q-Space imaging using small magnetic field gradient

A Bayesian approach to diffusional kurtosis imaging

PURPOSE

Diffusional kurtosis metrics show high performance for detecting pathological changes and are therefore expected to be disease biomarkers. Kurtosis maps, however, tend to be noisy. The maps' visual quality is crucial for disease diagnosis, even when kurtosis is being used quantitatively. A Bayesian method was proposed to curtail the large statistical error inherent in kurtosis estimation while maintaining potential application to biomarkers.

THEORY

Gaussian priors are determined from first-step estimations implemented using the least-square method (LSM). The likelihood-function variance is determined from the residuals of the estimation. Although the proposed approach is similar to a regularized LSM, regularization parameters do not have to be artificially adjusted. An appropriate balance between denoising and preventing false shrinkages of metric dispersions is automatically achieved.

METHODS

Map qualities achieved using the conventional and proposed methods were compared. The receiver-operating characteristic analysis was performed for glioma-grade differentiation using simulated low- and high-grade glioma DWI datasets. Noninferiority of the proposed method was tested for areas under the curves (AUCs).

RESULTS

The noisier the conventional maps, the better the proposed Bayesian method improved them. Noninferiority of the proposed method was confirmed by AUC tests for all kurtosis-related metrics. Superiority of the proposed method was also established for several metrics.

CONCLUSIONS

The proposed approach improved noisy kurtosis maps while maintaining their performances as biomarkers without increasing data acquisition requirements or arbitrarily choosing LSM regularization parameters. This approach may enable the use of higher-order terms in diffusional kurtosis imaging (DKI) fitting functions by suppressing overfitting, thereby improving the DKI-estimation accuracy.

Fast and robust estimation of diffusional kurtosis imaging (DKI) parameters by general closed-form expressions and their extensions

Diffusional kurtosis imaging (DKI) for clinical imaging involves time-consuming computation and demonstrates low robustness. Standard estimation of DKI parameters is based on an extension of Stejskal-Tanner's signal model with squared b-value term and is a least-squares fitting problem. The use of numerical methods for computation requires time, and estimation of DKI parameters is noise sensitive and often produces noisy results, such as images with pepper noise.In this study, we propose general closed-form solutions for DKI parameters to avoid numerical computation for least-squares fitting, solutions that can be applied to diffusion weighted imaging (DWI) datasets with any number of b-values more than three. Solutions are obtained through stationary-point conditions of an objective function that are minimized for fitting. We use 3 techniques to extend the solutions to increase robustness-b-value-dependent weighting in fitting, removal of outliers, and addition of neighbor sampling. Based on synthetic datasets and clinical datasets that both consist of 6 b-value and 3 b-value datasets, we detail and compare the 3 methods including a method by Jensen et al. are compared and investigated in detail. The synthetic data consist of several combinations of DKI parameters and some Rician noise. In addition to visually assessing result images, we also performed quantitative evaluation using a range of estimated parameters, positive-definiteness of the objective function for fitting, and root-mean-square error including estimation bias from the true value (synthetic data only). Methods that added neighbor sampling outperformed others in terms of low errors and visual smoothness. Though the solution by our method is to estimate DKI parameters in a single MPG direction, it can contribute to anisotropic analysis of diffusional kurtosis such as kurtosis tensor. More robust estimation is expected by combining techniques.

MR diffusion kurtosis imaging for neural tissue characterization

In conventional diffusion tensor imaging (DTI), water diffusion distribution is described as a 2nd-order three-dimensional (3D) diffusivity tensor. It assumes that diffusion occurs in a free and unrestricted environment with a Gaussian distribution of diffusion displacement, and consequently that diffusion weighted (DW) signal decays with diffusion factor (b-value) monoexponentially. In biological tissue, complex cellular microstructures make water diffusion a highly hindered or restricted process. Non-monoexponential decays are experimentally observed in both white matter and gray matter. As a result, DTI quantitation is b-value dependent and DTI fails to fully utilize the diffusion measurements that are inherent to tissue microstructure. Diffusion kurtosis imaging (DKI) characterizes restricted diffusion and can be readily implemented on most clinical scanners. It provides a higher-order description of water diffusion process by a 2nd-order 3D diffusivity tensor as in conventional DTI together with a 4th-order 3D kurtosis tensor. Because kurtosis is a measure of the deviation of the diffusion displacement profile from a Gaussian distribution, DKI analyses quantify the degree of diffusion restriction or tissue complexity without any biophysical assumption. In this work, the theory of diffusion kurtosis and DKI including the directional kurtosis analysis is revisited. Several recent rodent DKI studies from our group are summarized, and DKI and DTI compared for their efficacy in detecting neural tissue alterations. They demonstrate that DKI offers a more comprehensive approach than DTI in describing the complex water diffusion process in vivo. By estimating both diffusivity and kurtosis, it may provide improved sensitivity and specificity in MR diffusion characterization of neural tissues.

MRI quantification of non-Gaussian water diffusion by kurtosis analysis

Quantification of non-Gaussianity for water diffusion in brain by means of diffusional kurtosis imaging (DKI) is reviewed. Diffusional non-Gaussianity is a consequence of tissue structure that creates diffusion barriers and compartments. The degree of non-Gaussianity is conveniently quantified by the diffusional kurtosis and derivative metrics, such as the mean, axial, and radial kurtoses. DKI is a diffusion-weighted MRI technique that allows the diffusional kurtosis to be estimated with clinical scanners using standard diffusion-weighted pulse sequences and relatively modest acquisition times. DKI is an extension of the widely used diffusion tensor imaging method, but requires the use of at least 3 b-values and 15 diffusion directions. This review discusses the underlying theory of DKI as well as practical considerations related to data acquisition and post-processing. It is argued that the diffusional kurtosis is sensitive to diffusional heterogeneity and suggested that DKI may be useful for investigating ischemic stroke and neuropathologies, such as Alzheimer's disease and schizophrenia.