We use diverse approaches, including nonlinear dynamics, complex systems theory, probability
theory and statistical mechanics, to study how brain activity arises through the complex interaction
of numerous neurons. Theoretical models play an important role in bridging the gap between physical descriptions of cortical systems and empirical studies of brain functioning. We model brain activity at various physical scales using different levels of abstraction. Current projects range from large-scale biophysical models to finer scale spiking neuron models and Bayesian models of inference in single neurons. In particular, we aim at explaining and predicting data we obtained using EEG and fMRI related to cognitive functions, such as perception and decision making.
Oscillatory neuronal population dynamics
We study how large populations of neurons generate rhythmic
patterns in response to periodic input. We seek to understand how the intrinsic population dynamics arise from the interaction between neurons. By characterising the relationship between the population behaviour and the input pattern we investigate the biophysical mechanisms that underpin stimulus encoding in neuronal populations. Ultimately, this project seeks to illuminate the dynamic processes involved in sensory perception and inform our EEG projects.
Neural coding by spatio-temporal oscillation patterns
We use numerical simulation to explore a proposed role for spatio-temporal oscillation patterns in motor cortex as the neural code of movement. Spatial pattern formation in cortex is modelled using spatially-coupled neural oscillators. We show that the morphology of the ensuing cortical patterns can be discriminated by the descending fibers of the motor system. Our model demonstrates that specific spatio-temporal patterns in cortex can drive specific muscle movements in a simulated biomechanical limb. This research uses computational neuroscience to bridge the fields of human motor control and robotics.
Relationships between structure and dynamics in complex brain systems
We study the relationship between structure and dynamics in brain network models by incorporating reciprocal structural-dynamical interactions into these models. In one model, we represented interactions between brain regions via networks of coupled chaotic logistic maps. Coupling patterns between these maps enable the emergence of nontrivial dynamics, while these patterns are slowly modulated by the emergent dynamics via an activity-dependent unsupervised learning rule (Fig. 1). In another model, we represented interactions between brain regions via large networks of coupled spiking neuronal ensembles. These networks contain several neurobiologically realistic features, including leaky currents, spike-timing dependent plasticity, neuronal inhibition and axonal delays. We showed that realistic patterns of anatomical connectivity and spike-timing dependent plasticity in these networks enable the emergence of self-similar “critical” brain network dynamics.
Fig. 1 Central and peripheral nodes manifest distinctly different dynamics in complex brain systems. Peripheral nodes receive homogeneous inputs and consequently exhibit high synchrony and low-dimensional chaotic dynamics. Central hubs connect with nodes in multiple modules, receive discordant inputs, and consequently exhibit unsynchronized, high-dimensional stochastic dynamics. Figure from Rubinov et al., 2009.