Communications in Mathematical Sciences
Volume 17 (2019)
Dedicated to the memory of Professor David Shen Ou Cai
Fast algorithms for simulation of neuronal dynamics based on the bilinear dendritic integration rule
Pages: 1313 – 1331
We aim to develop fast algorithms for neuronal simulations to capture the dynamics of a neuron with realistic dendritic morphology. To achieve this, we perform the asymptotic analysis on a cable neuron model with branched dendrites. Using the second-order asymptotic solutions, we derive a bilinear dendritic integration rule to characterize the voltage response at the soma when receiving multiple spatiotemporal synaptic inputs from dendrites, with a dependency on the voltage state of the neuron at input arrival times. Based on the derived bilinear rule, we finally propose two fast algorithms and demonstrate numerically that, in comparison with solving the original cable neuron model numerically, the algorithms can reduce the computational cost of simulation for neuronal dynamics enormously while retaining relatively high accuracy in terms of both sub-threshold dynamics and firing statistics.
dendrites, cable equation, asymptotic analysis, dendritic integration, bilinear rule
2010 Mathematics Subject Classification
This work is funded by National Natural Science Foundation of China Grants 11901388, Shanghai Sailing Program 19YF1421400, Shanghai Chengguang program (S.L.), and Shanghai Rising-Star Program 15QA1402600, Natural Science Foundation of China Grants 11671259, 11722107, 91630208 (D.Z.), and by Student Innovation Center at Shanghai Jiao Tong University.
Received 3 January 2019
Accepted 15 July 2019
Published 6 December 2019