Diffusion-Weighted Magnetic Resonance Imaging (DWMRI or DWI) is a specialized imaging technique that can be used to quantify diffusivity of water molecules in biological tissues. Nerve fibers in nervous tissues consist of axon bundles which are highly directional microscopic tube-like structures with semi-permeable boundaries. Water molecules within fibers exhibit diffusion anisotropy due to preferential movement of the molecules along the direction of the fiber. The diffusion anisotropy can be measured by collecting data using a series of diffusion-encoding gradients (diffusion-encoding gradient scheme) in the DWI experiment and solving the inverse problem that characterizes the diffusion anisotropy process. The direction of highest diffusivity gives the direction of the nerve fibers. Hence, DWI provides a completely non-invasive technique to image nerve fibers and study nerve connectivity in the brain, the spinal cord or the peripheral nervous system. In model-based DWI methods (such as diffusion tensor imaging, DTI), the diffusion process is characterized by a parametric relation between the measured DWI signal and the diffusion model parameters (diffusivity, fiber orientation) as well as the experimental parameters (gradient strengths and directions in the scheme). The model parameters are estimated by solving the inverse problem corresponding to the diffusion process under a given experimental setting. The estimated model parameters are further used to compute secondary diffusion-related quantities (such as mean diffusivity and fractional anisotropy which are potential biomarkers of the health of the nerve fibers) or to reconstruct fiber tracts connecting different locations in the imaged structure (fiber tractography). It is important that the diffusion model parameters are precisely estimated since these directly affect any secondary processing step. The precision of the estimated model parameters depends on the selection of the experimental parameters and thus can be improved by optimal selection of these parameters. In this work, a framework to optimize the diffusion-encoding gradient scheme is developed for model-based DWI methods. The framework reduces the estimation uncertainty of diffusion model parameters (thus improves precision) by optimally selecting the diffusion-encoding gradients to minimize an analytical lower bound of the estimation uncertainty (known as the Cramer-Rao lower bound, CRLB). Focus has been on special structures, such as the spinal cord, where the axon bundles are oriented in specific direction known a priori.This availability of a priori information of the fiber orientation has been exploited and embedded into the optimization framework to reduce uncertainty of parameter estimation. The framework has been validated via Monte Carlo simulations as well as by conducting DTI experiments on human subjects. Also results from fiber tractography show improvement in the quality of tracked nerve fibers upon using the optimized gradient scheme. Thus, the use of the optimization framework can improve the quality of DWI diagnostics by improving precision of the imaging technique and encourage comparison of patient groups.
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