Faculty Bibliography

We report on an experimental observation of classical diffusion distinguishing between structural universality classes of disordered systems in one dimension. Samples of hyperuniform and short-range disorder were designed, characterized by the statistics of the placement of micrometer-thin parallel permeable barriers, and the time-dependent diffusion coefficient was measured by NMR methods over three orders of magnitude in time. The relation between the structural exponent, characterizing disorder universality class, and the dynamical exponent of the diffusion coefficient is experimentally verified. The experimentally established relation between structure and transport exemplifies the hierarchical nature of structural complexity-dynamics are mainly determined by the universality class, whereas microscopic parameters affect the nonuniversal coefficients. These results open the way for noninvasive characterization of structural correlations in porous media, complex materials, and biological tissues via a bulk diffusion measurement.

OBJECTIVE: To assess the association between peripheral lipid/fat profiles and cerebral gray matter (GM) and white matter (WM) in healthy Old Order Amish (OOA). METHODS: Blood lipids, abdominal adiposity, liver lipid contents, and cerebral microstructure were assessed in OOA (N = 64, 31 males/33 females, ages 18-77). Orthogonal factors were extracted from lipid and imaging adiposity measures. GM assessment used the Human Connectome Project protocol to measure whole-brain average cortical thickness. Diffusion-weighted imaging was used to derive WM fractional anisotropy and kurtosis anisotropy measurements. RESULTS: Lipid/fat measures were captured by three orthogonal factors explaining 80% of the variance. Factor one loaded on cholesterol and/or low-density lipoprotein cholesterol measurements; factor two loaded on triglyceride/liver measurements; and factor three loaded on abdominal fat measurements. A two-stage regression including age/sex (first stage) and the three factors (second stage) examined the peripheral lipid/fat effects. Factors two and three significantly contributed to WM measures after Bonferroni corrections (P < 0.007). No factor significantly contributed to GM. Blood pressure (BP) inclusion did not meaningfully alter the lipid/fat-WM relationship. CONCLUSIONS: Peripheral lipid/fat indicators were significantly and negatively associated with cerebral WM rather than with GM, independent of age and BP level. Dissecting the fat/lipid components contributing to different brain imaging parameters may open a new understanding of the body-brain connection through lipid metabolism.

OBJECTIVE: Prior studies in prostate diffusion-weighted magnetic resonance imaging (MRI) have largely explored the impact of b-value and diffusion directions on estimated diffusion coefficient D. Here we suggest varying diffusion time, t, to study time-dependent D(t) in prostate cancer, thereby adding an extra dimension in the development of prostate cancer biomarkers. METHODS: Thirty-eight patients with peripheral zone prostate cancer underwent 3-T MRI using an external-array coil and a diffusion-weighted image sequence acquired for b = 0, as well as along 12 noncollinear gradient directions for b = 500 s/mm using stimulated echo acquisition mode (STEAM) diffusion tensor imaging (DTI). For this sequence, 6 diffusion times ranging from 20.8 to 350 milliseconds were acquired. Tumors were classified as low-grade (Gleason score [GS] 3 + 3; n = 11), intermediate-grade (GS 3 + 4; n = 16), and high-grade (GS >/=4 + 3; n = 11). Benign peripheral zone and transition zone were also studied. RESULTS: Apparent diffusion coefficient (ADC) D(t) decreased with increasing t in all zones of the prostate, though the rate of decay in D(t) was different between sampled zones. Analysis of variance and area under the curve analyses suggested better differentiation of tumor grades at shorter t. Fractional anisotropy (FA) increased with t for all regions of interest. On average, highest FA was observed within GS 3 + 3 tumors. CONCLUSIONS: There is a measurable time dependence of ADC in prostate cancer, which is dependent on the underlying tissue and Gleason score. Therefore, there may be an optimal selection of t for prediction of tumor grade using ADC. Controlling t should allow ADC to achieve greater reproducibility between different sites and vendors. Intentionally varying t enables targeted exploration of D(t), a previously overlooked biophysical phenomenon in the prostate. Its further microstructural understanding and modeling may lead to novel diffusion-derived biomarkers.

