Auditory Evoked Potentials
The Quantification of Pure-tone Audiograms and Auditory Brain Stem Evoked Responses Using Mathematical Modeling Procedures Veronica Smyth, BA, MEdSt, PhD; S. Ravichandran, BSpThy(Hons); K. Capell, BSc, PhD Department of Speech and Hearing [V.S., S.R.] and Department of Mathematics [K.C.], University of Queensland, Queensland,Australia
ABSTRACT The relationship between quantified pure-tone audiometric variables (namely, pure-tone audiometric slope and the degree of hearing loss) and the slope of the wave V L-l (latency-intensity) function of the ABR was investigated. The influence of loudness recruitment on the relationship between audiogram slope and the wave V L-l slope was also studied. Fifty-five ears were selected and divided into two groups (a positive Metz group consisting of 35 ears and a negative Metz group comprising 20 ears) for statistical analyses. The results of the study indicated no significant relationship between the audiogram variables and the slope of the wave V L-l function. However, a significant relationship emerged between the degree of hearing loss and the slope of the L-l function. The results also suggested that neither loudness recruitment nor audiometric configuration influenced the slope of the L-I function. (Ear Hear 12 2:149-154)
THE USEFULNESS OF AUDIOLOGICAL tests in clinical practice is affected by the accuracy of test interpretation which has been influenced traditionally by the use of absolute measurements. For example, classification of subjects by the use of pure-tone average hearing levels may lead to the spurious inclusion in the same category of vastly differing audiometric configurations. Auditory brain stem responses (ABR) also are vulnerable to such degrading of clinical information, in particular the use of the latency-intensity (L-I) function attenuates the diagnostic yield of the ABR as such qualitative interpretation lacks measurement precision. Recently, studies which have sought to overcome the apparent deficiencies associated with traditional interpretation have adopted objective approaches through quantification of the pure tone audiometric configura-
tion (McGee, Kraus, & Wolters, 1988)and of the ABR/ L-I function (Gorga, Worthington, Reiland, Beauchaine, & Goldgar, 1985; Suter & Brewer, 1983). Interpretation of these studies is made difficult by lack of common method and by the use of small sample numbers and specific pathologic target groups which prevent extrapolation to wider clinical use. McGee et a1 (1988) specifically excluded subjects with neurological disorders from their mathematical modeling study of the audiogram configuration, but did not provide a definition of “neurological disorders” in their report. However, their positive approach warranted wider investigation as their concept of quantifying the audiogram provided an objective basis for further studies integrating test battery information. The first attempt to quantify the ABR/L-I function was made by Suter and Brewer (1983). These researchers used a linear regression line of latency on intensity to model just the lower intensity region of the L-I curve. The slope of this linear regression line represented the maximum steepness of the L-I function and incorporated the notion of a breakpoint or highpoint separating steeply sloping L-I functions from shallow ones in the regression equation. Gorga et a1 (1985) refined this approach by the use of an exponential model (equation 1) to fit the L-I function curve. Their model has the form y = A exp[-Bx], (1) where x represents the intensity of the click stimulus in dB nHL and y is the latency in msecs. The slope of equation 1 at any point (x, y) is given by the first derivative
y’ = AB exp[-Bx]. (2) To regard the “B” term “as the estimate of the slope of these functions” in the manner of Gorga et a1 ( 1985), though possibly useful, may be misleading. Indeed, even the initial slope (at x = 0, y = A) depends on A as well as B. Nevertheless, B remains important in its role as the attenuation parameter. Whereas the slope of equation 1 has this parameter as a factor, the rate of change of the slope has B2 as a factor, since it is given 0196/0202/91/1202-0149$O3.OO/O.EAR AND HEARING Copyright 0 1991 by The Williams & Wilkins Co:Printed in U S A . ~~
Ear and Hearing, Vol. 12, No. 2,1991
The Audiogram and ABR Quantification
149
