Electrical properties (EPs) of tissues facilitate early detection of cancerous tissues. Magnetic resonance electrical properties tomography (MREPT) is a technique to non-invasively probe the EPs of tissues from MRI measurements. Most MREPT methods rely on numerical differentiation (ND) to solve partial differential Equations (PDEs) to reconstruct the EPs. However, they are not practical for clinical data because ND is noise sensitive and the MRI measurements for MREPT are noisy in nature. Recently, Physics informed neural networks (PINNs) have been introduced to solve PDEs by substituting ND with automatic differentiation (AD). To the best of our knowledge, it has not been applied to MREPT due to the challenges in using PINN on MREPT as (i) a PINN requires part of ground-truth EPs as collocation points to optimize the network’s AD, (ii) the noisy input data disrupts the optimization of PINNs despite the noise-filtering nature of NNs and additional denoising processes. In this work, we propose a PINN-MREPT model based on a canonical analytic MREPT model. A reference padding layer with known EPs was added to surround the region of interest for providing additive collocation points. Moreover, an optimizable diffusion coefficient was embedded in the analytic MREPT model used in the PINN-MREPT. The noise robustness of the proposed PINN-MREPT for single-sample reconstruction was tested by using numerical phantoms of human brain with extra tumor-like tissues at different noise levels. The results of numerical experiments show that PINN-MREPT outperforms two typical numerical MREPT methods in terms of reconstruction accuracy, sensitivity to the extra tissues, and the correlations of line profiles in the regions of interest. The advantage of the PINN-MREPT is shown by the results of an experiment on phantom measurement, too. Moreover, it is found that the diffusion term plays an important role to achieve a noise-robust PINN-MREPT. This is an important step moving forward to a clinical application of MREPT.

To provide a stable surgical view in Minimally Invasive Surgery (MIS), it is necessary for a flexible endoscope applied in MIS to have adjustable stiffness to resist different external loads from surrounding organs and tissues. Pneumatic soft actuators are expected to fulfill this role, since they could feed the endoscope with an internal access channel and adjust their stiffness via an antagonistic mechanism. For that purpose, it is essential to estimate the external load. In this study, we proposed a neural network (NN)-based active load-sensing scheme and stiffness adjustment for a soft actuator for MIS support with antagonistic chambers for three degrees of freedom (DoFs) of control. To deal with the influence of the nonlinearity of the soft actuating system and uncertainty of the interaction between the soft actuator and its environment, an environment exploration strategy was studied for improving the robustness of sensing. Moreover, a NN-based inverse dynamics model for controlling the stiffness of the soft actuator with different flexible endoscopes was proposed too. The results showed that the exploration strategy with different sequence lengths improved the estimation accuracy of external loads in different conditions. The proposed method for external load exploration and inverse dynamics model could be used for in-depth studies of stiffness control of soft actuators for MIS support.