Abstract
Clickevoked otoacoustic emissions (CEOAEs) were studied by means of recurrence quantification analysis (RQA) and were found to be endowed with a relevant amount of deterministic structuring. Such a structure showed highly significant correlation with the clinical evaluation of the signal over a data set including 56 signals. Moreover, 1) one of the RQA variables, Trend, was very sensitive to phase transitions in the dynamical regime of CEOAEs, and2) appropriate use of principal component analysis proved able to isolate the individual character of the studied signals. These results are of general interest for the study of auditory signal transduction and generation mechanisms.
 recurrence quantification analysis
 nonlinear dynamics
 auditory system
 complexity
otoacoustic emissions (OAEs) are soundpressure oscillations generated by the outer hair cells inside the Corti's organ (6) that can be detected by a microphone put inside the external ear canal. They can be classified into two groups (8, 11). One group collects the emissions spontaneously present without external stimulation; the other is divided into three classes depending on the evoking stimuli: 1) stimulus frequency OAEs, in which the evoking stimulus is a pure tone; 2) distortionproduct OAEs, representing evoked responses consisting of new frequencies absent in the eliciting stimuli; and 3) transiently evoked OAEs, in which the responses are elicited by the use of a brief acoustic stimulus, generally of Gaussian or rectangular shape, but also single sinusoids or tone bursts (9, 11).
OAEs are related to the first active step in the auditory process, and their relevance can be assessed on both applicative and theoretical bases. In particular, the presence of evoked oscillations in the ear canal allows for a noninvasive and objective examination of the stimulusresponse relationships possibly associated with pathological events. Moreover, they provide clues to a careful analysis of cochlear functions and, more in general, to auditory signal transduction mechanisms. All in all, OAEs constitute a typical example of complex physiological signals not easily amenable to quantitative description despite their potential use as ideal probes for mechanical and neurological events related to the auditory function. At present, OAEs are mainly used to test the functionality of the inner ear, especially in the hearing screening of newborns, which cannot rely on the verbal competence of the subjects.
This work concerns the application of recurrence plots and of their quantitative description provided by recurrence quantification analysis (RQA) (4, 15) to appreciate subtle although physiologically relevant changes in the dynamical regime of transiently evoked OAEs. RQA aims at a direct and quantitative appreciation of the amount of deterministic structuring (10, 17) of signals, i.e., of the amount of their ruleobeying character, and has been shown to be an efficient and relatively simple tool in the nonlinear analysis of many physiological signals. Moreover, the technique allows for the identification of sudden phase changes possibly pointing to mechanistically relevant phenomena. RQA variables are potentially useful for OAE study but, because of the pure dataanalysis character of the technique, do not allow for any mechanistic speculation as such. Thus an empirical correlation between RQA variables and independent, pathophysiological variables is needed to work out an interpretation for our results (5). In the following sections, the existence of a rich deterministic structuring of OAEs is supplemented by a highly significant correlation between the description of the signals on the basis of RQA and their clinical evaluation by traditional methods (11). This type of statistical evidence also indicates a phase change identified along the time course of OAEs and, in any case, provides a firm basis for any subsequent mechanistic interpretation.
EXPERIMENTAL AND ANALYTIC METHODS
Signal detection.
The signals analyzed in this work are technically classified as clickevoked OAEs (CEOAEs). A rectangular stimulus (“click”) has been chosen because it is very brief and has a broadrange frequency spectrum, so that a complete and simultaneous stimulation of the Corti's organ can be obtained down its entire length (8, 9).
The ILO88 system (Otodynamics) is composed of analogtodigital and digitaltoanalog interfaces, a preamplifier, an acoustic probe (microphone), and software to manage the stimulus and to collect and elaborate data. Because the probe position can modify the stimulus' shape, checking the background noise level, shape, spectrum, and intensity level of the stimulus is mandatory. A response is valid if the intensity level is higher than the background level plus 3 dB. Responses were filtered with the use of a secondorder highpass filter at 500 Hz and a fourthorder lowpass filter at 5 kHz and were digitized at a rate of 25,000 samples/s.
Data collection.
