Average middle ear frequency response curves with preservation of curve morphology characteristics

Abstract

For the validation of modelling results or the comparison of middle ear interventions, such as prostheses placement, average responses of middle ear vibrations are needed. One such response is the amplitude and phase of the vibration of the stapes footplate as a function of frequency. Average responses and their standard deviation are commonly obtained by calculating the mean of a number of measured responses at each frequency. A typical middle ear magnitude response curve shows a number of distinct peaks, and the location of these peaks varies between ears. By simply taking an average along the magnitude or phase response axis, the typical fine structure of the response curve is flattened out, delivering an average curve which no longer has the typical morphology of an individual response curve. This paper introduces methods to avoid this problem by first aligning the typical curve features along the frequency axis prior to calculating the average along the magnitude or phase axis, resulting in average magnitude and phase curves which maintain the typical morphology of the curve obtained for an individual ear. In the method, landmark points on the response magnitude curves are defined and the frequencies at which these points occur are averaged. Next, these average frequencies are used to align the landmark points between curves, prior to averaging values along the magnitude or phase axes. Methods for semi-automatic and manual assignment of landmark points and curve alignment are presented. After alignment, the correspondence between the original landmark frequencies and aligned frequencies is obtained together with the warping function which maps each original magnitude curve to its aligned version. The phase curves are aligned using the warping functions determined from the corresponding magnitude curves. Finally, a method is proposed to compare the data set of an individual measurement or model result to an aligned average curve in terms of magnitude and frequency by applying the alignment procedure to the individual curve.

Methods and reference data for middle ear transfer functions

“…A recently published modal analysis of METF measurements shows a rather large standard deviation for the frequency distribution of the natural frequencies of the middle ear 37 , which contributes to the large interspecimen variance. A parametric evaluation of the METF data as published by Gladiné 38 may therefore be an interesting subject of further research.…”

Mimicking the Human Tympanic Membrane: The Significance of Scaffold Geometry

“…An averaging algorithm capable of preserving the curve morphology was implemented for the analysis of LDV measurements. [44] For each measurement, the first resonance frequency was defined as the only landmark to be registered. The code provided by Ramsay et al was utilized for this curve registration approach on MATLAB (R2018b, The MathWorks Inc., USA).…”

Mimicking the Human Tympanic Membrane: the Significance of Geometry

“…The statistical tests were performed with GraphPad Prism 8 (GraphPad Software, USA), where the statistical significances were determined by applying a one-way or two-way analysis of variance (ANOVA) followed by a Tukey’s honestly significant difference (HSD) post-hoc test (*p <0.05, **p <0.01, ***p <0.005, ****p <0.0001 and ns for p >0.05). An averaging algorithm capable of preserving the curve morphology was implemented for the analysis of LDV measurements [47]. For each measurement, the first resonance frequency was defined as the only landmark to be registered.…”