Jelle Veraart

Gliomas: Diffusion Kurtosis MR Imaging in Grading

PURPOSE To assess the diagnostic accuracy of diffusion kurtosis magnetic resonance imaging parameters in grading gliomas. MATERIALS AND METHODS The institutional review board approved this prospective study, and informed consent was obtained from all patients. Diffusion parameters-mean diffusivity (MD), fractional anisotropy (FA), mean kurtosis, and radial and axial kurtosis-were compared in the solid parts of 17 high-grade gliomas and 11 low-grade gliomas (P<.05 significance level, Mann-Whitney-Wilcoxon test, Bonferroni correction). MD, FA, mean kurtosis, radial kurtosis, and axial kurtosis in solid tumors were also normalized to the corresponding values in contralateral normal-appearing white matter (NAWM) and the contralateral posterior limb of the internal capsule (PLIC) after age correction and were compared among tumor grades. RESULTS Mean, radial, and axial kurtosis were significantly higher in high-grade gliomas than in low-grade gliomas (P = .02, P = .015, and P = .01, respectively). FA and MD did not significantly differ between glioma grades. All values, except for axial kurtosis, that were normalized to the values in the contralateral NAWM were significantly different between high-grade and low-grade gliomas (mean kurtosis, P = .02; radial kurtosis, P = .03; FA, P = .025; and MD, P = .03). When values were normalized to those in the contralateral PLIC, none of the considered parameters showed significant differences between high-grade and low-grade gliomas. The highest sensitivity and specificity for discriminating between high-grade and low-grade gliomas were found for mean kurtosis (71% and 82%, respectively) and mean kurtosis normalized to the value in the contralateral NAWM (100% and 73%, respectively). Optimal thresholds for mean kurtosis and mean kurtosis normalized to the value in the contralateral NAWM for differentiating high-grade from low-grade gliomas were 0.52 and 0.51, respectively. CONCLUSION There were significant differences in kurtosis parameters between high-grade and low-grade gliomas; hence, better separation was achieved with these parameters than with conventional diffusion imaging parameters.

Weighted linear least squares estimation of diffusion MRI parameters: Strengths, limitations, and pitfalls

PURPOSE Linear least squares estimators are widely used in diffusion MRI for the estimation of diffusion parameters. Although adding proper weights is necessary to increase the precision of these linear estimators, there is no consensus on how to practically define them. In this study, the impact of the commonly used weighting strategies on the accuracy and precision of linear diffusion parameter estimators is evaluated and compared with the nonlinear least squares estimation approach. METHODS Simulation and real data experiments were done to study the performance of the weighted linear least squares estimators with weights defined by (a) the squares of the respective noisy diffusion-weighted signals; and (b) the squares of the predicted signals, which are reconstructed from a previous estimate of the diffusion model parameters. RESULTS The negative effect of weighting strategy (a) on the accuracy of the estimator was surprisingly high. Multi-step weighting strategies yield better performance and, in some cases, even outperformed the nonlinear least squares estimator. CONCLUSION If proper weighting strategies are applied, the weighted linear least squares approach shows high performance characteristics in terms of accuracy/precision and may even be preferred over nonlinear estimation methods.

More accurate estimation of diffusion tensor parameters using diffusion kurtosis imaging

With diffusion tensor imaging, the diffusion of water molecules through brain structures is quantified by parameters, which are estimated assuming monoexponential diffusion‐weighted signal attenuation. The estimated diffusion parameters, however, depend on the diffusion weighting strength, the b‐value, which hampers the interpretation and comparison of various diffusion tensor imaging studies. In this study, a likelihood ratio test is used to show that the diffusion kurtosis imaging model provides a more accurate parameterization of both the Gaussian and non‐Gaussian diffusion component compared with diffusion tensor imaging. As a result, the diffusion kurtosis imaging model provides a b‐value‐independent estimation of the widely used diffusion tensor parameters as demonstrated with diffusion‐weighted rat data, which was acquired with eight different b‐values, uniformly distributed in a range of [0,2800 sec/mm2]. In addition, the diffusion parameter values are significantly increased in comparison to the values estimated with the diffusion tensor imaging model in all major rat brain structures. As incorrectly assuming additive Gaussian noise on the diffusion‐weighted data will result in an overestimated degree of non‐Gaussian diffusion and a b‐value‐dependent underestimation of diffusivity measures, a Rician noise model was used in this study. Magn Reson Med, 2010.

One diffusion acquisition and different white matter models: how does microstructure change in human early development based on WMTI and NODDI?

White matter microstructural changes during the first three years of healthy brain development are characterized using two different models developed for limited clinical diffusion data: White Matter Tract Integrity (WMTI) metrics from Diffusional Kurtosis Imaging (DKI) and Neurite Orientation Dispersion and Density Imaging (NODDI). Both models reveal a non-linear increase in intra-axonal water fraction and in tortuosity of the extra-axonal space as a function of age, in the genu and splenium of the corpus callosum and the posterior limb of the internal capsule. The changes are consistent with expected behavior related to myelination and asynchrony of fiber development. The intra- and extracellular axial diffusivities as estimated with WMTI do not change appreciably in normal brain development. The quantitative differences in parameter estimates between models are examined and explained in the light of each models assumptions and consequent biases, as highlighted in simulations. Finally, we discuss the feasibility of a model with fewer assumptions.

