Accelerated Microstructure Imaging via Convex Optimization (AMICO) from diffusion MRI data

Microstructure imaging from diffusion magnetic resonance (MR) data represents an invaluable tool to study non-invasively the morphology of tissues and to provide a biological insight into their microstructural organization. In recent years, a variety of biophysical models have been proposed to associate particular patterns observed in the measured signal with specific microstructural properties of the neuronal tissue, such as axon diameter and fiber density. Despite very appealing results showing that the estimated microstructure indices agree very well with histological examinations, existing techniques require computationally very expensive non-linear procedures to fit the models to the data which, in practice, demand the use of powerful computer clusters for large-scale applications. In this work, we present a general framework for Accelerated Microstructure Imaging via Convex Optimization (AMICO) and show how to re-formulate this class of techniques as convenient linear systems which, then, can be efficiently solved using very fast algorithms. We demonstrate this linearization of the fitting problem for two specific models, i.e. ActiveAx and NODDI, providing a very attractive alternative for parameter estimation in those techniques; however, the AMICO framework is general and flexible enough to work also for the wider space of microstructure imaging methods. Results demonstrate that AMICO represents an effective means to accelerate the fit of existing techniques drastically (up to four orders of magnitude faster) while preserving accuracy and precision in the estimated model parameters (correlation above 0.9). We believe that the availability of such ultrafast algorithms will help to accelerate the spread of microstructure imaging to larger cohorts of patients and to study a wider spectrum of neurological disorders.

Disentangling micro from mesostructure by diffusion MRI: A Bayesian approach

Diffusion-sensitized magnetic resonance imaging probes the cellular structure of the human brain, but the primary microstructural information gets lost in averaging over higher-level, mesoscopic tissue organization such as different orientations of neuronal fibers. While such averaging is inevitable due to the limited imaging resolution, we propose a method for disentangling the microscopic cell properties from the effects of mesoscopic structure. We further avoid the classical fitting paradigm and use supervised machine learning in terms of a Bayesian estimator to estimate the microstructural properties. The method finds detectable parameters of a given microstructural model and calculates them within seconds, which makes it suitable for a broad range of neuroscientific applications.

Diffusion MRI in the brain - Theory and concepts

Over the past two decades, diffusion MRI has become an essential tool in neuroimaging investigations. This is due to its sensitivity to the motion of water molecules as they diffuse through the microstructural environment, allowing diffusion MRI to be used as a 'probe' of tissue microstructure. Furthermore, this sensitivity is strongly direction-dependent, notably in brain white matter, due to the alignment of structures that restrict or hinder the motion of water molecules, notably axonal membranes. This provides a means of inferring the orientation of fibres in vivo, and by use of appropriate fibre-tracking algorithms, of delineating the path of white matter tracts in the brain. The ability to perform so-called tractography in humans in vivo non-invasively is unique to diffusion MRI, and is now used in applications such as neurosurgery planning and more broadly within investigations of brain connectomics. This review describes the theory and concepts of diffusion MRI and describes its most important areas of application in the brain, with a strong focus on tractography.

Post-mortem inference of the human hippocampal connectivity and microstructure using ultra-high field diffusion MRI at 11.7 T

The human hippocampus plays a key role in memory management and is one of the first structures affected by Alzheimer's disease. Ultra-high magnetic resonance imaging provides access to its inner structure in vivo. However, gradient limitations on clinical systems hinder access to its inner connectivity and microstructure. A major target of this paper is the demonstration of diffusion MRI potential, using ultra-high field (11.7 T) and strong gradients (750 mT/m), to reveal the extra- and intra-hippocampal connectivity in addition to its microstructure. To this purpose, a multiple-shell diffusion-weighted acquisition protocol was developed to reach an ultra-high spatio-angular resolution with a good signal-to-noise ratio. The MRI data set was analyzed using analytical Q-Ball Imaging, Diffusion Tensor Imaging (DTI), and Neurite Orientation Dispersion and Density Imaging models. High Angular Resolution Diffusion Imaging estimates allowed us to obtain an accurate tractography resolving more complex fiber architecture than DTI models, and subsequently provided a map of the cross-regional connectivity. The neurite density was akin to that found in the histological literature, revealing the three hippocampal layers. Moreover, a gradient of connectivity and neurite density was observed between the anterior and the posterior part of the hippocampus. These results demonstrate that ex vivo ultra-high field/ultra-high gradients diffusion-weighted MRI allows the mapping of the inner connectivity of the human hippocampus, its microstructure, and to accurately reconstruct elements of the polysynaptic intra-hippocampal pathway using fiber tractography techniques at very high spatial/angular resolutions.

