Time-division multiplexing (TDM) sequence removes bias in T2 estimation and relaxation-diffusion measurements.

Purpose: To compare the performance of multi-echo (ME) and time-division multiplexing (TDM) sequences for accelerated relaxation-diffusion MRI (rdMRI) acquisition and to examine their reliability in estimating accurate rdMRI microstructure measures. Method: The ME, TDM, and the reference single-echo (SE) sequences with six echo times (TE) were implemented using Pulseq with single-band (SB-) and multi-band 2 (MB2-) acceleration factors. On a diffusion phantom, the image intensities of the three sequences were compared, and the differences were quantified using the normalized root mean squared error (NRMSE). For the in-vivo brain scan, besides the image intensity comparison and T2-estimates, different methods were used to assess sequence-related effects on microstructure estimation, including the relaxation diffusion imaging moment (REDIM) and the maximum-entropy relaxation diffusion distribution (MaxEnt-RDD). Results: TDM performance was similar to the gold standard SE acquisition, whereas ME showed greater biases (3-4× larger NRMSEs for phantom, 2× for in-vivo). T2 values obtained from TDM closely matched SE, whereas ME sequences underestimated the T2 relaxation time. TDM provided similar diffusion and relaxation parameters as SE using REDIM, whereas SB-ME exhibited a 60% larger bias in the map and on average 3.5× larger bias in the covariance between relaxation-diffusion coefficients. Conclusion: Our analysis demonstrates that TDM provides a more accurate estimation of relaxation-diffusion measurements while accelerating the acquisitions by a factor of 2 to 3.

A review of algorithms and software for real-time electric field modeling techniques for transcranial magnetic stimulation.

Transcranial magnetic stimulation (TMS) is a device-based neuromodulation technique increasingly used to treat brain diseases. Electric field (E-field) modeling is an important technique in several TMS clinical applications, including the precision stimulation of brain targets with accurate stimulation density for the treatment of mental disorders and the localization of brain function areas for neurosurgical planning. Classical methods for E-field modeling usually take a long computation time. Fast algorithms are usually developed with significantly lower spatial resolutions that reduce the prediction accuracy and limit their usage in real-time or near real-time TMS applications. This review paper discusses several modern algorithms for real-time or near real-time TMS E-field modeling and their advantages and limitations. The reviewed methods include techniques such as basis representation techniques and deep neural-network-based methods. This paper also provides a review of software tools that can integrate E-field modeling with navigated TMS, including a recent software for real-time navigated E-field mapping based on deep neural-network models.

Reduced cross-scanner variability using vendor-agnostic sequences for single-shell diffusion MRI.

PURPOSE: To reduce the inter-scanner variability of diffusion MRI (dMRI) measures between scanners from different vendors by developing a vendor-neutral dMRI pulse sequence using the open-source vendor-agnostic Pulseq platform. METHODS: We implemented a standard EPI based dMRI sequence in Pulseq. We tested it on two clinical scanners from different vendors (Siemens Prisma and GE Premier), systematically evaluating and comparing the within- and inter-scanner variability across the vendors, using both the vendor-provided and Pulseq dMRI sequences. Assessments covered both a diffusion phantom and three human subjects, using standard error (SE) and Lin's concordance correlation to measure the repeatability and reproducibility of standard DTI metrics including fractional anisotropy (FA) and mean diffusivity (MD). RESULTS: Identical dMRI sequences were executed on both scanners using Pulseq. On the phantom, the Pulseq sequence showed more than a 2.5× reduction in SE (variability) across Siemens and GE scanners. Furthermore, Pulseq sequences exhibited markedly reduced SE in-vivo, maintaining scan-rescan repeatability while delivering lower variability in FA and MD (more than 50% reduction in cortical/subcortical regions) compared to vendor-provided sequences. CONCLUSION: The Pulseq diffusion sequence reduces the cross-scanner variability for both phantom and in-vivo data, which will benefit multi-center neuroimaging studies and improve the reproducibility of neuroimaging studies.

