HYDI-DSI revisited: Constrained non-parametric EAP imaging without q-space re-gridding

Producción CientíficaHybrid Diffusion Imaging (HYDI) was one of the first attempts to use multi-shell samplings of the q-space to infer diffusion properties beyond Diffusion Tensor Imaging (DTI) or High Angular Resolution Diffusion Imaging (HARDI). HYDI was intended as a flexible protocol embedding both DTI (for lower -values) and HARDI (for higher -values) processing, as well as Diffusion Spectrum Imaging (DSI) when the entire data set was exploited. In the latter case, the spherical sampling of the q-space is re-gridded by interpolation to a Cartesian lattice whose extent covers the range of acquired b-values, hence being acquisition-dependent. The Discrete Fourier Transform (DFT) is afterwards used to compute the corresponding Cartesian sampling of the Ensemble Average Propagator (EAP) in an entirely non-parametric way. From this lattice, diffusion markers such as the Return To Origin Probability (RTOP) or the Mean Squared Displacement (MSD) can be numerically estimated. We aim at re-formulating this scheme by means of a Fourier Transform encoding matrix that eliminates the need for q-space re-gridding at the same time it preserves the non-parametric nature of HYDI-DSI. The encoding matrix is adaptively designed at each voxel according to the underlying DTI approximation, so that an optimal sampling of the EAP can be pursued without being conditioned by the particular acquisition protocol. The estimation of the EAP is afterwards carried out as a regularized Quadratic Programming (QP) problem, which allows to impose positivity constraints that cannot be trivially embedded within the conventional HYDI-DSI. We demonstrate that the definition of the encoding matrix in the adaptive space allows to analytically (as opposed to numerically) compute several popular descriptors of diffusion with the unique source of error being the cropping of high frequency harmonics in the Fourier analysis of the attenuation signal. They include not only RTOP and MSD, but also Return to Axis/Plane Probabilities (RTAP/RTPP), which are defined in terms of specific spatial directions and are not available with the former HYDI-DSI. We report extensive experiments that suggest the benefits of our proposal in terms of accuracy, robustness and computational efficiency, especially when only standard, non-dedicated q-space samplings are available.Ministerio de Ciencia e Innovación (PID2021-124407NB-I00 and TED2021-130758B-I00)Ministry of Science and Higher Education (Poland) (PPN/BEK/ 2019/1/00421

Diffusion sampling schemes: A generalized methodology with nongeometric criteria

Producción CientíficaPurpose:The aim of this paper is to show that geometrical criteria for designingmultishellq-space sampling procedures do not necessarily translate into recon-struction matrices with high figures of merit commonly used in the compressedsensing theory. In addition, we show that a well-known method for visitingk-space in radial three-dimensional acquisitions, namely, the Spiral Phyllotaxis,is a competitive initialization for the optimization of our nonconvex objectivefunction.Theory and Methods:We propose the gradient design method WISH (WeIght-ing SHells) which uses an objective function that accounts for weighted dis-tances between gradients withinM-tuples of consecutive shells, withMrangingbetween 1 and the maximum number of shellsS. All theM-tuples share thesame weight�M. The objective function is optimized for a sample of theseweights, using Spiral Phyllotaxis as initialization. State-of-the-art General Elec-trostatic Energy Minimization (GEEM) and Spherical Codes (SC) were used forcomparison. For the three methods, reconstruction matrices of the attenuationsignal using MAP-MRI were tested using figures of merit borrowed from theCompressed Sensing theory (namely, Restricted Isometry Property —RIP— andCoherence); we also tested the gradient design using a geometric criterion basedon Voronoi cells.Results:For RIP and Coherence, WISH got better results in at least one com-bination of weights, whilst the criterion based on Voronoi cells showed anunrelated pattern.Conclusion:The versatility provided by WISH is supported by better results.Optimization in the weight parameter space is likely to provide additionalimprovements. For a practical design with an intermediate number of gradients,our results recommend to carry out the methodology here used to determine theappropriate gradient table.Agencia Estatal de Investigación,(under Grants RTI2018-094569-B-I00,PID2020-115339RB-I00 and TED2021-130090B-I00)ESAOTE, Ltd (Grant/Award Number: 18IQBM

Efficient estimation of propagator anisotropy and non‐Gaussianity in multishell diffusion MRI with micro‐structure adaptive convolution kernels and dual Fourier integral transforms

