Master
2022/2023
Mathematical Aspects of EEG and MEG Based Neuroimaging
Category 'Best Course for New Knowledge and Skills'
Type:
Elective course (Cognitive Sciences and Technologies: From Neuron to Cognition)
Area of studies:
Psychology
Delivered by:
School of Psychology
When:
1 year, 3 module
Mode of studies:
offline
Open to:
students of one campus
Master’s programme:
Cognitive Sciences and Technologies: From Neuron to Cognition
Language:
English
ECTS credits:
3
Contact hours:
56
Course Syllabus
Abstract
The course “ Mathematical Aspects of EEG and MEG Based Neuroimaging” aims to introduce masters graduate students to basic theory of inverse modelling used to analyze the distribution of neuronal sources on the basis of EEG or MEG data. This shall prove to be useful for the students who are interested in learning mathematical aspects behind the process of converting non-invasively recor neuronal behavior and show the ways to motivate model choice as well as relations between the features of neuronal activity and dynamical properties of the models.ded data into the dynamic maps of neural activity. During the course we will briefly explore the forward model that describes the way the neuronal sources are mixed into sensor signals. The major portion of the class will be devoted to studying three classes of the approaches used to tackle the underdetermined inverse problem of EEG and MEG that lies in the heart of the transition from the sensor space to source space. The course can be considered as a deep dive into the engineering mathematics behind EEG and MEG based neuroimaging, one of the topics presented during the introductory “Neuroimaging techniques” class. We will start exploration of the inverse modelling from the classification of different types of approaches to reconstruction of neuronal sources from the multichannel EEG and MEG data. Then we will explore several representative solutions for the three main classes of these methods, will see how they behave when applied to modelled and real data, will learn the basic assumptions behind these methods and the effect of their parameters. The course provides students with the basic understanding of the inverse modelling philosophy in application to MEG and EEG, prepares them for comprehending modern methodological literature and attempts to build a landshaft for reasoning to support an educated choice of an inverse solver to apply in a specific study.
Learning Objectives
- Gain understanding of the basic terms of forward and inverse models of EEG and MEG: volume conductor, equivalent current dipole, gain matrix, topography, lead field, ill-posed problem, regularization, global vs. local optimization, resolution kernel.
- Gain understanding of principles underlying the classification of EEG and MEG inverse solvers.
- Gain skills in applying an inverse solver to a real MEG\EEG data and tune its parameters to achieve the desired trade-off between the accuracy and the stability\reproducibility of the obtained solution.
- Gain skills in applying the existing software (MNE Python \ Brainstorm) and building pipelines for solving the inverse problem and presenting the results.
- Gain skills in implementing from scratch an inverse solver of their choice.
Expected Learning Outcomes
- Be capable of implementing from scratch and applying an inverse solver of their choice.
- Know basic terms of forward and inverse models of EEG and MEG: volume conductor, equivalent current dipole, gain matrix, topography, lead field, ill-posed problem, regularization, global vs. local optimization, resolution kernel.
- Know how to apply the existing software (MNE Python \ Brainstorm) and build pipelines for solving the inverse problem and present the results.
- Know principles underlying the classification of EEG and MEG inverse solvers.
- Possess skills in applying an inverse solver to a real MEG\EEG data and tune its parameters to achieve the desired tradeoff between the accuracy and the stability\reproducibility of the obtained solution
Course Contents
- EEG and MEG data origin.
- Inverse problem in non-parametric formulation.
- Inferring prior distribution from the data.
- Parametric methods.
- Local optimization.
- EEG and MEG data preprocessing.
- Brainstorm and MNE-Python software.
Bibliography
Recommended Core Bibliography
- Hari, R., & Puce, A. (2017). MEG-EEG Primer. New York, NY: Oxford University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=2097017
- Ilmoniemi, R., & Sarvas, J. (2019). Brain Signals : Physics and Mathematics of MEG and EEG. Cambridge: The MIT Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=2118154
Recommended Additional Bibliography
- Cohen, M. X. (2014). Analyzing Neural Time Series Data : Theory and Practice. Cambridge, Massachusetts: The MIT Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=689432
- Sekihara, K., & Nagarajan, S. S. (2008). Adaptive Spatial Filters for Electromagnetic Brain Imaging. Springer.