Neural orientation distribution fields for estimation and uncertainty quantification in diffusion MRI.

Inferring brain connectivity and structure in-vivo requires accurate estimation of the orientation distribution function (ODF), which encodes key local tissue properties. However, estimating the ODF from diffusion MRI (dMRI) signals is a challenging inverse problem due to obstacles such as significant noise, high-dimensional parameter spaces, and sparse angular measurements. In this paper, we address these challenges by proposing a novel deep-learning based methodology for continuous estimation and uncertainty quantification of the spatially varying ODF field. We use a neural field (NF) to parameterize a random series representation of the latent ODFs, implicitly modeling the often ignored but valuable spatial correlation structures in the data, and thereby improving efficiency in sparse and noisy regimes. An analytic approximation to the posterior predictive distribution is derived which can be used to quantify the uncertainty in the ODF estimate at any spatial location, avoiding the need for expensive resampling-based approaches that are typically employed for this purpose. We present empirical evaluations on both synthetic and real in-vivo diffusion data, demonstrating the advantages of our method over existing approaches.

DDParcel: Deep Learning Anatomical Brain Parcellation From Diffusion MRI.

Parcellation of anatomically segregated cortical and subcortical brain regions is required in diffusion MRI (dMRI) analysis for region-specific quantification and better anatomical specificity of tractography. Most current dMRI parcellation approaches compute the parcellation from anatomical MRI (T1- or T2-weighted) data, using tools such as FreeSurfer or CAT12, and then register it to the diffusion space. However, the registration is challenging due to image distortions and low resolution of dMRI data, often resulting in mislabeling in the derived brain parcellation. Furthermore, these approaches are not applicable when anatomical MRI data is unavailable. As an alternative we developed the Deep Diffusion Parcellation (DDParcel), a deep learning method for fast and accurate parcellation of brain anatomical regions directly from dMRI data. The input to DDParcel are dMRI parameter maps and the output are labels for 101 anatomical regions corresponding to the FreeSurfer Desikan-Killiany (DK) parcellation. A multi-level fusion network leverages complementary information in the different input maps, at three network levels: input, intermediate layer, and output. DDParcel learns the registration of diffusion features to anatomical MRI from the high-quality Human Connectome Project data. Then, to predict brain parcellation for a new subject, the DDParcel network no longer requires anatomical MRI data but only the dMRI data. Comparing DDParcel's parcellation with T1w-based parcellation shows higher test-retest reproducibility and a higher regional homogeneity, while requiring much less computational time. Generalizability is demonstrated on a range of populations and dMRI acquisition protocols. Utility of DDParcel's parcellation is demonstrated on tractography analysis for fiber tract identification.

SlicerTMS: Real-Time Visualization of Transcranial Magnetic Stimulation for Mental Health Treatment.

We present a real-time visualization system for Transcranial Magnetic Stimulation (TMS), a non-invasive neuromodulation technique for treating various brain disorders and mental health diseases. Our solution targets the current challenges of slow and labor-intensive practices in treatment planning. Integrating Deep Learning (DL), our system rapidly predicts electric field (E-field) distributions in 0.2 seconds for precise and effective brain stimulation. The core advancement lies in our tool's real-time neuronavigation visualization capabilities, which support clinicians in making more informed decisions quickly and effectively. We assess our system's performance through three studies: First, a real-world use case scenario in a clinical setting, providing concrete feedback on applicability and usability in a practical environment. Second, a comparative analysis with another TMS tool focusing on computational efficiency across various hardware platforms. Lastly, we conducted an expert user study to measure usability and influence in optimizing TMS treatment planning. The system is openly available for community use and further development on GitHub: https://github.com/lorifranke/SlicerTMS.

A domain-agnostic MR reconstruction framework using a randomly weighted neural network.

