Department of Mechanical Engineering, Polytechnic School, University of São Paulo, São Paulo 05508-900, Brazil.
IEEE Trans Biomed Eng. 2010 Feb;57(2):422-31. doi: 10.1109/TBME.2009.2032529. Epub 2009 Sep 29.
One of the electrical impedance tomography objectives is to estimate the electrical resistivity distribution in a domain based only on electrical potential measurements at its boundary generated by an imposed electrical current distribution into the boundary. One of the methods used in dynamic estimation is the Kalman filter. In biomedical applications, the random walk model is frequently used as evolution model and, under this conditions, poor tracking ability of the extended Kalman filter (EKF) is achieved. An analytically developed evolution model is not feasible at this moment. The paper investigates the identification of the evolution model in parallel to the EKF and updating the evolution model with certain periodicity. The evolution model transition matrix is identified using the history of the estimated resistivity distribution obtained by a sensitivity matrix based algorithm and a Newton-Raphson algorithm. To numerically identify the linear evolution model, the Ibrahim time-domain method is used. The investigation is performed by numerical simulations of a domain with time-varying resistivity and by experimental data collected from the boundary of a human chest during normal breathing. The obtained dynamic resistivity values lie within the expected values for the tissues of a human chest. The EKF results suggest that the tracking ability is significantly improved with this approach.
电阻抗断层成像的目标之一是仅根据边界处的电位测量值来估计域中的电阻率分布，这些测量值是通过在边界处施加电流分布产生的。在动态估计中使用的一种方法是卡尔曼滤波器。在生物医学应用中，随机游走模型通常用作演化模型，在这种情况下，扩展卡尔曼滤波器（EKF）的跟踪能力很差。目前还无法使用解析开发的演化模型。本文研究了与 EKF 并行的演化模型识别，并以一定的周期性更新演化模型。通过基于灵敏度矩阵的算法和牛顿-拉普森算法获得的估计电阻率分布的历史，识别演化模型转移矩阵。使用 Ibrahim 时域方法来数值识别线性演化模型。通过对随时间变化的电阻率域的数值模拟以及从正常呼吸期间人体胸部边界收集的实验数据进行研究。得到的动态电阻率值在人体胸部组织的预期值范围内。EKF 结果表明，该方法可以显著提高跟踪能力。
