# Quantifying Time-Varying Sources in Magnetoencephalography -- A Discrete Approach

## TL;DR

This paper introduces a novel discrete dynamic framework for localizing and quantifying time-varying brain sources in MEG data, addressing non-linear relationships and providing comprehensive temporal source distribution insights.

## Contribution

The paper develops a new discrete dynamic approach for estimating source location distributions in MEG, overcoming limitations of existing linear methods and enabling full temporal source characterization.

## Key findings

- The method accurately tracks source location changes over time.
- It provides detailed source distribution insights from entire measurement sets.
- The approach outperforms traditional methods in simulation and real data.

## Abstract

We study the distribution of brain source from the most advanced brain imaging technique, Magnetoencephalography (MEG), which measures the magnetic fields outside the human head produced by the electrical activity inside the brain. Common time-varying source localization methods assume the source current with a time-varying structure and solve the MEG inverse problem by mainly estimating the source moment parameters. These methods use the fact that the magnetic fields linearly depend on the moment parameters of the source, and work well under the linear dynamic system. However, magnetic fields are known to be non-linearly related to the location parameters of the source. The existing work on estimating the time-varying unknown location parameters is limited. We are motivated to investigate the source distribution for the location parameters based on a dynamic framework, where the posterior distribution of the source is computed in a closed form discretely. The new framework allows us not only to directly approximate the posterior distribution of the source current, where sequential sampling methods may suffer from slow convergence due to the large volume of measurement, but also to quantify the source distribution at any time point from the entire set of measurements reflecting the distribution of the source, rather than using only the measurements up to the time point of interest. Both a dynamic procedure and a switch procedure are proposed for the new discrete approach, balancing estimation accuracy and computational efficiency when multiple sources are present. In both simulation and real data, we illustrate that the new method is able to provide comprehensive insight into the time evolution of the sources at different stages of the MEG and EEG experiment.