29 The Acoustic Reflex at a 1000 Hz Probe Frequency: Phasor and Vector Analysis Judy Ferguson and Louise Reynolds Department of Logopaedics, University of Cape Town. ABSTRACT Phasor plots of reflex growth functions have been inconclusive concerning the effect of the reflex for mass dominated ears. The present study aimed to establish whether vector plots clarified the effects of the reflex for phasors not showing a clear circular shape. Measured admittance data (ipsilateral reflexes across a wide intensity range) was represented as both phasor diagrams and converted to impedance quantities, represented as vectors. The results analysed for 34 ears showed few unclassifiable phasor diagrams. In addition, all growth functions showed increased stiffness on vector analysis. Resistance changes appeared to be variable. The results suggest that vector diagrams may be a useful way of representing data that is not clearly represented via phasor diagrams. The current study, however, does not clarify the pattern for mass dominated ears. OPSOMMING Fasor-uitstippeling van refleksiewe groeifunksies was tot nog toe onafdoende ten opsigte van die refleks se uitwerking by massa-gedomineerde ore. Die onderhawige studie het as mikpuntgehad om vas te stel of vektor-uitstippeling die uitwerking van die refleks opgeklaar het ten aansien van fasore wat nie 'n duidelik sirkulere vorm vertoon het nie. Gemete toegangsdata (ipsi-laterale reflekse oor 'n wye intensiteits-spektrum) is weergegee sowel as fasor-diagramme as omgesit in skynweerstand- syfers, aangebied in vektore-vorm. Die uitslae ten aansien van 34 ore wat ontleed is, het weining onklassifiseerbare fasor- diagramme opgelewer. Bowendien, alle groeifunksies het verhoogde styfheid vertoon by vektor-ontleding. Weerstandsveranderinge was skynbaar wisselend. Die resultate wys in die rigtingdat vektor-diagramme moontlik 'n nuttige manier mag wees om data weer te gee wat nie duidelik deur fasor-diagramme weergegee word nie. Die huidige studie klaar egter nie die patroon vir massa-gedomineerde ore op nie. KEY WORDS: immittance,! reflex measures, high probe frequency, phasors, vectors INTRODUCTION The middle ear acts as a transducer of sound from the external environment to the cochlea (Berlin & Cullen, 1980). The effects of the acoustic reflex on the transmis- sion of sound through the middle ear can be observed in- directly through immittance measures (Wiley & Block, 1985). This technique has been used extensively in the literature to describe the effects of the reflex on transmis- sion properties of the middle ear at low probe frequencies (226 and 678 Hz). However, the effects of the reflex re- corded at higher probe frequencies using immittance meas- ures, have not been fully investigated in the literature. This is of particular interest given that baseline trans- mission properties differ across the frequency range in human ears (Berlin & Cullen, 1980). There are several ways of representing the quantities of the relationship between admittance and impedance components (Van Camp & Creten, 1976). Rectangular notation represents the magnitudes of both components of admittance (susceptance (B) and conductance (G)) or impedance (reactance (X) and resistance (R)) as co-ordi- nates (B;G) or (X;R). Polar notation represents the com- ponents of admittance or impedance as having both mag- / nitude and phase angle (degree) (magnitude ; <0). Dy- namic aspects of middle ear function, such as reflex growth functions, may be represented as phasor diagrams, using rectangular notation (joining up the coordinates). This method has been used by Lutman (1984) and Reynolds and Morton (1995) to investigate the effect of the acoustic reflex. Vector diagrams, as used by Bennett and Weatherby (1979) show the dynamic aspects of the reflex by selecting points along the dynamic process and repre- senting aspects of the reflex in both polar and rectangular notation. Immittance recordings of the acoustic reflex are usually made in admittance rather than impedance com- ponents, because there is a linear relationship between the admittance components at the probe tip and the plane of the tympanic membrane (Margolis, 1981). However, impedance quantities are usually used to explain immittance patterns (Van Camp & Creten, 1976). It is possible to correct measurements made at the probe tip to the level of the tympanic membrane, and to convert these components from admittance to impedance, using the for- mulae shown in Table 1. Researchers agree that the major effect of the reflex at low probe frequencies (220 and 660 Hz) is an increase in stiffness or negative reactance (Feldman & Williams, 1976; Die Suid-Afrikaanse Tydskrif vir Kommunikasieafwykings, Vol. 42, 1995 R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 01 2) 30 Judy Ferguson and Louise Reynolds Bennett & Weatherby, 1979, Lutman, McKenzie & Swan, 1984; Reynolds and Morton, 1994). This is made clear in phasor diagrams, which show circular, anticlockwise move- ment. This same effect is shown as