Mean-Field Modeling of Spiking Neural Network Dynamics
One of the projects I worked on during my PhD and continue to work on is the derivation and analysis of so-called mean-field models. Mean-field models can be derived from the mathematical equations that govern the dynamics of spiking neural networks and they capture how average quantities such as the average firing rate or the average membrane potential develop over time in these networks. These average quantities are much easier to record in living brains than single neuron properties. Thus, these mean-field models allow to relate recordings of neural population averages to the underlying spiking network activity. They are a great tool to bridge multiple scales of brain organization and allow to apply a wide range of dynamical systems analysis methods. The relationship between mean-field model and spiking neural network dynamics is depicted in the figure below for a network of quadratic integrate-and-fire (QIF) neurons.
My PhD work on mean-field models of spiking neural dynamics was mostly concerned with the effects that different forms of plasticity have on the network dynamics [1,2]. Plasticity thereby refers to properties of neurons or synapses that undergo changes, depending on the level of activity of the neuron or synapse. An example for that is spike-frequency adaptation, which leads to a reduction of the firing rate response of a neuron to a given input current, if the neuron fired at a high rate prior to the input already. My co-authors and I derived the mean-field equations for a network of spiking neurons with spike-frequency adaptation and analyzed its role in neural synchronization in .
As part of my first postdoc with Ann Kennedy, we built up on this previous work to derive mean-field equations for a new mathematical model of single neurons (the Izhikevich neuron model) with distributed spiking thresholds .
 Gast et al. (2020) Neural computation.
 Gast et al. (2021) Physical Review E.
 Gast et al. (2023) Physical Review E.
Neural Synchronization Properties in the Basal Ganglia
The basal ganglia are a set of interconnected neural populations, deep in the brain, that are involved in various important brain functions such as learning, habit formation, and motor control. Damage to or malfunctioning of the basal ganglia has been found in various neurological disorders such as Parkinson's disease, Tourette syndrome, or Huntington's disease. Typically, malfunctioning of the basal ganglia is associated with increased synchrony in the activity of basal ganglia neurons. For example, the decline in motor control in Parkinson's disease seems to be related to the tendency of large parts of basal ganglia neurons to fire in concert at frequencies between 12-30 Hz (beta frequency band), thus reducing their information encoding capacities.
In this project, I use mathematical modeling and computer simulations to examine the conditions under which neurons in the basal ganglia start to fire in synchrony. During my PhD, I built a mathematical model of the external pallidum, a central part of the basal ganglia, and analyzed the neural synchronization properties of the model under normal and dopamine depleted conditions . Furthermore, my co-authors and I showed via this model how the complex features of parkinsonian neural synchronization that have been found in human patients could emerge at the level of the external pallidum [4, 5].
 Gast et al. (2021) Journal of Neuroscience.
 Gong et al. (2021) Brain.