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 It has been shown that the measurement of the apparent diffusion coefficient (ADC) of water in articular cartilage by nuclear magnetic techniques has the potential to detect early-stage osteoarthritis (1-6). However, the success of the technique in discriminating between healthy and diseased tissues will depend to a large extent on the precision with which both a single value and a range of ADC values can be determined in the clinical setting. As the precision of diffusion measurements depends on both the signal-tonoise ratio (SNR) of the image and the applied b-value sampling scheme, it is important to optimize both in order to obtain the best quality measurements. Unfortunately, the characteristics of cartilage make it a very demanding tissue to scan: it requires high spatial resolution scans because of its small dimensions and, furthermore, the proton resonances of its water have short T 2 values. Consequently, the SNR of cartilage is inherently low, leading to difficulty in the precise measurement of ADC values.The majority of previous water diffusion studies in cartilage have used either NMR (3-5) of bulk material or NMR microscopy of small excised samples (1,2) where high spatial resolution and high SNR are readily achieved via the strong gradients, high magnetic field strengths, and short echo times produced by the imaging hardware. In addition, since the measurement time is not generally an important factor for NMR studies, the required SNR can be improved by signal averaging. In clinical MRI, however, neither the equivalent hardware performance nor the same timescales are available; consequently, the SNR of the measurements is substantially reduced and the precision of the measurement compromised.Diffusion measurements based on ultra-fast scanning techniques such as echo planar imaging (EPI) (7) or...

Optimization of Scan Parameters to Reduce Acquisition Time for Diffusion Kurtosis Imaging at 1.5T

“…Previous studies revealed that larger numbers of unique diffusion directions are more beneficial for robust estimation of DTI and DKI parameters. [21][22][23][24][25] However, our results suggest that compared to a combination of b-values and NSA, the number of diffusion directions has a weaker influence on the accuracy of the MK maps. The number of diffusion directions can thus be compromised to some extent when scanning time is shortened.…”

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