Towards Optimal Sampling in Diffusion MRI

The methodology outlined in this chapter is intended to provide a tool for the generation of sets of MRI diffusion encoding waveforms that are optimal for tissue micro-structure estimation. The methodology presented has five distinct components: 1. Defining the class of waveforms allowed, i.e. defining the measurement space. 2. Specifying the expected distribution of microstructure features present in the targeted tissue. 3. Learning the metric in the chosen measurement space. 4. Designing a continuous parametric functional suitable for approximation of the estimated metric. 5. Finding a distribution of a chosen number of waveforms that is optimal given the continuous metric. The tissue is modeled as a collection of simple elliptical compartments with varying size and shape. Two waveform classes are tested: The classical Stejskal-Tanner waveform and an idealized Laun long-short waveform. The estimation of the metric is based on correlations between measurements obtained at given points in the measurement space using an information theoretical approach. Optimal sets of waveforms are found using a simulated annealing inspired energy minimizing approach. The superior performance of the methodology is demonstrated for a number of different cases by means of simulations.