by the second derivative y” = AB2 exp[-Bx]. (3) This attenuation parameter B is therefore closely related to the extent of the increase in latency over a typical range of decreasing click intensities for a given ear. This suggests that B may be indicative of the degree of hearing loss. For convenience, -B will still be referred to as the slope of the L-I function. In the study reported here the application of mathematical models to the audiogram and the ABR is examined with reference to selected clinical populations, taking into account the presence or absence of positive signs of loudness recruitment measured objectively via the Metz test in the study subjects. Testing acoustic stapedius reflex threshold measurements compared to thresholds for pure tones was introduced by Metz in 1946 (Terkildsen & Nielsen, 1976). Such reflexes are demonstrable in response to acoustic stimuli at subjective loudness levels between 70 and 90 dB. In cochlear hearing loss accompanied by recruitment of loudness this intensity difference between pure-tone thresholds and reflex thresholds is reduced in proportion to the degree of hearing loss. It is a decibel for decibel trade (Jerger & Hayes, 1980). The purpose of this study was ( 1 ) to validate further the McGee et a1 (1988) formula, (2) to investigate model relationships between the audiogram and ABR/L-I function using curve fitting techniques to establish the data base, and (3) to determine the effect of cochlear distortion predicted by a positive Metz response on the outcome of ( 1 ) and (2). METHOD
Subjects Fifty-five ears were drawn retrospectively from a serial (year) clinical population within the University of Queensland Audiology Clinic. Selection criteria specified were (1) age range 15 years to 65 years, (2) test ears to be classified Jerger type A tympanograms, (3) test ears to exhibit either clearly positive (+ve) or clearly negative (-ve) Metz test results (60 dB sensation level cut-off). Using such criteria, 55 ears, 35 exhibiting +ve Metz and 20 exhibiting -ve Metz test results, were available for study. Instrumentation 1. Audiograms were obtained using a Peters AP6 clinical audiometer calibrated to current Australian (SAA) and IS0 standards. 2. Tympanometry and reflexometry were obtained using an Amplaid 702 Impedance Meter. 3. ABR measures were obtained using a Medelec MS92 dedicated system with an Amplaid CK63 click generator to deliver 20 pulses per second click stimuli via TDH 49 earphones. Filter settings were 200 and 2000 Hz with 12 dB octave roll-off. Medi-trace electrodes with ipsilateral mastoid reference, forehead active and contralateral ground electrodes were adopted for the recording montage as normative profiles were established for this configuration in the particular clinical setting. 150
Smyth et al.
Data Analysis The McGee et a1 (1988) hyperbolic tangent function, given by equation 4 T
=
a tanh[F - c)/b]
+d
(4)
and illustrated in Figure 1, was used to quantify the audiometric data for each ear. A least squares nonlinear technique was used to determine the parameters in the hyperbolic tangent function. Curve fits were executed on an IBM compatible 386 with 80387 coprocessor, using the built-in functions of the MATLAB software package. The tolerance limits for curve fits were consistently set at 0. I and fitted values of a, b, c, and d (refer Fig. 1) were then obtained for each audiogram. The tolerance limit of 0.1 is arbitrarily chosen but was set at a low enough value to give credance to the results. Curve fits were not performed where the estimated value of a was between -5 and +5 (n = 9 ears). This criterion was in accord with the recognition by McGee et a1 (1988) that the hyperbolic tangent function is inappropriate when a is small. Using an IBM compatible STATGRAPHICS software package, exponential regression analyses were performed in order to obtain correlation coefficients for the fitted exponential [A exp(-Bx)] curves. Through linear regression analyses the slope-B was then related to each of the audiogram parameters a/b (slope), c (central frequency), and d (hearing loss). Analyses were included as indicated in Table I , in order to establish the relative contribution of +ve and -ve Metz subject classification as variables and the effect of audiogram configuration on regression outcome. RESULTS
Audiogram Curve Fitting (tolerance limit 0.1) Successful curve fits were obtained for all except one audiogram using the hyperbolic tangent model. Figure 2 illustrates a clinical audiogram plotted against the same axes as the mathematical model. The nonmonotonic character of one audiogram from the 55 accounted for failure to fit such a function in this isolated case, which was excluded from further analysis. Similarly McGee et a1 (1988) found only 19 from 148 audiograms to be nonmonotonic.
C
1
2;O
500
1K
2K
4K
6K
FREOUENCY (Hr) Figure 1. Hyperbolic tangent function fit to the range of audiometric values. Point (c, d) denotes the midpoint of the sloping portion of the audiogram; a equals one-half of the dB difference between the lowand high-frequency asymptotes; and b corresponds to the breadth of the sloping portion of the audiogram. (From McGee et al. 1988).
Ear and Hearing, Vol. 12, No. 2,1991
Table 1. Format of data analysis.
