Determination of the appropriate b value and number of gradient directions for high-angular-resolution diffusion-weighted imaging.

High-angular-resolution diffusion-weighted imaging (HARDI) is one of the most common MRI acquisition schemes for use with higher order models of diffusion. However, the optimal b value and number of diffusion-weighted (DW) directions for HARDI are still undetermined, primarily as a result of the large number of available reconstruction methods and corresponding parameters, making it impossible to identify a single criterion by which to assess performance. In this study, we estimate the minimum number of DW directions and optimal b values required for HARDI by focusing on the angular frequency content of the DW signal itself. The spherical harmonic (SH) series provides the spherical analogue of the Fourier series, and can hence be used to examine the angular frequency content of the DW signal. Using high-quality data acquired along 500 directions over a range of b values, we estimate that SH terms above l = 8 are negligible in practice for b values up to 5000 s/mm(2), implying that a minimum of 45 DW directions is sufficient to fully characterise the DW signal. l > 0 SH terms were found to increase as a function of b value, levelling off at b = 3000 s/mm(2), suggesting that this value already provides the highest achievable angular resolution. In practice, it is recommended to acquire more than the minimum of 45 DW directions to avoid issues with imperfections in the uniformity of the DW gradient directions and to meet signal-to-noise requirements of the intended reconstruction method.