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In vivo pelvis conductivity mapping with a 3D patch-based convolutional neural network trained on in silico MR data

Soraya Gavazzi¹, Cornelis AT van den Berg^1,2, Mark HF Savenije^1,2, H Petra Kok³, Lukas JA Stalpers³, Jan JW Lagendijk¹, Hans Crezee³, and Astrid LHMW van Lier¹
¹Radiotherapy Department, University Medical Center Utrecht, Utrecht, Netherlands, ²Computational Imaging Group for MR diagnostic & therapy, University Medical Center Utrecht, Utrecht, Netherlands, ³Radiation Oncology Department, Amsterdam University Medical Center, Amsterdam, Netherlands

Synopsis

Pelvis conductivity is typically reconstructed with Helmholtz-based EPT. To overcome typical limitations of Helmholtz-based EPT in this challenging body site we explored reconstructing pelvis conductivity with deep learning. A 3D patch-based convolutional neural network was trained on in silica MR data (either a full complex B₁⁺ field or transceive phase only) with realistic noise levels. These data were related to realistic pelvic anatomies and electrical properties. Preliminary results indicate that the network retrieved anatomically-detailed conductivity maps, without a priori anatomical knowledge given in input. Quantitatively, conductivity estimates on in vivo volunteer MR data were in line with literature.

Introduction

Conductivity mapping of the human pelvis with so-called Helmholtz Electrical Properties Tomography (H-EPT) is challenging because of experimental and fundamental reasons. Firstly, H-EPT is based upon finite derivatives applied to experimental |B₁⁺| and B₁⁺ phase maps, which imposes high SNR requirements^1,2. Furthermore, respiration and bowel peristalsis induce motion artefacts that largely propagate in finite derivatives. Finally, the transceive phase assumption underpinning B₁⁺ phase retrieval is generally invalid in the pelvis at 3T³. These issues result in poor quality pelvis conductivity maps with H- EPT^1–3.
Recently, deep learning EPT (DL-EPT) has shown robustness to noise, bypassing transceive phase assumption and boundary errors, as demonstrated by preliminary brain results⁴. By conceptually extending that framework⁴, here we explored DL-EPT for pelvis conductivity mapping. We trained a 3D patch-based convolutional neural network (CNN) on 3D data obtained from realistic, sequence-specific MR simulations in the pelvis at 3T. Two network configurations were examined, based on full B₁⁺ information, i.e. |B₁⁺| and transceive phase, and on transceive phase only information. Both configurations were tested on simulated and in vivo MR data.

Methods

Human pelvic models
Forty-two pelvic models were reconstructed from CT scans of 42 cervical cancer patients by tissue segmentation using an in-house-developed software package⁵. Every segmented tissue (fat, muscle, bone, bladder, tumour) in the models was randomly assigned 5 permutations of conductivity and permittivity, resulting in 210 dielectric pelvic models. Permutations were selected from realistic, tissue-specific EP values at 128MHz. Tumour tissue was assigned muscle EPs of muscle in 1 permutation per model, to emulate healthy subjects. For the overall EP distribution, see Figure 1.

EM and MR simulations
EM simulations were performed in Sim4Life (ZTM AG, Zurich, Switzerland) for all 210 dielectric models. The models were placed inside a 3T birdcage coil, driven at 128MHz in quadrature/anti-quadrature mode for transmission/reception. Amplitude of B₁⁺ field, |B₁^+,em|, and transceive phase, ϕ^±,em, were retrieved in each simulation. Subsequently, these magnetic fields were used as inputs to Bloch simulations replicating AFI⁶ and SE sequences⁷. The resulting noiseless MR signals were corrupted by sequence-specific Gaussian noise levels and noisy |B₁^+,mr| and ϕ^±,mrwere calculated. Adopted noise levels were based on experimental SNR maps (SNRB₁≈200 and SNRϕ^±≈ 290 in muscle).

