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. 2018 Mar 1:12:122.
doi: 10.3389/fnins.2018.00122. eCollection 2018.

The Energy Coding of a Structural Neural Network Based on the Hodgkin-Huxley Model

Zhenyu Zhu  1 , Rubin Wang  1 , Fengyun Zhu  1
Affiliations

The Energy Coding of a Structural Neural Network Based on the Hodgkin-Huxley Model

Zhenyu Zhu et al. Front Neurosci. .

Abstract

Based on the Hodgkin-Huxley model, the present study established a fully connected structural neural network to simulate the neural activity and energy consumption of the network by neural energy coding theory. The numerical simulation result showed that the periodicity of the network energy distribution was positively correlated to the number of neurons and coupling strength, but negatively correlated to signal transmitting delay. Moreover, a relationship was established between the energy distribution feature and the synchronous oscillation of the neural network, which showed that when the proportion of negative energy in power consumption curve was high, the synchronous oscillation of the neural network was apparent. In addition, comparison with the simulation result of structural neural network based on the Wang-Zhang biophysical model of neurons showed that both models were essentially consistent.

Keywords: energy distribution; negative energy; neural energy coding; power consumption curve; synchronous oscillation.

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Figures

Figure 1
Figure 1
The equivalent circuit diagram of the Hodgkin–Huxley model.
Figure 2
Figure 2
The action potential and corresponding power consumption curve.
Figure 3
Figure 3
The schematic of a fully connected structural neural network.
Figure 4
Figure 4
Total power consumed by the overall network of 20 neurons and the spike record under continuous stimulus. The coupling strength is uniformly distributed in [0, 0.5]; the signal transmitting delay is uniformly distributed in [0.3 ms, 1.8 ms].
Figure 5
Figure 5
The total power consumption and the spike record of the overall network under continuous stimulus. The number of neurons in (A–D) are 30, 50, 100, 200, respectively. The coupling strength is uniformly distributed in [0, 0.5]; the signal transmitting delay is uniformly distributed in [0.3 ms, 1.8 ms]. The periodicity of the total power consumption curve is increasingly apparent and the spike record exhibits clear streaks with the increasing size of the network which indicates the synchronization of neuronal activity is getting stronger.
Figure 6
Figure 6
The total power consumption and the spike record of the overall network under continuous stimulus. The distribution interval of the coupling strength in (A–E) are [0, 0.05], [0, 0.1], [0, 0.3], [0, 0.5], [0, 1], respectively. The number of neurons is 100 and the signal transmitting delay is uniformly distributed in [0.3 ms, 1.8 ms]. The periodicity of the total power consumption curve and the synchronization of the network are positively correlated to the coupling strength.
Figure 7
Figure 7
(A) The total power consumption and the spike record of the overall network under continuous stimulus. The distribution interval of the signal transmitting delay in (A–D) are [0.1 ms, 1.6 ms], [0.3 ms, 1.8 ms], [0.5 ms, 2.0 ms], [0.7 ms, 2.2 ms], respectively. The number of neurons is 100 and the coupling strength is uniformly distributed in [0, 1]. The periodicity of the total power consumption curve and the synchronization of the network are negatively correlated to the signal transmitting delay.
Figure 8
Figure 8
(A) The curve of α and ρmean varies as a function of the number of neurons in the network based on the Hodgkin–Huxley model; (B) The curves of α and ρmean vary as a function of the number of neurons in the network based on Wang–Zhang biophysics model (Wang et al., ; Wang and Wang, 2014).
Figure 9
Figure 9
(A) The curve of α and ρmean varies with different distribution intervals of coupling strength in the network based on the Hodgkin–Huxley model; (B) The curves of α and ρmean varies with different distribution intervals of coupling strength in the network based on Wang–Zhang biophysical model (Wang et al., ; Wang and Wang, 2014).
Figure 10
Figure 10
(A) The curve of α and ρmean varies with different distribution intervals of signal transmitting delay in the network based on the Hodgkin–Huxley model; (B) The curve of α and ρmean varies with different distribution intervals of signal transmitting delay in the network based on Wang–Zhang biophysical model (Wang et al., ; Wang and Wang, 2014).
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