Efficient numerical simulation of neuron models with spatial structure on graphics processing units

Abstract

Computer simulation of multi-compartment neuron models is difficult, because writing the computer program is tedious but complicated, and it requires sophisticated numerical methods to solve partial differential equations (PDEs) that describe the current flow in a neuron robustly. For this reason, dedicated simulation software such as NEURON and GENESIS have been used widely. However, these simulators do not support hardware acceleration using graphics processing units (GPUs). In this study, we implemented a conjugate gradient (CG) method to solve linear equations efficiently on a GPU in our own software. CG methods are known much faster and more efficient than the Gaussian elimination, when the matrix is huge and sparse. As a result, our software succeeded to carry out a simulation of Purkinje cells developed by De Schutter and Bower (1994) on a GPU. The GPU (Tesla K40c) version realized 3 times faster computation than that a single-threaded CPU version for 15 Purkinje cells.