^{a)}

^{a)}A preliminary form of this research was presented at the 2012 meeting of the Association for Research in Otolaryngology.

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### Abstract

A click-evoked otoacoustic emission (CEOAE) has group delay and spread as first- and second-order temporal moments varying over frequency, and instantaneous frequency and bandwidth as first- and second-order spectral moments varying over time. Energy-smoothed moments were calculated from a CEOAE database over 0.5–15 kHz bandwidth and 0.25–20 ms duration. Group delay and instantaneous frequency were calculated without phase unwrapping using a coherence synchrony measure that accurately classified ears with hearing loss. CEOAE moment measurements were repeatable in individual ears. Group delays were similar for CEOAEs and stimulus-frequency OAEs. Group spread is a frequency-specific measure of temporal spread in an emission, related to spatial spread across tonotopic generation sites along the cochlea. In normal ears, group delay and spread increased with frequency and decreased with level. A direct measure of cochlear tuning above 4 kHz was analyzed using instantaneous frequency and bandwidth. Synchronized spontaneous OAEs were present in most ears below 4 kHz, and confounded interpretation of moments. In ears with sensorineural hearing loss, group delay and spread varied with audiometric classification and amount of hearing loss; group delay differed between older males and females. CEOAE moments reveal clinically relevant information on cochlear tuning in ears with normal and impaired hearing.

The author is grateful to the following individuals. John Ellison, Denis Fitzpatrick, and Shawn Goodman assisted in OAE data collection, database management and helpful discussions, Daniel Rasetshwane performed the microphone calibration, Dawna Lewis discussed patterns of hearing loss found in patients receiving medical services at BTNRH, and Judy Dubno shared audiometric data in older subjects from the Medical University of South Carolina. This research was supported by NIH Grant No. DC003784 with core support from Grant No. DC04662.

I. INTRODUCTION

A. Background on CEOAE timing in adult ears

II. METHODS

A. Subjects

B. General OAE procedures

C. CEOAE procedures

D. SSOAE procedures

E. Analytic signal

F. Multi-window analyses to improve SNR

III. THEORY UNDERLYING CEOAE MOMENTS

A. Phase and level gradient calculations

B. Smoothing of moments

C. OAE detection criteria based on SNR and CSM

IV. RESULTS

A. Individual ear results

1. SSOAEs

2. CEOAEs

B. Group results on SSOAEs

C. Group results on CEOAE moments

D. OAE predictions of SNHL

E. CEOAE moments in ears with sloping SNHL

F. Frequency-specific GD and GS in ears with SNHL

G. CEOAEs in older adults with SNHL

V. DISCUSSION

A. CEOAE moments in ears with normal hearing

B. CEAOE moments as measures of tuning

C. Improved CEOAE procedures to detect SNHL

D. CEOAE moments in ears with SNHL

E. Aging effects

VI. CONCLUDING REMARKS

## Figures

(Color online) Temporal SNR plotted (subject A) for originally measured CEOAE waveform (“no window” in legend), and waveforms from low-, mid-, and high-frequency bandpass-filtered spectra (line styles in legend). SNR plotted as level (in dB).

(Color online) Temporal SNR plotted (subject A) for originally measured CEOAE waveform (“no window” in legend), and waveforms from low-, mid-, and high-frequency bandpass-filtered spectra (line styles in legend). SNR plotted as level (in dB).

Cumulative sums of phasors of CEOAE spectrum plotted at three frequencies close to 8 kHz (left) and close to 15 kHz (right). Solid-line circle is circle of radius one; dashed-line circle is a circle ofradius Circle marker at the end of each line segment denotes its CSM across all 32 buffers. Each cumulative sum of phasors labeled by its spectral frequency (in kHz).

Cumulative sums of phasors of CEOAE spectrum plotted at three frequencies close to 8 kHz (left) and close to 15 kHz (right). Solid-line circle is circle of radius one; dashed-line circle is a circle ofradius Circle marker at the end of each line segment denotes its CSM across all 32 buffers. Each cumulative sum of phasors labeled by its spectral frequency (in kHz).

SSOAE response vs frequency (subject A) in left column (left ear) and right column (right ear) for tests 1 and 2. Row 1: CSM (lines), triangle markers at SSOAE peak frequencies: apex up for SSOAEs in test 1 and down for test 2. (dotted line). Row 2: in test 1 for SSOAEs (solid line) and noise (dotted line). Triangles specify peaks from CSM in row 1. Row 3: in test 2 using similar format to row 2. Row 4: CSM Sum. Upper row of numbers are # of SSOAEs at each frequency for test 1, and lower row for test 2.

