Magnetic Resonance Imaging of Anomalous Diffusion and Entropy in Neural Tissue

The novelty in this project lies in the cross-pollination of distinct disciplines in physics, information theory, and bioengineering to provide new insight about biological tissue structure. Magnet Resonance Imaging is an ideal tool to non-invasively probe biological tissue and is flexible to allow for measurements at a wide range of temporal and spatial resolutions. By utilizing a generalized mathematical model to interpret the diffusion dynamics, the data is free of statistical assumptions and is allowed to `talk', such that the continuous time random walk model `listens' as it converges to a fit that describes a class of diffusion, whether it is normal, sub-, or even super-. Furthermore, this approach is firmly cast in the probabilistic regime with the continuous time random walk so that diffusion decay signal is simply the characteristic function (i.e., Fourier transform) of the probability density function. Consequently, we can integrate information theory via entropy measurements of the characteristic function to formulate the problem of anomalous diffusion as one of statistical `uncertainty' or `information', inspired by C. E. Shannon. Most importantly, this project has been designed with a scope intended to demonstrate these methods are not only viable research tools, but also translatable to a clinical setting that poses additional hardware and scan time constraints. With these pilot studies, we intend to present a pipeline of new `information' starting with ex vivo healthy adolescent and adult neural tissue in animals and ending with new `information' in in vivo neural anatomy in humans.