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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Bayesian inversion for electrical-impedance tomography in medical imaging using the nonlinear Poisson-Boltzmann equation
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Bayesian inversion for electrical-impedance tomography in medical imaging using the nonlinear Poisson-Boltzmann equation

机译：使用非线性Poisson-Boltzmann方程的医学成像在医学成像中的贝叶斯逆转

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摘要

We develop an electrical-impedance tomography (EIT) inverse model problem in an infinite-dimensional setting by introducing a nonlinear elliptic PDE as a new EIT forward model. The new model completes the standard linear model by taking the transport of ionic charge into account, which was ignored in the standard equation. We propose Bayesian inversion methods to extract electrical properties of inhomogeneities in the main body, which is essential in medicine to screen the interior body and detect tumors or determine body composition. We also prove well-definedness of the posterior measure and well-posedness of the Bayesian inversion for the presented nonlinear model. The new model is able to distinguish between liquid and tissues and the state-of-the-art delayed-rejection adaptive-Metropolis (DRAM) algorithm is capable of analyzing the statistical variability in the measured data in various EIT experimental designs. This leads to design a reliable device with higher resolution images which is crucial in medicine for diagnostic purposes. We first test the validation of the presented nonlinear model and the proposed inverse method using synthetic data on a simple square computational domain with an inclusion. Then we establish the new model and robustness of the proposed inversion method in solving the ill-posed and nonlinear EIT inverse problem by presenting numerical results of the corresponding forward and inverse problems on a real-world application in medicine and healthcare. The results include the extraction of electrical properties of human leg tissues using measurement data. (C) 2020 Elsevier B.V. All rights reserved.
机译：通过将非线性椭圆PDE引入新的EIT前向模型，我们在无限尺寸的设置中开发了一种电阻抗断层扫描（EIT）逆模型问题。新模型通过将离子电荷运输考虑，在标准方程中忽略了标准线性模型。我们提出了贝叶斯倒反转方法，以提取主体中不均匀性的电性能，这对于药物来说是必不可少的，以筛选内部身体并检测肿瘤或确定体组成。我们还证明了呈现的非线性模型的贝叶斯反演的后测量和良好的良好度。新模型能够区分液体和组织，并且最先进的延迟抑制自适应 - 大都会（DRAM）算法能够分析各种EIT实验设计中测量数据中的统计变异性。这导致设计具有更高分辨率图像的可靠装置，该图像在医学中至关重要以用于诊断目的。我们首先测试所提出的非线性模型的验证以及在简单方形计算域上的合成数据的验证以及包含的综合数据。然后，我们建立了拟议的反演方法的新模型和稳健性，通过呈现了在医学和医疗保健中的实际应用上的相应前向和逆问题的数值结果来解决不良和非线性EIT逆问题。结果包括使用测量数据提取人腿组织的电性质。 （c）2020 Elsevier B.v.保留所有权利。

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