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Deep Learning based MR Electrical Properties Tomography
Stefano Mandija1,2, Ettore F. Meliadò1,2, Niek R.F. Huttinga1,2, Peter R. Luijten1,2, and Cornelis A.T. van den Berg1,2

1University Medical Center Utrecht, Utrecht, Netherlands, 2Utrecht University, Utrecht, Netherlands

Synopsis

The inability of Magnetic Resonance Electrical Properties Tomography to accurately reconstruct tissue electrical properties severely limits its clinical use, e.g. as a biomarker in oncology. We demonstrate that the electrical properties reconstruction problem can be casted as a supervised deep learning task. Deep learning based electrical properties reconstructions for simulations and MR measurements (3 Tesla) on phantoms and human brains demonstrate great improvement in the quality of reconstructed electrical properties maps. This could be major step forward to turn electrical properties tomography into a reliable biomarker where pathological conditions can be revealed and characterized by abnormalities in tissue electrical properties.

Introduction

MR-Electrical Properties Tomography (MR-EPT) is a non-invasive technique aiming at reconstructing tissue electrical properties (EPs: conductivity σ, and relative permittivity εr) from MR measurements of the transmit $$$\tilde{B}_1^+$$$ field[1]. According to the Helmholtz-MR-EPT (H-EPT) reconstruction model, EPs maps can be obtained by computing spatial derivatives of $$$\tilde{B}_1^+$$$ fields. Since, this operation is sensitive to the noise in the MRI measurements, large derivative kernels, imaging filters and large voxels are used at the cost of errors at tissue boundaries[2-4]. Furthermore, MR-EPT techniques require electromagnetic quantities that are not directly accessible with MRI (e.g. the phase of the MR transmit field).

Instead of employing conventional MR-EPT models based on electromagnetic theory, which prescribes rigidly the required electromagnetic quantities that need to be measured, we investigate for the first time the feasibility of using a data driven, supervised deep learning approach (DL-EPT) for EPs reconstructions. In DL-EPT a surrogate model based only on accessible MR quantities ($$$\tilde{B}_1^+$$$ field magnitude and transceive phase) can be learnt. DL-EPT reconstructions from simulated and measured data on phantom and in-vivo are shown. Comparison with H-EPT is performed for EPs reconstructions from simulated data. Although several MR-EPT reconstructions methods are nowadays available, we use H-EPT[4] as a reference since it provides good EPs reconstructions for simulated data.

Materials and Methods

42 homogeneous phantom and 20 head models with piecewise constant EPs (variations of Duke and Ella) were created in Sim4Life[5]. Different EPs values were assigned to each phantom and to the WM/GM/CSF of the head models[5]. Complex $$$\tilde{B}_1^+$$$ fields were obtained from electromagnetic simulations using the QBC coil model (128 MHz, same of MR experiments), and including Gaussian noise (SNR ≈ 100) (Fig. 1). Paired training of two conditional-generative-adversarial networks (cGAN)[6] implemented in TensorFlow[7] was performed:

  • cGANmask: trained using 2014 $$$\tilde{B}_1^+$$$ fields from phantom/head model simulations, except for phantom #12 and #24 used for validation, phantom #38, #42 and Duke #1 used for testing. 3 inputs were provided: $$$\tilde{B}_1^+$$$ magnitude fields, phase maps (half of the transceive phase), and binary masks (1:tissue, 0:air), giving the name cGANmask to this network.
  • cGANtissue: trained using 1064 $$$\tilde{B}_1^+$$$ field distributions from brain models, except Duke #1 used for testing. Pseudo-MRI tissue contrast maps (known a-priori information) were provided as third input, giving the name cGANtissue to this network.

These networks were trained separately for conductivity and permittivity reconstructions.

MR measurements were performed at 3 Tesla (Ingenia, Philips HealthCare, Best, The Netherlands, QBC in transmit and 15-channel head coil in receive mode) on an agar-based phantom (σ:0.88 S/m, εr:80, from probe measurements, 21oC), and human brains (three healthy subjects, after obtaining written inform consent).

The $$$\tilde{B}_1^+$$$ magnitude was measured using a dual-TR sequence[8]. For the transceive phase (φ±),two single-echo Spin-Echo (SE) sequences with opposite readout gradient polarities were combined[9]: φ±=(φSE1-φSE2)/2. For comparison, H-EPT reconstructions were performed for the phantom #42 and Duke #1 using the simulated 3D complex $$$\tilde{B}_1^+$$$ fields. Second order derivatives were computed using a 3D noise-robust kernel[4].

