Method development for co-simulation of electrical-chemical systems in Neuroscience

Multiscale modeling and simulation is a powerful approach for studying such phenomena in nature as learning and memory. In computational neuroscience, historically, methods and tools for neuronal modeling and simulations have been developed for studies focused on a single level of the neuronal organization. Once the community realized that the interaction of multiple systems acting at different temporal and spatial scales can lead to emerging properties of the phenomena under study, the interest in and need for models encompassing processes acting at multiple scales of time and space increased. Such models are called multiscale models. Multiscale modeling and simulation can be achieved in different ways. One of the possible solutions is to use an already existing foundation of formalisms and methods, and couple existing numerical algorithms and models during a simulation in a co-simulation, i.e. a joint simulation of subsystems. However, there are several obstacles on the way. First, a lack of interoperability of simulation environments makes it non-trivial to couple existing models in a single environment that supports multiscale simulation. Second, there is a decision to make regarding which variables to communicate between subsystems. The communication signal has a significant impact on the behavior of the whole multiscale system. Last but not least, an absence of a theory or general approach for the numerical coupling of existing mathematical formalisms makes the coupling of the numerical solvers a challenging task. The main contribution of this thesis is a numerical framework for multiscale co-simulation of electrical and chemical systems in neuroscience. A multiscale model that integrates a subcellular signaling system with the electrical activity of the neuron was developed. The thesis emphasizes the importance of numerically correct and efficient coupling of the systems of interest. Two coupling algorithms, named singlerate and multirate, differ in the rate of communication between the coupling subsystems, were proposed in the thesis. The algorithms, as well as test cases, were implemented in the MATLAB® environment. MATLAB was used to validate the accuracy and efficiency of the algorithms. Both algorithms showed an expected second order accuracy with the simulated electrical-chemical system. The guaranteed accuracy in the singlerate algorithm can be used as a trade-off for efficiency in the multirate algorithm. Thus, both algorithms can find its application in the proposed numerical framework for multiscale co-simulations. The framework exposes a modular organization with natural interfaces and could be used as a basis for the development of a generic tool for multiscale co-simulations. The thesis also presents an implementation of a new numerical method in the NEURON simulation environment, with benchmarks. The method can replace the standard discretization schema for the Hodgkin-Huxley type models. It can be beneficial in a co-simulation of large models where the Jacobian evaluation of the whole system becomes a very expensive operation. Finally, the thesis describes an extension of the MUlti-SImulation Coordinator tool (MUSIC). MUSIC is a library that is mainly used for co-simulations of spiking neural networks on a cluster. A series of important developments was done in MUSIC as the first step towards multiscale co-simulations. First, a new algorithm and an improvement of the existing parallel communication algorithms were implemented as described in the thesis. Then, a new communication scheduling algorithm was developed and implemented in the MUSIC library and analyzed. The numerical framework presented in the thesis could be implemented with MUSIC to allow efficient co-simulations of electrical-chemical systems.QC 20200127