Estimation of fiber orientations using neighborhood information

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.

Denoising of Diffusion MRI Data via Graph Framelet Matching in x-q Space

Diffusion magnetic resonance imaging (DMRI) suffers from lower signal-to-noise-ratio (SNR) due to MR signal attenuation associated with the motion of water molecules. To improve SNR, the non-local means (NLM) algorithm has demonstrated state-of-the-art performance in noise reduction. However, existing NLM algorithms do not take into account explicitly the fact that DMRI signal can vary significantly with local fiber orientations. Applying NLM naïvely can hence blur subtle structures and aggravate partial volume effects. To overcome this limitation, we improve NLM by performing neighborhood matching in non-flat domains and removing noise with information from both x -space (spatial domain) and q -space (wavevector domain). Specifically, we first encode the q -space sampling domain using a graph. We then perform graph framelet transforms to extract robust rotation-invariant features for each sampling point in x-q space. The resulting features are employed for robust neighborhood matching to locate recurrent information. Finally, we remove noise via an NLM framework. To adapt to the various types of noise in multi-coil MR imaging, we transform the signal before denoising so that it is Gaussian-distributed, allowing noise removal to be carried out in an unbiased manner. Our method is able to more effectively locate recurrent information in white matter structures with different orientations, avoiding the blurring effects caused by naïvely applying NLM. Experiments on synthetic, repetitively-acquired, and infant DMRI data demonstrate that our method is able to preserve subtle structures while effectively removing noise.

Reconstructing High-Quality Diffusion MRI Data from Orthogonal Slice-Undersampled Data Using Graph Convolutional Neural Networks

Diffusion MRI (dMRI), while powerful for the characterization of tissue microstructure, suffers from long acquisition times. In this paper, we propose a super-resolution (SR) reconstruction method based on orthogonal slice-undersampling for accelerated dMRI acquisition. Instead of scanning full diffusion-weighted (DW) image volumes, only a subsample of equally-spaced slices need to be acquired. We show that complementary information from DW volumes corresponding to different diffusion wave-vectors can be harnessed using graph convolutional neural networks for reconstruction of the full DW volumes. We demonstrate that our SR reconstruction method outperforms typical interpolation methods and mitigates partial volume effects. Experimental results indicate that acceleration up to a factor of 5 can be achieved with minimal information loss.

XQ-SR: Joint x-q space super-resolution with application to infant diffusion MRI

Diffusion MRI (DMRI) is a powerful tool for studying early brain development and disorders. However, the typically low spatio-angular resolution of DMRI diminishes structural details and limits quantitative analysis to simple diffusion models. This problem is aggravated for infant DMRI since (i) the infant brain is significantly smaller than that of an adult, demanding higher spatial resolution to capture subtle structures; and (ii) the typically limited scan time of unsedated infants poses significant challenges to DMRI acquisition with high spatio-angular resolution. Post-acquisition super-resolution (SR) is an important alternative for increasing the resolution of DMRI data without prolonging acquisition times. However, most existing methods focus on the SR of only either the spatial domain (x-space) or the diffusion wavevector domain (q-space). For more effective resolution enhancement, we propose a framework for joint SR in both spatial and wavevector domains. More specifically, we first establish the signal relationships in x-q space using a robust neighborhood matching technique. We then harness the signal relationships to regularize the ill-posed inverse problem associated with the recovery of high-resolution data from their low-resolution counterpart. Extensive experiments on synthetic, adult, and infant DMRI data demonstrate that our method is able to recover high-resolution DMRI data with remarkably improved quality.

Multifold Acceleration of Diffusion MRI via Deep Learning Reconstruction from Slice-Undersampled Data

Diffusion MRI (dMRI), while powerful for characterization of tissue microstructure, suffers from long acquisition time. In this paper, we present a method for effective diffusion MRI reconstruction from slice-undersampled data. Instead of full diffusion-weighted (DW) image volumes, only a subsample of equally-spaced slices need to be acquired. We show that complementary information from DW volumes corresponding to different diffusion wavevectors can be harnessed using graph convolutional neural networks for reconstruction of the full DW volumes. The experimental results indicate a high acceleration factor of up to 5 can be achieved with minimal information loss.

