Faculty Bibliography

There is a need for accurate quantitative non-invasive biomarkers to monitor myelin pathology in vivo and distinguish myelin changes from other pathological features including inflammation and axonal loss. Conventional MRI metrics such as T2, magnetization transfer ratio and radial diffusivity have proven sensitivity but not specificity. In highly coherent white matter bundles, compartment-specific white matter tract integrity (WMTI) metrics can be directly derived from the diffusion and kurtosis tensors: axonal water fraction, intra-axonal diffusivity, and extra-axonal radial and axial diffusivities. We evaluate the potential of WMTI to quantify demyelination by monitoring the effects of both acute (6weeks) and chronic (12weeks) cuprizone intoxication and subsequent recovery in the mouse corpus callosum, and compare its performance with that of conventional metrics (T2, magnetization transfer, and DTI parameters). The changes observed in vivo correlated with those obtained from quantitative electron microscopy image analysis. A 6-week intoxication produced a significant decrease in axonal water fraction (p<0.001), with only mild changes in extra-axonal radial diffusivity, consistent with patchy demyelination, while a 12-week intoxication caused a more marked decrease in extra-axonal radial diffusivity (p=0.0135), consistent with more severe demyelination and clearance of the extra-axonal space. Results thus revealed increased specificity of the axonal water fraction and extra-axonal radial diffusivity parameters to different degrees and patterns of demyelination. The specificities of these parameters were corroborated by their respective correlations with microstructural features: the axonal water fraction correlated significantly with the electron microscopy derived total axonal water fraction (rho=0.66; p=0.0014) but not with the g-ratio, while the extra-axonal radial diffusivity correlated with the g-ratio (rho=0.48; p=0.0342) but not with the electron microscopy derived axonal water fraction. These parameters represent promising candidates as clinically feasible biomarkers of demyelination and remyelination in the 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 mum. 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.

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

PURPOSE: To estimate the spatially varying noise map using a redundant series of magnitude MR images. METHODS: We exploit redundancy in non-Gaussian distributed multidirectional diffusion MRI data by identifying its noise-only principal components, based on the theory of noisy covariance matrices. The bulk of principal component analysis eigenvalues, arising due to noise, is described by the universal Marchenko-Pastur distribution, parameterized by the noise level. This allows us to estimate noise level in a local neighborhood based on the singular value decomposition of a matrix combining neighborhood voxels and diffusion directions. RESULTS: We present a model-independent local noise mapping method capable of estimating the noise level down to about 1% error. In contrast to current state-of-the-art techniques, the resultant noise maps do not show artifactual anatomical features that often reflect physiological noise, the presence of sharp edges, or a lack of adequate a priori knowledge of the expected form of MR signal. CONCLUSIONS: Simulations and experiments show that typical diffusion MRI data exhibit sufficient redundancy that enables accurate, precise, and robust estimation of the local noise level by interpreting the principal component analysis eigenspectrum in terms of the Marchenko-Pastur distribution. Magn Reson Med, 2015. (c) 2015 Wiley Periodicals, Inc.

PURPOSE: To study and reduce the effect of Gibbs ringing artifact on computed diffusion parameters. METHODS: We reduce the ringing by extrapolating the k-space of each diffusion weighted image beyond the measured part by selecting an adequate regularization term. We evaluate several regularization terms and tune the regularization parameter to find the best compromise between anatomical accuracy of the reconstructed image and suppression of the Gibbs artifact. RESULTS: We demonstrate empirically and analytically that the Gibbs artifact, which is typically observed near sharp edges in magnetic resonance images, has a significant impact on the quantification of diffusion model parameters, even for infinitesimal diffusion weighting. We find the second order total generalized variation to be a good choice for the penalty term to regularize the extrapolation of the k-space, as it provides a parsimonious representation of images, a practically full suppression of Gibbs ringing, and the absence of staircasing artifacts typical for total variation methods. CONCLUSIONS: Regularized extrapolation of the k-space data significantly reduces truncation artifacts without compromising spatial resolution in comparison to the default option of window filtering. In particular, accuracy of estimating diffusion tensor imaging and diffusion kurtosis imaging parameters improves so much that unconstrained fits become possible. Magn Reson Med, 2015. (c) 2015 Wiley Periodicals, Inc.