Subjects
Statistic Linear regressions -b(L-I) on a/b audiogram -b(L-I) on c audiograrn -b(L-I) on d audiogram Multiple regressions -b(L-I) on a/b&d audiogram -b(L-I) on a/b&c audiogram -b(L-I) on a/b, c&d audiogram t-tests Mann-Whitney, Wilcoxin Audiogram curve fitting L-l function curve fitting
+ve Metz ears
-ve Metz ears
-ve Metz excluding normal ears
J
4
J
J
4
J
+ve and -ve Metz ears pooled data
Ss with flat audiograrn configurations
J J J
J
J
J
J
J
J
J
J
J
J
J
J
J
Comparing +ve and -ve Metz Ss in all audiogram parameters (a/b, c, and d) and in the L-l function (-b) Comparing L-l functions in sloping-rising audiogram configurations, in slopingfalling audiogram configurations and in normal audiograrns Tolerance limit 0.1 Criterion adopted: r
The Quantification of Pure-tone Audiograms and Auditory Brain Stem Evoked Responses Using Mathematical Modeling Procedures Veronica Smyth, BA, MEdSt, PhD; S. Ravichandran, BSpThy(Hons); K. Capell, BSc, PhD Department of Speech and Hearing [V.S., S.R.] and Department of Mathematics [K.C.], University of Queensland, Queensland,Australia
ABSTRACT The relationship between quantified pure-tone audiometric variables (namely, pure-tone audiometric slope and the degree of hearing loss) and the slope of the wave V L-l (latency-intensity) function of the ABR was investigated. The influence of loudness recruitment on the relationship between audiogram slope and the wave V L-l slope was also studied. Fifty-five ears were selected and divided into two groups (a positive Metz group consisting of 35 ears and a negative Metz group comprising 20 ears) for statistical analyses. The results of the study indicated no significant relationship between the audiogram variables and the slope of the wave V L-l function. However, a significant relationship emerged between the degree of hearing loss and the slope of the L-l function. The results also suggested that neither loudness recruitment nor audiometric configuration influenced the slope of the L-I function. (Ear Hear 12 2:149-154)
THE USEFULNESS OF AUDIOLOGICAL tests in clinical practice is affected by the accuracy of test interpretation which has been influenced traditionally by the use of absolute measurements. For example, classification of subjects by the use of pure-tone average hearing levels may lead to the spurious inclusion in the same category of vastly differing audiometric configurations. Auditory brain stem responses (ABR) also are vulnerable to such degrading of clinical information, in particular the use of the latency-intensity (L-I) function attenuates the diagnostic yield of the ABR as such qualitative interpretation lacks measurement precision. Recently, studies which have sought to overcome the apparent deficiencies associated with traditional interpretation have adopted objective approaches through quantification of the pure tone audiometric configura-
tion (McGee, Kraus, & Wolters, 1988)and of the ABR/ L-I function (Gorga, Worthington, Reiland, Beauchaine, & Goldgar, 1985; Suter & Brewer, 1983). Interpretation of these studies is made difficult by lack of common method and by the use of small sample numbers and specific pathologic target groups which prevent extrapolation to wider clinical use. McGee et a1 (1988) specifically excluded subjects with neurological disorders from their mathematical modeling study of the audiogram configuration, but did not provide a definition of “neurological disorders” in their report. However, their positive approach warranted wider investigation as their concept of quantifying the audiogram provided an objective basis for further studies integrating test battery information. The first attempt to quantify the ABR/L-I function was made by Suter and Brewer (1983). These researchers used a linear regression line of latency on intensity to model just the lower intensity region of the L-I curve. The slope of this linear regression line represented the maximum steepness of the L-I function and incorporated the notion of a breakpoint or highpoint separating steeply sloping L-I functions from shallow ones in the regression equation. Gorga et a1 (1985) refined this approach by the use of an exponential model (equation 1) to fit the L-I function curve. Their model has the form y = A exp[-Bx], (1) where x represents the intensity of the click stimulus in dB nHL and y is the latency in msecs. The slope of equation 1 at any point (x, y) is given by the first derivative
y’ = AB exp[-Bx]. (2) To regard the “B” term “as the estimate of the slope of these functions” in the manner of Gorga et a1 ( 1985), though possibly useful, may be misleading. Indeed, even the initial slope (at x = 0, y = A) depends on A as well as B. Nevertheless, B remains important in its role as the attenuation parameter. Whereas the slope of equation 1 has this parameter as a factor, the rate of change of the slope has B2 as a factor, since it is given 0196/0202/91/1202-0149$O3.OO/O.EAR AND HEARING Copyright 0 1991 by The Williams & Wilkins Co:Printed in U S A . ~~
Ear and Hearing, Vol. 12, No. 2,1991
The Audiogram and ABR Quantification
149