MR experiments
A healthy volunteer was scanned on a 3T clinical scanner (Ingenia, Philips, The Netherlands). |B₁⁺| was acquired with AFI⁶ (FA=60°, TE/TR1/TR2=2.5/30/210ms) and ϕ^± with SE (FA=90°, TE/TR=6.2/1200ms). FOV: 370x259x120 mm³.Resolution:2.5x2.5x7.5mm³.

Conductivity mapping with DL-EPT
The compact, 3D CNN architecture by Li et al⁸, currently implemented in NiftyNet⁹under the name of “highres3dnet”, was used for DL-EPT reconstruction. Selected hyper-parameters are shown in Table1. Training/testing was performed in 7-fold cross-validation on 180/30 models for two configurations:

Net_MR-B1: with measurable B₁⁺ field |B₁^+,mr|·exp(i·ϕ^±,mr) as input (‘Full B₁⁺ information’).
Net_MR-ϕ^±: trained on ϕ^±,mr only (‘Transceive phase only information’).

Mean absolute error (MAE) for conductivity was assessed for each test dataset in each fold.
As reference, Helmholtz-based conductivity was reconstructed on acquired data with transceive phase assumption^1,2.

Results

Conductivity maps obtained in silico with Net_MR-B1 and Net_MR-ϕ^± showed detailed anatomical structures, with striking improvement over Helmholtz-based conductivity regarding tissue interface reconstruction (Figure 2). Net_MR-B1 performed better than Net_MR-ϕ^± in reconstructing tissue interfaces. Overall, both configurations had comparable mean errors in all pelvic tissues and were robust when tested among different folds (Figure 3).
Figure 4 shows in vivo results: over-/under-shooting errors at tissue interfaces and global anti-symmetry due to transceive phase assumption (e.g. in muscle) in H-EPT conductivity were absent in DL-EPT conductivity reconstructions, which resulted in more homogeneous intra-tissue estimations. However, imaging artefacts affecting underlying B₁⁺ and ϕ^± maps, such as breathing-induced ghosting, disturbed conductivity reconstruction in both Net_MR-B1 and Net_MR-ϕ^±and also in H-EPT (for example, in proximity of hip bones and bladder). Quantitatively, DL-EPT conductivity showed less spread of values within tissue ROIs than H-EPT (Figure 4). Median DL-EPT values were in line with literature values, but varied slightly between network configurations.

Discussion & Conclusion

Our preliminary results showed that pelvis conductivity maps reconstructed with a 3D patch-based CNN trained on in silica data presented reduced boundary errors and noise sensitivity with respect to H-EPT. Similar findings were reported in brain with a 2D CNN⁴. Unlike ref4, a 3D CNN was used to better mimic the 3D nature of EPT problem. Furthermore, Bloch simulations (performed after EM simulations, see ref7) were used for training, to account for sequence-specific propagation of noise and systematic errors that influence |B₁⁺| and ϕ^± measurements.
The comparable quality of conductivity maps reconstructed with Net_MR-B1 and Net_MR-Φ^± suggests that conductivity information was learnt predominantly from ϕ^±. This reflects underlying physics, where conductivity is primarily encoded in Φ^± rather than |B₁⁺|. Interestingly, highres3dnet retrieved large local variations in pelvic anatomy without any a priori anatomical information provided as image contrast data, as opposed to Mandija et al⁴. In silico, we observed that tissue interfaces were reconstructed slightly better in Net_MR-B1. This could suggest that the network exploited |B₁⁺| information to aid detecting high spatial frequencies (e.g. anatomical boundaries). This advantage, however, could become a drawback when artefacts (e.g. ghosting) affect underlying |B₁⁺| map.
In conclusion, we showed that mapping pelvis conductivity with a 3D patch-based CNN trained on in silica data is feasible.

Acknowledgements

We thank Robin Navest, Janot Tokaya, Stefano Mandija and Maarten Terpstra for help and discussions of this project.

References

1. Katscher U, van den Berg CAT. Electric properties tomography: Biochemical, physical and technical background, evaluation and clinical applications. NMR in Biomedicine. 2017;30:e3729.