an increase in nega- tive phase angle on vector diagrams. TABLE 1: Formulae to convert admittance (Y) com- ponents to components to impedance (Z) compo- nents (Margolis, 1981). jX = -jB/(B2 + G2) R = G/(B2 + G2) X = Reactance Β = Susceptance R = Resistance G = Conductance Reynolds and Morton (1995) examined whether phasor plots at 1000 Hz, where normal ears may not be stiffness dominated, followed the circular, anti-clockwise phasor diagram, indicating the constant resistance, stiffness change model proposed by Lutman (1984). While the majority of their phasor diagrams matched Lutman's (1984) model, some of their plots were difficult to inter- pret, particularly those derived from ears that were mass dominated at the probe frequency used (1000 Hz). The reasons for some phasor plots deviating from the standard model proposed by Lutman (1984) could have been due to procedural variables, such as the nonsimultaneous recording of susceptance and conduct- ance, or could be due to the effect of the reflex on systems where transmission properties are at or above resonance. Previous researchers have found variable effects of the reflex on resistance. This variability influences the over- all effect at higher probe frequencies due to smaller reac- tance effects which cannot so easily mask the resistance changes that are occurring, as happens for low probe fre- quencies (Sprague, Wiley & Block, 1981; Bennett & Weatherby, 1979; and Feldman & Williams, 1976). It is possible that phasor diagrams are unclassifiable when sig- nificant resistance changes occur, and as they interact with reactance changes, cause irregularities in the shape of the phasor. If this were the case, then phasor diagrams may not be the clearest means to show the effect of the reflex, for high probe frequencies or mass dominated ears, but the true effect of the reflex may be clarified through rep- resenting the effect of the reflex through plotting the re- sistance and reactance changes as vectors. This study aimed to explore whether unclassifiable phasor representations of admittance measures could be explained by means of vector representations of imped- ance values derived from the same reflex measures. Of further interest was whether mass dominated systems were always responsible for unclassifiable phasor plots as suggested by Reynolds and Morton (1995) and the present study therefore also investigated the relationship between baseline transmission and the phasor plots obtained. Clarification as to whether deviations from the constant resistance, stiffness change model were related to the means of representation was therefore the focus of the study. METHODOLOGY SUBJECTS Thirty four normal hearing young adults served as sub- jects. Data was collected from one ear per subject to pre- vent duplication of results due to the very small inter-au- ral differences reported in subjects by Hall (1979) and Creten, Van der Heyning and Van Camp (1985). Subjects were required to be within 18 and 30 years of age, and to have no known history of ear pathology. Normal hearing was determined as pure tone air and bone conduction thresholds within normal limits (-10 and 25 dB HL), as defined by Goodman (1965, cited by Yantis, 1985). Air and bone conduction thresholds were required to be within 10 dB of each other to exclude any middle ear pathology not known to the subject. In addition, normal middle ear func- tioning was required, and this was established on the ba- sis of tympanometry and acoustic reflex measurements. Subjects were required to have a single peaked admittance tympanogram at 226 Hz probe frequency, and ipsilateral acoustic reflex thresholds within normal limits (70 - 1 0 0 dB HL), as defined by Northern, Gabbard and Kinder (1985), for 500, 1000 and 2000 Hz stimulus frequencies, measured at a 226 Hz probe frequency. APPARATUS Hearing thresholds for all subjects were established using either a GSI10 Clinical Audiometer, with TDH-50P headphones and B71 bone vibrator, or a Beltone 2000 Au- diometer, with TDH-50P headphones and B71 bone vibra- tor. Both audiometers are calibrated in hearing level and meet the ANSI S.26-1981 standard for clinical audiom- eters. Immittance measurements were carried out using a GSI-33 (Version 2) Middle Ear Analyser, which meets the ANSI S.3.39-1987 standard for acoustic-immittance instru- ments. The instrument was calibrated for the specific al- titude of the test environment (98 m above sea level). Cali- bration checks, following the manufacturer's instructions, were carried out on each day of the data collection. All hearing threshold measurements were carried out in acoustically treated audiometric suites (LAC 109), meet- ing the SABS 0182 (1982) code of practice. PROCEDURE Baseline information for each subject was established first in order to relate phasor and vector classifications to trans- mission at 1000 Hz. Baseline transmission at 1000 Hz for both susceptance (B) and conductance (G), recorded simul- taneously, was established for each ear according to the