PURPOSE: To disentangle the free diffusivity (D0 ) and cellular membrane restrictions, by means of their surface-to-volume ratio (S/V), using the frequency-dependence of the diffusion coefficient D(omega), measured in brain tumors in the short diffusion-time regime using oscillating gradients (OGSE). METHODS: In vivo and ex vivo OGSE experiments were performed on mice bearing the GL261 murine glioma model (n = 10) to identify the relevant time/frequency (t/omega) domain where D(omega) linearly decreases with omega-1/2 . Parametric maps (S/V, D0 ) are compared with conventional DWI metrics. The impact of frequency range and temperature (20 degrees C versus 37 degrees C) on S/V and D0 is investigated ex vivo. RESULTS: The validity of the short diffusion-time regime is demonstrated in vivo and ex vivo. Ex vivo measurements confirm that the purely geometric restrictions embodied in S/V are independent from temperature and frequency range, while the temperature dependence of the free diffusivity D0 is similar to that of pure water. CONCLUSION: Our results suggest that D(omega) in the short diffusion-time regime can be used to uncouple the purely geometric restriction effect, such as S/V, from the intrinsic medium diffusivity properties, and provides a nonempirical and objective way to interpret frequency/time-dependent diffusion changes in tumors in terms of objective biophysical tissue parameters. Magn Reson Med, 2015. (c) 2015 Wiley Periodicals, Inc.

Diffusion MRI combined with biophysical modeling allows for the description of a white matter (WM) fiber bundle in terms of compartment specific white matter tract integrity (WMTI) metrics, which include intra-axonal diffusivity (Daxon), extra-axonal axial diffusivity (De||), extra-axonal radial diffusivity (De upper left and right quadrants), axonal water fraction (AWF), and tortuosity (alpha) of extra-axonal space. Here we derive these parameters from diffusion kurtosis imaging to examine their relationship to concentrations of global WM N-acetyl-aspartate (NAA), creatine (Cr), choline (Cho) and myo-Inositol (mI), as measured with proton MR spectroscopy (1H-MRS), in a cohort of 25 patients with mild traumatic brain injury (MTBI). We found statistically significant (p<0.05) positive correlations between NAA and Daxon, AWF, alpha, and fractional anisotropy; negative correlations between NAA and De, upper left and right quadrants and the overall radial diffusivity (D upper left and right quadrants). These correlations were supported by similar findings in regional analysis of the genu and splenium of the corpus callosum. Furthermore, a positive correlation in global WM was noted between Daxon and Cr, as well as a positive correlation between De|| and Cho, and a positive trend between De|| and mI. The specific correlations between NAA, an endogenous probe of the neuronal intracellular space, and WMTI metrics related to the intra-axonal space, combined with the specific correlations of De|| with mI and Cho, both predominantly present extra-axonally, corroborate the overarching assumption of many advanced modeling approaches that diffusion imaging can disentangle between the intra- and extra-axonal compartments in WM fiber bundles. Our findings are also generally consistent with what is known about the pathophysiology of MTBI, which appears to involve both intra-axonal injury (as reflected by a positive trend between NAA and Daxon) as well as axonal shrinkage, demyelination, degeneration, and/or loss (as reflected by correlations between NAA and De upper left and right quadrants, AWF, and alpha).

Interpreting brain diffusion MRI measurements in terms of neuronal structure at a micrometer level is an exciting unresolved problem. Here we consider diffusion transverse to a bundle of fibers, and show theoretically, as well as using Monte Carlo simulations and measurements in a phantom made of parallel fibers mimicking axons, that the time dependent diffusion coefficient approaches its macroscopic limit slowly, in a (lnt)/t fashion. The logarithmic singularity arises due to short range disorder in the fiber packing. We identify short range disorder in axonal fibers based on histological data from the splenium, and argue that the time dependent contribution to the overall diffusion coefficient from the extra-axonal water dominates that of the intra-axonal water. This dominance may explain the bias in measuring axon diameters in clinical settings. The short range disorder is also reflected in the linear frequency dependence of the diffusion coefficient measured with oscillating gradients, in agreement with recent experiments. Our results relate the measured diffusion to the mesoscopic structure of neuronal tissue, uncovering the sensitivity of diffusion metrics to axonal arrangement within a fiber tract, and providing an alternative interpretation of axonal diameter mapping techniques.

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 model's assumptions and consequent biases, as highlighted in simulations. Finally, we discuss the feasibility of a model with fewer assumptions.