SSOAE response vs frequency (subject A) in left column (left ear) and right column (right ear) for tests 1 and 2. Row 1: CSM (lines), triangle markers at SSOAE peak frequencies: apex up for SSOAEs in test 1 and down for test 2. (dotted line). Row 2: in test 1 for SSOAEs (solid line) and noise (dotted line). Triangles specify peaks from CSM in row 1. Row 3: in test 2 using similar format to row 2. Row 4: CSM Sum. Upper row of numbers are # of SSOAEs at each frequency for test 1, and lower row for test 2.

CEOAE data in subject A (left ear) shown in columns 1 and 2 for test 1, and columns 3 and 4 for test 2. Columns 1 and 3 with time abscissa*—*Row 1: Mean CEOAE waveform. Row 2: CSM (left ordinate, solid line) and (dotted line). SNR (right ordinate, dashed line) and (dash-dot line). Row 3: Mean SE of IF (solid line) and IB (dashed line). Mean SE of CEOAE waveform zero-crossing rate () (dash-dot line). Dotted line slope of −1. Columns 2 and 4 with frequency abscissa*—*Row 1: CEOAE spectrum level (solid line). Mean CEOAE signal spectrum level (black line, marker ○); mean CEOAE noise spectrum level (dashed line, marker ×). Triangles placed above SSOAE frequencies as in Fig. 3. Row 2: CSM (left ordinate, solid line) and (dotted line). SNR (right ordinate, dashed line) and (dash-dot line). Row 3: Mean SE of GD (solid line) and GS (dashed line). Dotted line slope of −1.

CEOAE data in subject A (left ear) shown in columns 1 and 2 for test 1, and columns 3 and 4 for test 2. Columns 1 and 3 with time abscissa*—*Row 1: Mean CEOAE waveform. Row 2: CSM (left ordinate, solid line) and (dotted line). SNR (right ordinate, dashed line) and (dash-dot line). Row 3: Mean SE of IF (solid line) and IB (dashed line). Mean SE of CEOAE waveform zero-crossing rate () (dash-dot line). Dotted line slope of −1. Columns 2 and 4 with frequency abscissa*—*Row 1: CEOAE spectrum level (solid line). Mean CEOAE signal spectrum level (black line, marker ○); mean CEOAE noise spectrum level (dashed line, marker ×). Triangles placed above SSOAE frequencies as in Fig. 3. Row 2: CSM (left ordinate, solid line) and (dotted line). SNR (right ordinate, dashed line) and (dash-dot line). Row 3: Mean SE of GD (solid line) and GS (dashed line). Dotted line slope of −1.

SSOAE normal group data using mean SE. Test 1 data in left column; magnitude difference data from tests 1 and 2 plotted in right column. Left column*—*Row 1: Number (NF) of SSOAEs per frequency bin. Row 2: CSM Sum. Separate plots for left/right ears slightly displaced along abscissa for clarity. Right column*—*Row 1: , magnitude difference in NF. Row 2: Sum, magnitude difference in CSM Sum.

SSOAE normal group data using mean SE. Test 1 data in left column; magnitude difference data from tests 1 and 2 plotted in right column. Left column*—*Row 1: Number (NF) of SSOAEs per frequency bin. Row 2: CSM Sum. Separate plots for left/right ears slightly displaced along abscissa for clarity. Right column*—*Row 1: , magnitude difference in NF. Row 2: Sum, magnitude difference in CSM Sum.

CEOAE-moment normal group data using mean SE. Left column, time abscissa*—*Row 1: CSM (solid line) and (dotted line) [left ordinate], and SNR (dashed line) and (dashed-dotted line) [right ordinate]. Row 2: IF and IB. # of ears at each time listed at bottom for detected IF and IB. Dotted line slope of −1. Right column, frequency abscissa*—*Row 1: CSM (solid line) and (dotted line) [left ordinate], and SNR (dashed line) and (dashed-dotted line) [right ordinate]. Row 2: GD and GS. # of ears at each frequency listed at bottom for detected GD and GS. Dotted line slope of −1.

CEOAE-moment normal group data using mean SE. Left column, time abscissa*—*Row 1: CSM (solid line) and (dotted line) [left ordinate], and SNR (dashed line) and (dashed-dotted line) [right ordinate]. Row 2: IF and IB. # of ears at each time listed at bottom for detected IF and IB. Dotted line slope of −1. Right column, frequency abscissa*—*Row 1: CSM (solid line) and (dotted line) [left ordinate], and SNR (dashed line) and (dashed-dotted line) [right ordinate]. Row 2: GD and GS. # of ears at each frequency listed at bottom for detected GD and GS. Dotted line slope of −1.