Purpose: To design a randomly-weighted neural network that performs domain-agnostic MR image reconstruction from undersampled k-space data without the need for ground truth or extensive in-vivo training datasets. The network performance must be similar to the current state-of-the-art algorithms that require large training datasets. Methods: We propose a Weight Agnostic randomly weighted Network method for MRI reconstruction (termed WAN-MRI) which does not require updating the weights of the neural network but rather chooses the most appropriate connections of the network to reconstruct the data from undersampled k-space measurements. The network architecture has three components, i.e. (1) Dimensionality Reduction Layers comprising of 3d convolutions, ReLu, and batch norm; (2) Reshaping Layer is Fully Connected layer; and (3) Upsampling Layers that resembles the ConvDecoder architecture. The proposed methodology is validated on fastMRI knee and brain datasets. Results: The proposed method provides a significant boost in performance for structural similarity index measure (SSIM) and root mean squared error (RMSE) scores on fastMRI knee and brain datasets at an undersampling factor of R=4 and R=8 while trained on fractal and natural images, and fine-tuned with only 20 samples from the fastMRI training k-space dataset. Qualitatively, we see that classical methods such as GRAPPA and SENSE fail to capture the subtle details that are clinically relevant. We either outperform or show comparable performance with several existing deep learning techniques (that require extensive training) like GrappaNET, VariationNET, J-MoDL, and RAKI. Conclusion: The proposed algorithm (WAN-MRI) is agnostic to reconstructing images of different body organs or MRI modalities and provides excellent scores in terms of SSIM, PSNR, and RMSE metrics and generalizes better to out-of-distribution examples. The methodology does not require ground truth data and can be trained using very few undersampled multi-coil k-space training samples.

Accelerating joint relaxation-diffusion MRI by integrating time division multiplexing and simultaneous multi-slice (TDM-SMS) strategies.

PURPOSE: To accelerate the acquisition of relaxation-diffusion imaging by integrating time-division multiplexing (TDM) with simultaneous multi-slice (SMS) for EPI and evaluate imaging quality and diffusion measures. METHODS: The time-division multiplexing (TDM) technique and SMS method were integrated to achieve a high slice-acceleration (e.g., 6×) factor for acquiring relaxation-diffusion MRI. Two variants of the sequence, referred to as TDM3e-SMS and TDM2s-SMS, were developed to simultaneously acquire slice groups with three distinct TEs and two slice groups with the same TE, respectively. Both sequences were evaluated on a 3T scanner with in vivo human brains and compared with standard single-band (SB) -EPI and SMS-EPI using diffusion measures and tractography results. RESULTS: Experimental results showed that the TDM3e-SMS sequence with total slice acceleration of 6 (multiplexing factor (MP) = 3 × multi-band factor (MB) = 2) provided similar image intensity and microstructure measures compared to standard SMS-EPI with MB = 2, and yielded less bias in intensity compared to standard SMS-EPI with MB = 4. The three sequences showed a similar positive correlation between TE and mean kurtosis (MK) and a negative correlation between TE and mean diffusivity (MD) in white matter. Multi-fiber tractography also shows consistency of results in TE-dependent measures between different sequences. The TDM2s-SMS sequence (MP = 2, MB = 2) also provided imaging measures similar to standard SMS-EPI sequences (MB = 2) for single-TE diffusion imaging. CONCLUSIONS: The TDM-SMS sequence can provide additional 2× to 3× acceleration to SMS without degrading imaging quality. With the significant reduction in scan time, TDM-SMS makes joint relaxation-diffusion MRI a feasible technique in neuroimaging research to investigate new markers of brain disorders.

White matter markers and predictors for subject-specific rTMS response in major depressive disorder.

