to each user-selected model, which can be used during fiber tractography to dissect and terminate the tracking without need for additional structural data. The optimal weighting of multi-shell data in the fit and the robustness to noise and to partial volume effects of GRL was studied with synthetic data. Subsequently, we investigated the performance of GRL in comparison to dRL and to multi-shell constrained spherical deconvolution (MSCSD) on a high-resolution diffusion MRI dataset from the Human Connectome Project and on an MRI dataset acquired at 3T on a clinical scanner. In line with previous studies, we described the signal of the cerebrospinal-fluid and of the grey matter with isotropic diffusion models, whereas four diffusion models were considered to describe the white matter. With a third dataset including small diffusion weightings, we studied the feasibility of including intra-voxel incoherent motion effects due to blood pseudo-diffusion in the modelling. Further, the reliability of GRL was demonstrated with a test-retest scan of a subject acquired at 3T. Results of simulations show that GRL can robustly disentangle different tissue types at SNR above 20 with respect to the non-weighted image, and that it improves the angular accuracy of the FOD estimation as compared to dRL. On real data, GRL provides signal fraction maps that are physiologically plausible and consistent with those obtained with MSCSD, with correlation coefficients between the two methods up to 0.96. When considering IVIM effects, a high blood pseudo-diffusion fraction is observed in the medial temporal lobe and in the sagittal sinus. In comparison to dRL and MSCSD, GRL provided sharper FODs and less spurious peaks in presence of partial volume effects, but the FOD reconstructions are also highly dependent on the chosen modelling of white matter. When performing fiber tractography, GRL allows to terminate fiber tractography using the signal fraction maps, which results in a better tract termination at the grey-white matter interface or at the outer cortical surface. In terms of inter-scan reliability, GRL performed similarly to or better than compared methods. In conclusion, GRL offers a new modular and flexible framework to perform spherical deconvolution of multi-shell data.

Enforcing necessary non-negativity constraints for common diffusion MRI models using sum of squares programming.

In this work we investigate the use of sum of squares constraints for various diffusion-weighted MRI models, with a goal of enforcing strict, global non-negativity of the diffusion propagator. We formulate such constraints for the mean apparent propagator model and for spherical deconvolution, guaranteeing strict non-negativity of the corresponding diffusion propagators. For the cumulant expansion similar constraints cannot exist, and we instead derive a set of auxiliary constraints that are necessary but not sufficient to guarantee non-negativity. These constraints can all be verified and enforced at reasonable computational costs using semidefinite programming. By verifying our constraints on standard reconstructions of the different models, we show that currently used weak constraints are largely ineffective at ensuring non-negativity. We further show that if strict non-negativity is not enforced then estimated model parameters may suffer from significant errors, leading to serious inaccuracies in important derived quantities such as the main fiber orientations, mean kurtosis, etc. Finally, our experiments confirm that the observed constraint violations are mostly due to measurement noise, which is difficult to mitigate and suggests that properly constrained optimization should currently be considered the norm in many cases.

Impact of b-value on estimates of apparent fibre density.

Recent advances in diffusion magnetic resonance imaging (dMRI) analysis techniques have improved our understanding of fibre-specific variations in white matter microstructure. Increasingly, studies are adopting multi-shell dMRI acquisitions to improve the robustness of dMRI-based inferences. However, the impact of b-value choice on the estimation of dMRI measures such as apparent fibre density (AFD) derived from spherical deconvolution is not known. Here, we investigate the impact of b-value sampling scheme on estimates of AFD. First, we performed simulations to assess the correspondence between AFD and simulated intra-axonal signal fraction across multiple b-value sampling schemes. We then studied the impact of sampling scheme on the relationship between AFD and age in a developmental population (n = 78) aged 8-18 (mean = 12.4, SD = 2.9 years) using hierarchical clustering and whole brain fixel-based analyses. Multi-shell dMRI data were collected at 3.0T using ultra-strong gradients (300 mT/m), using 6 diffusion-weighted shells ranging from b = 0 to 6,000 s/mm2 . Simulations revealed that the correspondence between estimated AFD and simulated intra-axonal signal fraction was improved with high b-value shells due to increased suppression of the extra-axonal signal. These results were supported by in vivo data, as sensitivity to developmental age-relationships was improved with increasing b-value (b = 6,000 s/mm2 , median R2 = .34; b = 4,000 s/mm2 , median R2 = .29; b = 2,400 s/mm2 , median R2 = .21; b = 1,200 s/mm2 , median R2 = .17) in a tract-specific fashion. Overall, estimates of AFD and age-related microstructural development were better characterised at high diffusion-weightings due to improved correspondence with intra-axonal properties.

