Wave speed in excitable random networks with spatially constrained connections

Area of Science:

• Neuroscience
• Computational Biology
• Network Science

Background:

• Very fast oscillations (VFO) precede epileptic seizures in the neocortex.
• Evidence suggests VFO arise from pyramidal neuron networks with axonal gap junctions.
• Electrocorticography (ECoG) reveals spatio-temporal waves of activity.

Purpose of the Study:

• Investigate the speed of activity propagation in neuron networks with axonal gap junctions.
• Develop a predictive model for wave propagation speed.
• Understand the influence of network topology and connection properties on wave speed.

Main Methods:

• Simulated wave propagation using excitable cellular automata (CA) on spatially constrained random networks.
• Derived a mean field theory from the CA model.
• Developed and tested a novel hyperbolic partial differential equation (PDE) for wave speed prediction.
• Analyzed wave speed dependence on network degree, connection length, and degree distributions.

Main Results:

• The proposed hyperbolic PDE accurately predicts wave speed, which saturates with increasing network degree ().
• Maximum connection length is a better predictor of wave speed than mean connection length.
• Wave speed is strongly dependent on the ratio of network moments (/), not just the mean degree ().
• Wave speeds were consistent across diverse network topologies (regular, Poisson, exponential, power law).

Conclusions:

• The developed mean field theory and hyperbolic PDE provide accurate predictions for wave propagation speed in electrically coupled neuronal networks.
• Network topology, particularly connection length and higher-order moments of degree distribution, significantly impacts wave speed.
• The findings offer practical insights for understanding epileptic seizure dynamics and can be applied to other network phenomena like epidemic spread.