Repetitive transcranial magnetic stimulation (rTMS) has established therapeutic efficacy for major depressive disorder (MDD). While translational research has focused primarily on understanding the mechanism of action of TMS on functional activation and connectivity, the effects on structural connectivity remain largely unknown especially when rTMS is applied using subject-specific brain targets. This study aims to use novel diffusion magnetic resonance imaging (dMRI) analysis to examine microstructural changes related to rTMS treatment response using a unique cohort of 21 patients with MDD treated using rTMS with subject-specific targets. White matter dMRI microstructural measures and clinical scores were captured before and after the full course of treatment. We defined disease-relevant fiber bundles connected to different subregions of the left prefrontal cortex and analyzed changes in diffusion properties as well as correlations between the changes of dMRI measures and the changes in Hamilton Depression Rating Scale (HAMD). No significant changes were observed in tracts connected to the TMS targets. rTMS significantly increased the extra-axonal free-water volume, fractional anisotropy and decreased the radial diffusivity in anterior-medial prefrontal fiber bundles but did not lead to raw changes in lateral prefrontal tracts. That said, the microstructural changes in the lateral prefrontal white matter were significantly correlated with treatment response. Moreover, pre-rTMS dMRI measures of the dorsal anterior cingulate cortex and lateral prefrontal cortex connections are correlated with changes in HAMD scores. Microstructural changes in the anterior-medial and lateral prefrontal white matter are potentially involved in treatment response to TMS, though further investigation is needed using larger datasets.

Rapid whole-brain electric field mapping in transcranial magnetic stimulation using deep learning.

Transcranial magnetic stimulation (TMS) is a non-invasive neurostimulation technique that is increasingly used in the treatment of neuropsychiatric disorders and neuroscience research. Due to the complex structure of the brain and the electrical conductivity variation across subjects, identification of subject-specific brain regions for TMS is important to improve the treatment efficacy and understand the mechanism of treatment response. Numerical computations have been used to estimate the stimulated electric field (E-field) by TMS in brain tissue. But the relative long computation time limits the application of this approach. In this paper, we propose a deep-neural-network based approach to expedite the estimation of whole-brain E-field by using a neural network architecture, named 3D-MSResUnet and multimodal imaging data. The 3D-MSResUnet network integrates the 3D U-net architecture, residual modules and a mechanism to combine multi-scale feature maps. It is trained using a large dataset with finite element method (FEM) based E-field and diffusion magnetic resonance imaging (MRI) based anisotropic volume conductivity or anatomical images. The performance of 3D-MSResUnet is evaluated using several evaluation metrics and different combinations of imaging modalities and coils. The experimental results show that the output E-field of 3D-MSResUnet provides reliable estimation of the E-field estimated by the state-of-the-art FEM method with significant reduction in prediction time to about 0.24 second. Thus, this study demonstrates that neural networks are potentially useful tools to accelerate the prediction of E-field for TMS targeting.

Accelerated diffusion and relaxation-diffusion MRI using time-division multiplexing EPI.

PURPOSE: To develop a time-division multiplexing echo-planar imaging (TDM-EPI) sequence for approximately two- to threefold acceleration when acquiring joint relaxation-diffusion MRI data with multiple TEs. METHODS: The proposed TDM-EPI sequence interleaves excitation and data collection for up to 3 separate slices at different TEs and uses echo-shifting gradients to disentangle the overlapping echo signals during the readout period. By properly arranging the sequence event blocks for each slice and adjusting the echo-shifting gradients, diffusion-weighted images from separate slices can be acquired. Therefore, we present 2 variants of the sequence. A single-TE TDM-EPI is presented to demonstrate the concept. Next, a multi-TE TDM-EPI is presented to highlight the advantages of the TDM approach for relaxation-diffusion imaging. These sequences were evaluated on a 3 Tesla scanner with a water phantom and in vivo human brain data. RESULTS: The single-TE TDM-EPI sequence can simultaneously acquire 2 slices with a maximum b value of 3000 s/mm2 and 2.5 mm isotropic resolution using interleaved readout windows with TE ≈ 78 ms. With the same b value and resolution, the multi-TE TDM-EPI sequence can simultaneously acquire 2 or 3 separate slices using interleaved readout sections with shortest TE ≈ 70 ms and ΔTE ≈ 30 ms. Phantom and in vivo experiments have shown that the proposed TDM-EPI sequences can provide similar image quality and diffusion measures as conventional EPI readouts with multiple echoes but can reduce the overall relaxation-diffusion protocol scan time by approximately two- to threefold. CONCLUSION: TDM-EPI is a novel approach to acquire diffusion imaging data at multiple TEs. This enables a significant reduction in acquisition time for relaxation-diffusion MRI experiments but without compromising image quality and diffusion measurements, thus removing a significant barrier to the adoption of relaxation-diffusion MRI in clinical research studies of neurological and mental disorders.

