Computational simulation is an invaluable tool for analyzing, understanding, and predicting the behavior of complex systems. Simulation is especially useful whenever access to the real system is impossible, inappropriate, or simply too expensive. Neuroscientists have increasingly been using computational models of neurons and developing simulation environments, with the goal simulating, and recreating in silico, the functionality of significant parts of the human brain. This has led to the development of many projects of varying dimension and ambition, which range from the study and characterization of individual neurons to large research programs such as the Human Brain Project (in Europe), the Human Connectome Project (in the US) and the Brain/MINDS project (in Japan), directed at understanding whole brains.
The behavior of large networks of biological neurons is most commonly simulated at the electrical level, given that the relevant behaviors of neurons at this scale result from the electrical properties of the neuron membranes, first understood by the pioneering work of Hodgkin and Huxley [Hodgin1959]. Therefore, a wide range of simulation techniques developed for the purpose of simulating electrical networks can be directly applied to the simulation of networks of biological neurons. It is now possible to simulate networks with thousands of neurons and tens of millions of electrical elements [Reinmann2013]. Ultimately, the target is to simulate complete brains or brain sections, with billions of neurons, or even a complete human brain, which exhibits close to a hundred billion neurons. Clearly, new approaches are required for problems with this dimension. In other domains, such as electronic systems design, larger and larger systems have been the target of the simulations, as the technology evolved. The key issue is to retain the relevant features of the system or phenomena being simulated while neglecting unneeded information. In many similar contexts, model order reduction techniques have been applied in order to compress models to smaller descriptions that, however, retain the relevant behavior characteristics. In electronic design automation (EDA), for instance, model order reduction has been successfully applied to reduce large interconnect networks, transforming networks with millions of nodes into compact systems that can be efficiently simulated. Such techniques, well known and exploited in EDA, have seen little usage in brain simulation. However, they promise to be able to compress the detailed representation of very large, realistic, neuronal networks while accurately tracking the behavior at relevant points in the network.
In this project we will apply model reduction techniques to the problem of simulating large networks of realistic neuron models, at the electrical level. We expect to obtain significant gains in speed and accuracy, making it possible to simulate much larger networks of neurons than what is possible today.