Magnitude difference (mean SE) in subset of normal ears () between tests 1 and 2 for CSM and SNR, and CEOAE moments. Left column, time abscissa*—*Row 1: (solid line) and (dotted line) [left ordinate], and (dashed line) and (dashed-dotted line) [right ordinate]. Row 2: and . Dotted line slope of −1. Right column, frequency abscissa*—*Row 1: CSM (solid line) and (dotted line) [left ordinate], and SNR (dashed line) and (dashed-dotted line) [right ordinate]. Row 2: and . Dotted line slope of −1.

Magnitude difference (mean SE) in subset of normal ears () between tests 1 and 2 for CSM and SNR, and CEOAE moments. Left column, time abscissa*—*Row 1: (solid line) and (dotted line) [left ordinate], and (dashed line) and (dashed-dotted line) [right ordinate]. Row 2: and . Dotted line slope of −1. Right column, frequency abscissa*—*Row 1: CSM (solid line) and (dotted line) [left ordinate], and SNR (dashed line) and (dashed-dotted line) [right ordinate]. Row 2: and . Dotted line slope of −1.

Normalized GD and GS (mean SE) as ratios of GD and GS, respectively, to sample period (units, # periods) over stimulus peSPL range 43–73 dB. Left: Normalized GD from CEOAEs. Fit line of normalized GD for SFOAEs (dotted line) with 90th percentiles of fit (gray shading) (Shera *et al.*, 2010). CEOAE latency at 73 dB peSPL (Goodman *et al.*, 2009). Right: Normalized GS from CEOAEs. (Data displaced horizontally for clarity.)

Normalized GD and GS (mean SE) as ratios of GD and GS, respectively, to sample period (units, # periods) over stimulus peSPL range 43–73 dB. Left: Normalized GD from CEOAEs. Fit line of normalized GD for SFOAEs (dotted line) with 90th percentiles of fit (gray shading) (Shera *et al.*, 2010). CEOAE latency at 73 dB peSPL (Goodman *et al.*, 2009). Right: Normalized GS from CEOAEs. (Data displaced horizontally for clarity.)

Normalized IF and IB (mean SE) as products of IF and IB, respectively, and sample period (units, # cycles) over stimulus peSPL range 43–73 dB. Left: normalized IF from CEOAEs. Mean standard deviation of normalized zero-crossing rate (Kemp, 1978). Right: normalized IB from CEOAEs. (Data displaced horizontally for clarity.)

Normalized IF and IB (mean SE) as products of IF and IB, respectively, and sample period (units, # cycles) over stimulus peSPL range 43–73 dB. Left: normalized IF from CEOAEs. Mean standard deviation of normalized zero-crossing rate (Kemp, 1978). Right: normalized IB from CEOAEs. (Data displaced horizontally for clarity.)

Mean IF (dashed line) and inverse GD (solid line) in normal group plotted at stimulus peSPLs of 73 dB (left) and 67 dB (right). Dotted line shows (tonal frequency versus inverse of its period).

Mean IF (dashed line) and inverse GD (solid line) in normal group plotted at stimulus peSPLs of 73 dB (left) and 67 dB (right). Dotted line shows (tonal frequency versus inverse of its period).

Parametric scatter plots of vs in normal ears at stimulus peSPLs from 73 dB down to 55 dB. Regression model fit (solid line) and 95% CI (dashed lines). Model intercept at ms and exponent i.e.,

Parametric scatter plots of vs in normal ears at stimulus peSPLs from 73 dB down to 55 dB. Regression model fit (solid line) and 95% CI (dashed lines). Model intercept at ms and exponent i.e.,

Parametric scatter plots of vs in normal ears at stimulus peSPLs from 73 dB down to 55 dB. Regression model fit (solid line) and 95% CI (dashed lines) for subset of data with kHz. Model intercept at kHz and exponent i.e.,

Parametric scatter plots of vs in normal ears at stimulus peSPLs from 73 dB down to 55 dB. Regression model fit (solid line) and 95% CI (dashed lines) for subset of data with kHz. Model intercept at kHz and exponent i.e.,

AUC at stimulus peSPLs of 73 dB (upper left), 67 dB (upper right) and 61 dB (lower left) using CEOAE predictors CSM(t), CSM(f), SNR(f), and CSM(t,f). As specified by markers at bottom of legend, tops rows in each panel list frequencies at which one of a pair of predictors is more accurate than another (at ).

AUC at stimulus peSPLs of 73 dB (upper left), 67 dB (upper right) and 61 dB (lower left) using CEOAE predictors CSM(t), CSM(f), SNR(f), and CSM(t,f). As specified by markers at bottom of legend, tops rows in each panel list frequencies at which one of a pair of predictors is more accurate than another (at ).

