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Med Phys. 2011 Feb;38(2):975-82.

A variable echo-number method for estimating R2 in MRI-based polymer gel dosimetry.

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  • 1Department of Therapeutic Radiology, University of Minnesota, Minneapolis, Minnesota 55455, USA.



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.

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