Not all voxels are created equal: Reducing estimation bias in regional NODDI metrics using tissue-weighted means

Neurite orientation dispersion and density imaging (NODDI) estimates microstructural properties of brain tissue relating to the organisation and processing capacity of neurites, which are essential elements for neuronal communication. Descriptive statistics of NODDI tissue metrics are commonly analyzed in regions-of-interest (ROI) to identify brain-phenotype associations. Here, the conventional method to calculate the ROI mean weights all voxels equally. However, this produces biased estimates in the presence of CSF partial volume. This study introduces the tissue-weighted mean, which calculates the mean NODDI metric across the tissue within an ROI, utilising the tissue fraction estimate from NODDI to reduce estimation bias. We demonstrate the proposed mean in a study of white matter abnormalities in young onset Alzheimer's disease (YOAD). Results show the conventional mean induces significant bias that correlates with CSF partial volume, primarily affecting periventricular regions and more so in YOAD subjects than in healthy controls. Due to the differential extent of bias between healthy controls and YOAD subjects, the conventional mean under- or over-estimated the effect size for group differences in many ROIs. This demonstrates the importance of using the correct estimation procedure when inferring group differences in studies where the extent of CSF partial volume differs between groups. These findings are robust across different acquisition and processing conditions. Bias persists in ROIs at higher image resolution, as demonstrated using data obtained from the third phase of the Alzheimer's disease neuroimaging initiative (ADNI); and when performing ROI analysis in template space. This suggests that conventional ROI means of NODDI metrics are biased estimates under most contemporary experimental conditions, the correction of which requires the proposed tissue-weighted mean. The tissue-weighted mean produces accurate estimates of ROI means and group differences when ROIs contain voxels with CSF partial volume. In addition to NODDI, the technique can be applied to other multi-compartment models that account for CSF partial volume, such as the free water elimination method. We expect the technique to help generate new insights into normal and abnormal variation in tissue microstructure of regions typically confounded by CSF partial volume, such as those in individuals with larger ventricles due to atrophy associated with neurodegenerative disease.

Data-Driven multi-Contrast spectral microstructure imaging with InSpect: INtegrated SPECTral component estimation and mapping

•

Unsupervised learning technique for spectroscopic analysis of quantitative MRI.

•

Shares information across voxels to improve estimation of multi-dimensional or single-dimensional spectra.

•

Spectral maps are dramatically improved compared to existing approaches.

•

Can potentially identify and map tissue environments; in placental diffusion-relaxometry MRI we demonstrate that it identifies components that correspond to distinct tissue types.

We introduce and demonstrate an unsupervised machine learning technique for spectroscopic analysis of quantitative MRI experiments. Our algorithm supports estimation of one-dimensional spectra from single-contrast data, and multidimensional correlation spectra from simultaneous multi-contrast data. These spectrum-based approaches allow model-free investigation of tissue properties, but require regularised inversion of a Laplace transform or Fredholm integral, which is an ill-posed calculation. Here we present a method that addresses this limitation in a data-driven way. The algorithm simultaneously estimates a canonical basis of spectral components and voxelwise maps of their weightings, thereby pooling information across whole images to regularise the ill-posed problem. We show in simulations that our algorithm substantially outperforms current voxelwise spectral approaches. We demonstrate the method on multi-contrast diffusion-relaxometry placental MRI scans, revealing anatomically-relevant sub-structures, and identifying dysfunctional placentas. Our algorithm vastly reduces the data required to reliably estimate spectra, opening up the possibility of quantitative MRI spectroscopy in a wide range of new applications. Our InSpect code is available at github.com/paddyslator/inspect.