Vanhuyse, Creten and Van Camp (1975) classification. Tympanometric values were recorded at pressure' values of-350 daPa, and tympanometric peak, in order to (correct the values to the plane of the tympanic membrane (Shanks, Wilson and Cambron, 1993). A positive-to-negative (+200 daPa to -400 daPa) pressure sweep procedure was used. Pressure was varied at a rate of 50 daPa per second (Grason-Stadler, 1987). Shanks and Lilly (1981) and Margolis, Van Camp, Wilson, and Creten (1985) found that positive to negative pressure sweeps result in less com- plex tympanometric patterns than negative to positive pressure sweeps. Acoustic reflexes were recorded at stimulus frequen- cies of 500 Hz and 1000 Hz at a 1000 Hz probe frequency, for susceptance, followed by conductance, as these meas- ures could not be displayed simultaneously. The inten- sity range used was 66-106 dB HL. A 4 dB increment size was used. This increment size has been used in other stud- ies (for example, Reynolds and Morton, 1995). The The South African Journal of Communication Disorders, Vol. 42, 1995 R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 01 2) The Acoustic Reflex at a 1000 Hz Probe Frequency: Phasor and Vector Analysis 31 m i l l i m h o change (magnitude of the reflex growth) at each intensity level was recorded as well as the direction of the reflex growth (i.e., whether it was positive or negative). The stimulus duration was kept constant at 1.5 seconds, as time related aspects were not being investigated in this study. Susceptance recording always preceded conductance recordings, and measurements at 500 Hz preceded meas- u r e m e n t s at 1000 Hz. Each subject's testing was completed within one day. DATA ORGANISATION AND DATA ANALYSIS: Data was corrected to the plane of the tympanic mem- brane by subtracting the susceptance and conductance values at -350 daPa from those values at tympanometric peak, as suggested by Shanks et al. (1993). Observed re- flex values (x) were added to the corrected baseline values (Bc;Gc) for each intensity level: (Be + x; Gc + x). Frequency counts of the number of phasor plots classified as above were recorded in table form. Vector diagrams: All corrected susceptance and conductance values were converted to reactance and resistance values by means of the formulae presented in Table 1 (Margolis, 1981). These corrected and converted reactance and resistance values were plotted on vector diagrams, which allowed for ex- amination of the impedance data. Vectors were classified as showing an increase in stiffness (+S), a decrease in stiff- ness (-S), or no change in stiffness (oS), and an increase in resistance (+R), a decrease in resistance (-R), no change in resistance (oR) or variable resistance (vR) at threshold and suprathreshold levels. From this, the effects of the reflex on reactance (increase or decrease in stiffness) and changes in resistance could be extracted and presented in table form. Phasor representation: Corrected susceptance and conductance values were represented in the form of phasor diagrams for each re- flex growth function recorded. In such diagrams, conduct- ance values are represented on the X-axis and susceptance values on the Y-axis. A phasor trajectory was obtained by joining up the coordinates at each point and the shape of the trajectory was then classified. The axes used for each graph were standard for all graphs, but the scaling for each graph was different. This was done in order to maxi- mize the visual representation of each phasor plot. The resulting phasors were classified as either: 1. Fitting with the Lutman (1984) model of an anti-clock- wise circular movement, indicating constant resistance, and an increase in stiffness. These were termed classi- fiable. 2. Phasor plots not fitting the Lutman (1984) model. These were termed unclassifiable. RESULTS AND DISCUSSION The distribution of ears used in the study across types of baseline characteristics is shown in Table 2. As expected, the majority of ears were at resonance at this frequency, with only a small number of ears being stiffness domi- nated. The ten mass dominated ears at the 1000 Hz probe frequency were of particular interest, given the focus of the study. As normal ears are expected to be close to resonance at 1000 Hz (Colletti, 1977), it would be necessary to use a higher probe frequency to measure the reflex for many mass dominated ears, and the ten were considered to be a sufficient number to clarify the research question. Table 3 shows, that similarly to Reynolds and Morton (1995), the majority of phasor plots obtained were matched to the constant resistance, stiffness change model ex- plained by Lutman (1984). An example of this is provided in Figure 1. TABLE 2: Summary of | baseline transmission characteristics of subjects in this study. (n=34). ! Number of Subjects Van Huyse Classification Stiffness dominated eairs ! 