Previous studies on the forward problem of magnetic induction tomography (MIT) have used simplified Maxwell's equations which assume a constant and position-independent total current density (TCD) inside the coils (ignoring skin effect). Moreover, they assume that TCD is independent of relative position of the coils (ignoring proximity effect). This article presents an improved finite element (FE) modeling for the two-dimensional (2D) forward problem of MIT by incorporating skin and proximity effects in the exciter and sensor coils. Consideration of skin and proximity effects requires the use of a position-dependent TCD in Maxwell's equations inside the coil domain. The FE method implementation of the improved forward method is validated with a simple analytical test problem. To evaluate the performance of the improved method in possible medical and industrial applications with low conductivity regions, a 16 coils 2D MIT system is modeled and the FE method is employed to solve the forward problem using a synthetic phantom. Results show the difference between the real parts of induced voltages obtained from the early and improved method falls into the range which is meaningful in terms of achievable conductivity contrast from the improved one. This discrepancy can generate considerable errors in image reconstruction. By considering skin and proximity effects, the improved method generates lower voltages in the coils suggesting the use of more precise hardware to detect inclusion. Findings show the importance and necessity of using improved method for modeling 2D MIT coils especially at low conductivity applications where measured signals are inherently weak.

中文翻译：

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考虑线圈中趋肤效应和邻近效应的二维麻省理工学院前向问题的解决方案

先前对磁感应断层扫描 (MIT) 前向问题的研究使用了简化的麦克斯韦方程，该方程假设线圈内的总电流密度 (TCD) 是恒定且与位置无关的（忽略趋肤效应）。此外，他们假设 TCD 与线圈的相对位置无关（忽略邻近效应）。本文通过在励磁器和传感器线圈中加入趋肤效应和邻近效应，为麻省理工学院的二维 (2D) 正向问题提出了一种改进的有限元 (FE) 建模。考虑趋肤效应和邻近效应需要在线圈域内的麦克斯韦方程中使用位置相关的 TCD。改进前向方法的有限元方法实现通过一个简单的分析测试问题得到验证。为了评估改进方法在具有低电导率区域的可能的医疗和工业应用中的性能，对 16 线圈 2D MIT 系统进行建模，并采用 FE 方法来解决使用合成体模的前向问题。结果表明，早期方法和改进方法获得的感应电压实部之间的差异在可实现的电导率对比方面与改进方法之间的差异是有意义的。这种差异会在图像重建中产生相当大的误差。通过考虑趋肤效应和邻近效应，改进的方法在线圈中产生较低的电压，这表明使用更精确的硬件来检测夹杂物。