Accuracy and precision of Cartilage T2-relaxation time Quantification: Impact of the Fit method

Introduction: T2 relaxation time quantification has high potential for the diagnostic work up of cartilage, especially in early osteoarthritis. T2 calculation relies on fitting data acquired at different echo times (TE) from multi-echo sequences (MES) to an exponential equation, which is assumed to reflect transverse magnetization decay. The low T2 times in articular cartilage (between 10 and 50 ms) and the high resolution necessary to resolve the cartilage layers unavoidably result in low-SNR data for T2 calculation. Noise in MRI has a non-vanishing mean, so that (noise) signal intensities do not decrease at long TEs [1]. Therefore, fitting to an exponential function results in systematic overestimation of T2. Our objective was to assess the influence of the fitting procedure on the accuracy and precision of T2 relaxation times in articular cartilage. Methods: Four different fit methods have been considered: a linear regression of the logarithmized signal intensities (LR); a non linear fit (Levenberg-Marquardt) to an exponential function (EXP); a voxel-based extension of the method proposed by Miller et al. [2], in which the squared signal intensities minus two times the variation of noise are fitted to an exponential function (SQEXP); and a newly introduced fit to a noise corrected exponential function (NCEXP). Accuracy (deviation of the calculated T2 values from the exact T2 values) and precision (spread of the calculated T2 values) were estimated for each method. Synthetic MRI images (n=1200, range of T2 from 10 to 110 ms and SNR at TE=0 between 15 and 120), and phantom MES image data acquired on nine test tubes (T2 range from 15 to 60 ms, SNR between 16 and 320) were used for accuracy and precision assessment. In simulations exact T2 were a priori known, whereas in phantom measurements the exact T2 times were assumed to be the T2 calculated in the highest SNR image. The accuracy was assessed by testing the coincidence of the mean of calculated T2 and the exact T2 (Wilcoxon test). Measured precision was compared with the theoretically predicted highest precision given by the Crámer-Rao lower bound (CRLB) (Levene test).