Viewing the Audiogram through a Mathematical Model*

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Abstract
In an effort to better quantify audiometric results, audiograms were modeled with a hyperbolic tangent function of the form: t = a tanh [(f.sbd.c)/b] + d, where t = threshold and f = frequency. The parameters, a, b, c, and d, were determined for a specific audiogram via a least-squares nonlinear curve fitting technique. The parameters describe salient features of the audiogram. The point (c,d) is the midpoint of the sloping portion of the audiogram, while a and b describe the slope. Other features of the configuration can be described by combinations fo the parameters. This approach quantifies the entire audiogram and allows simple correlations of routinely gathered clinical data. To demonstrate the application of the model, a small data set of 500 Hz ABR and behavioral thresholds recorded from 28 ears (23 subjects) was analyzed. The model showed that agreement between the thresholds varied with audiometric configuration.