A Deterministic Approach to Quantifying Hearing Temporary Threshold Shift

This study investigates the dynamics of cochlear hair cell populations under environmental stressors such as prolonged exposure to loud noise from earphones. To understand potential temporary hearing loss dynamics due to earphones, a mathematical model is developed in this investigation to capture the behavior of healthy, fatigued, and impaired hair cells in response to varying sound intensities, described by differential equations incorporating sound intensity and its regulation. The model is scaled and analysis of the system's steady states show that two endemic equilibria exist, with local asymptotic stability investigated using the Jacobian matrix. Results show that there is a critical level of sound exposure above which the auditory system can no longer maintain a healthy state, leading to long-term hearing impairment. Simulation results show that for a given intensity level, hearing loss is inevitable for certain for specific Temporary Threshold Shift (TTS). We are able to quantify healthy and acceptable TTS levels, beyond which there are no healthy, fatigued or impaired hair cells. The results can be used to predict hearing impairment outcomes and guide evidence-based interventions to mitigate the adverse effects of prolonged low-pressure sound exposure on auditory health.