Opening a new window on MR-based Electrical Properties Tomography with deep learning

Electrical properties (EPs) of tissues, conductivity and permittivity, are modulated by the ionic and water content, which change in presence of pathologies. Therefore, information on tissues EPs can be used e.g. as an endogenous biomarker in oncology. MRElectrical Properties Tomography (MR-EPT) aims to reconstruct tissue EPs by solving an electromagnetic inverse problem relating MR measurements of the transmit radiofrequency (RF) field to the EPs. However, current MR-EPT reconstructions highly suffer from noise in the RF field maps, which limits their clinical applicability. Instead of employing electromagnetic models posing strict requirements on the measured electromagnetic quantities, we propose to use a data driven approach where the inverse transformation is learned by means of a neural network. Supervised training of a conditional generative adversarial neural network was performed using simulated realistic RF field maps and realistic human head dielectric models. Deep learning EPT (DL-EPT) reconstructions are presented for in-silica MR data and MR measurements at 3 Tesla on phantoms and human brains. DL-EPT shows high quality EP maps, demonstrating good accuracy and greatly improved precision compared to conventional MR-EPT. Moreover, DLEPT allows permittivity reconstructions at 3 Tesla, which is not possible with state-of-art MR-EPT techniques. The supervised learning-based approach leverages the strength of tailored electromagnetic simulations, allowing inclusion of a priori information (e.g. coil setup) and circumvention of inaccessible MR electromagnetic quantities. Since DL-EPT is highly noise-robust, the requirements for MRI data acquisitions can be relaxed, allowing faster acquisitions and higher resolutions. We believe that DL-EPT greatly improves the quality and applicability of EPT opening a new window for an endogenous biomarker in MRI diagnostics that reflects differences in ionic tissue content. Significant Statement The inability of MR-Electrical Properties Tomography (MR-EPT) to accurately reconstruct tissue electrical properties (EPs) severely limits the clinical use of EPs mapping e.g. as a biomarker in oncology. We demonstrate that the EPT reconstruction problem can be casted as a supervised deep learning (DL) task. The presented DL-EPT reconstructions for both in-silica and experimental MR data at 3 Tesla on phantoms and human brains demonstrate a great improvement. This could be a key innovation step to turn EPT into a reliable biomarker revealing information on tissue ionic composition as a surrogate of a different metabolism caused by pathological conditions. Introduction Non-invasive measurements of human tissue Electrical Properties (EPs), namely conductivity σ and relative permittivity εr, is a challenge that attracted several research groups in the past decades (1, 2). These properties determine how electromagnetic (EM) fields, such as the MR radiofrequency fields (RF: 64-300 MHz), interact with human tissues. Tissue EPs depend on the tissue structure and composition (water content and ionic concentration). In particular, tissue conductivity is modulated by the total ionic content, which varies in presence of pathologies. Several studies already showed a change in tissue conductivity in presence of tumors (3–7). Therefore, non-invasive measurements of tissue EPs could in principle be used as a new endogenous biomarker in oncology for diagnostic purposes and treatment monitoring (7). In the early 1990s, an MR-based technique has been suggested to non-invasively measure tissue EPs at the Larmor frequency (64-300 MHz for clinical MR systems), which depends on the exact MR magnetic field strength (8). However, systematic research only started in the last decade, creating a new branch of research called MR-Electrical Properties Tomography (MR-EPT) (9). First MR-EPT approaches aimed to reconstruct tissue EPs by measuring the RF transmit magnetic field, i.e. the circularly polarized transverse magnetic field referred to as the B̃1 + field. This B̃1 + field consists of incident and scattered field terms, where the latter component includes contributions from conduction and displacement currents and thus contains the desired EPs information. By applying the homogenous Helmholtz equation to the measured B̃1 + field, EPs map can be reconstructed. According to this analytical reconstruction model, tissue EPs can be obtained by computing second order spatial derivatives of the B̃1 + field (10, 11). Spatial derivatives can be computed by applying a filter (in this case a 2 order finite difference filter) to the B̃1 + field data, resulting directly in EPs maps. However, this operation is highly sensitive to the intrinsic noise in the MR measurements, and consequently the reconstructed EPs maps lack precision (12, 13). In particular, for clinical MRI systems (1.5 and 3 Tesla) permittivity reconstructions are not yet feasible since the electromagnetic