Empirical reproducibility, sensitivity, and optimization of acquisition protocol, for Neurite Orientation Dispersion and Density Imaging using AMICO

Neurite Orientation Dispersion and Density Imaging (NODDI) has been gaining prominence for estimating multiple diffusion compartments from MRI data acquired in a clinically feasible time. To establish a pathway for adoption of NODDI in clinical studies, it is important to understand the sensitivity and reproducibility of NODDI metrics on empirical data in the context of acquisition protocol and brain anatomy. Previous studies addressed reproducibility across the 3 T scanners and within session and between subject reproducibility at 1.5 T and 3 T. However, empirical reproducibility on the performance of NODDI metrics based on b-value and diffusion-sensitized directions has not yet been addressed. In this study, we investigate a high angular resolution dataset with 11 repeats of a study with five b-values shells (1000, 1500, 2000, 2500 and 3000 s/mm2) and 96 directions per shell on a single subject. We validated the findings with a dataset from second subject with 10 repeats and 3 b-value shells (1000, 2000, 3000 s/mm2). The NODDI model was estimated using Accelerated Microstructure Imaging via Convex Optimization (AMICO) for different b-values and gradient directions on two-shell High Angular Resolution Density Imaging (HARDI) data fixing the lower shell at b = 1000 s/mm2. NODDI model applied to all acquired imaging data was used as a baseline gold standard for comparison. Additionally, we characterize orientation dispersion index (ODI) reproducibility using single-shell data. The experimental findings confirmed the sensitivity of intracellular volume fraction (Vic) with the choice of outer shell b-value more than with the choice of gradient directions. On the other hand, ODI is more sensitive to the number of gradient directions compared to b-value selection. Single-shell results for ODI are more comparable to 2-shell data at lower b-values than higher b-values. Recommended settings by region of interest and acquisition time are reported for the researchers considering using NODDI in human studies and/or comparing results across acquisition protocols.

Inferring spatial variations of microstructural properties from macroscopic mechanical response

Disease alters tissue microstructure, which in turn affects the macroscopic mechanical properties of tissue. In elasticity imaging, the macroscopic response is measured and is used to infer the spatial distribution of the elastic constitutive parameters. When an empirical constitutive model is used, these parameters cannot be linked to the microstructure. However, when the constitutive model is derived from a microstructural representation of the material, it allows for the possibility of inferring the local averages of the spatial distribution of the microstructural parameters. This idea forms the basis of this study. In particular, we first derive a constitutive model by homogenizing the mechanical response of a network of elastic, tortuous fibers. Thereafter, we use this model in an inverse problem to determine the spatial distribution of the microstructural parameters. We solve the inverse problem as a constrained minimization problem and develop efficient methods for solving it. We apply these methods to displacement fields obtained by deforming gelatin-agar co-gels and determine the spatial distribution of agar concentration and fiber tortuosity, thereby demonstrating that it is possible to image local averages of microstructural parameters from macroscopic measurements of deformation.