A deep network for tissue microstructure estimation using modified LSTM units

Diffusion magnetic resonance imaging (dMRI) offers a unique tool for noninvasively assessing tissue microstructure. However, accurate estimation of tissue microstructure described by complicated signal models can be challenging when a reduced number of diffusion gradients are used. Deep learning based microstructure estimation has recently been developed and achieved promising results. In particular, optimization-based learning, where deep network structures are constructed by unfolding the iterative processes performed for solving optimization problems, has demonstrated great potential in accurate microstructure estimation with a reduced number of diffusion gradients. In this work, using the optimization-based learning strategy, we propose a deep network structure that is motivated by the use of historical information in iterative optimization for tissue microstructure estimation, and such incorporation of historical information has not been previously explored in the design of deep networks for microstructure estimation. We assume that (1) diffusion signals can be sparsely represented by a dictionary and its coefficients jointly in the spatial and angular domain, and (2) tissue microstructure can be computed from the sparse representation. Following these assumptions, our network comprises two cascaded stages. The first stage takes image patches as input and computes the spatial-angular sparse representation of the input with learned weights. Specifically, the network structure in the first stage is constructed by unfolding an iterative process for solving sparse reconstruction problems, where historical information is incorporated. The components in this network can be shown to correspond to modified long short-term memory (LSTM) units. In the second stage, fully connected layers are added to compute the mapping from the sparse representation to tissue microstructure. The weights in the two stages are learned jointly by minimizing the mean squared error of microstructure estimation. Experiments were performed on dMRI scans with a reduced number of diffusion gradients. For demonstration, we evaluated the estimation of tissue microstructure described by three signal models: the neurite orientation dispersion and density imaging (NODDI) model, the spherical mean technique (SMT) model, and the ensemble average propagator (EAP) model. The results indicate that the proposed approach outperforms competing methods.

Noise reduction in diffusion MRI using non-local self-similar information in joint x-q space

Diffusion MRI affords valuable insights into white matter microstructures, but suffers from low signal-to-noise ratio (SNR), especially at high diffusion weighting (i.e., b-value). To avoid time-intensive repeated acquisition, post-processing algorithms are often used to reduce noise. Among existing methods, non-local means (NLM) has been shown to be particularly effective. However, most NLM algorithms for diffusion MRI focus on patch matching in the spatial domain (i.e., x-space) and disregard the fact that the data live in a combined 6D space covering both spatial domain and diffusion wavevector domain (i.e., q-space). This drawback leads to inaccurate patch matching in curved white matter structures and hence the inability to effectively use recurrent information for noise reduction. The goal of this paper is to overcome this limitation by extending NLM to the joint x-q space. Specifically, we define for each point in the x-q space a spherical patch from which we extract rotation-invariant features for patch matching. The ability to perform patch matching across q-samples allows patches from differentially orientated structures to be used for effective noise removal. Extensive experiments on synthetic, repeated-acquisition, and HCP data demonstrate that our method outperforms state-of-the-art methods, both qualitatively and quantitatively.

Tracking and validation techniques for topographically organized tractography

Topographic regularity of axonal connections is commonly understood as the preservation of spatial relationships between nearby neurons and is a fundamental structural property of the brain. In particular the retinotopic mapping of the visual pathway can even be quantitatively computed. Inspired from this previously untapped anatomical knowledge, we propose a novel tractography method that preserves both topographic and geometric regularity. We make use of parameterized curves with Frenet-Serret frame and introduce a highly flexible mechanism for controlling geometric regularity. At the same time, we incorporate a novel local data support term in order to account for topographic organization. Unifying geometry with topographic regularity, we develop a Bayesian framework for generating highly organized streamlines that accurately follow neuroanatomy. We additionally propose two novel validation techniques to quantify topographic regularity. In our experiments, we studied the results of our approach with respect to connectivity, reproducibility and topographic regularity aspects. We present both qualitative and quantitative comparisons of our technique against three algorithms from MRtrix3. We show that our method successfully generates highly organized fiber tracks while capturing bundle anatomy that are geometrically challenging for other approaches.

A Multi-Tissue Global Estimation Framework for Asymmetric Fiber Orientation Distributions

In connectomics, tractography involves tracing connections across gray-white matter boundaries in gyral blades of complex cortical convolutions. To date, most tractography algorithms exhibit gyral bias with fiber streamlines preferentially terminating at gyral crowns rather than sulcal banks or fundi. In this work, we will demonstrate that a multi-tissue global estimation framework of the asymmetric fiber orientation distribution function (AFODF) will mitigate the effects of gyral bias and will allow fiber streamlines at gyral blades to make sharper turns into the cortical gray matter. This is validated using in-vivo data from the Human Connectome Project (HCP), showing that, in a typical gyral blade with high curvature, the fiber streamlines estimated using AFODFs bend more naturally into the cortex than FODFs. Furthermore, we show that AFODF tractography results in better cortico-cortical connectivity.