by the second derivative y” = AB2 exp[-Bx]. (3) This attenuation parameter B is therefore closely related to the extent of the increase in latency over a typical range of decreasing click intensities for a given ear. This suggests that B may be indicative of the degree of hearing loss. For convenience, -B will still be referred to as the slope of the L-I function. In the study reported here the application of mathematical models to the audiogram and the ABR is examined with reference to selected clinical populations, taking into account the presence or absence of positive signs of loudness recruitment measured objectively via the Metz test in the study subjects. Testing acoustic stapedius reflex threshold measurements compared to thresholds for pure tones was introduced by Metz in 1946 (Terkildsen & Nielsen, 1976). Such reflexes are demonstrable in response to acoustic stimuli at subjective loudness levels between 70 and 90 dB. In cochlear hearing loss accompanied by recruitment of loudness this intensity difference between pure-tone thresholds and reflex thresholds is reduced in proportion to the degree of hearing loss. It is a decibel for decibel trade (Jerger & Hayes, 1980). The purpose of this study was ( 1 ) to validate further the McGee et a1 (1988) formula, (2) to investigate model relationships between the audiogram and ABR/L-I function using curve fitting techniques to establish the data base, and (3) to determine the effect of cochlear distortion predicted by a positive Metz response on the outcome of ( 1 ) and (2). METHOD
Subjects Fifty-five ears were drawn retrospectively from a serial (year) clinical population within the University of Queensland Audiology Clinic. Selection criteria specified were (1) age range 15 years to 65 years, (2) test ears to be classified Jerger type A tympanograms, (3) test ears to exhibit either clearly positive (+ve) or clearly negative (-ve) Metz test results (60 dB sensation level cut-off). Using such criteria, 55 ears, 35 exhibiting +ve Metz and 20 exhibiting -ve Metz test results, were available for study. Instrumentation 1. Audiograms were obtained using a Peters AP6 clinical audiometer calibrated to current Australian (SAA) and IS0 standards. 2. Tympanometry and reflexometry were obtained using an Amplaid 702 Impedance Meter. 3. ABR measures were obtained using a Medelec MS92 dedicated system with an Amplaid CK63 click generator to deliver 20 pulses per second click stimuli via TDH 49 earphones. Filter settings were 200 and 2000 Hz with 12 dB octave roll-off. Medi-trace electrodes with ipsilateral mastoid reference, forehead active and contralateral ground electrodes were adopted for the recording montage as normative profiles were established for this configuration in the particular clinical setting. 150
Smyth et al.
Data Analysis The McGee et a1 (1988) hyperbolic tangent function, given by equation 4 T
=
a tanh[F - c)/b]
+d
(4)
and illustrated in Figure 1, was used to quantify the audiometric data for each ear. A least squares nonlinear technique was used to determine the parameters in the hyperbolic tangent function. Curve fits were executed on an IBM compatible 386 with 80387 coprocessor, using the built-in functions of the MATLAB software package. The tolerance limits for curve fits were consistently set at 0. I and fitted values of a, b, c, and d (refer Fig. 1) were then obtained for each audiogram. The tolerance limit of 0.1 is arbitrarily chosen but was set at a low enough value to give credance to the results. Curve fits were not performed where the estimated value of a was between -5 and +5 (n = 9 ears). This criterion was in accord with the recognition by McGee et a1 (1988) that the hyperbolic tangent function is inappropriate when a is small. Using an IBM compatible STATGRAPHICS software package, exponential regression analyses were performed in order to obtain correlation coefficients for the fitted exponential [A exp(-Bx)] curves. Through linear regression analyses the slope-B was then related to each of the audiogram parameters a/b (slope), c (central frequency), and d (hearing loss). Analyses were included as indicated in Table I , in order to establish the relative contribution of +ve and -ve Metz subject classification as variables and the effect of audiogram configuration on regression outcome. RESULTS
Audiogram Curve Fitting (tolerance limit 0.1) Successful curve fits were obtained for all except one audiogram using the hyperbolic tangent model. Figure 2 illustrates a clinical audiogram plotted against the same axes as the mathematical model. The nonmonotonic character of one audiogram from the 55 accounted for failure to fit such a function in this isolated case, which was excluded from further analysis. Similarly McGee et a1 (1988) found only 19 from 148 audiograms to be nonmonotonic.
C
1
2;O
500
1K
2K
4K
6K
FREOUENCY (Hr) Figure 1. Hyperbolic tangent function fit to the range of audiometric values. Point (c, d) denotes the midpoint of the sloping portion of the audiogram; a equals one-half of the dB difference between the lowand high-frequency asymptotes; and b corresponds to the breadth of the sloping portion of the audiogram. (From McGee et al. 1988).
Ear and Hearing, Vol. 12, No. 2,1991
Table 1. Format of data analysis.
Subjects
Statistic Linear regressions -b(L-I) on a/b audiogram -b(L-I) on c audiograrn -b(L-I) on d audiogram Multiple regressions -b(L-I) on a/b&d audiogram -b(L-I) on a/b&c audiogram -b(L-I) on a/b, c&d audiogram t-tests Mann-Whitney, Wilcoxin Audiogram curve fitting L-l function curve fitting
+ve Metz ears
-ve Metz ears
-ve Metz excluding normal ears
J
4
J
J
4
J
+ve and -ve Metz ears pooled data
Ss with flat audiograrn configurations
J J J
J
J
J
J
J
J
J
J
J
J
J
J
J
Comparing +ve and -ve Metz Ss in all audiogram parameters (a/b, c, and d) and in the L-l function (-b) Comparing L-l functions in sloping-rising audiogram configurations, in slopingfalling audiogram configurations and in normal audiograrns Tolerance limit 0.1 Criterion adopted: r
