Uncertainty- and Sensitivity Analysis of Coupled Systems Composed of an Electromagnetic Field Problem and a Dynamic Nonlinear Network Using Spectral Methods
Final Report Abstract
A central object of the project was the development of new approaches and methods for an efficient uncertainty and sensitivity analysis of high-dimensional and discontinuous model functions. For this purpose, the classical generalized polynomial chaos (gPC) approach was extended with respect to numerous new methods. This included the development of adaptive gPC algorithms, which adjust the modeling accuracy depending on the complexity of the underlying model function. Furthermore, modern concepts of digital signal processing such as compressed sensing and optimized sampling methods were integrated into the gPC approach. This has significantly increased the efficiency of the method and now also enables the analysis of high-dimensional problems. To enable uncertainty analysis of discontinuous model function, the gPC was extended by a multi-element approach (ME- gPC). Modern image processing and machine learning techniques were used to identify the discontinuity boundary. The methods were applied in the field of noninvasive brain stimulation to quantify the prediction quality of the electric fields induced in the brain, which are significantly affected by uncertainties in the electrical conductivities of the biological tissue. All methodological approaches have been published in the Python software package pygpc and made freely available to the scientific community. The documentation contains numerous examples and explanations of the algorithms to make the introduction to the topic as accessible as possible and to make it easier for outsiders to use the software. As a result, pygpc got reputation from other scientists and has already found application in various scientific fields such as neurophysiological research, cancer therapy, and battery and power engineering for uncertainty and sensitivity analysis of complex and computationally expensive models. Furthermore, a precise method for localizing cortical muscle representations with transcranial magnetic stimulation (TMS) was developed. The developed measurement protocol and software for it was published in the journal Nature Protocols. In contrast to previous approaches, the developed protocol is particularly easy to implement, very efficient, much more robust, and therefore very well suited for a practical and clinical application. The routine not only provides insights into structure-function relationships in the brain, but also lays the foundation for future TMS dosage metrics based on individual cortical electric field thresholds. Later in the project, an efficient and easy-to-implement coupling model for noninvasive brain stimulation was developed that allows the electric fields induced in the brain to be coupled into neuronal structures. The model was derived from numerous simulations of realistic neurons of different morphologies and allows for the first time a realistic coupling between macroscopic electric fields and the activation of neurons at the meso- and microscopic scale. The work represents an important contribution to neuroscience research and opens up numerous new insights into how transcranial brain stimulation works. This work laid the foundation for the development of an overall model for modeling motor evoked potentials by TMS. Using the developed localization procedure and coupling model, the electric fields could be selectively coupled into the upper motor neurons. Their output signals in the form of D and I waves are transmitted to the lower motor neurons, which eventually activate the individual motor units in the hand muscles and can be combined into an overall signal in the form of a motor evoked potential. The model has the potential to be able to describe certain motor disease patterns, but this needs to be investigated further in the future.
Publications
- “A principled approach to conductivity uncertainty analysis in electric field calculations”, NeuroImage, vol. 188, pp. 821-834, 2019
G. B. Saturnino, A. Thielscher, K. H. Madsen, T. R. Knösche, K. Weise
(See online at https://doi.org/10.1016/j.neuroimage.2018.12.053) - A novel approach to localize cortical TMS effects. NeuroImage, 209, 116486, 2020
K. Weise, O. Numssen O., A. Thielscher, G. Hartwigsen, T. R. Knösche
(See online at https://doi.org/10.1016/j.neuroimage.2019.116486) - Left posterior inferior parietal cortex causally supports the retrieval of action knowledge. NeuroImage, 117041, 2020
P. Kuhnke, M. C. Beaupain, V. K. Cheung, K. Weise, M. Kiefer, G. Hartwigsen
(See online at https://doi.org/10.1016/j.neuroimage.2020.117041) - Pygpc: A sensitivity and uncertainty analysis toolbox for Python. SoftwareX, 11, 100450, 2020
K. Weise, L. Poßner, E. Müller, R. Gast, T. R. Knösche
(See online at https://doi.org/10.1016/j.softx.2020.100450) - Boundary element fast multipole method for modeling electrical brain stimulation with voltage and current electrodes. Journal of Neural Engineering, 18(4), 0460d4, 2021
S. N. Makarov, L. Golestanirad, W. A. Wartman, B. T. Nguyen, G. M. Noetscher, J. P. Ahveninen, K. Fujimoto, K. Weise, A. R. Nummenmaa
(See online at https://doi.org/10.1088/1741-2552/ac17d7) - Efficient high-resolution TMS mapping of the human motor cortex by nonlinear regression. NeuroImage, 245, 118654, 2021
O. Numssen, A. L. Zier, A. Thielscher, G. Hartwigsen, T. Knosche, K. Weise
(See online at https://doi.org/10.1016/j.neuroimage.2021.118654) - Comparison of the performance and reliability between improved sampling strategies for polynomial chaos expansion, AIMS Mathematical Biosciences and Engineering, 19(8), pp: 7425-7480, 2022
K. Weise, E. Müller, L. Poßner, T. R. Knösche
(See online at https://doi.org/10.3934/mbe.2022351) - Localization of cortical TMS effects and accurate motor threshold determination
K. Weise, O. Numssen, B. Kalloch, A. L. Zier, A. Thielscher, G. Hartwigsen, T. Knosche
(See online at https://doi.org/10.21203/rs.3.pex-1780/v2) - The effect of meninges on the electric fields in TES and TMS. Numerical modeling with adaptive mesh refinement, Brain Stimulation, 15(3), pp: 654-663, 2022
K. Weise, W. Wartmann, T. R. Knösche, A. Nummenmaa, S. Makarov
(See online at https://doi.org/10.1016/j.brs.2022.04.009)
