How does large-scale brain activity, such as EEG signals, emerge from the complex dynamics of interacting neurons in the brain? And how do interventions such as neurostimulation influence this dynamics and the cognitive functions it supports? Addressing these questions requires mathematical models that link biophysical mechanisms at the neuron level to population-level activity. Microscopic spiking neural network models provide detailed, biophysically grounded descriptions, but their complexity limits the interpretability and scalability. In contrast, macroscopic models such as neural-mass models are computationally efficient yet lack a clear link to the underlying neuronal mechanisms. Bridging these scales calls for a principled multiscale framework.

In this talk, I present a bottom-up approach that derives mesoscopic models from microscopic neural dynamics. Mesoscopic models bridge the gap by describing the coarse-grained activity of neuronal populations at an intermediate, mesoscopic scale (50-2000 neurons). Because of these relatively small numbers, a critical challenge is the treatment of “finite-size” fluctuations–an essential feature of mesoscopic dynamics. Starting from a realistic spiking neuron model (generalized integrate-and-fire neurons), we derive a stochastic integral equation governing the dynamics of the population activities. This formulation accurately reproduces nonstationary dynamics and variability of large spiking networks while substantially reducing the computational cost, as demonstrated in a cortical column model with 80,000 neurons.

Finally, I show how this mesoscopic description can be further reduced to low-dimensional stochastic differential equations, yielding extremely fast neural-mass models that remain consistent with microscopic dynamics. This framework enables efficient, biophysically grounded simulations of large-scale brain activity and provides a powerful tool to study the effects of neurostimulation on cognitive dynamics.