Identification of Dipoles in Bioengineering

生物工程中偶极子的识别

• 批准号: 11650068
• 负责人: OHNAKA Kohzaburo
• 金额: $ 1.09万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11650068/
• 关键词: Inverse Source Problem; Dipole Model; Poisson Equation; Boundary Integral; Charge Simulation Method; Magnetoencephalogram; 数値計算アルゴリズム

An important problem in bioengineering is to identify the activity of human brain from observation data of magnetic fields called Magneto Encephalo Gram. Many researchers assume spherically symmetric conductor model for the human head and dipole model for the activity of human brain. Our problem is to identify locations, moments, and number of dipoles in human brain from observations of magnetic induction outside of human head.Before this project, we have already proposed the following two methods.Method 1: Local search method based on weighted integrals for the two-dimensional caseMethod 2: Global search method based on an extension of observations to the interior of three-dimensional domainIn this project, we extend Method 1 to three-dimensional problem, and give error estimates of identified results. However, Method 1 needs a priori information of locations, moments, and number of dipoles. Method 2 is applicable without any a priori information of dipoles. We construct a new method combining Method 1 and Method 2. Our proposed method gives reasonable identification results with practical error estimation.At the present time, we are preparing a paper with respect to the proposed identification method. Further discussions are needed for the error caused by numerical integrations and noisy observations, and also needed for the arrangement of observation points

生物工程中的一个重要问题是从脑磁信号中识别人脑的活动。许多研究者假设人脑的活动是球对称导体模型，而人脑的活动是偶极子模型。我们的问题是从人头部外的磁感应的观测中识别人大脑中偶极子的位置、矩和数量。在这个项目之前，我们已经提出了以下两种方法。方法1：二维情况下基于加权积分的局部搜索方法方法2：基于观测值向三维域内部扩展的全局搜索方法在本项目中，我们将方法1推广到三维问题，并给出了辨识结果的误差估计。然而，方法1需要偶极子的位置、矩和数量的先验信息。方法2是适用的，没有任何先验信息的偶极子。我们结合方法1和方法2构造了一种新的方法。我们所提出的方法给出了合理的识别结果与实际的误差估计。目前，我们正在准备一份文件，就所提出的识别方法。对于数值积分和观测噪声引起的误差以及观测点的布置问题还需要进一步讨论

项目成果

K.Yamatani: "An Identification Method of Electric Current Dipoles in Spherically Symmetric Conductor"J.Computational and Applied Matematics. (in press).

K.Yamatani：“球对称导体中电流偶极子的识别方法”J.计算与应用数学。

S.Kajihara: "Application of Moditied Simplex Method to Biomagnetic Inverse Problem"Biomag 2000 : Proc. 12th Internet, Conterence on Bio-magnetism, J. Nenomen, R.J.Llmonieri, and T.Katila(eds.). 729-732 (2001)

S.Kajihara：“改进单纯形法在生物磁逆问题中的应用”Biomag 2000：Proc。

M.Ikehata: "Numerical Method for finding the Convex Hull of Polygonal Cavities using Enclosure Method"Inverse Problems. (in press).

M.Ikehata：“使用包围法寻找多边形空腔凸包的数值方法”反问题。

Sang-Uk Rye, A. Yagi: "Optimal Control of Keller-Segel Equations"Journal of Mathematical Analysis and Applications. 256-1. 45-66 (2001)

Sang-Uk Rye，A. Yagi：“Keller-Segel 方程的最优控制”数学分析与应用杂志。

S. Kajihara, K. Yamatani, N. S. Yamaki, A. Arakawa, and Y. Yoshida: "Application of Modified simplex Method to Biomagnetic Inverse Problem"Biomag 2000, Proc. 12th International Conference on Biomagnetism, J. Neuromen, R. J. Limonieri, and T. Katila (eds.)

S. Kajihara、K. Yamatani、N. S. Yamaki、A. Arakawa 和 Y. Yoshida：“改进单纯形法在生物磁反问题中的应用”Biomag 2000，Proc。