Model design for networks of heterogeneous Hodgkin–Huxley neurons

We present a novel modular, scalable and adaptable modelling framework to accurately model neuronal networks composed of neurons with different dynamic properties and distinct firing patterns based on a control-inspired feedback structure. We consider three important classes of neurons: inhibitory Fast spiking neurons, excitatory regular spiking with adaptations neurons, and excitatory intrinsic bursting neurons. We also take into consideration two basic means of neuronal interconnection: electrical and chemical synapses. By separating the neuronal dynamics from the network dynamics, we have developed a fully flexible feedback structure that can be further augmented to incorporate additional types of neurons and/or synapses. We use an augmented version of the Hodgkin–Huxley model to describe the individual neuron dynamics and graph theory to define the network structure. We provide simulation results for small fundamental neuron motifs as well as bigger neuronal networks and we verify the accuracy, flexibility and scalability of the proposed method. Therefore, we provide the basis for a comprehensive modelling framework that is able to imitate the dynamics of individual neurons and neuronal networks and is able to replicate basic normal brain function. The structure of the proposed framework is ideal for applications of control and optimization methods both for modelling the effect of pharmacological substances as well as for modelling diseased neuron and network conditions.