Department of Therapeutic Radiology, University of Minnesota, Minneapolis, Minnesota 55455, USA.
Med Phys. 2011 Feb;38(2):975-82. doi: 10.1118/1.3544659.
Spin-spin relaxation rate R2 is commonly used to quantify absorbed dose for magnetic resonance imaging (MRI)-based polymer gel dosimetry. R2 is estimated by applying a parameter fitting algorithm to a train of spin-echo signals. However, a careless application of a large number of echoes can result in anomalous R2 values because the echo signal intensity decreases to the background signal offset level for a long echo time. In this article, the authors proposed and evaluated a variable echo-number (VAREC) method to remedy the problem.
The VAREC algorithm uses only echo signals, whose intensities are greater than a preset threshold. Here, the threshold is defined as the standard deviation of Gaussian noise times a multiplier alpha. The authors implemented three R2 estimation methods in an in-house program: The nonlinear least-squares algorithm (NLLS), the VAREC method, and the maximum likelihood estimator with the Rician signal intensity distribution (MLE_R). Those methods were used to estimate the R2 values of test phantoms with known R2 values and BANG3-type polymer gels, which were irradiated to 12 different doses ranging from 0 to 50 Gy. The R2 values were measured by using a 32-echo CPMG pulse sequence on 3 T MRI scanners. The R2 values of the VAREC method were compared with those of NLLS and MLE_R.
The R2 values of the NLLS method incorrectly decreased to the zero-dose level for doses greater than 10 Gy. The R2 values of the VAREC method with alpha=2 agreed with those of MLE_R within the measurement uncertainty. The uncertainties of the R2 values were the smallest for alpha=2 or 3 among various alpha values.
The VAREC algorithm is simple, fast, and robust for the R2 estimation. The authors recommend this method with alpha=2 or 3 for R2 estimation using multispin echo MRI protocols.
自旋-自旋弛豫率 R2 常用于磁共振成像（MRI）基聚合物凝胶剂量测定中的吸收剂量定量。R2 通过对一组自旋回波信号应用参数拟合算法来估计。然而，大量回波的粗心应用可能会导致异常的 R2 值，因为回波信号强度对于长回波时间会降至背景信号偏移水平。在本文中，作者提出并评估了一种可变回波数（VAREC）方法来解决该问题。
VAREC 算法仅使用强度大于预设阈值的回波信号。这里，阈值定义为高斯噪声的标准偏差乘以倍增器 alpha。作者在内部程序中实现了三种 R2 估计方法：非线性最小二乘算法（NLLS）、VAREC 方法和具有瑞利信号强度分布的最大似然估计器（MLE_R）。这些方法用于估计具有已知 R2 值的测试体模和 BANG3 型聚合物凝胶的 R2 值，这些体模被照射到 12 个从 0 到 50 Gy 的不同剂量。使用 3 T MRI 扫描仪上的 32 回波 CPMG 脉冲序列测量 R2 值。将 VARC 方法的 R2 值与 NLLS 和 MLE_R 的 R2 值进行比较。
NLLS 方法的 R2 值对于大于 10 Gy 的剂量错误地降至零剂量水平。VAREC 方法的 R2 值与 MLE_R 在测量不确定度内一致。在各种 alpha 值中，alpha=2 或 3 的 R2 值的不确定度最小。
VAREC 算法用于 R2 估计既简单又快速且稳健。作者推荐在使用多自旋回波 MRI 协议进行 R2 估计时使用此方法和 alpha=2 或 3。
