Probing Cell Sizes Using Short Diffusion Times

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A new magnetic resonance imaging (MRI) technique will be developed with the capability to infer micron-scale restrictions to water diffusion in samples with complicated geometries.Over the next five years the method will be developed to work on live subjects and extended to use more accurate geometric models of white matter which include orientation dispersion, exchange between compartments and cerebrospinal fluid. In short, the current method uses a simplified model of the geometry of the sample; in our case we model axons in fibres as a distribution of parallel impermeable cylinders of varying diameters. An analytical expression is found for the diffusion of water measured perpendicular to the cylinders as a function of frequency. Data from experiments or Monte Carlo simulations are fitted to this analytical model to obtain the fraction of axons with different diameters.We will improve the model to include permeable membranes for more accurate results in white matter. With permeable membranes, water molecules can diffuse distances longer than an axon diameter. The failure of the current model to take this into account could skew the results making axons seem larger than they actually are.We will also surround the axons with myelin bilayers. Myelin lipid bilayers will add more diffusion barriers, the effect of which has not been fully studied. In addition, water within the myelin lipid bilayers has a very short relaxation time compared to water in other parts of the central nervous system. While the myelin will cause more restriction to the signal, the magnetization of the water within the myelin bilayers will relax much quicker possibly to the point that that water does not contribute to the signal. We will find analytical formulae for the model and test the geometries and assumptions with Monte Carlo simulations and corpus callosum and spinal cord samples.We will also optimize the new method so it will be a key in solving the problem with kissing or crossing fibres in MR tractography. MR tractography uses sophisticated methods collecting images using many gradient directions to determine geometrically whether fibres kiss or cross at junctions. Measuring the axon diameter distributions of fibres on either side of the junction will allow a simple determination of whether the fibres kiss or cross if the two fibres contain axons of different diameters. This is of extreme importance to neuroscience because tractography is being used to understand which regions of the brain are connected to each other. The new method will be optimized in terms of the selection of gradient frequencies, amplitudes, and directions to work at junctions with the goal of making a more accurate and faster method for tractography at junctions.The method will be verified using white matter, vegetables, and other micron-scale porous samples such as cement and lung airspaces.