INTRODUCTION

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OTOACOUSTIC EMISSIONS (OAEs) are sound-pressure 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) distortion-product 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 stimulus-response 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 rule-obeying 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 data-analysis 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

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Signal detection. The signals analyzed in this work are technically classified as click-evoked OAEs (CEOAEs). A rectangular stimulus ("click") has been chosen because it is very brief and has a broad-range frequency spectrum, so that a complete and simultaneous stimulation of the Corti's organ can be obtained down its entire length (8, 9).

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 and 2) any systematic pharmacological treatment within 3 mo from the record. Signals were recorded in a sound-attenuated 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 80-µs duration with a repetition rate of 50 Hz. Five hundred twelve digitized response points were collected for each stimulus in the 2.5- to 20.48-ms interval after the stimulus was triggered.

View larger version (21K): [in this window] [in a new window]   Fig. 1.   Waveforms of a click-evoked otoacoustic emission (CEOAE) signal. A and B are two waveforms of a typical CEOAE signal (no. 33 in Table 1) recorded by the ILO88 system after a "nonlinear click" stimulus (see text for details). Five hundred twelve data points correspond to 20.48 ms. Waveform B has been shifted by 0.12 ms for sake of clarity. This shift should by no means be confused with sliding windows mechanism used in recurrence quantification over epochs (RQE) analysis (see EXPERIMENTAL AND ANALYTICAL METHODS). au, Arbitrary units.

Clinical evaluation. The two waveforms of each signal (Fig. 1) collected in separate buffers were cross-correlated 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, 12-18). 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).

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 least-square sense), noise-filtered, monodimensional description of the original space.

	RESULTS

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Figure 2 shows the recurrence plots derived from a typical CEOAE and its shuffled counterpart. The presence of a rich deterministic structuring (Fig. 2A), completely destroyed by the shuffling (Fig. 2B), is self-evident 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.

View larger version (43K): [in this window] [in a new window]   Fig. 2.   Recurrence plots of a CEOAE waveform. A and B are recurrence plots before and after random reshuffling, respectively, of waveform A in Fig. 1. Corresponding samplings of waveforms are shown at bottom. Vertical line in bottom left marks starting point (175 ms) for recurrence quantification analysis (RQA; see text). Notice that, in B, recurrence structure disappears completely. RQA variables: percent of recurrence (Rec) = 52.71, percent of determinism (Det) = 98.10 (A); Rec = 0.96, Det = 26.74 (B).

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 time-series 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 (shuffling-sensitive) 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.

View larger version (9K): [in this window] [in a new window]   Fig. 3.   Correlation (reproducibility) between 2 waveforms of otoacoustic emission signal (Repro) values and first principal component (PC1) over RQA variables. Corresponding Pearson r score = 0.84 (see text). (It is worth noting that PC1 still measures differences between deterministic structuring of signals in region PC1 > 0 in which Repro reaches a plateau phase.)

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.

View larger version (18K): [in this window] [in a new window]   Fig. 4.   Dynamical analysis of a CEOAE in the sliding window mode (RQE); a-c refer to same CEOAE as in Figs. 1 and 2, analyzed by overlapping sliding windows of 4-ms length (100 points) and shift = 1 point (overlap = 99 points). Variables are plotted in central position in standardized units (su), i.e., after subtracting average value from absolute values and dividing by standard deviation in each window. a: Mean and SD profiles of waveform A. Corresponding profile for waveform B is practically indistinguishable. b: Profile of slope of linear relationship between distance from main diagonal and number of scored recurrences (Trend) for waveforms A and B. c: Rec, Det, and entropy (Ent) difference profiles for waveforms A and B.

Individual variability in OAEs. Figure 5 shows the location of the 56 signals in our data set over the PC2-PC3 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 PC2-PC3 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 PC2-PC3 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.

View larger version (7K): [in this window] [in a new window]   Fig. 5.   Individual features of CEOAEs in a principal component space. A representation is shown of the signals in Table 1 over their own second- and third- principal component (PC2, PC3) plane (). Arrows indicate signals recorded from same ear of same subject. , Signals recorded from same ear of same subject over different recording sessions.

	DISCUSSION

TOP ABSTRACT INTRODUCTION EXPERIMENTAL AND ANALYTIC... RESULTS DISCUSSION REFERENCES

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 "rule-obeying" (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 well-known high sensitivity of RQA to fine details of signals is directly demonstrated in the case of CEOAEs by comparing the cross-correlation of the two waveforms of the same signal with the cross-correlation 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. 4b) 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 defective-hearing 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 of RESULTS (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.