How to discern external acoustic waves in a piezoelectric neuron under noise?

Abstract

Biological neurons keep sensitive to external stimuli and appropriate firing modes can be triggered to give effective response to external chemical and physical signals. A piezoelectric neural circuit can perceive external voice and nonlinear vibration by generating equivalent piezoelectric voltage, which can generate an equivalent trans-membrane current for inducing a variety of firing modes in the neural activities. Biological neurons can receive external stimuli from more ion channels and synapse synchronously, but the further encoding and priority in mode selection are competitive. In particular, noisy disturbance and electromagnetic radiation make it more difficult in signals identification and mode selection in the firing patterns of neurons driven by multi-channel signals. In this paper, two different periodic signals accompanied by noise are used to excite the piezoelectric neural circuit, and the signal processing in the piezoelectric neuron driven by acoustic waves under noise is reproduced and explained. The physical energy of the piezoelectric neural circuit and Hamilton energy in the neuron driven by mixed signals are calculated to explain the biophysical mechanism of auditory neuron when external stimuli are applied. It is found that the neuron prefers to respond to the external stimulus with higher physical energy and the signal which can increase the Hamilton energy of the neuron. For example, stronger inputs used to inject higher energy and it is detected and responded more sensitively. The involvement of noise is helpful to detect the external signal under stochastic resonance, and the additive noise changes the excitability of neuron as the external stimulus. The results indicate that energy controls the firing patterns and mode selection in neurons, and it provides clues to control the neural activities by injecting appropriate energy into the neurons and network.

Keywords: Firing patterns; Hamilton energy; Noise; Piezoelectric neuron; Stochastic resonance.

Fig. 1

Schematic diagram for signal encoding in the auditory neurons in the brain in presence of two signal sources under noise

Fig. 2

Schematic diagram for piezoelectric neural circuit driven by more than two acoustic waves in presence of Gaussian white noise. NR represents a nonlinear resistor, PC denotes a piezoelectric ceramic, C, L and E describe the capacitor, induction coil, and constant voltage source, respectively. R_s and R are linear resistors and the constant E is used to describe the reversal potential of the ion channel

Fig. 3

Evolution of firing patterns, Hamilton energy, SNR, and ISI bifurcation in the piezoelectric neuron driven by periodic signals. For (a), F₁ is applied with A₁ = 0.26, f₁ = 0.015, then F₁ is applied and noise intensity is changed for getting SNR; (b) F₂ is applied with A₂ = 0.31, f₂ = 0.015, then F₂ is applied and noise intensity is changed for getting SNR; (c) F₃ is applied with A₃ = 1.07, f₃ = 0.015, then F₃ is applied and noise intensity is changed for getting SNR. The parameters are selected as a = 0.7, b = 0.8, c = 0.1, and ξ = 0.175, and the initial values are selected as (0.2, 0.1) in Eq. (5). The inserted subfigure shows the formed attractors under the same parameter setting

Fig. 4

(a) Evolution of membrane potential and Hamilton energy in the neuron driven by two periodic signals (F₁ + F₂) synchronously in absence of noise. (b) SNR distribution and ISI bifurcation under noise. (c) Firing patterns and Hamilton energy under noise D = 3. The parameters are selected as a = 0.7, b = 0.8, c = 0.1, ξ = 0.175, A₁ = 0.26, f₁ = 0.015, A₂ = 0.31, and f₂ = 0.015, and the initial values are selected as (0.2, 0.1) in Eq. (5). The inserted subfigure shows the formed attractors under the same parameters setting

Fig. 5

(a) Evolution of membrane potential and Hamilton energy in the neuron driven by two periodic signals (F₁ + F₃) synchronously in absence of noise. (b) SNR distribution and ISI bifurcation under noise. (c) Firing patterns and Hamilton energy under noise D = 17. The parameters are selected as a = 0.7, b = 0.8, c = 0.1, ξ = 0.175, A₁ = 0.26, f₁ = 0.015, A₂ = 1.07, and f₂ = 0.015, and the initial values are selected as (0.2, 0.1) in Eq. (5). The inserted subfigure shows the formed attractors under the same parameters setting

Fig. 6

Evolution of firing patterns (a); Hamilton energy (b); SNR (c); and ISI bifurcation (d) in the auditory neuron driven by chaotic signals under noise. The parameters are fixed at α = 10, β = 16, γ = 0.01, m₀ =  − 1.296, m₁ =  − 0.7364, a = 0.7, b = 0.8, c = 0.1, ξ = 0.175, A₁ = 0.26, and f₁ = 0.015_, and initial values are selected as (0.2, 0.1) in Eq. (5), and (0.01, 0.1, 1.0) in Eq. (10). The inserted subfigure shows the formed attractors under the same parameters setting

Fig. 7

(a) Evolution of membrane potential and Hamilton energy in the neuron driven by periodic and chaotic signals (F₁ + F₄) synchronously in absence of noise. (b) SNR distribution and ISI bifurcation under noise. (c) Firing patterns and Hamilton energy under noise D = 90. The parameters are fixed at α = 10, β = 16, γ = 0.01, m₀ =  − 1.296, m₁ =  − 0.7364, a = 0.7, b = 0.8, c = 0.1, ξ = 0.175, A₁ = 0.26, and f₂ = 0.015, and initial values are selected as (0.2, 0.1) in Eq. (5), and (0.01, 0.1, 1.0) in Eq. (10). The inserted subfigure shows the formed attractors under the same parameters setting

Fig. 8

(a) Evolution of membrane potential and Hamilton energy in the neuron driven by periodic and chaotic signals (F₃ + F₄) synchronously in absence of noise. (b) SNR distribution and ISI bifurcation under noise. (c) Firing patterns and Hamilton energy under noise D = 17. The parameters are fixed at α = 10, β = 16, γ = 0.01, m₀ =  − 1.296, m₁ =  − 0.7364, a = 0.7, b = 0.8, c = 0.1, ξ = 0.175, A₃ = 1.07, and f₂ = 0.015, and initial values are selected as (0.2, 0.1) in Eq. (5), and (0.01, 0.1, 1.0) in Eq. (10). The inserted subfigure shows the formed attractors under the same parameters setting