Producción CientíficaPurpose:We seek to reformulate the so-called Propagator Anisotropy (PA) andNon-Gaussianity (NG), originally conceived for the Mean Apparent Propagatordiffusion MRI (MAP-MRI), to the Micro-Structure adaptive convolution ker-nels and dual Fourier Integral Transforms (MiSFIT). These measures describerelevant normalized features of the Ensemble Average Propagator (EAP).Theory and Methods:First, the indices, which are defined as the EAP’sdissimilarity from an isotropic (PA) or a Gaussian (NG) one, are analyticallyreformulated within the MiSFIT framework. Then a comparison between theresulting maps is drawn by means of a visual analysis, a quantitative assess-ment via numerical simulations, a test-retest study across the MICRA dataset (6subjects scanned five times) and, finally, a computational time evaluation.Results:Findings illustrate the visual similarity between the indices computedwith either technique. Evaluation against synthetic ground truth data, however,demonstrates MiSFIT’s improved accuracy. In addition, the test–retest studyreveals MiSFIT’s higher degree of reliability in most of white matter regions.Finally, the computational time evaluation shows MiSFIT’s time reduction upto two orders of magnitude.Conclusions:Despite being a direct development on the MAP-MRI represen-tation, the PA and the NG can be reliably and efficiently computed withinMiSFIT’s framework. This, together with the previous findings in the originalMiSFIT’s article, could mean the difference that definitely qualifies diffusionMRI to be incorporated into regular clinical settings.Ministerio de Educación, Junta de Castilla y León y Fondo Social Europeo, (Grant/Award Number: OrdenEDU/1100/2017 12/12)Ministerio de Ciencia e Innovación, Grant/AwardNumbers: (RTI2018-094569-B-I00),(PID2021-124407NB-I00)Ministry of Science and Higher Education of Poland,(Grant/Award Number:692/STYP/13/2018)Narodowa Agencja Wymiany Akademickiej, (Grant/AwardNumber: PPN/BEK/2019/1/00421

Apparent propagator anisotropy from single-shell diffusion MRI acquisitions

Purpose The apparent propagator anisotropy (APA) is a new diffusion MRI metric that, while drawing on the benefits of the ensemble averaged propagator anisotropy (PA) compared to the fractional anisotropy (FA), can be estimated from single‐shell data. Theory and Methods Computation of the full PA requires acquisition of large datasets with many diffusion directions and different b‐values, and results in extremely long processing times. This has hindered adoption of the PA by the community, despite evidence that it provides meaningful information beyond the FA. Calculation of the complete propagator can be avoided under the hypothesis that a similar sensitivity/specificity may be achieved from apparent measurements at a given shell. Assuming that diffusion anisotropy (DiA) is nondependent on the b‐value, a closed‐form expression using information from one single shell (ie, b‐value) is reported. Results Publicly available databases with healthy and diseased subjects are used to compare the APA against other anisotropy measures. The structural information provided by the APA correlates with that provided by the PA for healthy subjects, while it also reveals statistically relevant differences in white matter regions for two pathologies, with a higher reliability than the FA. Additionally, APA has a computational complexity similar to the FA, with processing‐times several orders of magnitude below the PA. Conclusions The APA can extract more relevant white matter information than the FA, without any additional demands on data acquisition. This makes APA an attractive option for adoption into existing diffusion MRI analysis pipelines

Micro-structure diffusion scalar measures from reduced MRI acquisitions

In diffusion MRI, the Ensemble Average diffusion Propagator (EAP) provides relevant microstructural information and meaningful descriptive maps of the white matter previously obscured by traditional techniques like the Diffusion Tensor. The direct estimation of the EAP, however, requires a dense sampling of the Cartesian q-space. Due to the huge amount of samples needed for an accurate reconstruction, more efficient alternative techniques have been proposed in the last decade. Even so, all of them imply acquiring a large number of diffusion gradients with different b-values. In order to use the EAP in practical studies, scalar measures must be directly derived, being the most common the return-to-origin probability (RTOP) and the return-to-plane and return-to-axis probabilities (RTPP, RTAP). In this work, we propose the so-called “Apparent Measures Using Reduced Acquisitions” (AMURA) to drastically reduce the number of samples needed for the estimation of diffusion properties. AMURA avoids the calculation of the whole EAP by assuming the diffusion anisotropy is roughly independent from the radial direction. With such an assumption, and as opposed to common multi-shell procedures based on iterative optimization, we achieve closed-form expressions for the measures using information from one single shell. This way, the new methodology remains compatible with standard acquisition protocols commonly used for HARDI (based on just one b-value). We report extensive results showing the potential of AMURA to reveal microstructural properties of the tissues compared to state of the art EAP estimators, and is well above that of Diffusion Tensor techniques. At the same time, the closed forms provided for RTOP, RTPP, and RTAP-like magnitudes make AMURA both computationally efficient and robust

