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Testing an Explicit Method for Multi-compartment Neuron Model Simulation on a GPU

A Correction to this article was published on 02 March 2022

This article has been updated


Large-scale simulation of multi-compartment models is important for understanding the role of morphological structures of individual neurons for information processing in the brain. In a simulation, partial differential equations (PDEs) that describe the dynamics of neurons have to be solved numerically for each time step. To solve PDEs, numerical methods called implicit methods are used for stability. Implicit methods need to solve simultaneous equations, which can make numerical simulation slow on graphics processing units (GPUs) hardware accelerators for parallel computing. To overcome this problem, we investigated the use of explicit methods for multi-compartment model simulation. We applied the Runge–Kutta–Chebyshev (RKC) method to several cerebellar neuron models including Purkinje cells, granule cells, Golgi cells, and inferior olive cells. Next, we implemented a cerebellar cortical model composed of granule cells, Golgi cells, and Purkinje cells, while using different numerical methods for different cell types. Although explicit methods can be unstable against PDEs, using the RKC method showed sufficient stability for most cases, better computational performance than implicit methods on a GPU, and good reproducibility. In the network simulation, choosing the suitable numerical methods for each cell type achieved faster simulation than that used an implicit method solely. Our results suggest that explicit methods are applicable to multi-compartment models and can accelerate computational speed of simulations. Furthermore, to conduct large-scale simulation of multi-compartment models, choosing efficient numerical methods will be more important.

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We would like to thank Messrs. Tsukasa Tsuyuki and Yuki Yamamoto for preliminary investigation of multi-compartment models. We also thank Professors Junichiro Makino in Kobe University and Toshikazu Ebisuzaki in RIKEN for their comments on the use of explicit methods for diffusion equations. This study was supported by MEXT/JSPS Kakenhi Grant Numbers 17H06310 and 20K06850, Japanese Neural Network Society 30th Anniversary Fund, and an intramural fund of the University of Electro-Communications.

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Correspondence to Tadashi Yamazaki.

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Kobayashi, T., Kuriyama, R. & Yamazaki, T. Testing an Explicit Method for Multi-compartment Neuron Model Simulation on a GPU. Cogn Comput (2021).

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  • Multi-compartment model
  • Cerebellum
  • Runge–Kutta–Chebyshev method