Estimating non‐gaussian diffusion model parameters in the presence of physiological noise and rician signal bias

Abstract

Purpose: To assess the effects of Rician bias and physiological noise on parameter estimation for non-Gaussian diffusion models. Materials and Methods:At high b-values, there are deviations from monoexponential signal decay known as nonGaussian diffusion. Magnitude images have a Rician distribution, which introduces a bias that appears as non-Gaussian diffusion. A second factor that complicates parameter estimation is physiological noise. It has an intensity that depends on the b-value in a complicated manner. Hence, the signal distribution is unknown a priori. By measuring a large number of averages, however, the variance at each b-value can be estimated. Using Monte Carlo simulations, we compared uncorrected estimation to a corrected scheme that involves fitting to the mean value of the Rician distribution. We also evaluated effects of weighting with the inverse of the estimated variance in least-squares fitting. A human brain experiment illustrates parameter estimation effects and identifies brain regions affected by physiological noise. Results:The simulations show that the corrected estimator is very accurate. The uncorrected estimator is heavily biased. In the human brain experiment, the magnitude of the relative bias ranges from 6%-31%, depending on the diffusion model. Weighting has negligible effects on accuracy, but improves precision in the presence of physiological noise. At low b-values, physiological noise is prominent in cerebrospinal fluid. At high b-values there is physiological noise in white matter structures near the ventricles.Conclusion: Bias correction is essential and weighting may be beneficial. Physiological noise has significant effects.

Non-Gaussian Diffusion Imaging for Enhanced Contrast of Brain Tissue Affected by Ischemic Stroke

“…The maps are shown for 4 different slices in animal 1. At b  = 1 µm −2 ms, the χ 2 -maps look rather homogeneous but exhibit increasing contrast between GM and WM (see the “brightening” of WM tracts such as the corpus callosum) in accordance with similar findings in human brain [68]. Moreover, stroke lesions cannot be recognised in χ 2 -maps for b ≤1 µm −2 ms (see anatomic RARE-maps for their locations) but become strikingly enhanced for larger b .…”

“…BEDTA, on the other hand, was applicable only in range 2. In comparison to the other investigated models, BEDTA is less robust as it contains one more fitting parameter (3, if signal intensities are normalised), and is more vulnerable to low signal-to-noise ratio [36], [68]. Therefore, it is less beneficial for stroke analysis as it demands more scanning time.…”

A Majorize-Minimize Framework for Rician and Non-Central Chi MR Images

“…Gaussian approximation is quite common, and there are a number of methods that are designed to reduce the noise bias without directly optimizing the NCC NLL. Examples include approximately transforming the NCC distribution to a Gaussian distribution [26], [30] and various simplified forms of nonlinear bias compensation [10], [12], [14], [18], [28], [41]–[43]. While these simplifications improve computation speed, performance is typically worse than would be obtained from the statistically-optimal ML or PML solutions.…”

Influence of Noise Correction on Intra- and Inter-Subject Variability of Quantitative Metrics in Diffusion Kurtosis Imaging

“…along the fibers in the WM). When the signal is about or below the noise floor, the noise introduces a significant bias artificially enhancing the measured signal intensity [26]. The noise is then interpreted as true signal and, if not corrected, leads to an overestimation of kurtosis [27]–[29].…”

“…For that purpose, different methods using either image background areas or the image object itself have been reviewed in [44]. In the case of DKI, only the second approach has been investigated [26], [29]. The impact of noise, both thermal and physiological, on diffusion metrics has been studied previously for different non-Gaussian models [26], in the case of Rician noise distribution only.…”