Anisotropy measure from three diffusion-encoding gradient directions

Producción CientíficaWe propose a method that can provide information about the anisotropy and orientation of diffusion in the brain from only 3 orthogonal gradient directions without imposing additional assumptions. The method is based on the Diffusion Anisotropy (DiA) that measures the distance from a diffusion signal to its isotropic equivalent. The original formulation based on a Spherical Harmonics basis allows to go down to only 3 orthogonal directions in order to estimate the measure. In addition, an alternative simplification and a color-coding representation are also proposed. Acquisitions from a publicly available database are used to test the viability of the proposal. The DiA succeeded in providing anisotropy information from the white matter using only 3 diffusion-encoding directions. The price to pay for such reduced acquisition is an increment in the variability of the data and a subestimation of the metric on those tracts not aligned with the acquired directions. Nevertheless, the calculation of anisotropy information from DMRI is feasible using fewer than 6 gradient directions by using DiA. The method is totally compatible with existing acquisition protocols, and it may provide complementary information about orientation in fast diffusion acquisitions.Ministerio de Ciencia e Innovación (grant RTI2018-094569-B-I00)Wellcome Trust Investigator Award (award 096646/Z/11/Z)Wellcome Trust Strategic Award (award 104943/Z/14/Z

Moment-based representation of the diffusion inside the brain from reduced DMRI acquisitions: Generalized AMURA

Producción CientíficaAMURA (Apparent Measures Using Reduced Acquisitions) was originally proposed as a method to infer micro-structural information from single-shell acquisitions in diffusion MRI. It reduces the number of samples needed and the computational complexity of the estimation of diffusion properties of tissues by assuming the diffusion anisotropy is roughly independent on the b-value. This simplification allows the computation of simplified expressions and makes it compatible with standard acquisition protocols commonly used even in clinical practice. The present work proposes an extension of AMURA that allows the calculation of general moments of the diffusion signals that can be applied to describe the diffusion process with higher accuracy. We provide simplified expressions to analytically compute a set of scalar indices as moments of arbitrary orders over either the whole 3-D space, particular directions, or particular planes. The existing metrics previously proposed for AMURA (RTOP, RTPP and RTAP) are now special cases of this generalization. An extensive set of experiments is performed on public data and a clinical clase acquired with a standard type acquisition. The new metrics provide additional information about the diffusion processes inside the brain.Ministerio de Ciencia, Innovación y Universidades (grant RTI2018-094569-B-I00)Polish National Agency for Academic Exchange (grant PN/BEK/2019/1/00421)Ministry of Science and Higher Education of Poland (scholarship 692/STYP/13/2018)Junta de Castilla y León - Fondo Social Europeo (ID: 376062

Spherical means-based free-water volume fraction from diffusion MRI increases non-linearly with age in the white matter of the healthy human brain

Producción CientíficaThe term free-water volume fraction (FWVF) refers to the signal fraction that could be found as the cerebrospinal fluid of the brain, which has been demonstrated as a sensitive measure that correlates with cognitive performance and various neuropathological processes. It can be quantified by properly fitting the isotropic component of the magnetic resonance (MR) signal in diffusion-sensitized sequences. Using healthy subjects (178F/109M) aged 25-94, this study examines in detail the evolution of the FWVF obtained with the spherical means technique from multi-shell acquisitions in the human brain white matter across the adult lifespan, which has been previously reported to exhibit a positive trend when estimated from single-shell data using the bi-tensor signal representation. We found evidence of a noticeably non-linear gain after the sixth decade of life, with a region-specific variate and varying change rate of the spherical means-based multi-shell FWVF parameter with age, at the same time, a heteroskedastic pattern across the adult lifespan is suggested. On the other hand, the FW corrected diffusion tensor imaging (DTI) leads to a region-dependent flattened age-related evolution of the mean diffusivity (MD) and fractional anisotropy (FA), along with a considerable reduction in their variability, as compared to the studies conducted over the standard (single-component) DTI. This way, our study provides a new perspective on the trajectory-based assessment of the brain and explains the conceivable reason for the variations observed in FA and MD parameters across the lifespan with previous studies under the standard diffusion tensor imaging.Ministerio de Ciencia e Innovación (MCIN-AEI) y FEDER-UE (grant PID2021-124407NB-I00)Ministerio de Ciencia e Innovación (MCIN-AEI) - Unión Europea “NextGenerationEU/PRTR” (grant TED2021-130758B-I00)Ministry of Science and Higher Education (Poland) - Bekker programme (grant PPN/BEK/2019/1/00421)Norwegian ExtraFoundation for Health and Rehabilitation (2015/FO5146)European Union's Horizon 2020 research and Innovation program (ERC 802998

