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Constrained spherical deconvolution (CSD) has become one of the most widely used methods to extract white matter (WM) fibre orientation information from diffusion-weighted MRI (DW-MRI) data, overcoming the crossing fibre limitations inherent in the diffusion tensor model. It is routinely used to obtain high quality fibre orientation distribution function (fODF) estimates and fibre tractograms and is increasingly used to obtain apparent fibre density (AFD) measures. Unfortunately, CSD typically only supports data acquired on a single shell in q-space. With multi-shell data becoming more and more prevalent, there is a growing need for CSD to fully support such data. Furthermore, CSD can only provide high quality fODF estimates in voxels containing WM only. In voxels containing other tissue types such as grey matter (GM) and cerebrospinal fluid (CSF), the WM response function may no longer be appropriate and spherical deconvolution produces unreliable, noisy fODF estimates. The aim of this study is to incorporate support for multi-shell data into the CSD approach as well as to exploit the unique b-value dependencies of the different tissue types to estimate a multi-tissue ODF. The resulting approach is dubbed multi-shell, multi-tissue CSD (MSMT-CSD) and is compared to the state-of-the-art single-shell, single-tissue CSD (SSST-CSD) approach. Using both simulations and real data, we show that MSMT-CSD can produce reliable WM/GM/CSF volume fraction maps, directly from the DW data, whereas SSST-CSD has a tendency to overestimate the WM volume in voxels containing GM and/or CSF. In addition, compared to SSST-CSD, MSMT-CSD can substantially increase the precision of the fODF fibre orientations and reduce the presence of spurious fODF peaks in voxels containing GM and/or CSF. Both effects translate into more reliable AFD measures and tractography results with MSMT-CSD compared to SSST-CSD. •Constrained spherical deconvolution is extended to support multi-shell DW data.•We use the unique b-value dependency of each tissue to estimate a multi-tissue ODF.•We obtain reliable WM/GM/CSF volume fraction maps directly from the DW data.•We obtain more precise WM fibre orientation estimates at the tissue interfaces.•This leads to more accurate apparent fibre density and more reliable fibre tracking.

This article proposes a new measure called Apparent Fibre Density (AFD) for the analysis of high angular resolution diffusion-weighted images using higher-order information provided by fibre orientation distributions (FODs) computed using spherical deconvolution. AFD has the potential to provide specific information regarding differences between populations by identifying not only the location, but also the orientations along which differences exist. In this work, analytical and numerical Monte-Carlo simulations are used to support the use of the FOD amplitude as a quantitative measure (i.e. AFD) for population and longitudinal analysis. To perform robust voxel-based analysis of AFD, we present and evaluate a novel method to modulate the FOD to account for changes in fibre bundle cross-sectional area that occur during spatial normalisation. We then describe a novel approach for statistical analysis of AFD that uses cluster-based inference of differences extended throughout space and orientation. Finally, we demonstrate the capability of the proposed method by performing voxel-based AFD comparisons between a group of Motor Neurone Disease patients and healthy control subjects. A significant decrease in AFD was detected along voxels and orientations corresponding to both the corticospinal tract and corpus callosal fibres that connect the primary motor cortices. In addition to corroborating previous findings in MND, this study demonstrates the clear advantage of using this type of analysis by identifying differences along single fibre bundles in regions containing multiple fibre populations.

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. Presurgical white matter mapping using probabilistic CSD tractography is more accurate and sensitive than manual DTI FACT or automated probabilistic DTI tractography. This study included 22 patients with DES data, which was used as the ground truth. Distance in mm between tractograms and DES data resulted in 860 datapoints, 685 of which belonged to the CST and were used for linear modeling; AUC, area under the curve; CSD, constrained spherical deconvolution; DTI, diffusion tensor imaging; FWE, family‐wise error rate; TCK, tractogram/tractography.