Test-retest reliability and long-term stability of three-tissue constrained spherical deconvolution methods for analyzing diffusion MRI data.

PURPOSE: Several recent studies have used a three-tissue constrained spherical deconvolution pipeline to obtain quantitative metrics of brain tissue microstructure from diffusion-weighted MRI data. The three tissue compartments, consisting of white matter, gray matter, and CSF-like (free water) signals, are potentially useful in the evaluation of brain microstructure in a range of pathologies. However, the reliability and long-term stability of these metrics have not yet been evaluated. METHODS: This study examined estimates of whole-brain microstructure for the three tissue compartments, in three separate test-retest cohorts. Each cohort had different lengths of time between baseline and retest, ranging from within the same scanning session in the shortest interval to 3 months in the longest interval. Each cohort was also collected with different acquisition parameters. RESULTS: The CSF-like compartment displayed the greatest reliability across all cohorts, with intraclass correlation coefficient (ICC) values being above 0.95 in each cohort. White matter-like and gray matter-like compartments both demonstrated very high reliability in the immediate cohort (both ICC > 0.90); however, this declined in the 3-month interval cohort to both compartments having ICC > 0.80. Regional CSF-like signal fraction was examined in bilateral hippocampus and had an ICC > 0.80 in each cohort. CONCLUSION: The three-tissue constrained spherical deconvolution techniques provide reliable and stable estimates of tissue-microstructure composition, up to 3 months longitudinally in a control population. This forms an important basis for further investigations using three-tissue constrained spherical deconvolution techniques to track changes in microstructure across a variety of brain pathologies.

White matter microstructure of the extended limbic system in male and female youth with conduct disorder.

BACKGROUND: Previous studies of conduct disorder (CD) have reported structural and functional alterations in the limbic system. However, the white matter tracts that connect limbic regions have not been comprehensively studied. The uncinate fasciculus (UF), a tract connecting limbic to prefrontal regions, has been implicated in CD. However, CD-related alterations in other limbic tracts, such as the cingulum and the fornix, have not been investigated. Furthermore, few studies have examined the influence of sex and none have been adequately powered to test whether the relationship between CD and structural connectivity differs by sex. We examined whether adolescent males and females with CD exhibit differences in structural connectivity compared with typically developing controls. METHODS: We acquired diffusion-weighted magnetic resonance imaging data from 101 adolescents with CD (52 females) and 99 controls (50 females). Data were processed for deterministic spherical deconvolution tractography. Virtual dissections of the UF, the three subdivisions of the cingulum [retrosplenial cingulum (RSC), parahippocampal and subgenual cingulum], and the fornix were performed and measures of fractional anisotropy (FA) and hindrance-modulated orientational anisotropy (HMOA) were analysed. RESULTS: The CD group had lower FA and HMOA in the right RSC tract relative to controls. Importantly, these effects were moderated by sex - males with CD significantly lower FA compared to male controls, whereas CD and control females did not differ. CONCLUSIONS: Our results highlight the importance of considering sex when studying the neurobiological basis of CD. Sex differences in RSC connectivity may contribute to sex differences in the clinical presentation of CD.

A multi-shell multi-tissue diffusion study of brain connectivity in early multiple sclerosis.