Cross-term-compensated gradient waveform design for tensor-valued diffusion MRI

Diffusion MRI uses magnetic field gradients to sensitize the signal to the random motion of spins. In addition to the prescribed gradient waveforms, background field gradients contribute to the diffusion weighting and thereby cause an error in the measured signal and consequent parameterization. The most prominent contribution to the error comes from so-called 'cross-terms.' In this work we present a novel gradient waveform design that enables diffusion encoding that cancels such cross-terms and yields a more accurate measurement. This is achieved by numerical optimization that maximizes encoding efficiency with a simultaneous constraint on the 'cross-term sensitivity' (c = 0). We found that the optimized cross-term-compensated waveforms were superior to previous cross-term-compensated designs for a wide range of waveform types that yield linear, planar, and spherical b-tensor encoding. The efficacy of the proposed design was also demonstrated in practical experiments using a clinical MRI system. The sensitivity to cross-terms was evaluated in a water phantom with a folded surface which provoked strong internal field gradients. In every comparison, the cross-term-compensated waveforms were robust to the effects of background gradients, whereas conventional designs were not. We also propose a method to measure background gradients from diffusion-weighted data, and show that cross-term-compensated waveforms produce parameters that are markedly less dependent on the background compared to non-compensated designs. Finally, we also used simulations to show that the proposed cross-term compensation was robust to background gradients in the interval 0 to 3 mT/m, whereas non-compensated designs were impacted in terms of a severe signal and parameter bias. In conclusion, we have proposed and demonstrated a waveform design that yields efficient cross-term compensation and facilitates accurate diffusion MRI in the presence of static background gradients regardless of their amplitude and direction. The optimization framework is compatible with arbitrary spin-echo sequence timing and RF events, b-tensor shapes, suppression of concomitant gradient effects and motion encoding, and is shared in open source.

On the need for bundle-specific microstructure kernels in diffusion MRI

Probing microstructure with diffusion magnetic resonance imaging (dMRI) on a scale orders of magnitude below the imaging resolution relies on biophysical modelling of the signal response in the tissue. The vast majority of these biophysical models of diffusion in white matter assume that the measured dMRI signal is the sum of the signals emanating from each of the constituent compartments, each of which exhibits a distinct behaviour in the b-value and/or orientation domain. Many of these models further assume that the dMRI behaviour of the oriented compartments (e.g. the intra-axonal space) is identical between distinct fibre populations, at least at the level of a single voxel. This implicitly assumes that any potential biological differences between fibre populations are negligible, at least as far as is measurable using dMRI. Here, we validate this assumption by means of a voxel-wise, model-free signal decomposition that, under the assumption above and in the absence of noise, is shown to be rank-1. We evaluate the effect size of signal components beyond this rank-1 representation and use permutation testing to assess their significance. We conclude that in the healthy adult brain, the dMRI signal is adequately represented by a rank-1 model, implying that biologically more realistic, but mathematically more complex fascicle-specific microstructure models do not capture statistically significant or anatomically meaningful structure, even in extended high-b diffusion MRI scans.

Estimating Tissue Microstructure with Undersampled Diffusion Data via Graph Convolutional Neural Networks

Advanced diffusion models for tissue microstructure are widely employed to study brain disorders. However, these models usually require diffusion MRI (DMRI) data with densely sampled q-space, which is prohibitive in clinical settings. This problem can be resolved by using deep learning techniques, which learn the mapping between sparsely sampled q-space data and the high-quality diffusion microstructural indices estimated from densely sampled data. However, most existing methods simply view the input DMRI data as a vector without considering data structure in the q-space. In this paper, we propose to overcome this limitation by representing DMRI data using graphs and utilizing graph convolutional neural networks to estimate tissue microstructure. Our method makes full use of the q-space angular neighboring information to improve estimation accuracy. Experimental results based on data from the Baby Connectome Project demonstrate that our method outperforms state-of-the-art methods both qualitatively and quantitatively.