Diffusion-weighted magnetic resonance imaging provides invaluable insights into in-vivo neurological pathways. However, accurate and robust characterization of white matter fibers microstructure remains challenging. Widely used spherical deconvolution algorithms retrieve the fiber Orientation Distribution Function (ODF) by using an estimation of a response function, i.e., the signal arising from individual fascicles within a voxel. In this paper, an algorithm of blind spherical deconvolution is proposed, which only assumes the axial symmetry of the response function instead of its exact knowledge. This algorithm provides a method for estimating the peaks of the ODF in a voxel without any explicit response function, as well as a method for estimating signals associated with the peaks of the ODF, regardless of how those peaks were obtained. The two stages of the algorithm are tested on Monte Carlo simulations, as well as compared to state-of-the-art methods on real in-vivo data for the orientation retrieval task. Although the proposed algorithm was shown to attain lower angular errors than the state-of-the-art constrained spherical deconvolution algorithm on synthetic data, it was outperformed by state-of-the-art spherical deconvolution algorithms on in-vivo data. In conjunction with state-of-the art methods for axon bundles direction estimation, the proposed method showed its potential for the derivation of per-voxel per-direction metrics on synthetic as well as in-vivo data.

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.

There is accumulating evidence that at current acquisition resolutions for diffusion-weighted (DW) MRI, the vast majority of white matter voxels contains “crossing fibers”, referring to complex fiber configurations in which multiple and distinctly differently oriented fiber populations exist. Spherical deconvolution based techniques are appealing to characterize this DW intra-voxel signal heterogeneity, as they provide a balanced trade-off between constraints on the required hardware performance and acquisition time on the one hand, and the reliability of the reconstructed fiber orientation distribution function (fODF) on the other hand. Recent findings, however, suggest that an inaccurate calibration of the response function (RF), which represents the DW signal profile of a single fiber orientation, can lead to the detection of spurious fODF peaks which, in turn, can have a severe impact on tractography results. Currently, the computation of this RF is either model-based or estimated from selected voxels that have a fractional anisotropy (FA) value above a predefined threshold. For both approaches, however, there are user-defined settings that affect the RF and, consequently, fODF estimation and tractography. Moreover, these settings still rely on the second-rank diffusion tensor, which may not be the appropriate model, especially at high b-values. In this work, we circumvent these issues for RF calibration by excluding “crossing fibers” voxels in a recursive framework. Our approach is evaluated with simulations and applied to in vivo and ex vivo data sets with different acquisition settings. The results demonstrate that with the proposed method the RF can be calibrated in a robust and automated way without needing to define ad-hoc FA threshold settings. Our framework facilitates the use of spherical deconvolution approaches in data sets in which it is not straightforward to define RF settings a priori. [Display omitted] •We propose robust response function estimation for spherical deconvolution.•This recursive framework is completely independent of the diffusion tensor model.•Method excludes crossing fiber voxels recursively using an fODF peak ratio threshold.•It is robust towards the threshold and less dependent on underlying data properties.•It can be applied to data sets with different acquisition settings and properties.

Spherical deconvolution methods have been applied to diffusion MRI to improve diffusion tensor tractography results in brain regions with multiple fibre crossing. Recent developments, such as the introduction of non-negative constraints on the solution, allow a more accurate estimation of fibre orientations by reducing instability effects due to noise robustness. Standard convolution methods do not, however, adequately model the effects of partial volume from isotropic tissue, such as gray matter, or cerebrospinal fluid, which may degrade spherical deconvolution results. Here we use a newly developed spherical deconvolution algorithm based on an adaptive regularization (damped version of the Richardson–Lucy algorithm) to reduce isotropic partial volume effects. Results from both simulated and in vivo datasets show that, compared to a standard non-negative constrained algorithm, the damped Richardson–Lucy algorithm reduces spurious fibre orientations and preserves angular resolution of the main fibre orientations. These findings suggest that, in some brain regions, non-negative constraints alone may not be sufficient to reduce spurious fibre orientations. Considering both the speed of processing and the scan time required, this new method has the potential for better characterizing white matter anatomy and the integrity of pathological tissue.