A total of 56 signals from the hundreds of files collected during 1997–1998 in the Audiology Department of the Palermo University from adult individuals (age >25 yr) was selected on the basis of the absence of 1) any pathophysiological objective sign of clinical relevance in the subjects except a suspected aural malfunction and2) any systematic pharmacological treatment within 3 mo from the record. Signals were recorded in a soundattenuated booth with the patient seated adjacent to the recording equipment, using an ILO88 system with standard adult ILO probes. The probe fit was evaluated by measuring the adequacy of stimuli, i.e., flat acoustic spectrum, across the frequency range of 0.5–5 kHz. Responses were recorded after nonlinear stimuli (three clicks of equal amplitude and polarity followed by a click of opposite polarity and triple amplitude) of 80μs duration with a repetition rate of 50 Hz. Five hundred twelve digitized response points were collected for each stimulus in the 2.5 to 20.48ms interval after the stimulus was triggered.
To analyze CEOAEs, the signals revealed by the microphone are averaged by timelocking to the transient stimuli and alternatively storing them into two separate buffers (A and B). Thus each of the two waveforms A and B (see Fig.1) corresponds to an average of 700 accumulated responses without any intervening lag. However, because CEOAEs appear after ∼7 ms from the stimulus (11), our global RQA analysis starts from point 175, corresponding to a 7ms lag from triggering.
Clinical evaluation.
The two waveforms of each signal (Fig. 1) collected in separate buffers were crosscorrelated by means of a product moment correlation coefficient. The entity of correlation is considered as a measure of the response reliability and hence as a score of the functional efficiency of the auditory system. In the ILO88 test, a value of the correlation (reproducibility) between two waveforms of an OAE signal index (Repro) >70 is considered as physiological (Repro = Pearson correlation coefficient between the two waveforms × 100); signal pairs having a Repro <70 indicate the presence of a possible hearing malfunction. Table 1 summarizes the Repro values as well as the RQA variables estimated from the 56 signal pairs (112 waveforms) in our data set. On the basis of the Repro values,signals 1–38 in Table 1 are associated with normally hearing ears.
Signal analysis by RQA.
RQA is a relatively new method of nonlinear analysis of time series, originally introduced within a theoretical physics context (4) and subsequently applied to many types of biologically meaningful series including ion channel gating, heart beat intervals, breathing patterns, electromyograms, protein sequences, molecular dynamics, and so forth (3, 5, 10, 1218). The main merit of the method lies in its independence from massive amounts of data, as for classical methods estimating time series dimensionality (17), and of stationarity assumptions, as for Fourier spectral analysis (7, 13, 14).
RQA projects the signal into a multidimensional space through the setup of an embedding matrix and identifies time correlations that cannot be observed in just one dimension. By computing the Euclidean distance between every i,j row pair in the embedding matrix, a distance matrix is worked out and visualized in the form of a recurrence plot. In this plot, each pair of rows whose Euclidean distance (d) falls below a userdefined threshold is considered as recurrent and the corresponding point is darkened. The general appearance of the plot (Fig. 2) inherits the features of the distance operator on which it is based: symmetry (d_{ij} = d_{ji}) and the presence of a darkened main diagonal (d_{ii} = 0). The nontrivial recurrences correspond to the “returns” of the system to alreadyvisited states of the dynamics and give a picture of its autocorrelation structure, because recurrences near to and far from the diagonal correspond, respectively, to short and longrange temporal correlation. Webber and Zbilut (15) developed a set of quantitative descriptors of recurrence plots, based on simple statistics on the number and distribution of recurrences in recurrence plots. In the present work, the following descriptors are used: percent recurrence (Rec), the fraction of the plot occupied by recurrent points, i.e., the number of epoch pairs whose distance is lower than a predefined cutoff; percent determinism (Det), the fraction of recurrent points aligned into upward diagonal segments (deterministic lines); entropy (Ent), a Shannon entropy estimated over the length distribution of deterministic lines; and Trend, the slope of the linear relation holding between the distance from the main diagonal and the number of scored recurrences.
Besides their operational definition, all these parameters are endowed with a casedependent, specific meaning. In general terms, Rec is a measure of the recurrent (both periodic and autosimilar) behavior, and Det indicates the degree of deterministic structuring due to the presence of “quasiattractors,” i.e., portions of the phase space in which the system lies for a longer time than expected by chance alone. Ent and Trend are linked to the richness of deterministic structuring and to the nonstationarity of the signal, respectively.
If RQA is carried out on an epochbyepoch basis, i.e., by the computation of many small distance matrices corresponding to consecutive and overlapping sliding windows (epochs) along the series, the changing values of RQA variables in the subsequent windows allow for the detection of abrupt changes in the dynamical regime of the signal. We used this procedure, recurrence quantification over epochs [RQE; see the seminal paper by Webber and Zbilut (15)], to test the presence of phase changes in CEOAEs reflecting different phases in the transduction process. RQE analysis was carried out by using the same parameter setting as for the global mode (RQA), plus the definition of a window length of 100 points (4 ms) and a shift of 1 point between consecutive windows.