Angular Upsampling in Infant Diffusion MRI Using Neighborhood Matching in - Space

Diffusion MRI requires sufficient coverage of the diffusion wavevector space, also known as the q-space, to adequately capture the pattern of water diffusion in various directions and scales. As a result, the acquisition time can be prohibitive for individuals who are unable to stay still in the scanner for an extensive period of time, such as infants. To address this problem, in this paper we harness non-local self-similar information in the x-q space of diffusion MRI data for q-space upsampling. Specifically, we first perform neighborhood matching to establish the relationships of signals in x-q space. The signal relationships are then used to regularize an ill-posed inverse problem related to the estimation of high angular resolution diffusion MRI data from its low-resolution counterpart. Our framework allows information from curved white matter structures to be used for effective regularization of the otherwise ill-posed problem. Extensive evaluations using synthetic and infant diffusion MRI data demonstrate the effectiveness of our method. Compared with the widely adopted interpolation methods using spherical radial basis functions and spherical harmonics, our method is able to produce high angular resolution diffusion MRI data with greater quality, both qualitatively and quantitatively.

Laplace-based modeling of fiber orientation in the tongue

Mechanical modeling of tongue deformation plays a significant role in the study of breathing, swallowing, and speech production. In the absence of internal joints, fiber orientations determine the direction of sarcomeric contraction and have great influence over real and simulated tissue motion. However, subject-specific experimental observations of fiber distribution are difficult to obtain; thus, models of fiber distribution are generally used in mechanical simulations. This paper describes modeling of fiber distribution using solutions of Laplace equations and compares the effectiveness of this approach against tractography from diffusion tensor magnetic resonance imaging. The experiments included qualitative comparison of streamlines from the fiber model against experimental tractography, as well as quantitative differences between biomechanical simulations focusing in the region near the genioglossus. The model showed good overall agreement in terms of fiber directionality and muscle positioning when compared to subject-specific imaging results and the literature. The angle between the fiber distribution model against tractography in the genioglossus and geniohyoid muscles averaged [Formula: see text] likely due to experimental noise. However, kinematic responses were similar between simulations with modeled fibers versus experimentally obtained fibers; average discrepancy in surface displacement ranged from 1 to 7 mm, and average strain residual magnitude ranged from [Formula: see text] to 0.2. The results suggest that, for simulation purposes, the modeled fibers can act as a reasonable approximation for the tongue's fiber distribution. Also, given its agreement with the global tongue anatomy, the approach may be used in model-based reconstruction of displacement tracking and diffusion results.

Dictionary-based fiber orientation estimation with improved spatial consistency

Diffusion magnetic resonance imaging (dMRI) has enabled in vivo investigation of white matter tracts. Fiber orientation (FO) estimation is a key step in tract reconstruction and has been a popular research topic in dMRI analysis. In particular, the sparsity assumption has been used in conjunction with a dictionary-based framework to achieve reliable FO estimation with a reduced number of gradient directions. Because image noise can have a deleterious effect on the accuracy of FO estimation, previous works have incorporated spatial consistency of FOs in the dictionary-based framework to improve the estimation. However, because FOs are only indirectly determined from the mixture fractions of dictionary atoms and not modeled as variables in the objective function, these methods do not incorporate FO smoothness directly, and their ability to produce smooth FOs could be limited. In this work, we propose an improvement to Fiber Orientation Reconstruction using Neighborhood Information (FORNI), which we call FORNI+; this method estimates FOs in a dictionary-based framework where FO smoothness is better enforced than in FORNI alone. We describe an objective function that explicitly models the actual FOs and the mixture fractions of dictionary atoms. Specifically, it consists of data fidelity between the observed signals and the signals represented by the dictionary, pairwise FO dissimilarity that encourages FO smoothness, and weighted ℓ1-norm terms that ensure the consistency between the actual FOs and the FO configuration suggested by the dictionary representation. The FOs and mixture fractions are then jointly estimated by minimizing the objective function using an iterative alternating optimization strategy. FORNI+ was evaluated on a simulation phantom, a physical phantom, and real brain dMRI data. In particular, in the real brain dMRI experiment, we have qualitatively and quantitatively evaluated the reproducibility of the proposed method. Results demonstrate that FORNI+ produces FOs with better quality compared with competing methods.

