Brain tractography involves mapping diffusion-weighted images (DWI) onto streamlines representing neural fibre bundles. Recent research avenues have framed tractography into a reinforcement learning (RL) framework with actor-critic models. However, previous RL-based methods may compromise geometrical relations between the input (DWI) and output (tractogram). More specifically, 3D rotations applied to the input of RL-based tractography are not adequately reflected in the output, indicating a lack of SO(3) equivariance. This study aims to restore the equivariance present in previous non-learning-based methods (e.g., iFOD2 from MRtrix3) to RL-based tractography. To achieve this, we introduce SO(3) equivariant and invariant components for the actors (direction prediction model) and critics (Q-value prediction model), respectively. We employ an SE(3)-equivariant transformer as the next direction prediction function. The fact that both the input DWI and the output directional update can be represented as spherical signals that transform under representations of SO(3) makes this formulation a natural fit for the present problem. The contribution of this work is twofold. First, we discuss rotational equivariance in streamline tractography on a theoretical level. Second, we propose a method that combines RL-based tractography with a rotationally equivariant model. We evaluate the equivariance of the proposed method both locally and globally with phantom and in vivo data. The results show that the proposed method restores the equivariance of Track-to-Learn, which is the state-of-the-art for RL-based tractography. Our code is available at https://github.com/minnelab/SO3TrackToLearn.

Tractometry, also known as tract profiling, is a powerful technique for probing microstructural properties along white matter (WM) tracts. A prerequisite for tractography-based tractometry is bundle parcellation—the subdivision of WM bundles into smaller segments where microstructural measures can be computed. However, existing parcellation methods lack consistency across bundles and timepoints, which reduces reproducibility and limits their utility for both longitudinal and cross-sectional studies. Moreover, these methods typically depend on tractography and bundle segmentation, two processes that are computationally expensive and often highly variable. In this work, we introduce BundleParc , a consistent and tractography-free bundle parcellation method. Instead of relying on streamline generation, BundleParc maps fiber orientation distribution function (fODF) volumes directly to label maps. Rigorous evaluation on research and clinical cohorts show that BundleParc is not only much simpler than state-of-the-art tract-based profiling methods, it is also consistently more accurate, robust and reproducible. With these results, BundleParc is a new solution for fast, easy-to-use, and off-the-shelf bundle segmentation and parcellation. • BundleParc produces parcellations for tractometry directly from FOD volumes. • BundleParc outperforms SOTA methods in accuracy, reproducibility in multiple cohorts. • BundleParc enables fast, reliable, robust and anatomically consistent parcellations.

Diffusion-relaxation MRI aims to extract quantitative measures that characterise microstructural tissue properties such as orientation, size, and shape, but long acquisition times are typically required. This work proposes a physics-informed learning framework to extract an optimal subset of diffusion-relaxation MRI measurements for enabling shorter acquisition times, predict non-measured signals, and estimate quantitative parameters. In vivo and synthetic brain 5D-Diffusion-T1-T2∗-weighted MRI data obtained from five healthy subjects were used for training and validation, and from a sixth participant for testing. One fully data-driven and two physics-informed machine learning methods were implemented and compared to two manual selection procedures and Cramér-Rao lower bound optimisation. The physics-informed approaches could identify measurement-subsets that yielded more consistently accurate parameter estimates in simulations than other approaches, with similar signal prediction error. Five-fold shorter protocols yielded error distributions of estimated quantitative parameters with very small effect sizes compared to estimates from the full protocol. Selected subsets commonly included a denser sampling of the shortest and longest inversion time, lowest echo time, and high b-value. The proposed framework combining machine learning and MRI physics offers a promising approach to develop shorter imaging protocols without compromising the quality of parameter estimates and signal predictions.