imprint of related displacement currents is too low at these frequencies. Recently, alternative analytical reconstruction techniques have been presented to improve the quality of MR-EPT reconstructions (14–18). However, these techniques typically require complex RF setups (multitransmit array) and high field MR scanners (7 Tesla) are needed to achieve sufficient signal-to-noise-ratio (SNR). From a fundamental point of view, these analytical reconstruction techniques are computationally fast but require data with high SNR. Instead, algebraic algorithms, which employ a more general inverse approach using iterative minimization, behave better under noisy conditions. However, this comes at the expense of a higher computational load, challenges related to local minima, more complex electromagnetic modeling, and the need for a priori information (e.g. incident MR electric field), which is not always available. Nevertheless, some promising results have been obtained for EPT (19–22). Instead of relying on analytical or algebraic reconstruction techniques derived from electromagnetic theory, in this work we investigate the feasibility of using data driven, supervised deep learning (DL) approach for EPs reconstructions. Deep learning approaches have recently been successfully applied to inverse problems including MRI image reconstruction (23–27). To the best of our knowledge, this is the first time that deep learning is used for EPs reconstructions. Hereafter, we refer to this approach as Deep Learning Electrical Properties Tomography (DLEPT). Given the promising performance of CNNs, and in particular of Conditional Generative Adversarial Network (cGAN) (28), in this work we train a cGAN to perform EPT reconstructions. Contrary to most MREPT techniques which make assumptions on electromagnetic quantities that are not directly accessible with MRI, in DL-EPT we can learn a surrogate analytical reconstruction model using only MR accessible quantities, such as the magnitude of the MR transmit field (B̃1 ) and the transceive phase (φ). The training dataset is generated by electromagnetic simulations including realistic RF coil models and body models. Nowadays, these datasets can be easily generated by exploiting the availability of sophisticated electromagnetic solvers, which allow realistic electromagnetic simulations (e.g. Sim4Life; CST; COMSOL; Remcom). In this way, a high degree of a priori knowledge, such as the MRI coil setup, can be introduced to obtain robustness towards noise. In this work, DL-EPT reconstructions from simulations on phantoms and human head models, as well as from phantom and in-vivo MR measurements using a clinically available MR setup are presented. The accuracy and precision of the reconstructed EPs maps is assessed, and the impact of different SNR levels has also been investigated. For comparison purposes, Helmholtz based MR-EPT reconstructions for the phantoms and head model simulations are presented as a reference. Although the aim of this study is a proof of principle of DL-EPT, and not an investigation into optimal network and choice of learning parameters, several options are considered. In particular, two cGANs are used: cGANmask, and cGANtissue. The former has as input the MR transit B̃1 + field magnitude, the phase φ̃ (proportional to the transceive phase φ), and a binary mask (1: tissue, 0: air). In the latter, the binary mask is replaced by pseudo Spin Echo MRI images providing tissue contrast information. To the best of our knowledge, with this work we show for the first time that deep learning can provide greatly improved reconstructions of electrical conductivity and permittivity using clinically available MRI scanners, coil setups, and realistic SNR levels. Results In Fig 1, standard MR-EPT and DL-EPT reconstructions are presented for the phantom model 42 with realistic noise levels. This phantom was used for in-silica testing of the selected cGANmask (see SI Appendix). Additionally, reconstructions from MRI measurements at 3T are presented for a cylindrical, homogeneous phantom with the same EPs values. The mean and standard deviation values of the reconstructed EPs maps are also reported in Fig. 1. To avoid boundary regions that cannot be reconstructed accurately in MR-EPT, a smaller region of interest was considered for this calculation (see SI Appendix). Phantom MR-EPT reconstructions on simulated data show accurate mean EPs values after exclusion of boundary regions. However, the reported high standard deviation values indicate strong variability in the reconstructed EPs values due to noise amplification (see absolute error maps in SI Appendix). The need of high SNR levels is one of the main limitation of current analytical MR-EPT reconstruction methods. On the contrary, DL-EPT reconstructions on simulated phantom data are less affected by noise (relative error < 5%) and show accurate EPs reconstructions in both homogeneous regions and at boundaries (see profiles in SI Appendix). DL-EPT reconstructions from MR me