Vivography™: A fast, accurate, and reliable new method for measuring DPOAE andASSR

Xinde Li, M.Sc.

Harold Wodlinger, Ph.D.

Yuri Sokolov, Ph.D., MBA

Vivosonic Inc., 56Aberfoyle Cr., Suite 620, Toronto, ON Canada M8X 2W4

Tel. 416-231-9997, toll-free 1-877-255-7685(Canada and the US),

Fax 416-231-2289,

E-mail vivo@vivosonic.com,

Web www.vivosonic.com

Abstract

Conventionally, DPOAE and ASSR signals are measured using timeaveraging and the Fast Fourier Transform (FFT) method.  In this method, signals are first dividedinto data blocks, and these blocks are then averaged over time to improve thesignal-to-noise ratio.  However, blockaveraging introduces significant time delays before the signal is known,especially in the presence of artefacts. Transient artefacts, like the slamming of a door or a person talking inDPOAE recording, or muscular artefacts in ASSR recording, when averaged intothe calculation, degrade the accuracy of the results.  In addition, the FFT method does not allow continuous recordingof DPOAE signals, making measurements of rapid changes of DPOAEsdifficult.  Such rapid changes may be ofinterest for the study of temporal characteristics of DPOAE suppression.

Vivography™ is a new, patented method [1] for analyzingphysiological signals that is faster and more accurate than the FFTmethod.   While the FFT method analyzesall of the frequency components in the signal, Vivography™ analyzes onlythe frequencies of interest: in case of DPOAE, the exact frequencies of eachprimary and of the distortion products, and in case of ASSR – the modulationfrequency.   Vivography™ concentratesthe processing power of the computer in looking only for a few frequencies,rather than spending these resources analyzing all frequencies. 

Vivography™ has three major advantages over the FFT method: betterresolution, the ability to continuously record signals, and superior artefactrejection.  In the presence of transientnoise exactly at the frequency of interest, it is impossible to distinguish thesignal from the noise.  However, whenthe noise intensity falls below the intensity of the signal for a period oftime, the signal predominates.  If thesignal is stable, then the measured signal will also be stable for this period.  Vivography™ rejects transient artefacts bylooking for periods of stable signal that also have good signal-to-noiseratio.  A signal is considered to be aresponse if it is stable to within certain level and time criteria. 

Vivography™ can accurately measure good responses even in thepresence of strong transient noise. This unique ability assures the clinician of accurate, fast, andreliable DPOAE and ASSR measurements in real-world environments.

Background

Otoacoustic Emissions (OAEs) are stimulated and non-stimulatedfaint sounds produced by oscillations of the Outer Hair Cells in theCochlea.  These sounds can be measuredin the occluded ear canal and provide valuable diagnosticinformation on the cochlear function [2]. Distortion Product Otoacoustic Emissions (DPOAEs) are pure toneselicited by a stimulus consisting of two pure tones, the primaries, presentedsimultaneously into the occluded ear canal. In humans, the most prominent DPOAE is the cubic distortion product. Specifically, if primaries of frequenciesf₁ and f₂ (f₁ < f₂) are presented, the cubicdistortion frequency is f_DP = 2f₁-f₂.  For example, if f₁ = 3000 Hz, and f₂ = 3600 Hz, then f_DP= (2 * 3000) - 3600 = 6000 - 3600 = 2400 Hz (Fig. 1).

Auditory Steady State Response (ASSR) is an auditory electrical evokedpotential elicited by amplitude- or frequency-modulated pure tones (carrierfrequencies), with modulation frequencies typically around 80-100 Hz, with amajor application to hearing threshold prediction in infants and young children[3].

ConventionalMeasurement Method – the Fast Fourier Transform

Every measured signal – sound, light, radio waves, etc., iscomposed of one or more signal elements with different frequencies andphases.  The Fast Fourier Transform(FFT) is a mathematical method for analyzing “all” of the frequency componentsof a signal [4].  First, the signal isrecorded digitally for a period of time. Next, this signal record is analyzed using FFT software.  The analysis shows the spectral signalelements at every frequency within the analysis window.  Figure 2 shows a pure sine-wave signal at1000 Hz, and a display of the FFT analysis; in this case, there is only asingle frequency element at 1000 Hz.

Fig 2. Sine-wave signal and its FFT

The ideal signal measured during a DPOAE test consists of twoprimaries and the resulting DP signal, all at different frequencies; the signaldisplay and FFT analysis is shown in Figure 3.

