Faculty Bibliography

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.

One overarching challenge of clinical magnetic resonance imaging (MRI) is to quantify tissue structure at the cellular scale of micrometers, based on an MRI acquisition with a millimeter resolution. Diffusion MRI (dMRI) provides the strongest sensitivity to the cellular structure. However, interpreting dMRI measurements has remained a highly ill-posed inverse problem. Here we propose a framework that resolves the above challenge for human white matter fibers, by unifying intra-voxel mesoscopic modeling with global fiber tractography. Our algorithm is based on a Simulated Annealing approach which simultaneously optimizes diffusion parameters and fiber locations. Each fiber carries its by their individual set of diffusion parameters which allows to link them structural relationships.

BACKGROUND AND PURPOSE:Along with cortical abnormalities, white matter microstructural changes such as axonal loss and myelin breakdown are implicated in the pathogenesis of Alzheimer disease. Recently, a white matter model was introduced that relates non-Gaussian diffusional kurtosis imaging metrics to characteristics of white matter tract integrity, including the axonal water fraction, the intra-axonal diffusivity, and the extra-axonal axial and radial diffusivities.MATERIALS AND METHODS:This study reports these white matter tract integrity metrics in subjects with amnestic mild cognitive impairment (n = 12), Alzheimer disease (n = 14), and age-matched healthy controls (n = 15) in an effort to investigate their sensitivity, diagnostic accuracy, and associations with white matter changes through the course of Alzheimer disease.RESULTS:With tract-based spatial statistics and region-of-interest analyses, increased diffusivity in the extra-axonal space (extra-axonal axial and radial diffusivities) in several white matter tracts sensitively and accurately discriminated healthy controls from those with amnestic mild cognitive impairment (AUC = 0.82-0.95), while widespread decreased axonal water fraction discriminated amnestic mild cognitive impairment from Alzheimer disease (AUC = 0.84). Additionally, these white matter tract integrity metrics in the body of the corpus callosum were strongly correlated with processing speed in amnestic mild cognitive impairment (r = |0.80-0.82|, P < .001).CONCLUSIONS:These findings have implications for the course and spatial progression of white matter degeneration in Alzheimer disease, suggest the mechanisms by which these changes occur, and demonstrate the viability of these white matter tract integrity metrics as potential neuroimaging biomarkers of the earliest stages of Alzheimer disease and disease progression.

A Comment on the Letter by N. Shemesh, C.-F. Westin, and Y. Cohen, Phys. Rev. Lett. 108, 058103 (2012).. The authors of the Letter offer a Reply.

The impairment of axonal transport by overexpression or hyperphosphorylation of tau is well documented for in vitro conditions; however, only a few studies on this phenomenon have been conducted in vivo, using invasive procedures, and with contradictory results. Here we used the non-invasive, Manganese-Enhanced Magnetic Resonance Imaging technique (MEMRI), to study for the first time a pure model of tauopathy, the JNPL3 transgenic mouse line, which overexpresses a mutated (P301L) form of the human tau protein. We show progressive impairment in neuronal transport as tauopathy advances. These findings are further supported by a significant correlation between the severity of the impairment in neuronal transport assessed by MEMRI, and the degree of abnormal tau assessed by histology. Unlike conventional techniques that focus on axonal transport measurement, MEMRI can provide a global analysis of neuronal transport, i.e. from dendrites to axons and at the macroscopic scale of fiber tracts. Neuronal transport impairment has been shown to be a key pathogenic process in Alzheimer's disease and numerous other neurodegenerative disorders. Hence, MEMRI provides a promising set of functional biomarkers to be used during preclinical trials to facilitate the selection of new drugs aimed at restoring neuronal transport in neurodegenerative diseases.

Many nanoscale systems are known to emit light intermittently under continuous illumination. In the fluorescence of single semiconductor nanoparticles, the distributions of bright and dark periods ('on' and 'off' times) follow Levy statistics. Although fluorescence from single-quantum dots and from macroscopic quantum dot ensembles has been studied, there has been little study of fluorescence from small ensembles. Here we show that blinking nanorods (NRs) interact with each other in a cluster, and the interactions affect the blinking statistics. The on-times in the fluorescence of a NR cluster increase dramatically; in a cluster with N NRs, the maximum on-time increases by a factor of N or more compared with the combined signal from N well-separated NRs. Our study emphasizes the use of statistical properties in identifying the collective dynamics. The scaling of this interaction-induced increase of on-times with number of NRs reveals a novel collective effect at the nanoscale

Restrictions to molecular motion by barriers (membranes) are ubiquitous in porous media, composite materials and biological tissues. A major challenge is to characterize the microstructure of a material or an organism nondestructively using a bulk transport measurement. Here we demonstrate how the long-range structural correlations introduced by permeable membranes give rise to distinct features of transport. We consider Brownian motion restricted by randomly placed and oriented membranes (d - 1 dimensional planes in d dimensions) and focus on the disorder-averaged diffusion propagator using a scattering approach. The renormalization group solution reveals a scaling behavior of the diffusion coefficient for large times, with a characteristically slow inverse square root time dependence for any d. Its origin lies in the strong structural fluctuations introduced by the spatially extended random restrictions, representing a novel universality class of the structural disorder. Our results agree well with Monte Carlo simulations in two dimensions. They can be used to identify permeable barriers as restrictions to transport, and to quantify their permeability and surface area

Restrictions to diffusion result in the dispersion of the bulk diffusion coefficient. We derive the exact universal high-frequency behavior of the diffusion coefficient in terms of the surface-to-volume ratio of the restrictions. This frequency dependence can be applied to quantify structure of complex samples with NMR using oscillating field gradients and static-gradient CPMG. We also demonstrate the inter-relations between different equivalent diffusion metrics, and describe how to calculate the effect of restrictions for arbitrary gradient waveforms

Multisite exchange models have been applied frequently to quantify measurements of transverse relaxation and diffusion in living tissues. Although the simplicity of such models is attractive, the precise relationship of the model parameters to tissue properties may be difficult to ascertain. Here, we investigate numerically a two-compartment exchange (Karger) model as applied to diffusion in a system of randomly packed identical parallel cylinders with permeable walls, representing cells with permeable membranes, that may serve particularly as a model for axons in the white matter of the brain. By performing Monte Carlo simulations of restricted diffusion, we show that the Karger model may provide a reasonable coarse-grained description of the diffusion-weighted signal in the long time limit, as long as the cell membranes are sufficiently impermeable, i.e. whenever the residence time in a cell is much longer than the time it takes to diffuse across it. For larger permeabilities, the exchange time obtained from fitting to the Karger model overestimates the actual exchange time, leading to an underestimated value of cell membrane permeability