A robust variational approach for simultaneous smoothing and estimation of DTI

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.

A Joint Framework for Denoising and Estimating Diffusion Kurtosis Tensors Using Multiple Prior Information

Diffusion kurtosis imaging (DKI) has been shown to be valuable in a wide range of neuroscientific and clinical applications. However, reliable estimation of DKI tensors is often compromised by noise, especially for the kurtosis tensor (KT). Here, we propose a joint denoising and estimating framework that integrates multiple sources of prior information, including nonlocal structural self-similarity (NSS), local spatial smoothness (LSS), physical relevance (PR) of the DKI model, and noise characteristics of magnitude diffusion MRI (dMRI) images for improved estimation of DKI tensors. The local and nonlocal spatial smoothing constraints are complementary to each other, making the proposed framework highly effective in reducing the noise fluctuations on DKI tensors, especially KT. As an additional refinement, we propose to impose a physically relevant constraint within our joint denoising and estimation framework. We further adopt the first-moment noise-corrected fitting model (M¹NCM) to remove the noncentral χ -distribution noise bias. The effectiveness of integrating multiple sources of priors into the joint framework is verified by comparing the proposed M¹NCM-NSS-LSS-PR method with various versions of M¹NCM-based estimators and two state-of-the-art methods. Results show that the proposed method outperformed the compared methods in simulations and in-vivo dMRI datasets of both spatially stationary and nonstationary noise distributions. The in-vivo experiments also show that the proposed M¹NCM-NSS-LSS-PR method was robust to the number of diffusion directions.

Structure Prior Constrained Estimation of Human Cardiac Diffusion Tensors

OBJECTIVE

The purpose of this paper is to increase the accuracy of human cardiac diffusion tensor (DT) estimation in diffusion magnetic resonance imaging (dMRI) with a few diffusion gradient directions.

METHODS

A structure prior constrained (SPC) method is proposed. The method consists in introducing two regularizers in the conventional nonlinear least squares estimator. The two regularizers penalize the dissimilarity between neighboring DTs and the difference between estimated and prior fiber orientations, respectively. A novel numerical solution is presented to ensure the positive definite estimation.

RESULTS

Experiments on ex vivo human cardiac data show that the SPC method is able to well estimate DTs at most voxels, and is superior to state-of-the-art methods in terms of the mean errors of principal eigenvector, second eigenvector, helix angle, transverse angle, fractional anisotropy, and mean diffusivity.

CONCLUSION

The SPC method is a practical and reliable alternative to current denoising- or regularization-based methods for the estimation of human cardiac DT.

SIGNIFICANCE

The SPC method is able to accurately estimate human cardiac DTs in dMRI with a few diffusion gradient directions.

In Vivo Detection of Gray Matter Neuropathology in the 3xTg Mouse Model of Alzheimer's Disease with Diffusion Tensor Imaging

A diagnosis of Alzheimer's disease (AD), a neurodegenerative disorder accompanied by severe functional and cognitive decline, is based on clinical findings, with final confirmation of the disease at autopsy by the presence of amyloid-β (Aβ) plaques and neurofibrillary tangles. Given that microstructural brain alterations occur years prior to clinical symptoms, efforts to detect brain changes early could significantly enhance our ability to diagnose AD sooner. Diffusion tensor imaging (DTI), a type of MRI that characterizes the magnitude, orientation, and anisotropy of the diffusion of water in tissues, has been used to infer neuropathological changes in vivo. Its utility in AD, however, is still under investigation. The current study used DTI to examine brain regions susceptible to AD-related pathology; the cerebral cortex, entorhinal cortex, and hippocampus, in 12-14-month-old 3xTg AD mice that possess both Aβ plaques and neurofibrillary tangles. Mean diffusivity did not differ between 3xTg and control mice in any region. Decreased fractional anisotropy (p < 0.01) and axial diffusivity (p < 0.05) were detected only in the hippocampus, in which both congophilic Aβ plaques and hyperphosphorylated tau accumulation, consistent with neurofibrillary tangle formation, were detected. Pathological tau accumulation was seen in the cortex. The entorhinal cortex was largely spared from AD-related neuropathology. This is the first study to demonstrate DTI abnormalities in gray matter in a mouse model of AD in which both pathological hallmarks are present, suggesting the feasibility of DTI as a non-invasive means of detecting brain pathology in vivo in early-stage AD.

