Near-Hamiltonian dynamics and energy-like quantities of next-generation neural mass models

Neural mass models describe the mean-field dynamics of populations of neurons. In this work we illustrate how fundamental ideas of physics, such as energy and conserved quantities, can be explored for such models. We show that time-rescaling renders recent next-generation neural mass models Hamiltonian in the limit of a homogeneous population or strong coupling. The corresponding energy-like quantity provides considerable insight into the model dynamics even in the case of heterogeneity, and explain for example why orbits are near-ellipsoidal and predict spike amplitude during bursting dynamics. We illustrate how these energy considerations provide a possible link between neuronal population behavior and energy landscape theory, which has been used to analyze data from brain recordings. Our introduction of near-Hamiltonian descriptions of neuronal activity could permit the application of highly developed physics theory to get insight into brain behavior.