BACKGROUND: The potential of multi-shell diffusion imaging to produce accurate brain connectivity metrics able to unravel key pathophysiological processes in multiple sclerosis (MS) has scarcely been investigated. OBJECTIVE: To test, in patients with a clinically isolated syndrome (CIS), whether multi-shell imaging-derived connectivity metrics can differentiate patients from controls, correlate with clinical measures, and perform better than metrics obtained with conventional single-shell protocols. METHODS: Nineteen patients within 3 months from the CIS and 12 healthy controls underwent anatomical and 53-direction multi-shell diffusion-weighted 3T images. Patients were cognitively assessed. Voxel-wise fibre orientation distribution functions were estimated and used to obtain network metrics. These were also calculated using a conventional single-shell diffusion protocol. Through linear regression, we obtained effect sizes and standardised regression coefficients. RESULTS: Patients had lower mean nodal strength (p = 0.003) and greater network modularity than controls (p = 0.045). Greater modularity was associated with worse cognitive performance in patients, even after accounting for lesion load (p = 0.002). Multi-shell-derived metrics outperformed single-shell-derived ones. CONCLUSION: Connectivity-based nodal strength and network modularity are abnormal in the CIS. Furthermore, the increased network modularity observed in patients, indicating microstructural damage, is clinically relevant. Connectivity analyses based on multi-shell imaging can detect potentially relevant network changes in early MS.

Tractography and the connectome in neurosurgical treatment of gliomas: the premise, the progress, and the potential.

The ability of diffusion tensor MRI to detect the preferential diffusion of water in cerebral white matter tracts enables neurosurgeons to noninvasively visualize the relationship of lesions to functional neural pathways. Although viewed as a research tool in its infancy, diffusion tractography has evolved into a neurosurgical tool with applications in glioma surgery that are enhanced by evolutions in crossing fiber visualization, edema correction, and automated tract identification. In this paper the current literature supporting the use of tractography in brain tumor surgery is summarized, highlighting important clinical studies on the application of diffusion tensor imaging (DTI) for preoperative planning of glioma resection, and risk assessment to analyze postoperative outcomes. The key methods of tractography in current practice and crucial white matter fiber bundles are summarized. After a review of the physical basis of DTI and post-DTI tractography, the authors discuss the methodologies with which to adapt DT image processing for surgical planning, as well as the potential of connectomic imaging to facilitate a network approach to oncofunctional optimization in glioma surgery.

Sparse wars: A survey and comparative study of spherical deconvolution algorithms for diffusion MRI.

Spherical deconvolution methods are widely used to estimate the brain's white-matter fiber orientations from diffusion MRI data. In this study, eight spherical deconvolution algorithms were implemented and evaluated. These included two model selection techniques based on the extended Bayesian information criterion (i.e., best subset selection and the least absolute shrinkage and selection operator), iteratively reweighted l2- and l1-norm approaches to approximate the l0-norm, sparse Bayesian learning, Cauchy deconvolution, and two accelerated Richardson-Lucy algorithms. Results from our exhaustive evaluation show that there is no single optimal method for all different fiber configurations, suggesting that further studies should be conducted to find the optimal way of combining solutions from different methods. We found l0-norm regularization algorithms to resolve more accurately fiber crossings with small inter-fiber angles. However, in voxels with very dominant fibers, algorithms promoting more sparsity are less accurate in detecting smaller fibers. In most cases, the best algorithm to reconstruct fiber crossings with two fibers did not perform optimally in voxels with one or three fibers. Therefore, simplified validation systems as employed in a number of previous studies, where only two fibers with similar volume fractions were tested, should be avoided as they provide incomplete information. Future studies proposing new reconstruction methods based on high angular resolution diffusion imaging data should validate their results by considering, at least, voxels with one, two, and three fibers, as well as voxels with dominant fibers and different diffusion anisotropies.

Histologically derived fiber response functions for diffusion MRI vary across white matter fibers-An ex vivo validation study in the squirrel monkey brain.