Fig. 3 Ideal cubic DP signal and FFTspectrum

Unfortunately, real signals in DPOAE and ASSR measurements containacoustical and electronic noise respectfully. This makes it difficult to measure the amplitude of the signalsaccurately.  For example, a morerealistic cubic DPOAE signal and spectrum are shown in Figure 4.

Fig. 4 Typical DPOAE signal and FFT spectrum

Conventionally, DPOAE or ASSR signals are divided into data blocksand averaged to improve the Signal-to-Noise Ratio (SNR).  However, block averaging introducessignificant time delays before the signal is known, especially in the presenceof artefacts.  Artefacts that aretransient, like the slamming of a door or a person talking in DPOAE testing, ormuscular artefacts in ASSR testing, are averaged into the calculation,degrading the accuracy of the results.  In addition, the FFT method does not allow continuous recording ofsignals, making measurements of rapid signals changes difficult.  However, such rapid changes may be ofinterest, for example, for the study of dynamic characteristics of DPOAEsuppression.

New measurementmethod – Vivography™

Vivography is a new, patented method for analyzing DPOAE signalsthat is faster and more accurate than the FFT method.  While the FFT method analyzes all of the frequency components inthe signal, Vivography™ analyzes only the frequencies of interest: theprimaries and DPOAEs, or ASSR modulation frequency.   Vivography™ concentrates the processing power of the computer inlooking only for a few frequencies, rather than spending these resourcesanalyzing all frequencies.  Vivography™is like pointing a laser beam directly at a target only, while the FFT methodis like using a flashlight to illuminate a wide area containing the target andmany other objects.

Vivography™ is based on a digital signalprocessing technique known as Kalman filtering, which is a recursive solutionto the discrete-data linear filtering problem, first published in 1960 [5,6].  Since that time, due in large partto advances in digital computing the Kalman Filter has been the subject ofextensive research and application, particularly in the area of autonomous orassisted navigation.

The Kalman filter is a set of complexmathematical equations that provides an efficient computational solution of theleast-squares method. The filter is very powerful in several aspects: itsupports estimations of past, present, and future states, and it can do so evenwhen the precise nature of the modeled system is unknown.  The mathematical basis of Kalman filteringis described in the Appendix.

Vivography™ hasthree major advantages over the averaging/FFT method: higher resolution,continuous recording of signals, and transient artefact rejection.

Higher resolutionand speed

Vivography™ is soefficient that it can isolate the frequencies of the primaries and the signalwith much higher resolution than the FFT method.  The higher the resolution, the more accurate the measurement,because artefact that is close to, but not exactly at the signal frequency, willbe rejected.  For example, the FFT methodrequires at least 10 seconds of data in order to achieve a resolution of 0.1Hz.  The signal is averaged within this10-second interval.  Computation timedepends on processor speed, but would typically exceed one minute.  Vivography™ achieves the same resolution of0.1 Hz in a portion of a second without block data averaging.  High frequency resolution combined with thespeed of analysis makes it ideal for testing at multiple test frequencies thatis particularly important for multi-frequency ASSR testing. 

ContinuousRecording of signals

Unlike the FFTmethod, Vivography™ does not record the signal for a period of time beforeanalyzing it – rather, it analyzes the signal continuously.  Once the DPOAE signal has been acquired, itis followed and displayed in real time without any block averaging.  This makes Vivography™ the ideal method insuch applications as the study of DPOAE behavior over time, particularly withsuppression – because Vivography™ can measure not only the amplitude, but alsothe latency of the suppression accurately with one-millisecond resolution.  

Transient artefactrejection

By continuouslyrecording the signal, Vivography™ has the unique ability to identify and rejectnoise that is transient in nature; noises like talking, crying, doors slamming,muscular electric artefacts etc.  Sincemost noise covers a broad frequency range, there will usually be frequencycomponents of this noise that overlap with the signal. 

The left panel ofFigure 5 shows the spectrum of a DPOAE signal from a patient’s ear at afrequency of 800 Hz and a level of +2 dB SPL. In the right panel of Figure 5, a transient noise is introduced which,for a short period of time, contains energy of +8 dB SPL at 800 Hz.  In this case, the DPOAE signal will be“buried” in the noise, since the level of the noise at 800 Hz is higher thanthe level of the DPOAE signal.  In thisinstance, both the FFT and Vivography™ methods will measure only the level ofthe noise, i.e. +8 dB.    However, oncethe noise falls, Vivography™ can quickly adjust its bandwidth to approach theDPOAE signal alone, but the FFT method will continue to block-average,measuring an average of both the noise and DPOAE signals.  

