Optimal diffusion MRI acquisition for fiber orientation density estimation: an analytic approach.

An important challenge in the design of diffusion MRI experiments is how to optimize statistical efficiency, i.e., the accuracy with which parameters can be estimated from the diffusion data in a given amount of imaging time. In model-based spherical deconvolution analysis, the quantity of interest is the fiber orientation density (FOD). Here, we demonstrate how the spherical harmonics (SH) can be used to form an explicit analytic expression for the efficiency of the minimum variance (maximally efficient) linear unbiased estimator of the FOD. Using this expression, we calculate optimal b-values for maximum FOD estimation efficiency with SH expansion orders of L = 2, 4, 6, and 8 to be approximately b = 1,500, 3,000, 4,600, and 6,200 s/mm(2), respectively. However, the arrangement of diffusion directions and scanner-specific hardware limitations also play a role in determining the realizable efficiency of the FOD estimator that can be achieved in practice. We show how some commonly used methods for selecting diffusion directions are sometimes inefficient, and propose a new method for selecting diffusion directions in MRI based on maximizing the statistical efficiency. We further demonstrate how scanner-specific hardware limitations generally lead to optimal b-values that are slightly lower than the ideal b-values. In summary, the analytic expression for the statistical efficiency of the unbiased FOD estimator provides important insight into the fundamental tradeoff between angular resolution, b-value, and FOD estimation accuracy.