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

Yoichi Watanabe, Hitoshi Kubo

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


Purpose: 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. Methods: 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 α. 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. Results: 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 α=2 agreed with those of MLE-R within the measurement uncertainty. The uncertainties of the R2 values were the smallest for α=2 or 3 among various α values. Conclusions: The VAREC algorithm is simple, fast, and robust for the R2 estimation. The authors recommend this method with α=2 or 3 for R2 estimation using multispin echo MRI protocols.

Original languageEnglish (US)
Pages (from-to)975-982
Number of pages8
JournalMedical Physics
Issue number2
StatePublished - Feb 2011

Bibliographical note

Funding Information:
Some of the results in the current article were previously presented at the AAPM Annual Meeting (Anaheim, CA) in July 2009. One of authors (Y.W.) was previously supported by a Minnesota Medical Foundation grant, which was awarded to the preliminary study and the work was performed with Dr. Bruce Hammer at the Center for Innovative Applications of Magnetic Resonance of University of Minnesota. The Center for Magnetic Resonance Research (CMRR) was funded by NIH grants (Grant Nos. P30 NS057091 and P41 RR008079). The authors, in particular, the second author (H.K.), also would like to acknowledge the staff at the 3T MRI facility of Nagoya University for help.


  • CPMG
  • R2
  • maximum likelihood estimator
  • polymer gel dosimetry
  • quantitative MRI
  • radiation dose


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