A Neurophysiological Approach for Evaluating Noise-Induced Sleep Disturbance: Calculating the Time Constant of the Dynamic Characteristics in the Brainstem

Abstract

Chronic sleep disturbance induced by traffic noise is considered to cause environmental sleep disorder, which increases the risk of cardiovascular disease, stroke, diabetes and other stress-related diseases. However, noise indices for the evaluation of sleep disturbance are not based on the neurophysiological process of awakening regulated by the brainstem. In this study, through the neurophysiological approach, we attempted (1) to investigate the thresholds of awakening due to external stimuli in the brainstem; (2) to evaluate the dynamic characteristics in the brainstem and (3) to verify the validity of existing noise indices. Using the mathematical Phillips-Robinson model, we obtained thresholds of awakening in the brainstem for different durations of external stimuli. The analysis revealed that the brainstem seemed insensitive to short stimuli and that the response to external stimuli in the brainstem could be approximated by a first-order lag system with a time constant of 10-100 s. These results suggest that the brainstem did not integrate sound energy as external stimuli, but neuroelectrical signals from auditory nerve. To understand the awakening risk accumulated in the brainstem, we introduced a new concept of "awakening potential" instead of sound energy.

Keywords: Phillips–Robinson model; brainstem; neurophysiology; sleep disturbance; time constant.

Figure 1

Illustration of the schematic diagram of the Phillips–Robinson model. The monoaminergic (MA) and ventrolateral preoptic nucleus (VLPO) nuclei are activated by external drives that influence sleep stages, external stimuli, as well as internal circadian and homeostatic drives. Mutual inhibition between the MA and VLPO comprises the sleep-wake switch.

Figure 2

The behavior of the potential, $\mathbf{V}\left(t\right)$, in response to external stimuli. The nullclines of $V_v$ and $V_m$ and their intersection, ${\mathbf{V}}_{\mathbf{0}}$, were obtained from Equation (2). $\mathbf{V}\left(t\right)$ moves upward in response to a stimulus (thick black line) before returning to ${\mathbf{V}}_{\mathbf{0}}$ (grey line).

Figure 3

Relationship between the time to return to the sleep node, $t_{\mathrm{lat}}$, and the strength of the external stimulus, $D_{\mathrm{ext}}$. The neuroelectrical threshold of awakening, $D_{\mathrm{ext}}^{*}$, is defined as the point at which the return time ascent is the steepest.

Figure 4

Relationship between neuroelectrical thresholds of awakening in response to external stimuli and varied duration of external stimuli using different values of $D_v$ and A.

Figure 5

Relationship between neuroelectrical thresholds of awakening in response to external stimuli and varied duration of external stimuli, where a first-order lag system was applied to the thresholds (see Equation (7)) using different values of the time constant, $t_{\mathrm{c}}$.

Figure 6

Relationship between neuroelectrical thresholds of awakening in response to external stimuli and the duration of the external stimuli using different values of ${\tau }_m$ and ${\tau }_v$.

Figure 7

Experimental and mathematical results (see Table 1, white and black circles) and conversion curves of neuroelectrical stimuli to sound pressure levels. Note that the threshold falling after five minutes (black circle) was excluded from the calculation for obtaining conversions.

Figure 8

Average awakening levels using $L_{\mathrm{Amax},\mathrm{fast}}$ and sound exposure level (SEL), where $A=1.3$ (mV) and $D_v=3.0$ (mV). Equations (12) through (14) were used to convert neuroelectrical thresholds into sound levels.