title: A variable echo-number method for estimating R2 in MRI-based polymer gel dosimetry.
abstract: OBJECTIVE
  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 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.
  
  
  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 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.
  
  
  CONCLUSIONS
  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.
authors: Department of Therapeutic Radiology, University of Minnesota, Minneapolis, Minnesota 55455, USA. watan016@umn.edu
authors: Yoichi
authors: Y
authors: Watanabe
authors: Hitoshi
authors: H
authors: Kubo
mesh_terms: D000465:Algorithms; D005240:Feasibility Studies; D005782:Gels; D008279:Magnetic Resonance Imaging; D019047:Phantoms, Imaging; D011108:Polymers / Q000737:chemistry*; D011874:Radiometry / Q000379:methods*; D035501:Uncertainty
chemical_list: D005782:Gels; D011108:Polymers