Tissue microstructure estimation using a deep network inspired by a dictionary-based framework

Diffusion magnetic resonance imaging (dMRI) captures the anisotropic pattern of water displacement in the neuronal tissue and allows noninvasive investigation of the complex tissue microstructure. A number of biophysical models have been proposed to relate the tissue organization with the observed diffusion signals, so that the tissue microstructure can be inferred. The Neurite Orientation Dispersion and Density Imaging (NODDI) model has been a popular choice and has been widely used for many neuroscientific studies. It models the diffusion signal with three compartments that are characterized by distinct diffusion properties, and the parameters in the model describe tissue microstructure. In NODDI, these parameters are estimated in a maximum likelihood framework, where the nonlinear model fitting is computationally intensive. Therefore, efforts have been made to develop efficient and accurate algorithms for NODDI microstructure estimation, which is still an open problem. In this work, we propose a deep network based approach that performs end-to-end estimation of NODDI microstructure, which is named Microstructure Estimation using a Deep Network (MEDN). MEDN comprises two cascaded stages and is motivated by the AMICO algorithm, where the NODDI microstructure estimation is formulated in a dictionary-based framework. The first stage computes the coefficients of the dictionary. It resembles the solution to a sparse reconstruction problem, where the iterative process in conventional estimation approaches is unfolded and truncated, and the weights are learned instead of predetermined by the dictionary. In the second stage, microstructure properties are computed from the output of the first stage, which resembles the weighted sum of normalized dictionary coefficients in AMICO, and the weights are also learned. Because spatial consistency of diffusion signals can be used to reduce the effect of noise, we also propose MEDN+, which is an extended version of MEDN. MEDN+ allows incorporation of neighborhood information by inserting a stage with learned weights before the MEDN structure, where the diffusion signals in the neighborhood of a voxel are processed. The weights in MEDN or MEDN+ are jointly learned from training samples that are acquired with diffusion gradients densely sampling the q-space. We performed MEDN and MEDN+ on brain dMRI scans, where two shells each with 30 gradient directions were used, and measured their accuracy with respect to the gold standard. Results demonstrate that the proposed networks outperform the competing methods.

Fiber Orientation Estimation Guided by a Deep Network

Diffusion magnetic resonance imaging (dMRI) is currently the only tool for noninvasively imaging the brain's white matter tracts. The fiber orientation (FO) is a key feature computed from dMRI for tract reconstruction. Because the number of FOs in a voxel is usually small, dictionary-based sparse reconstruction has been used to estimate FOs. However, accurate estimation of complex FO configurations in the presence of noise can still be challenging. In this work we explore the use of a deep network for FO estimation in a dictionary-based framework and propose an algorithm named Fiber Orientation Reconstruction guided by a Deep Network (FORDN). FORDN consists of two steps. First, we use a smaller dictionary encoding coarse basis FOs to represent diffusion signals. To estimate the mixture fractions of the dictionary atoms, a deep network is designed to solve the sparse reconstruction problem. Second, the coarse FOs inform the final FO estimation, where a larger dictionary encoding a dense basis of FOs is used and a weighted ℓ₁-norm regularized least squares problem is solved to encourage FOs that are consistent with the network output. FORDN was evaluated and compared with state-of-the-art algorithms that estimate FOs using sparse reconstruction on simulated and typical clinical dMRI data. The results demonstrate the benefit of using a deep network for FO estimation.

Probabilistic tractography using Lasso bootstrap

Diffusion magnetic resonance imaging (dMRI) can be used for noninvasive imaging of white matter tracts. Using fiber tracking, which propagates fiber streamlines according to fiber orientations (FOs) computed from dMRI, white matter tracts can be reconstructed for investigation of brain diseases and the brain connectome. Because of image noise, probabilistic tractography has been proposed to characterize uncertainties in FO estimation. Bootstrap provides a nonparametric approach to the estimation of FO uncertainties and residual bootstrap has been used for developing probabilistic tractography. However, recently developed models have incorporated sparsity regularization to reduce the required number of gradient directions to resolve crossing FOs, and the residual bootstrap used in previous methods is not applicable to these models. In this work, we propose a probabilistic tractography algorithm named Lasso bootstrap tractography (LBT) for the models that incorporate sparsity. Using a fixed tensor basis and a sparsity assumption, diffusion signals are modeled using a Lasso formulation. With the residuals from the Lasso model, a distribution of diffusion signals is obtained according to a modified Lasso bootstrap strategy. FOs are then estimated from the synthesized diffusion signals by an algorithm that improves FO estimation by enforcing spatial consistency of FOs. Finally, streamlining fiber tracking is performed with the computed FOs. The LBT algorithm was evaluated on simulated and real dMRI data both qualitatively and quantitatively. Results demonstrate that LBT outperforms state-of-the-art algorithms.