A diffusion measurement in the short-time surface-to-volume ratio (S/V) limit (Mitra et al., Phys Rev Lett. 1992;68:3555) can disentangle the free diffusion coefficient from geometric restrictions to diffusion. Biophysical parameters, such as the S/V of tissue membranes, can be used to estimate microscopic length scales non-invasively. However, due to gradient strength limitations on clinical MRI scanners, pulsed gradient spin echo (PGSE) measurements are impractical for probing the S/V limit. To achieve this limit on clinical systems, an oscillating gradient spin echo (OGSE) sequence was developed. Two phantoms containing 10 fiber bundles, each consisting of impermeable aligned fibers with different packing densities, were constructed to achieve a range of S/V values. The frequency-dependent diffusion coefficient, D(omega), was measured in each fiber bundle using OGSE with different gradient waveforms (cosine, stretched cosine, and trapezoidal), while D(t) was measured from PGSE and stimulated-echo measurements. The S/V values derived from the universal high-frequency behavior of D(omega) were compared against those derived from quantitative proton density measurements using single spin echo (SE) with varying echo times, and from magnetic resonance fingerprinting (MRF). S/V estimates derived from different OGSE waveforms were similar and demonstrated excellent correlation with both SE- and MRF-derived S/V measures (rho >/= 0.99). Furthermore, there was a smoother transition between OGSE frequency f and PGSE diffusion time when using teffS/V=9/64f, rather than the commonly used teff = 1/(4f), validating the specific frequency/diffusion time conversion for this regime. Our well-characterized fiber phantom can be used for the calibration of OGSE and diffusion modeling techniques, as the S/V ratio can be measured independently using other MR modalities. Moreover, our calibration experiment offers an exciting perspective of mapping tissue S/V on clinical systems.

The time dependence of the diffusion coefficient is a hallmark of tissue complexity at the micrometer level. Here we demonstrate how biophysical modeling, combined with a specifically tailored diffusion MRI acquisition performing diffusion tensor imaging (DTI) for varying diffusion times, can be used to determine fiber size and membrane permeability of muscle fibers in vivo. We describe the random permeable barrier model (RPBM) and its assumptions, as well as the details of stimulated echo DTI acquisition, signal processing steps, and potential pitfalls. We illustrate the RPBM method on a few pilot examples involving human subjects (previously published as well as new), such as revealing myofiber size derived from RPBM increase after training in a calf muscle, and size decrease with atrophy in shoulder rotator cuff muscle. Finally, we comment on the potential clinical relevance of our results

