Time-Dependent Diffusion MRI in Cancer: Tissue Modeling and Applications

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.

We present the first in vivo application of the filter-exchange imaging protocol for diffusion MRI. The protocol allows noninvasive mapping of the rate of water exchange between microenvironments with different self-diffusivities, such as the intracellular and extracellular spaces in tissue. Since diffusional water exchange across the cell membrane is a fundamental process in human physiology and pathophysiology, clinically feasible and noninvasive imaging of the water exchange rate would offer new means to diagnose disease and monitor treatment response in conditions such as cancer and edema. The in vivo use of filter-exchange imaging was demonstrated by studying the brain of five healthy volunteers and one intracranial tumor (meningioma). Apparent exchange rates in white matter range from 0.8±0.08 s(-1) in the internal capsule, to 1.6±0.11 s(-1) for frontal white matter, indicating that low values are associated with high myelination. Solid tumor displayed values of up to 2.9±0.8 s(-1). In white matter, the apparent exchange rate values suggest intra-axonal exchange times in the order of seconds, confirming the slow exchange assumption in the analysis of diffusion MRI data. We propose that filter-exchange imaging could be used clinically to map the water exchange rate in pathologies. Filter-exchange imaging may also be valuable for evaluating novel therapies targeting the function of aquaporins.