     Fig. 5   Left - spectrum of a pure DPOAE signal

Right – spectrum of transient noise at the same instant of time

Figure 6 shows agraph of only the 800 Hz frequency component, measured over time.  The left panel shows the DPOAE signal, whichis stable.  The right panel shows thenoise signal, which varies with time due to its transient nature.  The bottom panel shows the sum of the DPOAEsignal and the noise signal, as a DPOAE instrument would measure it.  Note that the DPOAE signal rises above thenoise signal for 1.5 seconds beginning at time 2 seconds; that part of thesignal is displayed in red.

Figure 6:   Recording of the 800 Hz frequency component over time

Left – DPOAE signal (stable)

Right – transientnoise signal

Bottom – sum of the DPOAE and noisesignals.  The DPOAE signal can bemeasured during the time shown in red.

During transientnoise, it is impossible to distinguish the DPOAE signal from the noise.  However, when the noise level falls belowthe intensity of the DPOAE signal, the DPOAE signal predominates.  If the DPOAE is stable, then the measuredsignal will also be stable for this period of time.  Vivography™ rejects transient artefacts by looking for periods ofstable signal that also have good signal-to-noise ratio.   For example, a signal is considered to be aDPOAE response if it is stable to within ±1 dB SPL over a period of 400ms. 

Good DPOAE responsescan be accurately measured by Vivography™, even in the presence of strongtransient noise.  This unique abilityassures the clinician of accurate, reliable DPOAE and ASSR measurements inreal-world environments.

Clinicalapplications

Vivography™ isapplicable in those clinical situations where, on the one hand, the frequencyof the signal is known, while on the other hand, high speed and accuracy ofmeasurement are required.  Excellentclinical applications include DPOAE and ASSR measurements.  Vivography™ proved to be very fast,accurate, and reliable in real-life clinical settings.  Its accuracy and reliability is particularlyimportant for diagnostics and hearing-loss monitoring in ototoxicity and noise-and music-induced hearing loss, while its robustness in transient noises isimportant for hearing-screening settings where acoustic conditions are far fromthose in a soundproof booth.  Real-timerecording of DPOAEs using Vivography™ is effective for the study of MedialOlivo-cochlear Reflex (MOCR): it allows adequate temporal resolution to studythe latency of DPOAE suppression onset and offset [7, 8].

Implementation

Vivosonic hasimplemented DPOAE Vivography™ in its portable clinical audiometer Vivo 200 DPSVivoScan™ that measures DPOAEs and is highly appreciated by its users; the Vivo210 DPT VivoScan+™ that combines DPOAE and TEOAE; and the Vivo 600 R forreal-time DPOAE research.  We are nowimplementing Vivography™ for clinical ASSR testing in ICS Medical CHARTR®Evoked Potential System, as well as in the multi-functional Vivo 250 OEPVivoScan++™ that will combine DPOAE, TEOAE, ABR, and ASSR functions in oneportable instrument.

References

1.      Li, X.,Sokolov, Yu., Kunov, H.  System and method for processing lowsignal-to-noise ratio signals. United States Patent 6,463,411. Filed May 7, 2001, issued October 8,2002.

2.      Lonsbury-Martin,B.L., Martin, G.K.  Distortion Product Otoacoustic Emissions. In: OtoacousticEmissions: Clinical Applications.  Ed.M.S. Robinette and T.J. Glattke. Thieme, 1997, p. 83-109.

3.      Sininger,Y.S., Cone-Wesson, B.  Threshold prediction using auditorybrainstem response and steady-state evoked potentials with infants and youngchildren.  In: Handbook of ClinicalAudiology, 5^th ed.  Jack Katzed.  Lippincott, Williams, and Wolkins,2002, p. 298-322.

4.      Poularikas,A.D, et. al.. Digital Signal Processing.In: The Electrical Engineering Handbook. CRC Press, 1993, p. 229 – 278.

5.      Maybeck, P.S.Stochastic Models, Estimation, andControl, V.1. Academic Press, 1979.

6.      Anderson, B.,Moore, J.  Optimal Filtering, Prentice-Hall, 1979.

7.      James, A. L.,Mount, R. J., Harrison, R. V.  Contralateral suppression of DPOAEs measuredin real time.  Clin. Otolaryngol.,V. 27, p. 107-112.