4 1B1G Ears at resonance \© 3B1G Mass dominated ears 10 3B3G TABLE 3: Results of the phasor analysis of growth functions obtained for 500 and 1000 Hz stimuli (n = 68). Classified Phasors Unclassified Phasors Stifness dominated ears 6 2 Ears at resonance 34 6 Mass dominated ears 1 1 8 2 CO ο JC ε ε ω «μ* ω ο c « α ω ο <Λ CO 1.62 1.53 1.44 1.35 1.26 1.17. 1.08 0.99 0.90 0.81 4.99 5.04 5.09 5.14 5.19 5.24 5.29 5 3 4 5.39 Conductance (G) m m h o s FIGURE 1: Example of classifiable phasors demon- strating anticlockwise, circular movement form baseline to suprathreshold levels. Die Suid-Afrikaanse Tydskrif vir Kommunikasieafwykings, Vol. 42, 1995 R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 01 2) 32 Judy Ferguson and Louise Reynolds However, an unexpected result was the distribution of unclassifiable phasors across ears, regardless of baseline transmission properties. Unlike Reynolds and Morton (1995), who found that those phasors that deviated from the model were from mass dominated ears, the results of the present study indicated that unclassifiable phasors were obtained from stiffness dominated ears, ears at reso- nance, and mass dominated ears. Both the present study and the Reynolds and Morton (1995) study did not differ- entiate between degrees of mass domination within sub- jects. It is possible that the ears in the present study be- haved similarly to ears at resonance or stiffness domina- tion with the added stiffness effect of the reflex, which, as shown below, was demonstrated for the reflex patterns obtained. Given that normal ears are expected to be close to resonance at 1000 Hz, it may be necessary to use a higher probe frequency to demonstrate the effect of the reflex for mass dominated ears, although problems will be encountered in the measurement of such small immittance changes in mass dominated ears (Lutman, 1995). Of particular interest in the results of this study, is the nature of the deviation from the model. Clearly, as shown in the examples in Figure 2, the deviations from the con- stant resistance, stiffness change model are not marked in the present study, and all showed overall patterns that could be broadly described as circular, anticlockwise move- ment, at least for some portion of the phasor plot. These results are shown in Table 4, where a brief description of the phasors obtained is provided. It is evident from this table that the patterns which were not strictly showing anticlockwise movement with the activation of the reflex typically showed clockwise movement close to threshold, and then at suprathreshold levels the typical pattern of anticlockwise movement was seen. Examples of this are provided in Figure 2A. One contributing factor to this pattern may relate to the determination of reflex thresh- old, as it is possible that the threshold values obtained were not the actual thresholds of the subjects, and that true threshold was reached at higher intensity levels, where the pattern was consistent with.the model. The criteria used to determine threshold on the GSI 33, derived from Bennett and Weatherby (1979), may not be absolute threshold values. Lutman (1984) argues that there is some question regarding the accurateness of the criterion values given by Grason-Stadler (1987). It is there- fore possible that absolute thresholds were not obtained at the level at which they were recorded. This would mean that only two phasors did not actually match the model (see Table 4). These two demonstrated deviations from the model at suprathreshold intensity levels. An example is shown in Figure 2B. It is well documented that the reflex reaches saturation (Wilson and McBride, 1978), and it may be that the complex interaction of immittance com- ponents, coupled with saturation of the reflex contributed to the patterns obtained. In analyzing the results of the study using vector analy- sis, an attempt was made to clarify the effect of the re- flex, particularly for phasors which were not classifiable. In spite of the few unclassifiable phasors obtained, the vector analysis did provide some useful information, shown in Tables 5,6 and 7, particularly as regards the unresolved TABLE 4: Description and frequency count of unclassifiable phasors (N=10) Classifiable at threshold, & unclassifiable at suprathreshold levels 2 Unclassifiable at threshold, & classifiable at suprathreshold levels 8 Conductance (G) mmhos 4.85 5.02 520 5.38 5 56 5.74 5.92 6.10 6.28 6.46 0.55- Ο 0 β5 JC. I 0.75 m 0 . 