  Electrical properties (EP), namely permittivity and electric conductivity,
dictate the interactions between electromagnetic waves and biological tissue.
EP can be potential biomarkers for pathology characterization, such as cancer,
and improve therapeutic modalities, such radiofrequency hyperthermia and
ablation. MR-based electrical properties tomography (MR-EPT) uses MR
measurements to reconstruct the EP maps. Using the homogeneous Helmholtz
equation, EP can be directly computed through calculations of second order
spatial derivatives of the measured magnetic transmit or receive fields
$(B_{1}^{+}, B_{1}^{-})$. However, the numerical approximation of derivatives
leads to noise amplifications in the measurements and thus erroneous
reconstructions. Recently, a noise-robust supervised learning-based method
(DL-EPT) was introduced for EP reconstruction. However, the pattern-matching
nature of such network does not allow it to generalize for new samples since
the network's training is done on a limited number of simulated data. In this
work, we leverage recent developments on physics-informed deep learning to
solve the Helmholtz equation for the EP reconstruction. We develop deep neural
network (NN) algorithms that are constrained by the Helmholtz equation to
effectively de-noise the $B_{1}^{+}$ measurements and reconstruct EP directly
at an arbitrarily high spatial resolution without requiring any known
$B_{1}^{+}$ and EP distribution pairs.