Results

H-EPT reconstructions from simulated data (phantom #42) show accurate mean EPs values after excluding boundary regions, but high SD (lack of precision) (Fig. 2). DL-EPT reconstructions are more precise, but show small inaccuracies in the mean EPs values (relative error <5%). DL-EPT reconstructions from MR measurements confirm the results from simulations. Additionally, permittivity reconstructions are now feasible.

In Fig. 3, H-EPT reconstructions for Duke #1 are severely affected by noise and boundary errors. The high SD values indicate that H-EPT is not suitable to reconstruct EPs on a voxel basis. If cGANmask is used, the precision of EPs reconstructions is greatly improved. If cGANtissue is used, thus providing tissue contrast (pseudo-Spin-Echo MRI images) as a-priori information, the precision is further improved, and the mean EPs values agree with the ground truth values.

DL-EPT reconstructions from in-vivo MR measurements (Fig. 4) show good quality EPs maps with exception of the head periphery and the ventricles where cGANmask demonstrates less performance. If cGANtissue is used, errors at tissue boundaries are reduced, confirming the results from simulations.

Discussion and Conclusion

DL-EPT demonstrates high quality EPs reconstructions and greatly improved precision compared to conventional MR-EPT for clinically available MRI scanners, coil setups, and realistic SNR levels. Moreover, DL-EPT allows permittivity reconstructions at 3 Tesla, which are not possible with state-of-the-art MR-EPT techniques. The supervised learning approach leverages the strength of electromagnetic simulations, allowing inclusion of a-priori information (e.g. coil setup, tissue contrasts) and circumvention of inaccessible MRI electromagnetic quantities (e.g. the MRI transmit phase).

Acknowledgements

No acknowledgement found.

References

1 Katscher U, van den Berg CAT, NMR in Biomed 2017 Aug;30(8). doi: 10.1002/nbm.3729.

2 Lee S, et al. IEEE Trans Med Imaging. 2015 Nov;34(11):2220-32. doi: 10.1109/TMI.2015.2427236

3 Duan S, et al. NMR Biomed. 2016 Jun;29(6):744-50. doi: 10.1002/nbm.3522.

4 Mandija S, et al. Magn Reson Med. 2018 Jul;80(1):90-100. doi: 10.1002/mrm.27004.

5 Sim4Life (ZMT AG, Zurich, CH).

6 Isola P, et al. arXiv 2016. 1611.07004:1–16.

7 Abadi M, et al. arXiv 2016. 1603.04467:1–19.

8 Yarnykh VL. Magn Reson Med. 2007 Jan;57(1):192-200 doi: 10.1002/mrm.21120

9 van Lier ALHMW, et al. Magn Reson Med. 2012 Feb;67(2):552-61. doi: 10.1002/mrm.22995.

Figures

Fig. 1: Database construction and cGAN training. First, EM simulations were performed in Sim4Life (1). Then, data were combined, Gaussian noise was added, and the three inputs for the network were generated (2). Two cGAN networks were trained, one for conductivity and one for permittivity DL-EPT reconstructions. Each network was trained using as third input a mask or tissue contrast information (Pseudo MRI images) (3). Finally, the network was validated and tested on data which were excluded from the training set (4).

Fig. 2: Ground truth, H-EPT and DL-EPT conductivity and permittivity reconstruction are shown for the phantom #42, used for testing the cGANmask. Absolute error maps are also shown. This phantom was excluded from the training set. Additionally, DL-EPT reconstructions from phantom MR measurements using the same cGANmask adopted for the simulations are shown. In the table, the mean and standard deviation values computed in the region-of-interest (ROI) indicated in the figure are reported. Note the exclusion of boundary regions from the ROI, which would have an impact on the computation of H-EPT mean EPs values.

Fig. 3: Ground truth, H-EPT, cGANmask and cGANtissue conductivity and permittivity reconstruction are shown for the head model Duke #1, used for testing the cGANmask and cGANtissue EPs reconstructions. Absolute error maps are also shown. This model was excluded from the training set. In the table, the mean and standard deviation values computed in the WM/GM/CSF tissues are reported. These values were computed after eroding each tissue by 3 voxels to avoid boundary errors in H-EPT reconstructions.

Fig. 4: cGANmask and cGANtissue conductivity and permittivity reconstruction from in-vivo MRI measurements on three volunteers. In the table, the mean and standard deviation values computed in the WM/GM/CSF tissues are reported. These values were computed after eroding each tissue by 3 voxels to allow direct comparison to the simulation results.

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