8.      James, A. L.,Harrison, R. V., Pienkowski, M., Dajani, H. R., Mount, R. J. Dynamics of of real time DPOAE contralateralsuppression in chinchilla and humans. Audiol. & Neurootol.  (under review).

Appendix – Kalmanfiltering

Consider the problem of estimating the variables of some system. Indynamic systems (that is, systems that vary with time), the system variablesare often denoted by the term state variables.  Assume that the system variables, represented by the vector x,are governed by the equation x_k+1 = Ax_k + w_kwhere w_k is random process noise, and thesubscripts on the vectors represent the time step.  For instance, if our dynamic system consists of a spacecraft whichis accelerating with random bursts of gas from its Reaction Control Systemthrusters, the vector x might consist of position p and velocity v. Then the system equation would be

……………………(1)

where a_kis the random, time-varying acceleration and T is the time between step kand step k+1.   Now suppose wecan measure the position p.  Thenour measurement at time k can be denoted as follows

z_k = p_k + v_k ………………………………………………..(2)

where v_k is random measurement noise.

Equation 1 is usually called StateEquation and Equation 2 is called ObservationEquation.

Generally, we can write State Equation and Observation Equation in thefollowing form:

In Equations 3 and 4 above, is statevector,is processnoise,ismeasurement noise vector, is statetransition matrix, ismeasurement matrix.

The question that the Kalman Filter addresses is this: Given ourknowledge of the behavior of the system, and given our measurements, what isthe best estimate of position and velocity? We know how the system behavesaccording to the system equation, and we have measurements of the position, sohow can we determine the best estimate of the system variables? Certainly, wecan do better than just take each measurement at its face value, especially ifwe suspect that we have a lot of measurement noise.

The Kalman Filter is formulated as follows.  Suppose we assume that the process noise w_kis white Gaussian noise with a covariance matrix Q.  Further, assume that the measurement noise iswhite Gaussian noise with a covariance matrix R, and that it is notcorrelated with the process noise.  Wemight want to formulate an estimation algorithm such that the followingstatistical criteria hold:

1.    The expected valueof our estimate is equal to the expected value of the state. That is, "onaverage," our estimate of the state will be equal to the true state.

2.    We want anestimation algorithm that, of all possible estimation algorithms, minimizes theexpected value of the square of the estimation error. That is, "onaverage," our algorithm gives the "smallest" possible estimationerror.

It so happens that the Kalman Filter is the estimation algorithmthat satisfies these two criteria. There are many alternative ways to formulatethe Kalman Filter equations. One of the formulations is given in the followingEquations 5– 9:

In the above equations, the superscript -1 indicates matrixinversion and the superscript T indicates matrix transposition. Ris the covariance matrix of the measurement noise, Q is covariance matrix ofmodel noise (process noise), K is called the gain matrix, and Pis called the covariance of the estimation error.

Equation 6 is intuitive. The first term is our pre-knowledge aboutthe state at time k.  It is thestate estimate if we did not have a measurement. In other words, the stateestimate propagates in time just like the state vector (see Equation 1).  The second term in Equation 5 is called the correctorterm, and it represents how much to correct the propagated estimated due to ourmeasurement.  Inspection of Equation 5indicates that if the measurement noise is much greater than the process noise,K will be small (that is, we will not give much credence to themeasurement); if the measurement noise is much smaller than the process noise, Kwill be large (that is, we will give a lot of credence to the measurement).

To use Kalman Filter to process DPOAE or ASSR signal, we need firstto model the signal. Following is an example of modeling the recorded voltagefrom DPOAE probe.

In this model,  ,,  are actually the f₁, f₂,and f_DP components at time k.  Once the model is established, we can use Equations 5-9 toestimate vector x_k, by recursively applying Equations5-9, we can estimate both Stimuli waveform and DPOAE waveforms.

It is worth to point out that there are many ways to model therecorded signal: we can use time-invariant model as shown above or we can usetime-variant model to deal with time variant cases.  Vivography™ uses different models to meet different DPOAE or ASSRmeasurement needs.  It also has some featuresthat are not available in the “standard” Kalman Filter: for example, Vivography™provides two parameters to control the tracking speed and accuracy that make thesystem more flexible particularly for studying DPOAE dynamics.