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. Author manuscript; available in PMC: 2017 Sep 1.
Published in final edited form as: Magn Reson Med. 2015 Sep 4;76(3):953–962. doi: 10.1002/mrm.25913

Table 2. Accuracy and precision of fit parameters from Monte Carlo simulations.

Model Parameter SNR = 78,000 SNR = 100 SNR = 40

Accuracy (%) Precision (%) Accuracy (%) Precision (%) Accuracy (%) Precision (%)
Mono-exponential T2 3.36e-5 7.45e-4 -0.22 1.54 -1.13 3.75

Stretched exponential T2,se -8.54e-6 9.60e-4 0.12 2.27 0.06 5.89
αse -1.20e-4 1.37e-3 0.38 3.03 1.66 7.93

Stretched Mittag-Leffler T2,sml -4.57e-5 7.81e-4 -0.11 1.64 -0.34 5.12
αsml -3.56e-4 4.94e-4 -0.31 1.27 0.96 3.46

Biexponental w1 2.21e-3 2.58e-2 -25.47 35.27 -38.69 35.26
T2,1 7.14e-4 2.43e-2 -24.89 30.41 -30.29 45.25
T2,2 2.87e-4 4.17e-3 -3.25 5.36 -4.12 7.29

Each sample condition was simulated with 200 noise realizations. SNR = 78,000 was used, representing the average experimental SNR from in vitro BNC experiments. Two more modest levels, SNR = 100 and SNR = 40, were also simulated representing typical levels for clinical imaging. The average T2, α, and w values derived experimentally from control BNC were used as input values. Decay data for the high SNR condition were simulated using 1024 echoes with TE = 1.2 ms. Decay data using SNR = 100 and 40 were simulated using typical imaging parameters consisting of 64 echoes and TE= 8 ms. Accuracy is defined as fit parameter percent error, which is the difference between the true simulation input parameter and the average fit value over 200 noise realizations, divided by the true input simulation parameter value, all multiplied by 100. Precision is reported as the percent relative standard deviation, which is the standard deviation of fit residuals over 200 noise realizations divided by the mean fit value of the parameter, multiplied by 100.