This paper presents a novel method based on leveraging physics-informed neural networks for magnetic resonance electrical property tomography (MREPT). MREPT is a noninvasive technique that can retrieve the spatial distribution of electrical properties (EPs) of scanned tissues from measured transmit radiofrequency (RF) in magnetic resonance imaging (MRI) systems. The reconstruction of EP values in MREPT is achieved by solving a partial differential equation derived from Maxwell’s equations that lacks a direct solution. Most conventional MREPT methods suffer from artifacts caused by the invalidation of the assumption applied for simplification of the problem and numerical errors caused by numerical differentiation. Existing deep learning-based (DL-based) MREPT methods comprise data-driven methods that need to collect massive datasets for training or model-driven methods that are only validated in trivial cases. Hence we proposed a model-driven method that learns mapping from a measured RF, its spatial gradient and Laplacian to EPs using fully connected networks (FCNNs). The spatial gradient of EP can be computed through the automatic differentiation of FCNNs and the chain rule. FCNNs are optimized using the residual of the central physical equation of convection-reaction MREPT as the loss function ( ${{\mathcal {L}}}{)}$ . To alleviate the ill condition of the problem, we added multiconstraints, including the similarity constraint between permittivity and conductivity and the ${\ell }_{{{1}}}$ norm of spatial gradients of permittivity and conductivity, to the ${{\mathcal {L}}}$ . We demonstrate the proposed method with a three-dimensional realistic head model, a digital phantom simulation, and a practical phantom experiment at a 9.4T animal MRI system.

中文翻译：

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基于改进的物理信息神经网络和多约束的磁共振电学层析成像


本文提出了一种基于利用物理信息神经网络进行磁共振电特性断层扫描 （MREPT） 的新方法。MREPT 是一种无创技术，可以从磁共振成像 （MRI） 系统中测量的发射射频 （RF） 中检索扫描组织的电特性 （EP） 的空间分布。MREPT 中 EP 值的重建是通过求解从 Maxwell 方程组得出的偏微分方程来实现的，该方程缺乏直接解。大多数传统的 MREPT 方法都存在因用于简化问题的假设无效而导致的伪影，以及由数值微分引起的数值误差。现有的基于深度学习（基于 DL）的 MREPT 方法包括需要收集大量数据集进行训练的数据驱动方法，或仅在微不足道的情况下验证的模型驱动方法。因此，我们提出了一种模型驱动的方法，该方法使用全连接网络 （FCNN） 从测量的 RF、其空间梯度和拉普拉斯算子到 EP 中学习映射。EP 的空间梯度可以通过 FCNN 的自动微分和链式法则来计算。使用对流反应 MREPT 的中心物理方程的残差作为损失函数 （ ${{\mathcal {L}}}{）}$ 进行优化。为了缓解问题的病态，我们在 ${{\mathcal {L}}}$ 中添加了多重约束，包括介电常数和电导率之间的相似性约束以及介电常数和电导率的空间梯度的 ${\ell }_{{{1}}}$ 范数。我们通过 3D 逼真头部模型、数字体模模拟和 9.4T 动物 MRI 系统的实际体模实验演示了所提出的方法。