Extracting Gold Standard Relaxation Times and Field Map Estimates from the Balanced SSFP Frequency Profile by Neural Network Fitting
Rahel Heule1 and Klaus Scheffler1,2

1High Field Magnetic Resonance, Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2Department of Biomedical Magnetic Resonance, University of Tübingen, Tübingen, Germany


It has been observed that the balanced steady-state free precession (bSSFP) frequency profile exhibits asymmetries if the intra-voxel frequency content is inhomogeneous and asymmetric. Recent attempts to calculate T1 and T2 values of human brain tissues from the measured bSSFP profile fail to account for anisotropies in the tissue microenvironment and are thus subject to a considerable bias, in particular for white matter. To eliminate this bias, a feedforward neural network is trained with the bSSFP profile as input and a multi-parametric output (i.e., T1, T2, B1, ∆B0) using gold standard relaxation times and reference field maps as ground truth.


Phase-cycled balanced steady-state free precession (bSSFP) imaging allows sampling the characteristic tissue-specific frequency profile, which is sensitive to T1 and T2. In existing relaxometry techniques using phase-cycled bSSFP experiments such as MIRACLE 1 or PLANET 2, the estimated relaxation times of human brain tissues mismatch gold standard reference values. The observed bias is especially prominent in white matter and likely linked to an asymmetric intra-voxel frequency content 3,4 due to fiber tract geometry, in combination with multi-component relaxation, e.g. due to the presence of myelin. Here, we aim to use neural network fitting to recover the gold standard T1 and T2 values from the bSSFP frequency profile while simultaneously mapping B1 and B0 field inhomogeneity.


MR acquisition protocol.

3D sagittal bSSFP experiments were performed at 3T in four healthy volunteers. Twelve RF phase cycles were acquired covering a range of 360° in steps of 30°, with an isotropic resolution of 1.3x1.3x1.3 mm3, 128 slices, a TR/TE of 4.8 ms/2.4 ms, and a flip angle of 15°. Each phase-cycle acquisition was preceded by 256 dummy pulses and elliptical scanning was used, yielding a total acquisition time of 17min 13s. One volunteer was additionally scanned with a GRAPPA acceleration factor of 2, shortening the acquisition time to 10min 12s. Reference B1 and ∆B0 maps were obtained using a TurboFLASH sequence with preconditioning RF pulse for B1 5 and a standard dual-echo gradient-echo acquisition for ∆B0. Gold standard T1 and T2 values were derived from 2D multi-slice inversion recovery turbo-spin-echo (IR-TSE) scans with variable inversion times (TI = [100, 400, 800, 1600, 3200] ms) and 2D multi-slice single-echo spin-echo (SE) scans with variable echo times (TE = [10, 30, 60, 100] ms), respectively (in-plane resolution: 1.3x2.6 mm2, 30 axial slices, 2.6mm slice thickness, 100% slice gap). Overall scan time for the gold standard measurement was 17min 32s. For anatomical reference and segmentation purposes, a 3D sagittal MPRAGE acquisition was added to the protocol.

Neural network training.

The data of three volunteers was included into the training of a feedforward 4-layer deep neural network (NN) with in total 72 neurons in the three hidden layers, taking the magnitude and phase of the Fourier transformed complex bSSFP frequency response as input and the multi-parametric set [T1, T2, B1, ∆B0] available from the reference scans as target. The data set was divided randomly into three sets to prevent overfitting: training (70%), validation (15%), and testing (15%). Prior to input, the phase-cycled bSSFP data were registered onto the reference data and skull-stripped. The voxels containing CSF were excluded using the MPRAGE images for segmentation, yielding ~407000 voxels, which were included into training. The learned neural network was applied to trained data and untrained data from a fourth volunteer who was additionally scanned with GRAPPA-accelerated bSSFP. For comparison, T1 and T2 maps were derived using MIRACLE 1.


Representative magnitude and phase images of a phase-cycled bSSFP experiment in the human brain are shown in Figure 1a. Asymmetries in the bSSFP frequency profile can be observed, which are substantially more pronounced in white than in gray matter (cf. Fig. 1b). Neural network prediction of T1 and T2 for trained (cf. Fig. 2, columns 1+2) as well as untrained (cf. Fig. 3, columns 1+2) data yields high agreement with the measured gold standard whereas MIRACLE substantially underestimates WM T1 and T2 as well as GM T1 (cf. Table 1). Predicted B1 and ∆B0 maps show the expected spatial inhomogeneity patterns in agreement with the reference measurements (cf. Figs. 2+3, columns 3+4). The B1 predicted for data not contained in the training set tends to overestimate B1 in comparison to the reference by about 10% in the center of the brain (cf. Fig. 3, column 3). The GRAPPA-accelerated quantitative data are nearly identical to the unaccelerated results (cf. Table 1 and Fig. 3). The substantial T1 and T2 underestimation of MIRACLE in comparison to the NN prediction is evident in Figure 4a, and explored in Figure 4b to assess tissue microstructure by T2 ratio maps.

