Brain model state space reconstruction using an LSTM neural network

Abstract

Objective
Kalman filtering has previously been applied to track neural model states and parameters, particularly at the scale relevant to electroencephalography (EEG). However, this approach lacks a reliable method to determine the initial filter conditions and assumes that the distribution of states remains Gaussian. This study presents an alternative, data-driven method to track the states and parameters of neural mass models (NMMs) from EEG recordings using deep learning techniques, specifically a Long Short-Term Memory (LSTM) neural network.
Approach
An LSTM filter was trained on simulated EEG data generated by a neural mass model using a wide range of parameters. With an appopriately customised loss function, the LSTM filter can learn the behaviour of NMMs. As a result, it can output the state vector and parameters of NMMs given observation data as the input.
Main Results
Test results using simulated data yielded correlations with R squared of around 0.99 and verified that the method is robust to noise and can be more accurate than a nonlinear Kalman filter when the initial conditions of the Kalman filter are not accurate. As an example of real-world application, the LSTM filter was also applied to real EEG data that included epileptic seizures, and revealed changes in connectivity strength parameters at the beginnings of seizures.
Significance
Tracking the state vector and parameters of mathematical brain models is of great importance in the area of brain modelling, monitoring, imaging and control. This approach has no need to specify the initial state vector and parameters, which is very difficult to do in practice because many of the variables being estimated cannot be measured directly in physiological experiments. This method may be applied using any neural mass model and, therefore, provides a general, novel, efficient approach to estimate brain model variables that are often difficult to measure.