Optimization of diffusion measurements using Cramer‐Rao lower bound theory and its application to articular cartilage

Abstract

A novel approach to optimized diffusion measurements by minimizing the Cramer-Rao lower bound (CRLB) with respect to the b-values used for diffusion measurement was investigated. The applicability of the CRLB to these measurements is shown by the close agreement between the CRLB prediction and the actual precision obtained from experimental results. Where studies using a propagation-of-errors approach have restricted the optimization of the diffusion measurement to two b-values and to specific diffusion coefficient values, the CRLB approach sets no bounds on the number of b-values and is applicable to any system. The optimal number of b-values depends on the ratio of the maximum and minimum diffusion coefficients in the sample (the D_ratio) and on the number of acquisitions. For a D_ratio above 6.8 the optimal number of b-values increases to three; at a D_ratio of 21.8 it increases to four. The optimized sampling schemes for ADC measurements in a variety of representative tissues found in the human body are given. For cartilage the optimal five-point acquisition scheme requires one measurement at a b-value of 0 and four at 1036 sec mm⁻², whereas brain requires one at 0, three at 660, and one at 1987 sec mm⁻². Magn Reson Med 50:1069–1076, 2003.