Fast and Robust Estimation of Diffusional Kurtosis Imaging (DKI) Parameters by General Closed-form Expressions and their Extensions

Abstract

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 leastsquares 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 robustnessb-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, positivedefiniteness 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 methodis 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.

Kurtosis analysis of neural diffusion organization

“…However, the kurtosis and diffusion tensors contain the majority of the information obtainable with small diffusion weightings (Jensen and Helpern, 2010), and so this loss is likely to be minor when low b-value dMRI methods, such as DKI, are employed. In addition, by basing the modeling solely on these two tensors, KANDO can benefit from the advanced post-processing methods already available for DKI (André et al, 2014; Ghosh et al, 2014; Glenn et al, 2014; Kuder et al, 2012; Tabesh et al, 2011; Masutani and Aoki, 2014; Poot et al, 2010; Tax et al, 2014; Veraart et al, 2013; Veraart et al, 2011). …”

Diffusional Kurtosis Imaging in Idiopathic Normal Pressure Hydrocephalus: Correlation with Severity of Cognitive Impairment

“…HCU, Hiroshima, Japan). 31 Prior to DKI calculation, the amount of noise (η) was estimated from the mean value of signals at air region in the image. 20 The DKI parameters for a single direction can be determined with the following Equation (1) as described in previous studies 20 , 21 : where S is the diffusion-weighted signal intensity at the given b value, S 0 is the signal intensity at b = 0 s/mm 2 , D app is the mean diffusivity (MD), and K app is the apparent kurtosis coefficient (dimensionless).…”

“…Here voxels with MK value outside the physiologically reasonable range (0≦MK≦2) were judged as containing calculation error. 31 Though this range of acceptable MK value was set originally presuming normal white matter, recent studies have suggested that MK comes into this range even in severely pathological tissues like glioma and multiple sclerosis. 34 , 35 Using the back-projected FA skeleton as an ROI, the rates of error voxels were compared between the controls and the iNPH patients using Student’s t-test.…”

Diffusion-tensor-based method for robust and practical estimation of axial and radial diffusional kurtosis

“…The brief calculation procedure for each pixel was as follows. First, quadratic-function curve fitting was performed for the b-value-related signal changes in each encoding direction, separately (a closed-form method was applied) [ 10 , 14 ]. …”

“…However, the long acquisition time of DKI resulting from the requirements for multiple b-values and the large number of diffusion encoding directions (NEDs) of the raw diffusion-weighted images (DWIs) remains a problem [ 3 , 10 ]. A typical conventional protocol can consist of 30 uniformly distributed encoding directions in three to six different b-values between 0 and 3,000 s/mm 2 [ 3 ].…”