Improved gray matter surface based spatial statistics in neuroimaging studies

Neuroimaging often involves acquiring high-resolution anatomical images along with other low-resolution image modalities, like diffusion and functional magnetic resonance imaging. Performing gray matter statistics with low-resolution image modalities is a challenge due to registration artifacts and partial volume effects. Gray matter surface based spatial statistics (GS-BSS) has been shown to provide higher sensitivity using gray matter surfaces compared to that of skeletonization approach of gray matter based spatial statistics which is adapted from tract based spatial statistics in diffusion studies. In this study, we improve upon GS-BSS incorporating neurite orientation dispersion and density imaging (NODDI) based search (denoted N-GSBSS) by 1) enhancing metrics mapping from native space, 2) incorporating maximum orientation dispersion index (ODI) search along surface normal, and 3) proposing applicability to other modalities, such as functional MRI (fMRI). We evaluated the performance of N-GSBSS against three baseline pipelines: volume-based registration, FreeSurfer's surface registration and ciftify pipeline for fMRI and simulation studies. First, qualitative mean ODI results are shown for N-GSBSS with and without NODDI based search in comparison with ciftify pipeline. Second, we conducted one-sample t-tests on working memory activations in fMRI to show that the proposed method can aid in the analysis of low resolution fMRI data. Finally we performed a sensitivity test in a simulation study by varying percentage change of intensity values within a region of interest in gray matter probability maps. N-GSBSS showed higher sensitivity in the simulation test compared to the other methods capturing difference between the groups starting at 10% change in the intensity values. The computational time of N-GSBSS is 68 times faster than that of traditional surface-based or 86 times faster than that of ciftify pipeline analysis.

Hybrid Graph Transformer for Tissue Microstructure Estimation with Undersampled Diffusion MRI Data

Advanced contemporary diffusion models for tissue microstructure often require diffusion MRI (DMRI) data with sufficiently dense sampling in the diffusion wavevector space for reliable model fitting, which might not always be feasible in practice. A potential remedy to this problem is by using deep learning techniques to predict high-quality diffusion microstructural indices from sparsely sampled data. However, existing methods are either agnostic to the data geometry in the diffusion wavevector space ( q -space) or limited to leveraging information from only local neighborhoods in the physical coordinate space ( x -space). Here, we propose a hybrid graph transformer (HGT) to explicitly consider the q -space geometric structure with a graph neural network (GNN) and make full use of spatial information with a novel residual dense transformer (RDT). The RDT consists of multiple densely connected transformer layers and a residual connection to facilitate model training. Extensive experiments on the data from the Human Connectome Project (HCP) demonstrate that our method significantly improves the quality of microstructural estimations over existing state-of-the-art methods.

P2T2: A physically-primed deep-neural-network approach for robust T2 distribution estimation from quantitative T2-weighted MRI

Estimating T₂ relaxation time distributions from multi-echo T₂-weighted MRI (T₂W) data can provide valuable biomarkers for assessing inflammation, demyelination, edema, and cartilage composition in various pathologies, including neurodegenerative disorders, osteoarthritis, and tumors. Deep neural network (DNN) based methods have been proposed to address the complex inverse problem of estimating T₂ distributions from MRI data, but they are not yet robust enough for clinical data with low Signal-to-Noise ratio (SNR) and are highly sensitive to distribution shifts such as variations in echo-times (TE) used during acquisition. Consequently, their application is hindered in clinical practice and large-scale multi-institutional trials with heterogeneous acquisition protocols. We propose a physically-primed DNN approach, called P₂T₂, that incorporates the signal decay forward model in addition to the MRI signal into the DNN architecture to improve the accuracy and robustness of T₂ distribution estimation. We evaluated our P₂T₂ model in comparison to both DNN-based methods and classical methods for T₂ distribution estimation using 1D and 2D numerical simulations along with clinical data. Our model improved the baseline model's accuracy for low SNR levels (SNR<80) which are common in the clinical setting. Further, our model achieved a ∼35% improvement in robustness against distribution shifts in the acquisition process compared to previously proposed DNN models. Finally, Our P₂T₂ model produces the most detailed Myelin-Water fraction maps compared to baseline approaches when applied to real human MRI data. Our P₂T₂ model offers a reliable and precise means of estimating T₂ distributions from MRI data and shows promise for use in large-scale multi-institutional trials with heterogeneous acquisition protocols. Our source code is available at: https://github.com/Hben-atya/P2T2-Robust-T2-estimation.git.