Ex vivo tissue imaging for radiology-pathology correlation: a pilot study with a small bore 7-T MRI in a rare pigmented ganglioglioma exhibiting complex MR signal characteristics associated with melanin and hemosiderin

To advance magnetic resonance imaging (MRI) technologies further for in vivo tissue characterization with histopathologic validation, we investigated the feasibility of ex vivo tissue imaging of a surgically removed human brain tumor as a comprehensive approach for radiology–pathology correlation in histoanatomically identical fashion in a rare case of pigmented ganglioglioma with complex paramagnetic properties. Pieces of surgically removed ganglioglioma, containing melanin and hemosiderin pigments, were imaged with a small bore 7-T MRI scanner to obtain T1-, T2-, and T2*-weighted image and diffusion tensor imaging (DTI). Corresponding histopathological slides were prepared for routine hematoxylin and eosin stain and special stains for melanin and iron/hemosiderin to correlate with MRI signal characteristics. Furthermore, mean diffusivity (MD) maps were generated from DTI data and correlated with cellularity using image analysis. While the presence of melanin was difficult to interpret in in vivo MRI with certainty due to concomitant hemosiderin pigments and calcium depositions, ex vivo tissue imaging clearly demonstrated pieces of tissue exhibiting the characteristic MR signal pattern for melanin with pathologic confirmation in a histoanatomically identical location. There was also concordant correlation between MD and cellularity. Although it is still in an initial phase of development, ex vivo tissue imaging is a promising approach, which offers radiology–pathology correlation in a straightforward and comprehensive manner.

Denoise diffusion-weighted images using higher-order singular value decomposition

Noise usually affects the reliability of quantitative analysis in diffusion-weighted (DW) magnetic resonance imaging (MRI), especially at high b-values and/or high spatial resolution. Higher-order singular value decomposition (HOSVD) has recently emerged as a simple, effective, and adaptive transform to exploit sparseness within multidimensional data. In particular, the patch-based HOSVD denoising has demonstrated superb performance when applied to T1-, T2-, and proton density-weighted MRI data. In this study, we aim to investigate the feasibility of denoising DW data using the HOSVD transform. With the low signal-to-noise ratio in typical DW data, the patch-based HOSVD denoising suffers from stripe artifacts in homogeneous regions because of the HOSVD bases learned from the noisy patches. To address this problem, we propose a novel denoising method. It first introduces a global HOSVD-based denoising as a prefiltering stage to guide the subsequent patch-based HOSVD denoising stage. The HOSVD bases from the patch groups in prefiltered images are then used to transform the noisy patch groups in original DW data. Experiments were performed using simulated and in vivo DW data. Results show that the proposed method significantly reduces stripe artifacts compared with conventional patch-based HOSVD denoising methods, and outperforms two state-of-the-art denoising methods in terms of denoising quality and diffusion parameters estimation.

SR-HARDI: Spatially Regularizing High Angular Resolution Diffusion Imaging

High angular resolution diffusion imaging (HARDI) has recently been of great interest in mapping the orientation of intra-voxel crossing fibers, and such orientation information allows one to infer the connectivity patterns prevalent among different brain regions and possible changes in such connectivity over time for various neurodegenerative and neuropsychiatric diseases. The aim of this paper is to propose a penalized multi-scale adaptive regression model (PMARM) framework to spatially and adaptively infer the orientation distribution function (ODF) of water diffusion in regions with complex fiber configurations. In PMARM, we reformulate the HARDI imaging reconstruction as a weighted regularized least-squares regression (WRLSR) problem. Similarity and distance weights are introduced to account for spatial smoothness of HARDI, while preserving the unknown discontinuities (e.g., edges between white matter and grey matter) of HARDI. The L₁ penalty function is introduced to ensure the sparse solutions of ODFs, while a scaled L₁ weighted estimator is calculated to correct the bias introduced by the L₁ penalty at each voxel. In PMARM, we integrate the multiscale adaptive regression models (Li et al., 2011), the propagation-separation method (Polzehl and Spokoiny, 2000), and Lasso (least absolute shrinkage and selection operator) (Tibshirani, 1996) to adaptively estimate ODFs across voxels. Experimental results indicate that PMARM can reduce the angle detection errors on fiber crossing area and provide more accurate reconstruction than standard voxel-wise methods.

Adaptive anisotropic gaussian filtering to reduce acquisition time in cardiac diffusion tensor imaging

Diffusion tensor imaging (DTI) is used to quantify myocardial fiber orientation based on helical angles (HA). Accurate HA measurements require multiple excitations (NEX) and/or several diffusion encoding directions (DED). However, increasing NEX and/or DED increases acquisition time (TA). Therefore, in this study, we propose to reduce TA by implementing a 3D adaptive anisotropic Gaussian filter (AAGF) on the DTI data acquired from ex-vivo healthy and infarcted porcine hearts. DTI was performed on ex-vivo hearts [9-healthy, 3-myocardial infarction (MI)] with several combinations of DED and NEX. AAGF, mean (AVF) and median filters (MF) were applied on the primary eigenvectors of the diffusion tensor prior to HA estimation. The performance of AAGF was compared against AVF and MF. Root mean square error (RMSE), concordance correlation-coefficients and Bland-Altman's technique was used to determine optimal combination of DED and NEX that generated the best HA maps in the least possible TA. Lastly, the effect of implementing AAGF on the infarcted porcine hearts was also investigated. RMSE in HA estimation for AAGF was lower compared to AVF or MF. Post-filtering (AAGF) fewer DED and NEX were required to achieve HA maps with similar integrity as those obtained from higher NEX and/or DED. Pathological alterations caused in HA orientation in the MI model were preserved post-filtering (AAGF). Our results demonstrate that AAGF reduces TA without affecting the integrity of the myocardial microstructure.