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 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 differences in the alpha rhythm observed in EEG recorded from 20 people with epilepsy. We find that a small number of parameters can explain this difference and that, counterintuitively, the mean excitatory synaptic gain parameter is reduced in people with epilepsy compared to control. In addition, we propose that the MOEA could be used to mine for the presence of pathological rhythms, and demonstrate the application of this to epileptiform spike-wave discharges.Author summary: EEG is a useful tool to study large scale brain activity. Mathematical models have been developed to help improve the understanding of the generation of signals recorded from the EEG during different brain states. The dynamics of these models are dependent on their inputs (or parameters) and hence it is important to explore the parameter combinations that result in model dynamics that approximate data. This allows us to better understand how the data were generated. However, due to the relative complexity of these models, finding the parameter combinations that explain data can be a cumbersome task and hence many studies make simplifications about how model and data are compared. In this study, we introduce methods that do not require these simplifying assumptions. Using these methods we demonstrate that different choices in the way we compare models and data can lead to differences in what we infer about the underlying mechanisms. However, we find that combining different choices into the same algorithm allows us to better approximate features of the data and better constrain model parameters. We apply our method to try to understand differences observed in the resting EEG between patients with epilepsy and controls. We find that the model explains these differences predominately by a reduced excitatory synaptic gain in patients with epilepsy. We also demonstrate the potential of this method to “mine” for different kinds of dynamics in high dimensional models.