Besides amyloid deposition, white matter (WM) changes are involved in the early pathogenesis of Alzheimer's Disease (AD), including inflammation, demyelination and axonal loss. Using simultaneous PET and MRI, we investigated differences in WM microstructural integrity, measured with Diffusion Kurtosis Imaging (DKI), with respect to beta amyloid (Aa) deposition as measured with18F-Florbetapir PET. DKI is a clinically feasible diffusion MRI method that extends beyond Diffusion Tensor Imaging and probes non-Gaussian diffusion properties of nervous tissue, and allows for quantifying the microstructural index for the axonal water fraction (AWF), a specific marker for axonal degeneration and demyelination. Methods: 34 subjects were scanned on a 3T integrated PET-MRI system (Siemens Biograph mMR, VB20). 18FFlorbetapir (9 mCi, Eli Lilly) was injected intravenously and a static 20-minute PET image was reconstructed starting at 40 min post-injection using a UTE-based attenuation map. An anatomical MP-RAGE was acquired for cortical and sub-cortical segmentation using Freesurfer. Hippocampal volume was normalized to the estimated total intracranial volume. The standardized uptake values (SUV) in 5 cortical regions known for pathological uptake of Florbetapir (anterior and posterior cingulate, medial orbito-frontal, parietal and temporal), normalized to the cerebellum, yielded mean cortical relative SUV (SUVr). DKI provided parametric maps for the radial diffusivity (RD), radial kurtosis (RK), and the AWF. Using a lower and higher mean SUVr threshold of 1.0 and 1.1, age- and gender-controlled subjects were categorized into Aa negative (Aa-) (n = 13, 5 females, age = 69.8 +/- 5.1 yrs), Aa intermediate (Aai) (n = 13, 8 females, age = 68.9 +/- 4.8 yrs), or Aa positive (Aa+) (n = 8, 4 females, age = 70.6 +/- 5.3 yrs). Using Tract-Based Spatial Statistics (TBSS), skeletonized voxel-wise analysis was performed to identify areas of differences in the diffusion metrics while covarying for age. Separately, WM regions of interests (ROIs) were automatically segmented using atlas registration over which mean values were extracted. Analysis of covariance covarying for age was used to compare diffusion metrics and hippocampal volume among groups. Results: See figure. Results from both TBSS and ROI analysis demonstrated changes in the fornix and the genu of the corpus callosum. Between the Aa- and Aai groups, RD decreased while RK and AWF increased. Conversely, between the Aai and Aa+ groups, RD increased RD while RK and AWF decreased. A trend towards significantly higher hippocampal volume in the Aai group was observed. Conclusions: We report changes in RD, RK and AWF in opposite directions between Aa- and Aa~, and between Aa~ and Aa+, respectively, suggesting that different mechanisms affect the microstructure during different stages of AD. Early on, mechanisms including microglial activation may restrict diffusion, resulting in the observed decrease in RD and increase in RK and AWF. Later on, neurodegenerative effects such as demyelination and axonal loss may outweigh inflammation, resulting in the observed increase in RD and decrease in RK and AWF. [IMAGE PRESENTED]

We introduce and evaluate a post-processing technique for fast denoising 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, yielding 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/or spatial resolution.

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.

Solid tumor microstructure is related to the aggressiveness of the tumor, interstitial pressure and drug delivery pathways, which are closely associated with treatment response, metastatic spread and prognosis. In this study, we introduce a novel diffusion MRI data analysis framework, pulsed and oscillating gradient MRI for assessment of cell size and extracellular space (POMACE), and demonstrate its feasibility in a mouse tumor model. In vivo and ex vivo POMACE experiments were performed on mice bearing the GL261 murine glioma model (n = 8). Since the complete diffusion time dependence is in general non-analytical, the tumor microstructure was modeled in an appropriate time/frequency regime by impermeable spheres (radius Rcell , intracellular diffusivity Dics ) surrounded by extracellular space (ECS) (approximated by constant apparent diffusivity Decs in volume fraction ECS). POMACE parametric maps (ECS, Rcell , Dics , Decs ) were compared with conventional diffusion-weighted imaging metrics, electron microscopy (EM), alternative ECS determination based on effective medium theory (EMT), and optical microscopy performed on the same samples. It was shown that Decs can be approximated by its long time tortuosity limit in the range [1/(88 Hz)-31 ms]. ECS estimations (44 +/- 7% in vivo and 54 +/- 11% ex vivo) were in agreement with EMT-based ECS and literature on brain gliomas. Ex vivo, ECS maps correlated well with optical microscopy. Cell sizes (Rcell = 4.8 +/- 1.3 in vivo and 4.3 +/- 1.4 microm ex vivo) were consistent with EM measurements (4.7 +/- 1.8 microm). In conclusion, Rcell and ECS can be quantified and mapped in vivo and ex vivo in brain tumors using the proposed POMACE method. Our experimental results support the view that POMACE provides a way to interpret the frequency or time dependence of the diffusion coefficient in tumors in terms of objective biophysical parameters of neuronal tissue, which can be used for non-invasive monitoring of preclinical cancer studies and treatment efficacy

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.