CRAMER-RAO BOUNDS FOR 3-POINT DIXON IMAGING

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This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. INTRODUCTION In most applications of MRI, the diagnostic information is contained in the signal coming from the water in tissue. The fat component of the signal can obscure underlying pathology. For this reason, it is important to suppress or separate the fat signal. Dixon imaging uses images obtained at different times from the echo to separate the chemical species in each pixel. The most common application of this technique is the separation of fat and water using 3 measurements, i.e. 3-point Dixon imaging. The noise of the estimates for the magnitude of fat and water in 3-point Dixon imaging depends on many factors including the echo times, the field inhomogeneity, the fat-to-water ratio and the reconstruction algorithm1. The Cramer-Rao bound2 (CRB) is the lower bound on the variance of any unbiased estimate. It provides a measure of the minimum uncertainty of the estimates for a given data acquisition which is independent of the reconstruction algorithm. We use the CRB to optimize the choice of echo times and compare performance of our least-squares estimation algorithm with this theoretical limit. MATERIALS AND METHODS The CRB was computed for estimating the magnitude of the fat and water from measurements at any 3 echo times. An optimization was carried out to find choice of echo times with the least imaging time that optimized the noise performance. As a measure of noise performance, we used the number of signals averaged (NSA) which is the ratio of the variance of the original images over the variance of the water estimate. In our case, an NSA of 3 is the maximum possible. An NSA of 0 says that the water cannot be estimated from the measurements. To verify the theoretical result, an in-vitro experiment was carried out using a spherical phantom containing fat and water. By reconstructing an oblique slice with respect to the interface of the fat and water, we generated pixels with a range of fat-to-water ratios. CONCLUSION Cramer-Rao bounds provide a computationally efficient way to optimize the choice of echo times for Dixon imaging. Such an optimization was carried out to avoid the loss of NSA when a pixel contained equal parts fat and water. For this application, we have shown that the non-linear least squares algorithm is efficient (since it achieves the CRB). By combining the use of the CRB to choose our echo times and a reconstruction algorithm that is efficient, we have obtained an imaging method that is ideal in terms of the variance of the reconstructed water and fat images. REFERENCES 1. Reeder, et. al., submitted to MRM. 2. Pineda, et. al., to be submitted to TMI.