Discussion and Conclusion

Neural network fitting enables to obtain gold standard relaxation time maps from the bSSFP frequency profile with simultaneous B1 and B0 estimation. The ratio of the NN predicted relaxation times to MIRACLE T1 and T2 has potential to enhance the sensitivity to tissue microenvironment, such as myelin content, as demonstrated here for T2. In conclusion, neural network fitting of phase-cycled bSSFP data is a promising method for accurate multi-parametric mapping and suited for rapid acquisitions accelerated by parallel imaging.


No acknowledgement found.


1. Nguyen D, Bieri O. Motion-insensitive rapid configuration relaxometry. Magn Reson Med 2017;78(2):518-526.

2. Shcherbakova Y, van den Berg CAT, Moonen CTW, Bartels LW. PLANET: An ellipse fitting approach for simultaneous T1 and T2 mapping using phase-cycled balanced steady-state free precession. Magn Reson Med 2018;79(2):711-722.

3. Miller KL. Asymmetries of the balanced SSFP profile. Part I: theory and observation. Magn Reson Med 2010;63:385–395.

4. Miller KL. Asymmetries of the balanced SSFP profile. Part II: white matter. Magn Reson Med 2010;63:385–395.

5. Chung S, Kim D, Breton E, Axel L. Rapid B1+ mapping using a preconditioning RF pulse with TurboFLASH readout. Magn Reson Med 2010;64(2):439-446.


Figure 1. (a) Magnitude (left) and phase (right) pairs of a representative slice acquired with bSSFP experiments at twelve different phase-cycles φ in the range (0°,360°) in a healthy volunteer at 3T. For input into the neural network, the data was masked by skull-stripping and CSF removal as displayed here. (b) Region-of-interest (ROI) assessment for frontal white matter (blue) and gray matter (putamen, red), as indicated by the arrows in the bottom left image in (a). The magnitude (left) and phase (right) of the bSSFP frequency profile in the WM and GM ROI is plotted versus the RF phase increment (phase-cycle) φ.

Figure 2. Quantitative results for trained data. First row: Neural network prediction of T1, T2, B1 (here, B1 scaling factor cB1 = αactnom, i.e., actual/nominal flip angle), and ΔB0 maps for a data set included into training. Second row: Corresponding neural network target maps, i.e., gold standard T1 and T2 as well as B1 and ∆B0 acquired with reference methods.

Figure 3. Quantitative results for data from a volunteer who was not included into the training set, scanned additionally with a GRAPPA-accelerated phase-cycled bSSFP protocol. First and second row: Neural network prediction of T1, T2, B1 scaling factor cB1 (≡ αactnom), and ΔB0 maps for the default protocol (first row) and a protocol accelerated by GRAPPA (factor 2). Third row: Corresponding ground truth maps derived from gold standard T1 and T2 measurements as well as B1 and ∆B0 reference methods.

Table 1. T1 and T2 region-of-interest analysis for data from a volunteer included into the neural network training (cf. Fig. 2) and data from a volunteer not included into training (cf. Fig. 3). T1 and T2 values are assessed for frontal white matter (WM) and putamen (GM) at locations as indicated in Figure 1a. The performance of the NN is compared to MIRACLE and the gold standard measurements. In case of the untrained data, the NN is additionally validated for the GRAPPA-accelerated bSSFP experiment.

Figure 4. (a) Comparison between NN relaxation time prediction for untrained data (first row) and MIRACLE relaxometry (second row) obtained from sagittal phase-cycled bSSFP scans at isotropic resolution (1.3x1.3x1.3 mm3). It is clearly evident that MIRACLE substantially underestimates the T1 and T2 relaxation times in comparison to the NN output because of its sensitivity to tissue microstructure as reflected by profile asymmetries (cf. Fig. 1a). (b) Ratio maps of the NN T2 prediction to MIRACLE T2 for the same data set as shown in (a), exhibiting a strong gray-white matter contrast as can be seen in the sagittal, coronal, and axial views.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)