Uncertainty- and Sensitivity Analysis of Coupled Systems Composed of an Electromagnetic Field Problem and a Dynamic Nonlinear Network Using Spectral Methods

使用谱方法对由电磁场问题和动态非线性网络组成的耦合系统进行不确定性和灵敏度分析

• 批准号: 317335820
• 负责人: Dr.-Ing. Konstantin Weise
• 金额: --
• 依托单位: Max-Planck-Institut für Kognitions- und Neurowissenschaften
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/317335820?language=en
• 关键词: Uncertainty; Sensitivity; Analysis; Coupled; Systems

The present project addresses the uncertainty and sensitivity analysis of coupled systems composed of an electromagnetic field problem and a complex dynamic and nonlinear network including lumped parameters. Especially in case of coupled systems with a high number of variables it is of great interest to determine the most important model parameters.It is the goal to address this question in the scope of transcranial magnetic stimulation (TMS) and neural mass modelling (NMM). The electric field induced during TMS can be predicted by means of numerical techniques like the finite element method but depends on the electrical conductivities assigned to the neural tissues, which are subject to uncertainties. Besides that, NMM enable to model neural activity in consequence of external stimulation. They are described in accordance to electrical circuits by systems of differential equations. Those models involve a high number of parameters and can be declared as high-dimensional. Due to individual differences and their intrinsic nature, the parameters are subject to high variabilities. Those variabilities propagate through the system under investigation and directly affect the predicted output of it. This fact becomes even more apparent when multiple parameters undergo a certain amount of uncertainty at the same time, which makes it difficult to distinguish between individual effects and how they were caused. In this project, it is intended to couple the electromagnetic field induced during TMS with an NMM, taking into account the uncertainties of the parameters in both systems. Therefore, a stochastic coupling model between both systems is developed. The methodological basis rests on the generalized polynomial chaos technique (gPC). Since NMM are multistable and high-dimensional, it is the goal to further develop the gPC method in these terms. The stochastic analysis of the overall system composed of the induction problem in TMS, the coupling model and the NMM necessitates efficient algorithms. In order to ensure computational efficiency, it is the goal to utilize model order reduction techniques together with sparse grids and reduced basis polynomials. The obtained methodology is of general use and can be applied for a variety of engineering problems, such as electrical circuit design and nondestructive testing, where uncertainties are involved and could harm safety. In times characterized by a strong demand on technology and automation, safety is of the utmost priority. This underpins the need of highly efficient methods to analyse the impact of uncertainties in complex and coupled systems.

本项目针对由电磁场问题和包括集总参数的复杂动态非线性网络组成的耦合系统的不确定性和灵敏度分析。特别是在耦合系统的情况下，具有大量的变量，它是非常感兴趣的，以确定最重要的模型参数，这是目标，以解决这个问题的范围内的经颅磁刺激（TMS）和神经质量建模（NMM）。在TMS过程中感应的电场可以通过数值技术如有限元法来预测，但取决于分配给神经组织的电导率，这是不确定的。 除此之外，NMM还能够模拟外部刺激引起的神经活动。它们是按照电路用微分方程组来描述的。这些模型涉及大量的参数，可以被声明为高维。由于个体差异及其内在性质，这些参数具有很高的变异性。这些可变性通过被研究的系统传播并直接影响其预测输出。当多个参数同时经历一定量的不确定性时，这一事实变得更加明显，这使得难以区分个体效应以及它们是如何产生的。在这个项目中，它的目的是耦合在TMS与NMM期间感应的电磁场，考虑到两个系统中的参数的不确定性。因此，两个系统之间的随机耦合模型的开发。方法的基础上依赖于广义多项式混沌技术（gPC）。由于NMM是多稳态和高维的，因此目标是在这些方面进一步发展gPC方法。由TMS中的感应问题、耦合模型和NMM组成的整个系统的随机分析需要高效的算法。为了保证计算效率，它的目标是利用模型降阶技术与稀疏网格和减少基多项式。所得到的方法是通用的，可以应用于各种工程问题，如电路设计和无损检测，其中涉及的不确定性，可能会损害安全。在对技术和自动化需求强烈的时代，安全是最重要的。这就需要高效的方法来分析复杂和耦合系统中不确定性的影响。

项目成果

A principled approach to conductivity uncertainty analysis in electric field calculations

• DOI: 10.1016/j.neuroimage.2018.12.053
• 发表时间: 2019-03-01
• 期刊: NEUROIMAGE
• 影响因子: 5.7
• 作者: Saturnino, Guilherme B.;Thielscher, Axel;Weise, Konstantin
• 通讯作者: Weise, Konstantin

Boundary element fast multipole method for modeling electrical brain stimulation with voltage and current electrodes.

• DOI: 10.1088/1741-2552/ac17d7
• 发表时间: 2021-08-19
• 期刊: Journal of neural engineering
• 影响因子: 4
• 作者: Makarov SN;Golestanirad L;Wartman WA;Nguyen BT;Noetscher GM;Ahveninen JP;Fujimoto K;Weise K;Nummenmaa AR
• 通讯作者: Nummenmaa AR

The effect of meninges on the electric fields in TES and TMS. Numerical modeling with adaptive mesh refinement.

脑膜对 TES 和 TMS 电场的影响。

• DOI: 10.1016/j.brs.2022.04.009
• 发表时间: 2022
• 期刊: Brain stimulation
• 影响因子: 7.7
• 作者: Weise,Konstantin;Wartman,WilliamA;Knösche,ThomasR;Nummenmaa,AapoR;Makarov,SergeyN
• 通讯作者: Makarov,SergeyN

Left posterior inferior parietal cortex causally supports the retrieval of action knowledge

• DOI: 10.1016/j.neuroimage.2020.117041
• 发表时间: 2020-10-01
• 期刊: NEUROIMAGE
• 影响因子: 5.7
• 作者: Kuhnke, Philipp;Beaupain, Marie C.;Hartwigsen, Gesa
• 通讯作者: Hartwigsen, Gesa

Pygpc: A sensitivity and uncertainty analysis toolbox for Python

Pygpc：Python 的敏感性和不确定性分析工具箱

• DOI: 10.1016/j.softx.2020.100450
• 发表时间: 2020
• 期刊: SoftwareX
• 影响因子: 3.4
• 作者: K. Weise;L. Poßner;E. Müller;R. Gast;T. R. Knösche
• 通讯作者: T. R. Knösche