CEOAE moments at 73 dB peSPL in sloping SNHL re: normal group. Left column with frequency abscissa—Top: Audiometric HL for sloping-loss groups. Middle: in GD for SNHL re: normal groups. Significant changes () indicated by marker above frequency (top of panel). Similar plotting style used in remaining panels. Bottom: Right column with time abscissa—Middle: Bottom:

CEOAE moments at 73 dB peSPL in sloping SNHL re: normal group. Left column with frequency abscissa—Top: Audiometric HL for sloping-loss groups. Middle: in GD for SNHL re: normal groups. Significant changes () indicated by marker above frequency (top of panel). Similar plotting style used in remaining panels. Bottom: Right column with time abscissa—Middle: Bottom:

At 73 dB peSPL, the prevalence (in %) for CEOAE detection (left ordinate) for CSM (solid line) and SNR (dashed line) vs HL at octave frequencies 0.5, 1, 2, 4, and 8 kHz. Number of ears per HL bin (in 5 dB bins) also plotted (right ordinate, dotted line, diamond markers). Total # of test ears listed in title. (CSM/SNR data displaced horizontally for clarity.)

At 73 dB peSPL, the prevalence (in %) for CEOAE detection (left ordinate) for CSM (solid line) and SNR (dashed line) vs HL at octave frequencies 0.5, 1, 2, 4, and 8 kHz. Number of ears per HL bin (in 5 dB bins) also plotted (right ordinate, dotted line, diamond markers). Total # of test ears listed in title. (CSM/SNR data displaced horizontally for clarity.)

At 73 dB peSPL, normal-group median GD plotted (horizontal dashed line) with median listed to left of line (e.g., 4 periods at 0.5 kHz), and IQR plotted (gray shading). Scatter plot of SNHL ears shows GD vs HL with × marker. Regression model for SNHL ears (solid line) with 95% CI (dotted lines). Text lists regression slope (i.e., ) and

At 73 dB peSPL, normal-group median GD plotted (horizontal dashed line) with median listed to left of line (e.g., 4 periods at 0.5 kHz), and IQR plotted (gray shading). Scatter plot of SNHL ears shows GD vs HL with × marker. Regression model for SNHL ears (solid line) with 95% CI (dotted lines). Text lists regression slope (i.e., ) and

At 73 dB peSPL, normal-group median GS plotted (horizontal dashed line) with median listed to left of line (e.g., 0.8 periods at 0.5 kHz), and IQR plotted (gray shading). Scatter plot of SNHL ears shows GS vs HL with × marker. Regression model for SNHL ears (solid line) with 95% CI (dotted lines). Text lists regression slope (i.e., ) and

At 73 dB peSPL, normal-group median GS plotted (horizontal dashed line) with median listed to left of line (e.g., 0.8 periods at 0.5 kHz), and IQR plotted (gray shading). Scatter plot of SNHL ears shows GS vs HL with × marker. Regression model for SNHL ears (solid line) with 95% CI (dotted lines). Text lists regression slope (i.e., ) and

Audiograms in older males and females from MUSC study (Dubno *et al.*, 2008) and current study (BTNRH).

Audiograms in older males and females from MUSC study (Dubno *et al.*, 2008) and current study (BTNRH).

Rows 1 and 2—For older females tested at 73 dB peSPL, % prevalence for CEOAE detection (left ordinate) vs HL for CSM (solid line). Number of ears per HL bin (in 5 dB bins) also plotted (right ordinate, dotted line, diamond marker). Title lists audiometric frequency and total # of test ears. Rows 3 and 4 show similar results for older male ears.

Rows 1 and 2—For older females tested at 73 dB peSPL, % prevalence for CEOAE detection (left ordinate) vs HL for CSM (solid line). Number of ears per HL bin (in 5 dB bins) also plotted (right ordinate, dotted line, diamond marker). Title lists audiometric frequency and total # of test ears. Rows 3 and 4 show similar results for older male ears.

For tests at 73 dB peSPL, normalized GD vs HL of older female ears (marker ×). Regression model (solid line) with 95% CI (dotted lines). Text lists model slope and For comparison, median GD (horizontal dashed line) and IQR (gray shading) of younger normal group are shown; median GD listed (left of line). Five panels show data for older females at octaves 0.5–8 kHz. Lower right panel shows GD vs HL at 2.0 kHz for older males (marker ○).

For tests at 73 dB peSPL, normalized GD vs HL of older female ears (marker ×). Regression model (solid line) with 95% CI (dotted lines). Text lists model slope and For comparison, median GD (horizontal dashed line) and IQR (gray shading) of younger normal group are shown; median GD listed (left of line). Five panels show data for older females at octaves 0.5–8 kHz. Lower right panel shows GD vs HL at 2.0 kHz for older males (marker ○).

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