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Viewing the audiogram through a mathematical model.

T McGee1, N Kraus, C Wolters

  • 1Siegel Institute, Michael Reese Medical Center, Chicago, Illinois.

Ear and Hearing
|June 1, 1988
PubMed
Summary
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This study introduces a new mathematical model to quantify audiometric results using a hyperbolic tangent function. The model effectively describes audiogram features and their correlation with clinical data.

Area of Science:

  • Audiology
  • Biomedical Engineering
  • Mathematical Modeling

Background:

  • Accurate quantification of audiometric results is crucial for clinical diagnosis and research.
  • Traditional audiogram analysis may not fully capture the nuances of hearing thresholds across frequencies.
  • Developing advanced models can improve the interpretation of audiological data.

Purpose of the Study:

  • To develop and validate a hyperbolic tangent function model for quantifying audiometric results.
  • To describe salient features of audiograms using model parameters.
  • To assess the correlation between different audiometric thresholds using the proposed model.

Main Methods:

  • Modeled audiograms using the hyperbolic tangent function: t = a tanh [(f-c)/b] + d.

Related Experiment Videos

  • Determined model parameters (a, b, c, d) via least-squares nonlinear curve fitting.
  • Analyzed a dataset of 500 Hz Auditory Brainstem Response (ABR) and behavioral thresholds from 28 ears.

    • Main Results:

    • The hyperbolic tangent function effectively models audiogram data.
    • Model parameters (a, b, c, d) provide quantitative descriptions of audiogram features, including slope and midpoint.
    • The model revealed that agreement between ABR and behavioral thresholds varies with audiometric configuration.

    Conclusions:

    • The hyperbolic tangent function offers a robust method for quantifying entire audiograms.
    • This approach facilitates simple correlations with routinely collected clinical data.
    • The model's application demonstrates its utility in understanding the relationship between different hearing threshold measures.