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.
翻译:电磁波和生物组织之间的相互作用(EP),即允许性和电导性。EP可以是癌症等病理学定性的潜在生物标志,也可以是治疗模式的改进,例如放射频率超高热度和消融。MR-电磁特性透析(MR-EPT)使用MR测量法重建EP地图。使用同质的Helmholtz等方程式,EP可以直接计算测量磁波和生物组织之间的相互作用。但是,EP可以直接计算测得磁电波和生物组织之间的二等分空间衍生物。但是,在测量中,衍生物的数字近似会导致噪音放大,从而导致重建错误的治疗模式。最近,为EPS重建引入了以噪音-robust为主的基于学习的方法(DL-EPT)。然而,这种网络的模式匹配性质不允许它对新样本进行概括,因为网络培训的模拟数据数量有限。在这项工作中,我们利用物理学和深深层次的EPEPEP- $B1 和任何已知的平-N-N-N-N-Q-Q-Q-Q-Q-Q-QAR等等等等等平平压数据进行有效的重建。