Current brain white matter fiber tracking techniques show a number of problems, including: generating large proportions of streamlines that do not accurately describe the underlying anatomy; extracting streamlines that are not supported by the underlying diffusion signal; and under-representing some fiber populations, among others. In this paper, we describe a novel autoencoder-based learning method to filter streamlines from diffusion MRI tractography, and hence, to obtain more reliable tractograms. Our method, dubbed FINTA (Filtering in Tractography using Autoencoders) uses raw, unlabeled tractograms to train the autoencoder, and to learn a robust representation of brain streamlines. Such an embedding is then used to filter undesired streamline samples using a nearest neighbor algorithm. Our experiments on both synthetic and in vivo human brain diffusion MRI tractography data obtain accuracy scores exceeding the 90\% threshold on the test set. Results reveal that FINTA has a superior filtering performance compared to conventional, anatomy-based methods, and the RecoBundles state-of-the-art method. Additionally, we demonstrate that FINTA can be applied to partial tractograms without requiring changes to the framework. We also show that the proposed method generalizes well across different tracking methods and datasets, and shortens significantly the computation time for large (>1 M streamlines) tractograms. Together, this work brings forward a new deep learning framework in tractography based on autoencoders, which offers a flexible and powerful method for white matter filtering and bundling that could enhance tractometry and connectivity analyses.

Validation is arguably the bottleneck in the diffusion magnetic resonance imaging (MRI) community. This paper evaluates and compares 20 algorithms for recovering the local intra-voxel fiber structure from diffusion MRI data and is based on the results of the "HARDI reconstruction challenge" organized in the context of the "ISBI 2012" conference. Evaluated methods encompass a mixture of classical techniques well known in the literature such as diffusion tensor, Q-Ball and diffusion spectrum imaging, algorithms inspired by the recent theory of compressed sensing and also brand new approaches proposed for the first time at this contest. To quantitatively compare the methods under controlled conditions, two datasets with known ground-truth were synthetically generated and two main criteria were used to evaluate the quality of the reconstructions in every voxel: correct assessment of the number of fiber populations and angular accuracy in their orientation. This comparative study investigates the behavior of every algorithm with varying experimental conditions and highlights strengths and weaknesses of each approach. This information can be useful not only for enhancing current algorithms and develop the next generation of reconstruction methods, but also to assist physicians in the choice of the most adequate technique for their studies.

We propose an integral concept for tractography to describe crossing and splitting fibre bundles based on the fibre orientation distribution function (ODF) estimated from high angular resolution diffusion imaging (HARDI). We show that in order to perform accurate probabilistic tractography, one needs to use a fibre ODF estimation and not the diffusion ODF. We use a new fibre ODF estimation obtained from a sharpening deconvolution transform (SDT) of the diffusion ODF reconstructed from q-ball imaging (QBI). This SDT provides new insight into the relationship between the HARDI signal, the diffusion ODF, and the fibre ODF. We demonstrate that the SDT agrees with classical spherical deconvolution and improves the angular resolution of QBI. Another important contribution of this paper is the development of new deterministic and new probabilistic tractography algorithms using the full multidirectional information obtained through use of the fibre ODF. An extensive comparison study is performed on human brain datasets comparing our new deterministic and probabilistic tracking algorithms in complex fibre crossing regions. Finally, as an application of our new probabilistic tracking, we quantify the reconstruction of transcallosal fibres intersecting with the corona radiata and the superior longitudinal fasciculus in a group of eight subjects. Most current diffusion tensor imaging (DTI)-based methods neglect these fibres, which might lead to incorrect interpretations of brain functions.

We present a Diffusion Maps clustering method applied to diffusion MRI in order to segment complex white matter fiber bundles. It is well-known that diffusion tensor imaging (DTI) is restricted in complex fiber regions with crossings and this is why recent High Angular Resolution Diffusion Imaging (HARDI) such has Q-Ball Imaging (QBI) have been introduced to overcome these limitations. QBI reconstructs the diffusion orientation distribution function (ODF), a spherical function that has its maximum(a) agreeing with the underlying fiber population. In this paper, we use the ODF representation in a small set of spherical harmonic coefficients as input to the Diffusion Maps clustering method. We first show the advantage of using Diffusion Maps clustering over classical methods such as N-Cuts and Laplacian Eigenmaps. In particular, our ODF Diffusion Maps requires a smaller number of hypothesis from the input data, reduces the number of artifacts in the segmentation and automatically exhibits the number of clusters segmenting the Q-Ball image by using an adaptative scale-space parameter. We also show that our ODF Diffusion Maps clustering can reproduce published results using the diffusion tensor (DT) clustering with N-Cuts on simple synthetic images without crossings. On more complex data with crossings, we show that our method succeeds to separate fiber bundles and crossing regions whereas the DT- based methods generate artifacts and exhibit wrong number of clusters. Finally, we show results on a real brain dataset where we successfully segment the fiber bundles.