Implementing a Variable Echo Time Method for Reference T2 Mapping

Jack Allen,

For my PhD thesis [Allen2019], we produced a custom phantom for evaluating quantitative MRI pulse sequences. We compared fitted Magnetic Resonance Fingerprinting (MRF) parameters with those of reference gold standard sequences. In this post, I’ll share how we implemented a reference T2 method based on the gold standard approach with various echo times. This is related to my introductory post on T2.

For reference T2 estimates, we used a single-echo spin-echo Echo Planar Imaging (EPI) pulse sequence, varying the Echo Time (TE) across the measurements.

Data acquisition

Multiple single-slice images were acquired, each with a different TE, using a Siemens spin-echo EPI sequence. The echo times and repetition times were (min:increment:max) TE = [21:4:69, 80, 90, 110, 200, 400, 800, 1200, 1600, 3200] ms and TR = 30000ms, making the total scan time 660 seconds (i.e. 11 minutes). Other acquisition parameters were: field of view = 250mm × 250mm, in-plane pixel size = 3.9mm × 3.9mm, slice thickness = 5mm, readout bandwidth = 2298Hz per pixel and partial Fourier factor = 6/8.

Model and fitting

To estimate T2, an exponential decay model (Eq. 1) was fitted to the magnitude images. The model included an offset term C to account for positive signal offsets. Although a simple offset correction was used here (Eq. 1) it would be worth considering alternatives in future work, such as squaring the signal [He2008] or removing low SNR data points from the curve [Miller1993].

\begin{equation} S_{TE} = M_{0}\exp\left(\frac{-TE}{T_2}\right) + C \quad [1] \end{equation}

To perform the fit, the MATLAB fit function was used with the default algorithm. Fitted parameter maps of our custom phantom are shown in Fig. 1. Figure 2 shows the T2 distribution across the six inner compartment tubes in the phantom.

Figure 1: fitted parameters from the T2 decay model. The top row shows T2 for two colour scale ranges: a low range to highlight the six inner compartments of the phantom (top left) and a larger range to include the water T2 in the outer region of the phantom (top right). Note T2 values in the outer region are considerably larger than those of the inner compartments.
Figure 2: distributions of T2 in Regions Of Interest (ROI) in the 6 inner compartments of the phantom. The 6 ROIs are shown in the grayscale T2 map (left), with the corresponding T2 spreads plotted in the adjacent graph (right). T2 values were estimated by fitting a T2 decay model to spin-echo data acquired with various echo times.

Example fits for voxels from the tubes with the longest and shortest T2 are shown in Fig. 3, with corresponding Bland-Altman plots in Fig. 4. Bland-Altman plots provide a visual representation of measurement bias and confidence. Figure 4 shows the majority of the fitted points were within the 95% confidence interval. However, both plots in Fig. 4 show a positive bias.

Figure 3: Example T2 fits (using 22 different TEs) for a voxel from the tubes with the longest and shortest T2. The selected voxels are labelled (top), with the T2 decay curve fits shown for two echo time ranges (middle, bottom). The smaller echo time range (bottom) highlights the difference in the T2 decay curves of the two voxels.
Figure 4: Bland-Altman plots for the T2 fits for the voxel signal from the tubes with the shortest (left) and longest (right) T2 (i.e. the voxels used for Figure 3), showing the mean difference between the data and the fitted points (solid black horizontal line). For both plots, the mean difference line is slightly above zero, representing a small positive bias in the fitting. The dashed lines mark the 95% confidence intervals.

Minimum scan time

The scan time required by the T2 protocol can be reduced by acquiring fewer measurements. Table 1 compares the tube T2 values obtained from fitting with 22 and 9 measurements from the same data set. The 9 different TEs were [21, 33, 45, 65, 80, 110, 200, 400, 800] ms. Using 9 measurements reduces the scan duration for a single slice to 270 seconds (i.e. 4 minutes 30 seconds), for TR = 30 seconds. The two sets of values in Table 1 are in very close agreement and approximately cover the literature values for grey and white matter [82, 71]. The measured standard deviations in the tubes were between ≈6-10% of the respective means.

The minimum TR for this method can be derived from gold standard T1 measurements of the same phantom. In a separate experiment we measured the longest T1 as 1621ms +/- 23ms. The solution to the longitudinal term of the Bloch equation shows us that for the upper value of this T1 range (i.e. T1 = 1621ms + 23ms), after 10000ms the Mz has effectively recovered. Specifically, 10000ms after a complete inversion Mz will equal 0.995M0, where M0 is the thermal equilibrium value of Mz. By reducing the TR to 10000ms, the scan duration of our reference T2-mapping sequence could be reduced to 90 seconds (i.e. 1 minute 30 seconds) per slice. This would translate to a scan duration of 30 minutes to acquire 20 slices.

Table 1: a comparison of the phantom tube T2 values. Estimates are shown for fits with 22 and 9 different echo times. The 9-measurement experiment requires a shorter scan duration. In this case, the 9-measurement fitted T2 values are similar to those of the 22-point scan.

References and further reading:

  • Allen J. An Optimisation Framework for Magnetic Resonance Fingerprinting. Thesis. University of Oxford, UK. 2019. https://ora.ox.ac.uk/objects/uuid:14c92874-7b00-4f79-abce-87b05f9cb4d4
  • T. He, P. D. Gatehouse, G. C. Smith, R. H. Mohiaddin, D. J. Pennell, and D. N. Firmin. Myocardial T2* Measurements in Iron Overloaded Thalassemia: An In Vivo Study to Investigate the Optimal Methods of Quantification. Magnetic Resonance in Medicine, 60(5):1082–1089, 2008.
  • A. J Miller and P. M. Joseph. The Use of Power Images to Perform Quantitative Analysis on Low SNR MR Images. Magnetic Resonance Imaging, 11(7):1051–1056, 1993.
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