2. Liu J, Wang Y, Katscher U, He B. Electrical Properties Tomography Based on B1 Maps in MRI: Principles, Applications, and Challenges. IEEE Transactions on Biomedical Engineering. 2017;64(11):2515–30.

3. Balidemaj E, van Lier ALHMW, Crezee H, et al. Feasibility of Electric Property Tomography of pelvic tumors at 3T. Magnetic Resonance in Medicine. 2015;73(4):1505–13.

4. Mandija S, Meliadò EF, Huttinga NRF. et al Opening a new window on MR-based Electrical Properties Tomography with deep learning. Scientific Reports. 2019;9(1):1–9.

5. Kok HP, Kotte ANTJ, Crezee J. Planning, optimisation and evaluation of hyperthermia treatments. International Journal of Hyperthermia. 2017;33(6):593–607.

6. Yarnykh VL. Actual flip-angle imaging in the pulsed steady state: A method for rapid three-dimensional mapping of the transmitted radiofrequency field. Magnetic Resonance in Medicine. 2007;57(1):192–200.

7. Gavazzi S, van den Berg CAT, Sbrizzi A, et al. Accuracy and precision of electrical permittivity mapping at 3T: the impact of three mapping techniques. Magnetic Resonance in Medicine. 2019;81(6):3628–42.

8. Li W, Wang G, Fidon L, Ourselin S, et al. On the Compactness, Efficiency, and Representation of 3D Convolutional Networks: Brain Parcellation as a Pretext Task. In: Niethammer M, et al.(eds). Information Processing in Medical Imaging. Springer Cham; 2017. p. 348–60. (Lecture Notes in Computer Science, vol 10265).

9. Gibson E, Li W, Sudre C, et al. NiftyNet: a deep-learning platform for medical imaging. Computer Methods and Programs in Biomedicine. 2018;158:113–22.

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11. Balidemaj E, de Boer P, van Lier ALHMW, et al. In vivo electric conductivity of cervical cancer patients based on B1+ maps at 3T MRI. Physics in Medicine and Biology. 2016;61(4):1596–607.

Figures

Figure 1. Final distribution of conductivity and permittivity in the whole dataset (210 dielectric models).

Table 1. Settings used in both Net_MR-B1 and Net_MR-ϕ^± for training and inference. Input data were deprived of their mean value as pre-processing. The ground truth conductivity, given in training as regression target, was scaled with fixed factors. These factors were then used during inference to convert the conductivity inferred by the network from scaled values to absolute values.

Figure 2. DL-EPT conductivity of a pelvic model in a test dataset. Conductivity maps (σ, first and third rows) and conductivity difference maps (Δσ, second and forth rows), shown in both transversal and sagittal views. Ground truth conductivity (first column), conductivity reconstructed with Helmholtz-based EPT (second column), conductivity reconstructed with Net_MR-B1 (third column), conductivity reconstructed with Net_MR-Φ^± (fourth column).

Figure 3. Mean absolute error (MAE) for conductivity reconstructed with Net_MR-B1 and Net_MR-ϕ^± on test data during 7-fold cross-validation: MAE is reported for all pelvic tissues and for all folds. MAE was calculated within tissue segmentation without the outermost voxels. Each colour represents one fold. Each asterisk denotes a dielectric model in the test dataset. All 210 dielectric models were tested once within all 7 folds. The blue dashed lines for each pelvic tissue represent MAE averaged over all folds (also reported in blue on top of each graph).

Figure 4. Volunteer results. Top row, from left to right: magnitude image, conductivity reconstructed with H-EPT, conductivity reconstructed with Net_MR-B1, conductivity reconstructed with Net_MR-Φ^±. Bottom row: median conductivity values in pelvic tissues for H-EPT, Net_MR-B1 and Net_MR-Φ^±. Error bars denote 25^thand 75^th percentiles. These values were calculated in manually delineated ROIs comprising 5 adjacent slices (shown in magnitude image). Literature mean values, with maximum and minimum values when available, are shown (fat¹⁰,bone¹⁰,muscle¹¹, bladder¹¹).

Proc. Intl. Soc. Mag. Reson. Med. 28 (2020)

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