Degeneracy in model parameter estimation for multi-compartmental diffusion in neuronal tissue

The ultimate promise of diffusion MRI (dMRI) models is specificity to neuronal microstructure, which may lead to distinct clinical biomarkers using noninvasive imaging. While multi‐compartment models are a common approach to interpret water diffusion in the brain in vivo, the estimation of their parameters from the dMRI signal remains an unresolved problem. Practically, even when q space is highly oversampled, nonlinear fit outputs suffer from heavy bias and poor precision. So far, this has been alleviated by fixing some of the model parameters to a priori values, for improved precision at the expense of accuracy. Here we use a representative two‐compartment model to show that fitting fails to determine the five model parameters from over 60 measurement points. For the first time, we identify the reasons for this poor performance. The first reason is the existence of two local minima in the parameter space for the objective function of the fitting procedure. These minima correspond to qualitatively different sets of parameters, yet they both lie within biophysically plausible ranges. We show that, at realistic signal‐to‐noise ratio values, choosing between the two minima based on the associated objective function values is essentially impossible. Second, there is an ensemble of very low objective function values around each of these minima in the form of a pipe. The existence of such a direction in parameter space, along which the objective function profile is very flat, explains the bias and large uncertainty in parameter estimation, and the spurious parameter correlations: in the presence of noise, the minimum can be randomly displaced by a very large amount along each pipe. Our results suggest that the biophysical interpretation of dMRI model parameters crucially depends on establishing which of the minima is closer to the biophysical reality and the size of the uncertainty associated with each parameter. Copyright

Comprehensive framework for accurate diffusion MRI parameter estimation

During the last decade, many approaches have been proposed for improving the estimation of diffusion measures. These techniques have already shown an increase in accuracy based on theoretical considerations, such as incorporating prior knowledge of the data distribution. The increased accuracy of diffusion metric estimators is typically observed in well‐defined simulations, where the assumptions regarding properties of the data distribution are known to be valid. In practice, however, correcting for subject motion and geometric eddy current deformations alters the data distribution tremendously such that it can no longer be expressed in a closed form. The image processing steps that precede the model fitting will render several assumptions on the data distribution invalid, potentially nullifying the benefit of applying more advanced diffusion estimators. In this work, we present a generic diffusion model fitting framework that considers some statistics of diffusion MRI data. A central role in the framework is played by the conditional least squares estimator. We demonstrate that the accuracy of that particular estimator can generally be preserved, regardless the applied preprocessing steps, if the noise parameter is known a priori. To fulfill that condition, we also propose an approach for the estimation of spatially varying noise levels. Magn Reson Med, 70:972–984, 2013.

Denoising of diffusion MRI using random matrix theory

We introduce and evaluate a post-processing technique for fast denoising of diffusion-weighted MR images. By exploiting the intrinsic redundancy in diffusion MRI using universal properties of the eigenspectrum of random covariance matrices, we remove noise-only principal components, thereby enabling signal-to-noise ratio enhancements. This yields parameter maps of improved quality for visual, quantitative, and statistical interpretation. By studying statistics of residuals, we demonstrate that the technique suppresses local signal fluctuations that solely originate from thermal noise rather than from other sources such as anatomical detail. Furthermore, we achieve improved precision in the estimation of diffusion parameters and fiber orientations in the human brain without compromising the accuracy and spatial resolution.

In vivo observation and biophysical interpretation of time-dependent diffusion in human white matter.

The presence of micrometer-level restrictions leads to a decrease of diffusion coefficient with diffusion time. Here we investigate this effect in human white matter in vivo. We focus on a broad range of diffusion times, up to 600 ms, covering diffusion length scales up to about 30 μm. We perform stimulated echo diffusion tensor imaging on 5 healthy volunteers and observe a relatively weak time-dependence in diffusion transverse to major fiber tracts. Remarkably, we also find notable time-dependence in the longitudinal direction. Comparing models of diffusion in ordered, confined and disordered media, we argue that the time-dependence in both directions can arise due to structural disorder, such as axonal beads in the longitudinal direction, and the random packing geometry of fibers within a bundle in the transverse direction. These time-dependent effects extend beyond a simple picture of Gaussian compartments, and may lead to novel markers that are specific to neuronal fiber geometry at the micrometer scale.

Nonlocal maximum likelihood estimation method for denoising multiple-coil magnetic resonance images.

Effective denoising is vital for proper analysis and accurate quantitative measurements from magnetic resonance (MR) images. Even though many methods were proposed to denoise MR images, only few deal with the estimation of true signal from MR images acquired with phased-array coils. If the magnitude data from phased array coils are reconstructed as the root sum of squares, in the absence of noise correlations and subsampling, the data is assumed to follow a non central-χ distribution. However, when the k-space is subsampled to increase the acquisition speed (as in GRAPPA like methods), noise becomes spatially varying. In this note, we propose a method to denoise multiple-coil acquired MR images. Both the non central-χ distribution and the spatially varying nature of the noise is taken into account in the proposed method. Experiments were conducted on both simulated and real data sets to validate and to demonstrate the effectiveness of the proposed method.

Diffusion MRI noise mapping using random matrix theory.

To estimate the spatially varying noise map using a redundant series of magnitude MR images.