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A Discussion on the Algorithm Design of Electrical Impedance Tomography for Biomedical Applications

机译：浅谈生物医学应用的电阻抗断层扫描算法设计

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摘要

In this chapter, we present a discussion on the algorithm design of Electrical Impedance Tomography (EIT) for biomedical applications. Based on the Maxwell differential equations and the derived finite element (FE) linear equations, we first investigate the possibility to estimate the matrix that contains the impedance values based on Singular Value Decomposition (SVD) approximations. Secondly based on the biomedical properties we further explore the possibility to recover the impedance values uniquely by injecting various different types of currents with multi-frequency. Injecting various types of multi-frequency currents lead to a set of different measured voltages configurations, thus enhancing the possibility of uniquely recovering the impedance values in a stable way under the assumption that the biological cells respond to the different types of injecting currents in a different way. By converting the Maxwell differential equations into linear equations by Finite Element (FE) method, we are able to focus on the discussions based on the linear algebra method. We also explore some insights into the biological cells' electrical properties so that we can make use of the biological cell's electrical properties to make the numerical algorithm design more stable and robust.
机译：在本章中，我们讨论了生物医学应用的电阻抗断层扫描（EIT）算法设计。基于Maxwell差分方程和导出的有限元（FE）线性方程，首先研究估计基于奇异值分解（SVD）近似的阻抗值的矩阵的可能性。其次，基于生物医学特性，我们进一步探索了通过使用多频率注入各种不同类型的电流来唯一恢复阻抗值的可能性。注入各种类型的多频电流导致一组不同的测量电压配置，从而提高了在本假设中以稳定的方式唯一地恢复阻抗值的可能性，因为生物细胞在不同类型的注射电流响应不同类型的注入电流下道路。通过通过有限元（FE）方法将MaxWell微分方程转换为线性方程，我们能够专注于基于线性代数方法的讨论。我们还探讨了生物细胞的电气性能的一些见解，以便我们可以利用生物电池的电气性能来使数值算法设计更稳定和稳健。

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