The accurate estimation of fiber orientation distribution functions (fODFs) in diffusion magnetic resonance imaging (MRI) is crucial for understanding early brain development and its potential disruptions. Although supervised deep learning (DL) models have shown promise in fODF estimation from neonatal diffusion MRI (dMRI) data, the out‐of‐domain (OOD) performance of these models remains largely unexplored, especially under diverse domain shift scenarios. This study evaluated the robustness of three state‐of‐the‐art DL architectures: multilayer perceptron (MLP), transformer, and U‐Net/convolutional neural network (CNN) on fODF predictions derived from dMRI data. Using 488 subjects from the developing Human Connectome Project (dHCP) and the Baby Connectome Project (BCP) datasets, we reconstructed reference fODFs from the full dMRI series using single‐shell three‐tissue constrained spherical deconvolution (SS3T‐CSD) and multi‐shell multi‐tissue CSD (MSMT‐CSD) to generate reference fODF reconstructions for model training, and systematically assessed the impact of age, scanner/protocol differences, and input dimensionality on model performance. Our findings reveal that U‐Net consistently outperformed other models when fewer diffusion gradient directions were used, particularly with the SS3T‐CSD‐derived ground truth, which showed superior performance in capturing crossing fibers. However, as the number of input diffusion gradient directions increased, MLP and the transformer‐based model exhibited steady gains in accuracy. Nevertheless, performance nearly plateaued from 28 to 45 input directions in all models. Age‐related domain shifts showed asymmetric patterns, being less pronounced in late developmental stages (late neonates, and babies), with SS3T‐CSD demonstrating greater robustness to variability compared to MSMT‐CSD. To address inter‐site domain shifts, we implemented two adaptation strategies: the Method of Moments (MoM) and fine‐tuning. Both strategies achieved significant improvements (p<0.05 $$ p<0.05 $$ ) in over 95% of tested configurations, with fine‐tuning consistently yielding superior results and U‐Net benefiting the most from increased target subjects. This study represents the first systematic evaluation of OOD settings in DL applications to fODF estimation, providing critical insights into model robustness and adaptation strategies for diverse clinical and research applications. We quantify domain‐shift impacts of three state‐of‐the‐art deep learning models for fiber orientation estimation in dMRI of neonatal and baby brains, across age, scanner, input variations, target output ground truths, and demonstrate how fine‐tuning and data harmonization strategies improve model robustness for clinical and research applications.

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. •There is no single optimal SD method for all the different fiber configurations.•Sparse algorithms to resolve fiber crossings with small inter-fiber angles were found.•Algorithms promoting more sparsity are less accurate in detecting smaller fibers.•Future studies should validate their results by considering many fiber configurations.

Local fiber orientation distributions (FODs) can be computed from diffusion magnetic resonance imaging (dMRI). The accuracy and ability of FODs to resolve complex fiber configurations benefits from acquisition protocols that sample a high number of gradient directions, a high maximum b-value, and multiple b-values. However, acquisition time and scanners that follow these standards are limited in clinical settings, often resulting in dMRI acquired at a single shell (single b-value). In this work, we learn improved FODs from clinically acquired dMRI. We evaluate patch-based 3D convolutional neural networks (CNNs) on their ability to regress multi-shell FODs from single-shell FODs, using constrained spherical deconvolution (CSD). We evaluate U-Net and High-Resolution Network (HighResNet) 3D CNN architectures on data from the Human Connectome Project and an in-house dataset. We evaluate how well each CNN can resolve FODs 1) when training and testing on datasets with the same dMRI acquisition protocol; 2) when testing on a dataset with a different dMRI acquisition protocol than used to train the CNN; and 3) when testing on a dataset with a fewer number of gradient directions than used to train the CNN. This work is a step towards more accurate FOD estimation in time- and resource-limited clinical environments. •Improved estimation of fiber orientations distributions (FODs) for clinically acquired singleshell diffusion MRI (dMRI).•Evaluation of how well CNNs can resolve FODs for dMRI with the same and for different acquisition protocols.•A step towards more accurate FOD estimation in time- and resource-limited clinical environments.