CRAMER-RAO BOUNDS FOR 3-POINT DIXON IMAGING

这个子项目是利用由NIH/NCRR资助的中心拨款提供的资源的许多研究子项目之一。子项目和调查员(PI)可能从另一个NIH来源获得了主要资金，因此可能会出现在其他CRISE条目中。列出的机构是针对中心的，而不一定是针对调查员的机构。前言在磁共振成像的大多数应用中，诊断信息包含在来自组织中的水的信号中。信号中的脂肪成分可能会掩盖潜在的病理。因此，抑制或分离脂肪信号是很重要的。Dixon成像使用在不同时间从回波中获得的图像来分离每个像素中的化学物质。这项技术最常见的应用是使用三种测量方法来分离脂肪和水分，即三点狄克逊成像。三点Dixon成像中估计脂肪和水的大小的噪声取决于许多因素，包括回波时间、场不均匀、脂水比和重建算法1。克雷默-罗界(CRB)是任何无偏估计的方差的下界。它提供了对给定数据采集的估计的最小不确定性的度量，该度量独立于重建算法。我们使用CRB来优化回波时间的选择，并将我们的最小二乘估计算法的性能与这个理论极限进行了比较。材料和方法计算CRB，通过在任意3个回声时间的测量来估计脂肪和水的大小。对成像时间最短的回波次数进行了优化，使噪声性能达到最优。作为噪声性能的衡量标准，我们使用平均信号数(NSA)，它是原始图像的方差与水估计的方差之比。在我们的情况下，NSA为3是可能的最大值。国家安全局的值为0表示无法从测量结果中估计水量。为了验证理论结果，使用一个含有脂肪和水的球形体模进行了体外实验。通过重建相对于脂肪和水界面的倾斜切片，我们生成了具有一定范围的脂肪与水的比率的像素。结论Cramer-Rao边界为优化Dixon成像回波时间的选择提供了一种有效的计算方法。这样的优化是为了避免当像素含有相同比例的脂肪和水分时NSA的损失。对于这种应用，我们已经证明了非线性最小二乘算法是有效的(因为它实现了CRB)。通过使用CRB来选择我们的回波时间，并结合高效的重建算法，我们获得了一种从重建的水和脂肪图像的方差来看理想的成像方法。参考文献1.Reeder等人Al.提交给MRM。2.Pineda，et.Al.将提交给TMI。

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.