8 5 - W Φ Ο 0.95 Ι- α <0 Q. 105 Φ § 1 1 5 " U5 h 1.35- 1.62 CO 1.59 Ο -C Ε Ε m a> ο c ra a. a> υ CO 3 CO 1.56 1.53 1.50 1.47 1.44 1.41 1.38 1.35 A 244 2 5 0 2 5 6 2 6 2 2 6 8 274 2 8 0 2 8 6 2.92 Conductance (G) mmhos FIGURE 2: Examples of unclassifiable phasors. a) Represents clockwise movement at threshold, followed by anticlockwise circular movement. b) Represents anticlockwise movement at threshold, followed by deviations from the model at suprathreshold levels. / The South African Journal of Communication Disorders, Vol. 42, 1995 R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 01 2) The Acoustic Reflex at a 1000 Hz Probe Frequency: Phasor and Vector Analysis 33 question of the effect of the reflex on resistance. C o n s i s t e n t with all previous studies , for example L u t m a n et al. (1984) and Reynolds and Morton (1995), is that the effect of the reflex on reactance is an increase in stiffness. During the course of some of the reflex growth f u n c t i o n s obtained in the present study , there was some d e v i a t i o n from this pattern at threshold, but as mentioned above, this may have related to the definition of thresh- old I n t e r e s t i n g l y , two growth functions, both obtained from mass dominated ears showed decreased stiffness at s u p r a t h r e s h o l d levels, as shown in Table 5. However, these growth functions were classifiable within the model, as this pattern did not emerge for the unclassifiable phasors, as shown in the detailed analysis in Table 7. Thus, there did not appear to be any relationship between the reac- tance change and the classifiability of phasors. A variety of effects on resistance were observed, con- sistent with previous findings (for example Sprague et al., 1981). As shown in Table 6, the most common effects were decreased resistance at threshold, with most demonstrat- ing increased resistance at higher intensity levels. Sev- eral of these typical patterns were also obtained from u n c l a s s i f i a b l e phasors (see Table 7), thus indicating that there was no clear relationship between the resistance pattern and the classifiability of phasors. CONCLUSIONS While the reactance and resistance changes from classifi- able and unclassifiable phasors across ears with differing baseline properties were not differentiated in the results of this study, some interesting observations relating to phasor and vector analysis of reflex growth functions were nonetheless evident. As the complex interaction of reac- tance and resistance change was demonstrated in unclassifiable phasors, isolating the effects of the reflex on impedance quantities does allow for the identification of increased stiffness, in spite of fairly obscure phasor pat- terns, possibly making this a useful tool for clinical inter- pretation of obscure reflex patterns. However, identify- ing expected patterns for mass dominated ears appears to require either a more sophisticated form of recording re- flex phenomena, or more sophisticated form of analysis. Factors contributing to the lack of clarity of the effect may i TABLE 5: Vector Analysis: ̂ Effect of the reflex on stiff- ness reactance. j +S = increase in stiffness -S = decrease in stiffness ^ oS = no change in stiffness ; = shows the difference between baseline, thresh- old and suprathreshold levels. Stiffness Dominated Ears Ears at Resonance Mass Dominated Ears +S 8 24 7 -S;+S 0 10 11 oS;+S 0 6 0 +S;-S 0 1 0 2 relate to the nonsimultaneous recording of the reflex, but probably the most overriding factor is the use of a probe frequency where normal ears are typically at resonance. Thus in order to clarify the effect of the reflex for mass dominated ears, a higher probe frequency should be in- corporated for studies of normal ears, but this is not cur- rently possible using commercially available equipment, due to the increasing complexity of immittance recordings as ears deviate from simple stiff systems. One further TABLE 6: Vector Analysis: Effect of the reflex on re- sistance. +R = increase in resistance -R = decrease in resistance oR = no change in resistance vR = variable resistance changes ; = shows the difference between baseline, thres- hold and suprathreshold levels. Stiffness dominated ears Ears at resonance Mass dominated ears oR;+R 3 2 0 -R;+R 2 21 11 +R 0 0 4 oR;-R 0 2 0 -R 2 7 2 vR 0 4 1 oR 1 0 0 -R;oR 0 4 2 TABLE 7: Detailed vectorial description of the ten unclassifiable phasors. +S = increase in stiffness -S = decrease in stiffness oS = no change in stiffness +R = increase in resistance -R = decrease in resistance oR = no change in resistance vR = variable resistance changes ; = shows the difference between baseline, thres- hold and suprathreshold levels. Stiffness dominated ears Ears at resonance Mass dominated ears +S, oR;+R oS;+S, -R;+R -S;+S -R;+R +S, -R;+R +S, -R -S;+S -R;+R oS;+S, vR +S, -R;oR -S;+S, -R +S, -R;+R Die Suid-Afrikaanse Tydskrif vir Kommunikasieafwykings, Vol. 42, 1995 R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 01 2) 34 Judy Ferguson and Louise Reynolds possibility may be to investigate the pattern of reflex growth functions in pathological ears, or in ears selected because of their marked mass domination at the probe fre- quency, rather than in terms of simply a normal phenom- enon, as was the case in the present investigation. REFERENCES American National Standards Institute. (1987). Specifications for instruments to measure aural acoustic impedance and admittance. ANSI S 3. 39. New York, ANSI. American National Standards Institute. (1981). Specifications for audiometers. ANSI S 26. New York, ANSI. Bennett, M.J, & Weatherby, L.A. (1979). 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