Deep learning based segmentation of brain tissue from diffusion MRI.

Segmentation of brain tissue types from diffusion MRI (dMRI) is an important task, required for quantification of brain microstructure and for improving tractography. Current dMRI segmentation is mostly based on anatomical MRI (e.g., T1- and T2-weighted) segmentation that is registered to the dMRI space. However, such inter-modality registration is challenging due to more image distortions and lower image resolution in dMRI as compared with anatomical MRI. In this study, we present a deep learning method for diffusion MRI segmentation, which we refer to as DDSeg. Our proposed method learns tissue segmentation from high-quality imaging data from the Human Connectome Project (HCP), where registration of anatomical MRI to dMRI is more precise. The method is then able to predict a tissue segmentation directly from new dMRI data, including data collected with different acquisition protocols, without requiring anatomical data and inter-modality registration. We train a convolutional neural network (CNN) to learn a tissue segmentation model using a novel augmented target loss function designed to improve accuracy in regions of tissue boundary. To further improve accuracy, our method adds diffusion kurtosis imaging (DKI) parameters that characterize non-Gaussian water molecule diffusion to the conventional diffusion tensor imaging parameters. The DKI parameters are calculated from the recently proposed mean-kurtosis-curve method that corrects implausible DKI parameter values and provides additional features that discriminate between tissue types. We demonstrate high tissue segmentation accuracy on HCP data, and also when applying the HCP-trained model on dMRI data from other acquisitions with lower resolution and fewer gradient directions.

Probing tissue microstructure by diffusion skewness tensor imaging.

Probing the cellular structure of in vivo biological tissue is a fundamental problem in biomedical imaging and medical science. This work introduces an approach for analyzing diffusion magnetic resonance imaging data acquired by the novel tensor-valued encoding technique for characterizing tissue microstructure. Our approach first uses a signal model to estimate the variance and skewness of the distribution of apparent diffusion tensors modeling the underlying tissue. Then several novel imaging indices, such as weighted microscopic anisotropy and microscopic skewness, are derived to characterize different ensembles of diffusion processes that are indistinguishable by existing techniques. The contributions of this work also include a theoretical proof that shows that, to estimate the skewness of a diffusion tensor distribution, the encoding protocol needs to include full-rank tensor diffusion encoding. This proof provides a guideline for the application of this technique. The properties of the proposed indices are illustrated using both synthetic data and in vivo data acquired from a human brain.

Quantifying Genetic and Environmental Influence on Gray Matter Microstructure Using Diffusion MRI.

Early neuroimaging work in twin studies focused on studying genetic and environmental influence on gray matter macrostructure. However, it is also important to understand how gray matter microstructure is influenced by genes and environment to facilitate future investigations of their influence in mental disorders. Advanced diffusion MRI (dMRI) measures allow more accurate assessment of gray matter microstructure compared with conventional diffusion tensor measures. To understand genetic and environmental influence on gray matter, we used diffusion and structural MRI data from a large twin and sibling study (N = 840) and computed advanced dMRI measures including return to origin probability (RTOP), which is heavily weighted toward intracellular and intra-axonal restricted spaces, and mean squared displacement (MSD), more heavily weighted to diffusion in extracellular space and large cell bodies in gray matter. We show that while macrostructural features like brain volume are mainly genetically influenced, RTOP and MSD can together tap into both genetic and environmental influence on microstructure.

