The interaction between neural populations: Additive versus diffusive coupling
Authors: Lopes Marinho A. , Hamandi Khalid , Zhang Jiaxiang , Creaser Jennifer L. 
Published: November 2021

Models of networks of populations of neurons commonly assume that the interactions between neural populations are via additive or diffusive coupling. When using the additive coupling, a population’s activity is affected by the sum of the activities of neighbouring populations. In contrast, when using the diffusive coupling a neural population is affected by the sum of the differences between its activity and the activity of its neighbours. These two coupling functions have been used interchangeably for similar applications. Here, we show that the choice of coupling can lead to strikingly different brain network dynamics. We focus on a model of seizure transitions that has been used both with additive and diffusive coupling in the literature. We consider networks with two and three nodes, and large random and scale-free networks with 64 nodes. We further assess functional networks inferred from magnetoencephalography (MEG) from people with epilepsy and healthy controls. To characterize the seizure dynamics on these networks, we use the escape time, the brain network ictogenicity (BNI) and the node ictogenicity (NI), which are measures of the network’s global and local ability to generate seizures. Our main result is that the level of ictogenicity of a network is strongly dependent on the coupling function. We find that people with epilepsy have higher additive BNI than controls, as hypothesized, while the diffusive BNI provides the opposite result. Moreover, individual nodes that are more likely to drive seizures with one type of coupling are more likely to prevent seizures with the other coupling function. Our results on the MEG networks and evidence from the literature suggest that the additive coupling may be a better modelling choice than the diffusive coupling, at least for BNI and NI studies. Thus, we highlight the need to motivate and validate the choice of coupling in future studies.

Author summary

Most models of brain dynamics assume that distinct brain regions interact in either an additive or a diffusive way. With additive coupling, each brain region sums incoming signals. In contrast, with diffusive coupling, each region sums the differences between its own signal and incoming signals. Although they are different, these two couplings have been used for very similar applications, particularly within models of epilepsy. Here we assessed the effect of this choice on seizure behaviour. Using a model of seizures and both artificial and real brain networks, we showed that the coupling choice can lead to very different seizure dynamics. We found that networks that are more prone to seizures using one coupling, are less prone to them using the other. Likewise, individual brain regions that are more likely to drive seizures when using additive coupling, are more likely to prevent them when using diffusive coupling. Using real brain networks, we found that the additive coupling predicted higher seizure propensity in people with epilepsy compared to healthy controls, whereas the diffusive coupling did not. Our results highlight the need to justify the choice of coupling used and show that the additive coupling may be a better option in some applications.