Viability of AMURA biomarkers from single-shell diffusion MRI in clinical studies

Diffusion Tensor Imaging (DTI) is the most employed method to assess white matter properties using quantitative parameters derived from diffusion MRI, but it presents known limitations that restrict the evaluation of complex structures. The objective of this study was to validate the reliability and robustness of complementary diffusion measures extracted with a novel approach, Apparent Measures Using Reduced Acquisitions (AMURA), with a typical diffusion MRI acquisition from a clinical context in comparison with DTI with application to clinical studies. Fifty healthy controls, 51 episodic migraine and 56 chronic migraine patients underwent single-shell diffusion MRI. Four DTI-based and eight AMURA-based parameters were compared between groups with tract-based spatial statistics to establish reference results. On the other hand, following a region-based analysis, the measures were assessed for multiple subsamples with diverse reduced sample sizes and their stability was evaluated with the coefficient of quartile variation. To assess the discrimination power of the diffusion measures, we repeated the statistical comparisons with a region-based analysis employing reduced sample sizes with diverse subsets, decreasing 10 subjects per group for consecutive reductions, and using 5,001 different random subsamples. For each sample size, the stability of the diffusion descriptors was evaluated with the coefficient of quartile variation. AMURA measures showed a greater number of statistically significant differences in the reference comparisons between episodic migraine patients and controls compared to DTI. In contrast, a higher number of differences was found with DTI parameters compared to AMURA in the comparisons between both migraine groups. Regarding the assessments reducing the sample size, the AMURA parameters showed a more stable behavior than DTI, showing a lower decrease for each reduced sample size or a higher number of regions with significant differences. However, most AMURA parameters showed lower stability in relation to higher coefficient of quartile variation values than the DTI descriptors, although two AMURA measures showed similar values to DTI. For the synthetic signals, there were AMURA measures with similar quantification to DTI, while other showed similar behavior. These findings suggest that AMURA presents favorable characteristics to identify differences of specific microstructural properties between clinical groups in regions with complex fiber architecture and lower dependency on the sample size or assessing technique than DTI.Grants PID2021-124407NB-I00, TED2021-130758B-I00 - MCIN/AEI/10.13039/501100011033 and the European Union NextGenerationEU/PRT

Viability of AMURA biomarkers from single-shell diffusion MRI in clinical studies

Diffusion Tensor Imaging (DTI) is the most employed method to assess white matter properties using quantitative parameters derived from diffusion MRI, but it presents known limitations that restrict the evaluation of complex structures. The objective of this study was to validate the reliability and robustness of complementary diffusion measures extracted with a novel approach, Apparent Measures Using Reduced Acquisitions (AMURA), with a typical diffusion MRI acquisition from a clinical context in comparison with DTI with application to clinical studies. Fifty healthy controls, 51 episodic migraine and 56 chronic migraine patients underwent single-shell diffusion MRI. Four DTI-based and eight AMURA-based parameters were compared between groups with tract-based spatial statistics to establish reference results. On the other hand, following a region-based analysis, the measures were assessed for multiple subsamples with diverse reduced sample sizes and their stability was evaluated with the coefficient of quartile variation. To assess the discrimination power of the diffusion measures, we repeated the statistical comparisons with a region-based analysis employing reduced sample sizes with diverse subsets, decreasing 10 subjects per group for consecutive reductions, and using 5,001 different random subsamples. For each sample size, the stability of the diffusion descriptors was evaluated with the coefficient of quartile variation. AMURA measures showed a greater number of statistically significant differences in the reference comparisons between episodic migraine patients and controls compared to DTI. In contrast, a higher number of differences was found with DTI parameters compared to AMURA in the comparisons between both migraine groups. Regarding the assessments reducing the sample size, the AMURA parameters showed a more stable behavior than DTI, showing a lower decrease for each reduced sample size or a higher number of regions with significant differences. However, most AMURA parameters showed lower stability in relation to higher coefficient of quartile variation values than the DTI descriptors, although two AMURA measures showed similar values to DTI. For the synthetic signals, there were AMURA measures with similar quantification to DTI, while other showed similar behavior. These findings suggest that AMURA presents favorable characteristics to identify differences of specific microstructural properties between clinical groups in regions with complex fiber architecture and lower dependency on the sample size or assessing technique than DTI