Filtering RQA variables by principal components analysis.
Principal components analysis (PCA) is a very common descriptive statistical technique whose aim is projecting the original space of a multidimensional data set into a new orthogonal space of lower dimensionality on the basis of the correlation structure among the variables. The axes of the latter space are called “principal components” to stress the point that most of the nonredundant information in the data set can be recorded into a smaller number of variables. Because principal components are, by construction, orthogonal to each other and are extracted in order of explained variance, each of them represents an “autonomous” feature of the data set (1, 3), and the first of them (PC1) is the “optimal” (in a leastsquare sense), noisefiltered, monodimensional description of the original space.
In the context of the present work, PCA proved extremely useful in dissecting the total variance observed in the dynamical description of CEOAEs provided by RQA parameters. Thus PCA revealed1) macroscopic differences of possible clinical relevance, which should nonredundantly sum up into PC1, and 2) more subtle differences due to individual variability evidenced by the minor second and third components (PC2, PC3).
The PCA procedure applied to RQA descriptors gave the results displayed in Table 2 in terms of factor loadings. It is evident that PC1 can be considered a general score of the amount of deterministic structuring of the signals, whereas minor components point to subtle differences. This interpretation results from very high correlations (factor loadings) between PC1 and RQA variables.
RESULTS
Figure 2 shows the recurrence plots derived from a typical CEOAE and its shuffled counterpart. The presence of a rich deterministic structuring (Fig. 2 A), completely destroyed by the shuffling (Fig. 2 B), is selfevident and is confirmed by changes in the RQA variables (see Fig. 2 legend). This deterministic structuring can be considered to directly reflect the complex active mechanisms underlying OAEs.
Consistency between RQA and clinical descriptions.
For the data set used in this work, optimal tuning of RQA variables has been empirically found by using a delay of 1 between timeseries points, an embedding dimension of 10, a cutoff value of 15 to score recurrent points, and a minimum number of 5 consecutive recurrent points to score determinism (see Ref. 16 for further details). The actual variables worked out for each signal were subtracted from the averaged values relative to 10 corresponding shuffled series to take into consideration only the dynamical (shufflingsensitive) information. The Pearson correlation coefficient, r, between dynamical descriptors of CEOAEs and their clinical evaluation provided by Repro values is summarized in Table 3, in which the correlation coefficients between Repro values and the principal components extracted from RQA variables are also included.
The quite high correlation with Repro values, amounting to 0.69, 0.71, and 0.69 for Rec, Det, and Ent, respectively, all at P < 0.005, point to the clinical relevance of the description provided by RQA. The correlation between PC1 and Repro, shown in Fig.3, scored a Pearson r of 0.84 (P < 0.0001), higher than the correlation between Repro and single RQA variables; this illuminates a strong link between the global dynamical features of the signal and its reliability as well as a global correspondence between the RQA description and the clinical evaluation.
Fine details in the dynamical structure of CEOAE.
Having characterized the clinical significance of global RQA description of CEOAEs, we tried to identify the presence of phase changes along the dynamics by means of the RQE technique.
Figure 4 reports the results obtained from a typical signal using two “static” descriptors, mean value and standard deviation (a), and the RQA dynamical variables Trend, Det, Rec, and Ent (b and c). The mean value series corresponds to a simple smoothing of the signal, whereas the secondorder moment (standard deviation) series allows appreciation of the timedependent dampening of the oscillations. By contrast, RQA variables indicate at least one otherwise undetected sharp transition in the 16 to 17ms range.
Among RQA variables, Trend, being essentially a derivative, should be endowed with the highest sensitivity even to fine dynamical details. This is confirmed by the Trend profiles of both waveforms in Fig.4 b. Thus, in full agreement with previous observations (14), Trend appears to be the RQA variable of choice to underscore phase transitions in CEOAEs. It is worth noting that the main differences between waveforms for Rec, Det, and Ent also occur within essentially the same time span (Fig. 4 c). Because the various RQA variables represent specific and relatively independent facets of the deterministic structuring of the signal, this is a strong indication of the nonstochastic nature of the underlying phenomena.
Individual variability in OAEs.
