Classifying dynamic transitions in high dimensional neural mass models: A random forest approach.

Lauric A Ferrat,John R Terry,Marc Goodfellow,Levin Kuhlmann

doi:10.1371/journal.pcbi.1006009

Abstract

Neural mass models (NMMs) are increasingly used to uncover the large-scale mechanisms of brain rhythms in health and disease. The dynamics of these models is dependent upon the choice of parameters, and therefore it is crucial to be able to understand how dynamics change when parameters are varied. Despite being considered low dimensional in comparison to micro-scale, neuronal network models, with regards to understanding the relationship between parameters and dynamics, NMMs are still prohibitively high dimensional for classical approaches such as numerical continuation. Therefore, we need alternative methods to characterise dynamics of NMMs in high dimensional parameter spaces. Here, we introduce a statistical framework that enables the efficient exploration of the relationship between model parameters and selected features of the simulated, emergent model dynamics of NMMs. We combine the classical machine learning approaches of trees and random forests to enable studying the effect that varying multiple parameters has on the dynamics of a model. The method proceeds by using simulations to transform the mathematical model into a database. This database is then used to partition parameter space with respect to dynamic features of interest, using random forests. This allows us to rapidly explore dynamics in high dimensional parameter space, capture the approximate location of qualitative transitions in dynamics and assess the relative importance of all parameters in the model in all dimensions simultaneously. We apply this method to a commonly used NMM in the context of transitions to seizure dynamics. We find that the inhibitory sub-system is most crucial for the generation of seizure dynamics, confirm and expand previous findings regarding the ratio of excitation and inhibition, and demonstrate that previously overlooked parameters can have a significant impact on model dynamics. We advocate the use of this method in future to constrain high dimensional parameter spaces enabling more efficient, person-specific, model calibration.

Highlights

If the model has only one or two parameters, formal analysis is possible, understanding changes in system behaviour becomes increasingly difficult as the number of model parameters increases
In this article we introduce a method to overcome this challenge and use it to better elucidate the contribution of different mechanisms to the emergence of brain rhythms
Our method uses machine learning approaches to classify the dynamics of the model under different parameters and to calculate their variability

Summary

Introduction

Neural mass models (NMM) approximate the average behaviour of large populations of neurons and provide an efficient way to simulate electrographic data in order to understand the mechanisms of brain (dys-) function They have been used to understand a wide variety of physiological and pathophysiological activities of the brain, including the alpha rhythm [1, 2], sleep rhythms [3,4,5], brain resonance [6] or dynamics resulting from conditions such as epilepsy [7,8,9,10,11], schizophrenia [12] and dementia [13]. In order to reduce dimensionality, subsets of parameters can be fixed based on a priori assumptions Both the choice of initial values for parameters and the boundaries of the parameter space that are searched are often constrained [18]. In these early derivations of NMM, parameters that could be experimentally determined were estimated but their uncertainties were not always measured [1]

Objectives

Methods

Results

Discussion

Conclusion