Faculty Bibliography

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

Dynamic contrast enhanced (DCE) MRI has emerged as a reliable and diagnostically useful functional imaging technique. DCE protocol typically lasts 3-15 minutes and results in a time series of N volumes. For automated analysis, it is important that volumes acquired at different times be spatially coregistered. We have recently introduced a novel 4D, or volume time series, coregistration tool based on a user-specified target volume of interest (VOI). However, the relationship between coregistration accuracy and target VOI size has not been investigated. In this study, coregistration accuracy was quantitatively measured using various sized target VOIs. Coregistration of 10 DCE-MRI mouse head image sets were performed with various sized VOIs targeting the mouse brain. Accuracy was quantified by measures based on the union and standard deviation of the coregistered volume time series. Coregistration accuracy was determined to improve rapidly as the size of the VOI increased and approached the approximate volume of the target (mouse brain). Further inflation of the VOI beyond the volume of the target (mouse brain) only marginally improved coregistration accuracy. The CPU time needed to accomplish coregistration is a linear function of N that varied gradually with VOI size. From the results of this study, we recommend the optimal size of the VOI to be slightly overinclusive, approximately by 5 voxels, of the target for computationally efficient and accurate coregistration.

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.

The purpose of this work was to carry out diffusion tensor imaging (DTI) at multiple diffusion times Td in skeletal muscle in normal subjects and chronic exertional compartment syndrome (CECS) patients and analyze the data with the random permeable barrier model (RPBM) for biophysical specificity. Using an institutional review board approved HIPAA-compliant protocol, seven patients with clinical suspicion of CECS and eight healthy volunteers underwent DTI of the calf muscle in a Siemens MAGNETOM Verio 3 T scanner at rest and after treadmill exertion at four different Td values. Radial diffusion values lambdarad were computed for each of seven different muscle compartments and analyzed with RPBM to produce estimates of free diffusivity D0 , fiber diameter a, and permeability kappa. Fiber diameter estimates were compared with measurements from literature autopsy reference for several compartments. Response factors (post/pre-exercise ratios) were computed and compared between normal controls and CECS patients using a mixed-model two-way analysis of variance. All subjects and muscle compartments showed nearly time-independent diffusion along and strongly time-dependent diffusion transverse to the muscle fibers. RPBM estimates of fiber diameter correlated well with corresponding autopsy reference. D0 showed significant (p < 0.05) increases with exercise for volunteers, and a increased significantly (p < 0.05) in volunteers. At the group level, response factors of all three parameters showed trends differentiating controls from CECS patients, with patients showing smaller diameter changes (p = 0.07), and larger permeability increases (p = 0.07) than controls. Time-dependent diffusion measurements combined with appropriate tissue modeling can provide enhanced microstructural specificity for in vivo tissue characterization. In CECS patients, our results suggest that high-pressure interfiber edema elevates free diffusion and restricts exercise-induced fiber dilation. Such specificity may be useful in differentiating CECS from other disorders or in predicting its response to either physical therapy or fasciotomy

Measuring molecular diffusion is widely used for characterizing materials and living organisms noninvasively. This characterization relies on relations between macroscopic diffusion metrics and structure at the mesoscopic scale commensurate with the diffusion length. Establishing such relations remains a fundamental challenge, hindering progress in materials science, porous media, and biomedical imaging. Here we show that the dynamical exponent in the time dependence of the diffusion coefficient distinguishes between the universality classes of the mesoscopic structural complexity. Our approach enables the interpretation of diffusion measurements by objectively selecting and modeling the most relevant structural features. As an example, the specific values of the dynamical exponent allow us to identify the relevant mesoscopic structure affecting MRI-measured water diffusion in muscles and in brain, and to elucidate the structural changes behind the decrease of diffusion coefficient in ischemic stroke.

Abstract Mild traumatic brain injury (mTBI), although often presenting without the gross structural abnormalities seen in more severe forms of brain trauma, can nonetheless result in lingering cognitive and behavioral problems along with subtle alterations in brain structure and function. Repeated injuries are associated with brain atrophy and dementia in the form of chronic traumatic encephalopathy (CTE). The mechanisms underlying these dysfunctions are poorly understood. There is a growing body of evidence that brain iron is abnormal after TBI, and brain iron has also been implicated in a host of neurodegenerative disorders. The purpose of this article is to review evidence about the function of iron in the pathophysiology of mTBI and the role that advanced imaging modalities can play in further elucidating said function. MRI techniques sensitive to field inhomogeneities provide supporting evidence for both deep gray matter non-heme iron accumulation as well as focal microhemorrhage resulting from mTBI. In addition, there is evidence that iron may contribute to pathology after mTBI through a number of mechanisms, including generation of reactive oxygen species (ROS), exacerbation of oxidative stress from other sources, and encouragement of tau phosphorylation and the formation of neurofibrillary tangles. Finally, recent animal studies suggest that iron may serve as a therapeutic target in mitigating the effects of mTBI. However, research on the presence and role of iron in mTBI and CTE is still relatively sparse, and further work is necessary to elucidate issues such as the sources of increased iron and the chain of secondary injury.