We are continuing to develop novel Magnetic Resonance (MR) based displacement imaging methods, such as Diffusion Tensor MRI (DT-MRI or DTI). DTI measures a diffusion tensor of water within tissue. It consists of relating an effective diffusion tensor to the measured MR spin echo signal;estimating an effective diffusion tensor, D, in each pixel from a set of diffusion-weighted MR images;and calculating and displaying information derived from D. This information includes the local fiber-tract orientation, the mean-squared distance water molecules diffuse in any given direction, the orientationally-averaged mean diffusivity, and other scalar invariant quantities that are independent of the laboratory coordinate system. These scalar parameters are intrinsic properties of the tissue that we measure without requiring contrast agents or dyes. For example, one DTI parameter, the orientationally-averaged diffusivity (or Trace), has been the most successful imaging parameter used to date to visualize an acute stroke in progress. Moreover, we have shown that DTI is effective in identifying Wallerian degeneration often associated with chronic stroke. Studies with kittens have shown DTI to be useful in following early developmental changes occurring in cortical gray and white matter, which are not detectable using other means. The development of a method to color-encode nerve fiber orientation in the brain by Sinisa Pajevic and Carlo Pierpaoli has allowed us to identify and differentiate anatomical white matter pathways that have similar structure and composition, but different spatial orientations. Color maps of the human brain clearly show the main association, projection, and commissural white matter pathways. They have also allowed detailed studies of the brains structural anatomy to be performed, which was only possible previously using laborious, invasive histological methods. To assess anatomical connectivity between different functional regions in the brain, we also proposed and demonstrated a way to use DTI data to trace out nerve fiber tract trajectories, which we called DTI "tractography". This development was made possible by previous contributions of Sinisa Pajevic and Akram Aldroubi who implemented a general mathematical framework for obtaining a continuous, smooth approximation to the measured discrete, noisy, diffusion tensor field data. We have also developed non-parametric (bootstrap) methods for determining features of the statistical distribution of the diffusion tensor from experimental DTI data. Another innovation has been the development of a tensor variate Gaussian distribution that fully describes the variability of the diffusion tensor in an idealized DTI experiment, and can be used to improve the design and efficiency of DTI experiments. These collective developments are encouraging us to develop powerful hypothesis tests to address a wide variety of important biological and clinical questions that previously could only be tackled using ad hoc methods, if at all. We are currently addressing several key methodological issues that will enable us to perform quantitative longitudinal and multi-center DTI studies. More recently, we have been developing sophisticated mathematical models of water diffusion in tissues and have begun using these to infer additional microstructural details about tissue (primarily white matter in the brain) from MRI data. The composite hindered and restricted model of diffusion (CHARMED) framework is one example. Our recently proposed enhancement of CHARMED, AxCaliber, is another. AxCaliber allows us to estimate the axon diameter distribution within a nerve bundle from MR displacement imaging data and the volume fraction of axons. Sophisticated diffusion weighted NMR and MRI sequences, recently developed by Michael Komlosh, promise to allow us to characterize microscopic anisotropy within tissues like gray matter that are macroscopically isotropic, and appear like a homogeneous gel in DTI. She and Ferenc Horkay have developed physical phantoms to test and inteerrogate our mathematical models of water diffusion in such complex tissue. Evren Ozarslan has been developing novel ways to characterize anomalous diffusion observed in various tissue specimen. Parameters derived from these measurements may provide a new source of MR contrast for promising diagnostic applications such as Brodmann parcellation or cancer detection. He has also developed novel approaches to characterize non-Gaussian features of the displacement distribution measured using MRI. Evren, Valery Pikalov, and Wolfram Jarisch are all working on different methods to reconstruct the average propagator (average displacement distribution) using a relatively small number of diffusion weighted images (DWI). The average propagator is the "holy grail" of displacement imaging, which can by used to infer geometric features of microscopic restricted compartments as well as glean all of the information provided by DTI. Collectively, these methods represent a general framework for performing in vivo MRI histology, providing detailed microstructural and microarchitectural information that otherwise could only be obtained using laborious and invasive histological techniques applied on biopsied specimens. Our goal is to provide these structural assessment in vivo and non-invasively.