Cross-scanner and cross-protocol multi-shell diffusion MRI data harmonization: Algorithms and results.

Cross-scanner and cross-protocol variability of diffusion magnetic resonance imaging (dMRI) data are known to be major obstacles in multi-site clinical studies since they limit the ability to aggregate dMRI data and derived measures. Computational algorithms that harmonize the data and minimize such variability are critical to reliably combine datasets acquired from different scanners and/or protocols, thus improving the statistical power and sensitivity of multi-site studies. Different computational approaches have been proposed to harmonize diffusion MRI data or remove scanner-specific differences. To date, these methods have mostly been developed for or evaluated on single b-value diffusion MRI data. In this work, we present the evaluation results of 19 algorithms that are developed to harmonize the cross-scanner and cross-protocol variability of multi-shell diffusion MRI using a benchmark database. The proposed algorithms rely on various signal representation approaches and computational tools, such as rotational invariant spherical harmonics, deep neural networks and hybrid biophysical and statistical approaches. The benchmark database consists of data acquired from the same subjects on two scanners with different maximum gradient strength (80 and 300 â€‹mT/m) and with two protocols. We evaluated the performance of these algorithms for mapping multi-shell diffusion MRI data across scanners and across protocols using several state-of-the-art imaging measures. The results show that data harmonization algorithms can reduce the cross-scanner and cross-protocol variabilities to a similar level as scan-rescan variability using the same scanner and protocol. In particular, the LinearRISH algorithm based on adaptive linear mapping of rotational invariant spherical harmonics features yields the lowest variability for our data in predicting the fractional anisotropy (FA), mean diffusivity (MD), mean kurtosis (MK) and the rotationally invariant spherical harmonic (RISH) features. But other algorithms, such as DIAMOND, SHResNet, DIQT, CMResNet show further improvement in harmonizing the return-to-origin probability (RTOP). The performance of different approaches provides useful guidelines on data harmonization in future multi-site studies.

High-fidelity, accelerated whole-brain submillimeter in vivo diffusion MRI using gSlider-spherical ridgelets (gSlider-SR).

PURPOSE: To develop an accelerated, robust, and accurate diffusion MRI acquisition and reconstruction technique for submillimeter whole human brain in vivo scan on a clinical scanner. METHODS: We extend the ultra-high resolution diffusion MRI acquisition technique, gSlider, by allowing undersampling in q-space and radiofrequency (RF)-encoding space, thereby dramatically reducing the total acquisition time of conventional gSlider. The novel method, termed gSlider-SR, compensates for the lack of acquired information by exploiting redundancy in the dMRI data using a basis of spherical ridgelets (SR), while simultaneously enhancing the signal-to-noise ratio. Using Monte Carlo simulation with realistic noise levels and several acquisitions of in vivo human brain dMRI data (acquired on a Siemens Prisma 3T scanner), we demonstrate the efficacy of our method using several quantitative metrics. RESULTS: For high-resolution dMRI data with realistic noise levels (synthetically added), we show that gSlider-SR can reconstruct high-quality dMRI data at different acceleration factors preserving both signal and angular information. With in vivo data, we demonstrate that gSlider-SR can accurately reconstruct 860 µm diffusion MRI data (64 diffusion directions at b=2000s/mm2 ), at comparable quality as that obtained with conventional gSlider with four averages, thereby providing an eight-fold reduction in scan time (from 1 hour 20 to 10 minutes). CONCLUSIONS: gSlider-SR enables whole-brain high angular resolution dMRI at a submillimeter spatial resolution with a dramatically reduced acquisition time, making it feasible to use the proposed scheme on existing clinical scanners.

