Imagine your brain as a bustling orchestra, with different sections playing their own rhythms. Some come from the neurons firing, while others are orchestrated by higher brain processes. These rhythms have their own unique melodies, constantly evolving in amplitude and frequency. While scientists have successfully recreated gamma rhythms in computational models, they haven’t fully explored the irregular nature of these rhythms. In this study, researchers tackled the challenge of generating brain-like signals using simplified models. By tweaking the parameters of a two-variable model inspired by real neuronal systems, they were able to imitate the qualitative features of natural brain rhythms. Their model allowed them to capture the complex behaviors observed in gamma rhythms, paving the way for a deeper understanding of the brain’s symphony. To showcase the versatility of their approach, they simulated gamma rhythms in different brain states recorded during experiments. If you’re excited to delve into the intricacies of brain rhythms and how they can be recreated using mathematical models, check out the full article!

The brain produces rhythms in a variety of frequency bands. Some are likely by-products of neuronal processes; others are thought to be top-down. Produced entirely naturally, these rhythms have clearly recognizable beats, but they are very far from periodic in the sense of mathematics. The signals are broad-band, episodic, wandering in amplitude and frequency; the rhythm comes and goes, degrading and regenerating. Gamma rhythms, in particular, have been studied by many authors in computational neuroscience, using reduced models as well as networks of hundreds to thousands of integrate-and-fire neurons. All of these models captured successfully the oscillatory nature of gamma rhythms, but the irregular character of gamma in reduced models has not been investigated thoroughly. In this article, we tackle the mathematical question of whether signals with the properties of brain rhythms can be generated from low dimensional dynamical systems. We found that while adding white noise to single periodic cycles can to some degree simulate gamma dynamics, such models tend to be limited in their ability to capture the range of behaviors observed. Using an ODE with two variables inspired by the FitzHugh-Nagumo and Leslie-Gower models, with stochastically varying coefficients designed to control independently amplitude, frequency, and degree of degeneracy, we were able to replicate the qualitative characteristics of natural brain rhythms. To demonstrate model versatility, we simulate the power spectral densities of gamma rhythms in various brain states recorded in experiments.

Read Full Article (External Site)