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...

The present study assesses the effects of cross-term interactions between diffusion and imaging gradients in magnetic resonance imaging q-space analysis, and corrects for those effects for both spin echo and stimulated echo diffusionweighted sequences. These corrections are demonstrated experimentally in unrestricted media for water and theoretically by simulating the case of restricted diffusion in a sphere. By correcting for the cross-term interactions, large imaging gradients can be used without compromising the results. Ignoring cross-term interactions could lead to a misunderstanding of the q-space analysis; for instance, the microstructural size of the sample could be overestimated, or isotropic media could be misinterpreted as being anisotropic. In the early 1990s Callaghan (1) and Cory and Garroway (2) demonstrated that structural information too small to be detected by conventional nuclear magnetic resonance (NMR) methods can be inferred from the measurement of water diffusion. Their studies demonstrated that the echo attenuation in a spin echo sequence due to the effect of a pair of finite duration diffusion pulse field gradients, separated by a long diffusion time, could be related to the displacement probability of the observed spins following Fourier transformation (FT) of the echo intensity, E(q), with respect to the so-called "reciprocal spatial vector," q. This technique was termed q-space imaging, and it has since been used almost exclusively in bulk NMR spectroscopy. Recently, however, q-space imaging has been extended both to localized NMR spectroscopy (3) and to MRI (3-5).If additional magnetic field gradients (e.g., imaging gradients) are introduced into the diffusion sequence, however, these may contribute to the diffusion weighting, which in turn may translate into greater echo attenuation than would be expected from the diffusion gradients alone. This interaction between the imaging gradients and diffusion gradients is well known in standard diffusionweighted imaging (DWI) (7-9) and is generally referred to as "cross-term interaction." If those interactions are not accounted for in the experimental analysis, misinterpretation of the data can easily occur, particularly when the q-space experiments are performed using strong imaging gradients.For standard DWI experiments, Neeman et al. (7) and Eis and Hoehn-Berlage (8) solved this problem for unidirectional diffusion measurements, whereas Mattiello et al. (9) have done so for diffusion tensor measurements. However, if the q-space technique is to be implemented successfully in conjunction with imaging gradients, the cross-term interactions must also be evaluated for this sequence. In the present study, expressions for calculation of corrected qvalues, which account for cross-term interactions with imaging gradients, were derived and the practical implications of the imaging gradients in q-space imaging were examined. These corrections were determined for two sequences commonly used in q-space analysis, namely, the spin echo (10) and stimulat...