Understanding the relationship between the diffusion-weighted MRI signal and the arrangement of white matter fibers is fundamental for accurate voxel-wise reconstruction of the fiber orientation distribution (FOD) and subsequent fiber tractography. Spherical deconvolution reconstruction techniques model the diffusion signal as the convolution of the FOD with a response function that represents the signal profile of a single fiber orientation. Thus, given the signal and a fiber response function, the FOD can be estimated in every imaging voxel by deconvolution. However, the selection of the appropriate response function remains relatively under-studied, and requires further validation. In this work, using 3D histologically defined FODs and the corresponding diffusion signal from three ex vivo squirrel monkey brains, we derive the ground truth response functions. We find that the histologically derived response functions differ from those conventionally used. Next, we find that response functions statistically vary across brain regions, which suggests that the practice of using the same kernel throughout the brain is not optimal. We show that different kernels lead to different FOD reconstructions, which in turn can lead to different tractography results depending on algorithmic parameters, with large variations in the accuracy of resulting reconstructions. Together, these results suggest there is room for improvement in estimating and understanding the relationship between the diffusion signal and the underlying FOD.

Modelling white matter with spherical deconvolution: How and why?

Since the realization that diffusion MRI can probe the microstructural organization and orientation of biological tissue in vivo and non-invasively, a multitude of diffusion imaging methods have been developed and applied to study the living human brain. Diffusion tensor imaging was the first model to be widely adopted in clinical and neuroscience research, but it was also clear from the beginning that it suffered from limitations when mapping complex configurations, such as crossing fibres. In this review, we highlight the main steps that have led the field of diffusion imaging to move from the tensor model to the adoption of diffusion and fibre orientation density functions as a more effective way to describe the complexity of white matter organization within each brain voxel. Among several techniques, spherical deconvolution has emerged today as one of the main approaches to model multiple fibre orientations and for tractography applications. Here we illustrate the main concepts and the reasoning behind this technique, as well as the latest developments in the field. The final part of this review provides practical guidelines and recommendations on how to set up processing and acquisition protocols suitable for spherical deconvolution.

Crossing muscle fibers of the human tongue resolved in vivo using constrained spherical deconvolution.

BACKGROUND: Surgical resection of tongue cancer may impair swallowing and speech. Knowledge of tongue muscle architecture affected by the resection could aid in patient counseling. Diffusion tensor imaging (DTI) enables reconstructions of muscle architecture in vivo. Reconstructing crossing fibers in the tongue requires a higher-order diffusion model. PURPOSE: To develop a clinically feasible diffusion imaging protocol, which facilitates both DTI and constrained spherical deconvolution (CSD) reconstructions of tongue muscle architecture in vivo. STUDY TYPE: Cross-sectional study. SUBJECTS/SPECIMEN: One ex vivo bovine tongue resected en bloc from mandible to hyoid bone. Ten healthy volunteers (mean age 25.5 years; range 21-34 years; four female). FIELD STRENGTH/SEQUENCE: Diffusion-weighted echo planar imaging at 3 T using a high-angular resolution diffusion imaging scheme acquired twice with opposing phase-encoding for B0 -field inhomogeneity correction. The scan of the healthy volunteers was divided into four parts, in between which the volunteers were allowed to swallow, resulting in a total acquisition time of 10 minutes. ASSESSMENT: The ability of resolving crossing muscle fibers using CSD was determined on the bovine tongue specimen. A reproducible response function was estimated and the optimal peak threshold was determined for the in vivo tongue. The quality of tractography of the in vivo tongue was graded by three experts. STATISTICAL TESTS: The within-subject coefficient of variance was calculated for the response function. The qualitative results of the grading of DTI and CSD tractography were analyzed using a multilevel proportional odds model. RESULTS: Fiber orientation distributions in the bovine tongue specimen showed that CSD was able to resolve crossing muscle fibers. The response function could be determined reproducibly in vivo. CSD tractography displayed significantly improved tractography compared with DTI tractography (P = 0.015). DATA CONCLUSION: The 10-minute diffusion imaging protocol facilitates CSD fiber tracking with improved reconstructions of crossing tongue muscle fibers compared with DTI. LEVEL OF EVIDENCE: 2 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2019;50:96-105.