Neural Membrane Mutual Coupling Characterisation Using Entropy-Based Iterative Learning Identification

• Published in: IEEE access Vol. 8; pp. 205231 - 205243
• Main Authors: Tang, Xiafei, Zhang, Qichun, Dai, Xuewu, Zou, Yiqun
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Axons; Circuits; Consumer goods; Convergence; convergence analysis; Couplings; Differential equations; Entropy; equivalent electric circuit; extended Hodgkin-Huxley model; information entropy; Integrated circuit modeling; Ions; iterative learning; Iterative methods; kernel density estimation; Machine learning; Mathematical model; Mathematical models; Membrane potentials; Membranes; Mutual coupling; Neural coupling analysis; Ordinary differential equations; statistical description; System identification
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2020.3037816

This paper investigates the interaction phenomena of the coupled axons while the mutual coupling factor is presented as a pairwise description. Based on the Hodgkin-Huxley model and the coupling factor matrix, the membrane potentials of the coupled myelinated/unmyelinated axons are quantified which implies that the neural coupling can be characterised by the presented coupling factor. Meanwhile the equivalent electric circuit is supplied to illustrate the physical meaning of this extended model. In order to estimate the coupling factor, a data-based iterative learning identification algorithm is presented where the Rényi entropy of the estimation error has been minimised. The convergence of the presented algorithm is analysed and the learning rate is designed. To verified the presented model and the algorithm, the numerical simulation results indicate the correctness and the effectiveness. Furthermore, the statistical description of the neural coupling, the approximation using ordinary differential equation, the measurement and the conduction of the nerve signals are discussed respectively as advanced topics. The novelties can be summarised as follows: 1) the Hodgkin-Huxley model has been extended considering the mutual interaction between the neural axon membranes, 2) the iterative learning approach has been developed for factor identification using entropy criterion, and 3) the theoretical framework has been established for this class of system identification problems with convergence analysis.