Global nonlinear approach for mapping parameters of neural mass models

Neural mass models (NMMs) are important for helping us interpret observations of brain dynamics. They provide a means to understand data in terms of mechanisms such as synaptic interactions between excitatory and inhibitory neuronal populations. To interpret data using NMMs we need to quantitatively...

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Bibliographic Details
Published in:PLoS computational biology 2023-03, Vol.19 (3), p.e1010985-e1010985
Main Authors: Dunstan, Dominic M, Richardson, Mark P, Abela, Eugenio, Akman, Ozgur E, Goodfellow, Marc
Format: Article
Language:English
Subjects:
Algorithms
Biology and Life Sciences
Brain
Brain - physiology
Brain research
Computer and Information Sciences
Computer Simulation
EEG
Epilepsy
Evolutionary algorithms
Firing pattern
Genetic algorithms
Global optimization
Humans
Mapping
Mathematical models
Mathematical optimization
Medicine and Health Sciences
Models, Neurological
Multiple objective analysis
Neurons
Neurons - physiology
Nonlinear Dynamics
Nonlinearity
Parameter identification
Physical Sciences
Research and Analysis Methods
Subspaces
Time series
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Summary:Neural mass models (NMMs) are important for helping us interpret observations of brain dynamics. They provide a means to understand data in terms of mechanisms such as synaptic interactions between excitatory and inhibitory neuronal populations. To interpret data using NMMs we need to quantitatively compare the output of NMMs with data, and thereby find parameter values for which the model can produce the observed dynamics. Mapping dynamics to NMM parameter values in this way has the potential to improve our understanding of the brain in health and disease. Though abstract, NMMs still comprise of many parameters that are difficult to constrain a priori. This makes it challenging to explore the dynamics of NMMs and elucidate regions of parameter space in which their dynamics best approximate data. Existing approaches to overcome this challenge use a combination of linearising models, constraining the values they can take and exploring restricted subspaces by fixing the values of many parameters a priori. As such, we have little knowledge of the extent to which different regions of parameter space of NMMs can yield dynamics that approximate data, how nonlinearities in models can affect parameter mapping or how best to quantify similarities between model output and data. These issues need to be addressed in order to fully understand the potential and limitations of NMMs, and to aid the development of new models of brain dynamics in the future. To begin to overcome these issues, we present a global nonlinear approach to recovering parameters of NMMs from data. We use global optimisation to explore all parameters of nonlinear NMMs simultaneously, in a minimally constrained way. We do this using multi-objective optimisation (multi-objective evolutionary algorithm, MOEA) so that multiple data features can be quantified. In particular, we use the weighted horizontal visibility graph (wHVG), which is a flexible framework for quantifying different aspects of time series, by converting them into networks. We study EEG alpha activity recorded during the eyes closed resting state from 20 healthy individuals and demonstrate that the MOEA performs favourably compared to single objective approaches. The addition of the wHVG objective allows us to better constrain the model output, which leads to the recovered parameter values being restricted to smaller regions of parameter space, thus improving the practical identifiability of the model. We then use the MOEA to study dif
ISSN:1553-7358
1553-734X
1553-7358
DOI:10.1371/journal.pcbi.1010985