Smooth interpolation of covariance matrices and brain network estimation: Part II.

This work focuses on the modeling of time-varying covariance matrices using the state covariance of linear systems. Following concepts from optimal mass transport, we investigate and compare three types of covariance paths which are solutions to different optimal control problems. One of the covariance paths solves the Schrödinger bridge problem (SBP). The other two types of covariance paths are based on generalizations of the Fisher-Rao metric in information geometry, which are the major contributions of this work. The general framework is an extension of the approach in [1] which focuses on linear systems without stochastic input. The performances of the three covariance paths are compared using synthetic data and a real-data example on the estimation of dynamic brain networks using functional magnetic resonance imaging.

Detecting microstructural white matter abnormalities of frontal pathways in children with ADHD using advanced diffusion models.

Studies using diffusion tensor imaging (DTI) have documented alterations in the attention and executive system in children and adolescents with attention-deficit/hyperactivity disorder (ADHD). While abnormalities in the frontal lobe have also been reported, the associated white matter fiber bundles have not been investigated comprehensively due to the complexity in tracing them through fiber crossings. Furthermore, most studies have used a non-specific DTI model to understand white matter abnormalities. We present results from a first study that uses a multi-shell diffusion MRI (dMRI) data set coupled with an advanced multi-fiber tractography algorithm to probe microstructural measures related to axonal/cellular density and volume of fronto-striato-thalamic pathways in children with ADHD (N = 30) and healthy controls (N = 28). Head motion was firstly examined as a priority in order to assure that no group difference existed. We investigated 45 different white matter fiber bundles in the brain. After correcting for multiple comparisons, we found lower axonal/cellular packing density and volume in ADHD children in 8 of the 45 fiber bundles, primarily in the right hemisphere as follows: 1) Superior longitudinal fasciculus-II (SLF-II) (right), 2) Thalamus to precentral gyrus (right), 3) Thalamus to superior-frontal gyrus (right), 4) Caudate to medial orbitofrontal gyrus (right), 5) Caudate to precentral gyrus (right), 6) Thalamus to paracentral gyrus (left), 7) Caudate to caudal middlefrontal gyrus (left), and 8) Cingulum (bilateral). Our results demonstrate reduced axonal/cellular density and volume in certain frontal lobe white matter fiber tracts, which sub-serve the attention function and executive control systems. Further, our work shows specific microstructural abnormalities in the striato-thalamo-cortical connections, which have not been previously reported in children with ADHD.

Joint RElaxation-Diffusion Imaging Moments to Probe Neurite Microstructure.

Joint relaxation-diffusion measurements can provide new insight about the tissue microstructural properties. Most recent methods have focused on inverting the Laplace transform to recover the joint distribution of relaxation-diffusion. However, as is well-known, this problem is notoriously ill-posed and numerically unstable. In this work, we address this issue by directly computing the joint moments of transverse relaxation rate and diffusivity, which can be robustly estimated. To zoom into different parts of the joint distribution, we further enhance our method by applying multiplicative filters to the joint probability density function of relaxation and diffusion and compute the corresponding moments. We propose an approach to use these moments to compute several novel scalar indices to characterize specific properties of the underlying tissue microstructure. Furthermore, for the first time, we propose an algorithm to estimate diffusion signals that are independent of echo time based on the moments of the marginal probability density function of diffusion. We demonstrate its utility in extracting tissue information not contaminated with multiple intra-voxel relaxation rates. We compare the performance of four types of filters that zoom into tissue components with different relaxation and diffusion properties and demonstrate it on an in-vivo human dataset. Experimental results show that these filters are able to characterize heterogeneous tissue microstructure. Moreover, the filtered diffusion signals are also able to distinguish fiber bundles with similar orientations but different relaxation rates. The proposed method thus allows to characterize the neural microstructure information in a robust and unique manner not possible using existing techniques.