Figure 5 shows the location of the 56 signals in our data set over the PC2PC3 plane. It is evident how the PCA exploits the individual variability: the outliers of the distribution are used as “poles” to order all the units along the maximal variability and maximal discriminatory axes (PC2 and PC3, respectively). Notice the close vicinity of the only pair of signals pertaining to the same ear of the same subject (indicated on Fig. 5 by arrows) over the background of the uniform distribution of all other signals over the plane. To check the general and predictive power of the PC2PC3 plane for “individuality detection,” eight independent CEOAEs were subsequently recorded from the same ear of that subject. These eight signals (test set) were treated following the same RQA of the 56 signals in the data set (training set) and were embedded into the PC2PC3 plane by computation of their PC2 and PC3 scores from their RQA variables. The localization of these signals is a demonstration of the generalization ability of the principal component space and of the sensitivity of the technique to individual features.
DISCUSSION
The active micromechanical processes generating OAEs are not currently explained. However, their nonlinear nature has been well established and it is possible to work out models able to discriminate between their linear and nonlinear components (2, 7). RQA provides a further confirmation to that end and, moreover, reveals a rich deterministic structuring of OAEs with a direct relevance for the clinical evaluation of auditory system performance. It is worth noting that the reconstruction, by means of RQA, of a clinical score, Repro, was accomplished without any empirical estimate of the correlation between the two waveforms of each signal. On top of that, the correspondence between the degree of “deterministic structuring” of the signal and its reproducibility shows a direct link between the “ruleobeying” (and hence reliable) character of the signal, as estimated by RQA, and the actual OAE's reproducibility, as estimated by Repro. This means that RQA descriptors provide a basis for any further research aiming to 1) evaluate the pathological relevance of the response and 2) quantify the response of auditory systems to various experimental stimuli.
The wellknown high sensitivity of RQA to fine details of signals is directly demonstrated in the case of CEOAEs by comparing the crosscorrelation of the two waveforms of the same signal with the crosscorrelation of their respective “sliding window,” Trend. Within exactly the same range (7–20.48 ms), the two waveforms of Fig. 1 score a direct correlation of 0.927, whereas the two corresponding Trend series (Fig. 4 b) score 0.643. This means that RQA allows detection of otherwise hidden differences between the two time series.
More specifically, the peaks consistently shown by all RQA variables in the same time range (Fig. 4, b and c) indicate the presence of nonstochastic transitions in the dynamical regime of CEOAEs in the region where active effects, nonlinearly dependent on stimulation, are supposed to arise (7). Very similar peaks can be observed, under the same conditions, in the vast majority of the analyzed signals. Although any solid physiopathological explanation for them is still out of range, their characterization represents, in our opinion, an interesting subject for future work.
The role of PCA in reinforcing the statistical significance of the correlation between global dynamical features of CEOAEs and their clinical interpretation deserves special attention. Such a role has been specifically played by PC1 extracted from RQA variables, which allowed the emergence of two classes in the data set, the normal and defectivehearing ears (corresponding to high and low Repro values, respectively). In this context, also of particular interest, is the result depicted in Fig. 3, in which, for normal ears, under very high and “saturating” conditions of Repro values, PC1 still shows a considerable discriminatory power. Full exploitation of the heuristic power of PCA in the present case, however, may lead much further, because individual variability should emerge in the second and third components, which explain, respectively, 22 and 10% of the total variance in the data set and take into account relatively finer details of CEOAEs.
The results of the exercise described in the last paragraph ofresults (see Fig. 5) actually confirm the hypothesis: signals from the same subject (same ear) cluster within the same region of the plane defined by the second and third components, thus demonstrating the utility of the RQA/PCA analysis to detect signal individuality. It should be stressed that the eight test signals were not used to compute the PCA axes but were classified by the preexisting model, which shows a relevant generalization ability.
In conclusion, we can state that the proposed method constitutes an efficient way to quantitatively study OAEs in both physiological and pathological conditions.
Acknowledgments
Helpful observations and encouragement from Prof. Charles L. Webber, Jr. (Loyola University, Chicago, IL) are gratefully acknowledged.
Footnotes

Address for reprint requests and other correspondence: A. Colosimo, Dept. of Biochemical Sciences, Univ. of Rome “La Sapienza,” P.le A. Moro 5, 00185 Roma, Italy (Email:colosimo{at}caspur.it).

This work has been partially funded by Italian Ministero Pubblico Istruzione grants (40% and 60%) to A. Colosimo.

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 Copyright © 2000 the American Physiological Society