Abstract
The information is transmitted in neurons through axons, many of whom have myelin-covered sections, whose main purpose is to increase the speed of electrical signal transmission. Modeling the myelinated axons in a realistic way, by maintaining the physical meaning of components may lead to complex systems, described by high-dimensional systems of PDEs, whose solution is computationally demanding. Analysis of larger neuronal circuits including multiple myelinated axons therefore requires the generation of equivalent low-order models to control complexity. Such models must preserve the physical interpretation and properties of the original system including its passivity and stability. The axons’ port-based structure makes them suitable to be modeled as port-Hamiltonian systems. This paper uses a structure-preserving reduction method for port-Hamiltonian systems to reduce the description of a myelinated compartment into a model with comparable accuracy with the previously used vector fitting technique. The reduced system is synthesized into an equivalent passive circuit with no controlled sources and only positive elements, amenable for inclusion in standard neuronal simulators.
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Acknowledgements
This work was partially supported by Portuguese national funds through FCT, Fundação para a Ciência e a Tecnologia, under project UIDB/50021/2020 as well as project PTDC/EEI-EEE/31140/2017.
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Barbulescu, R., Ciuprina, G., Ionescu, T., Ioan, D., Silveira, L.M. (2021). Efficient Model Reduction of Myelinated Compartments as Port-Hamiltonian Systems. In: van Beurden, M., Budko, N., Schilders, W. (eds) Scientific Computing in Electrical Engineering. Mathematics in Industry(), vol 36. Springer, Cham. https://doi.org/10.1007/978-3-030-84238-3_1
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