A template-free approach for determining the latency of single events of auditory evoked M100

Size: px

Start display at page:

Download "A template-free approach for determining the latency of single events of auditory evoked M100"

Polly Warner
5 years ago
Views:

1 INSTITUTE OF PHYSICS PUBLISHING Phys. Med. Biol. 5 (25) N43 N48 PHYSICS IN MEDICINE AND BIOLOGY doi:1.188/ /5/3/n4 NOTE A template-free approach for determining the latency of single events of auditory evoked M1 M Burghoff 1,ALink 1, A Salajegheh 2, C Elster 1, D Poeppel 2,3,4 and L Trahms 1 1 Physikalisch-Technische Bundesanstalt (PTB), Berlin, Germany 2 Cognitive Neuroscience of Language Laboratory, University of Maryland College Park, MD, USA 3 Department of Linguistics, University of Maryland College Park, MD, USA 4 Department of Biology, University of Maryland College Park, MD, USA Received 24 June 24, in final form 2 December 24 Published 19 January 25 Online at stacks.iop.org/pmb/5/n43 Abstract The phase of the complex output of a narrow band Gaussian filter is taken to define the latency of the auditory evoked response M1 recorded by magnetoencephalography. It is demonstrated that this definition is consistent with the conventional peak latency. Moreover, it provides a tool for reducing the number of averages needed for a reliable estimation of the latency. Singleevent latencies obtained by this procedure can be used to improve the signal quality of the conventional average by latency adjusted averaging. Introduction Electroencephalographic (EEG) and magnetoencephalographic (MEG) recordings of evoked or event related responses are contaminated by perturbations originating from various sources such as instrumental noise, environmental interference and the brain s own background activity. To suppress the contribution of such perturbations, evoked and event related EEG and MEG responses are usually analysed in terms of their average. Averaging is a widely accepted and very successful data processing concept for studying all kinds of brain function. By definition, the average only reflects the reproducible part of single events, and information on possible variations is lost. But biosignals are not necessarily fully reproducible. Knowledge about their variation may contribute to a deeper understanding of higher cognitive functions, and maybe even of short latency responses (Liu and Ioannides 1996, Kisley and Gerstein 1999). In order to retrieve such information several approaches have been suggested (von Spreckelsen and Bromm 1988, Karjalainen et al 1999, Heinrich et al 1999, Jung et al 21), most of which characterize single events by their amplitude and latency deviation from a signal template (Woody 1967, Tuan et al 1987, Jaskowski and Verleger 1999). Our approach does not refer to a template, but is based on the assumption that relevant information can be found in a narrow frequency band. In most cases, a suitable bandwidth is /5/343+6$3. 25 IOP Publishing Ltd Printed in the UK N43

2 N44 M Burghoff et al evident from a simple-frequency analysis of the averaged signal. After applying an adequate narrow band Gaussian filter to an evoked response, the phase signal is derived from the complex filter output. This nonlinear transformation provides a measure for the latency that remains robust in the presence of a high-noise level (Salajegheh et al 24). Here, we show how latencies determined by this method depend on the number of events taken for averaging. In addition, we demonstrate how knowledge of single-event latencies may help us to improve the signal-to-noise ratio of the averaged signal by adjusting the latency of each single event before averaging. To this end we analysed MEG recordings of the auditory M1, sometimes also referred to by the notion Nm1, which is known to vary in latency as a function of the stimulation tone frequency (Jacobson et al 1992, Roberts et al 2). Methods Data acquisition A total of 6 binaural stimulations of three pseudorandomly interleaved sinusoidal tones (125 Hz, 25 Hz, 1 Hz) of 4 ms duration and matched loudness were presented to the subject. Auditory evoked fields were recorded in a magnetically and acoustically shielded room (AK3b, VAC, Hanau, Germany) by a whole-head MEG containing 93 axial gradiometers (Eagle Technology, Kanazawa, Japan) (Kado et al 1999). Magnetic fields were recorded continuously using a sampling rate of 5 Hz and a high pass of.1 Hz. A frequency analysis of the recorded evoked fields showed that the M1 intensity peaks around 1 Hz. So we focused our analysis on a frequency band of F = 3 Hz width around a centre frequency of F = 1 Hz. Signal processing The Gaussian band-pass filter characterized by the coefficients ) h(l) = h norm exp( jω l)exp ( l2, l = L,...,,...L, (1) 2β 2 has an optimal time-bandwidth product and does not generate a phase shift (Link et al 21). For a large number of filter coefficients, e.g., for L = 4, both transfer function and impulse response receive a Gaussian shape, and the bandwidth of the transfer function depends on β by the approximation f =.13/β. The response of this filter to a real input function x(n) is a complex output function y(n) = y re (n) +jy im (n), n =,...,N 1, (2) where the real and the imaginary component, defined by the convolutions y re (n) = x(n) h re (n) and y im (n) = x(n) h im (n), are Hilbert transforms of each other. Alternatively, y can be decomposed into its envelope r(n) = yre 2 (n) + y2 im (n) and its phase ψ(n) = arctan(y im (n)/y re (n)), so that y(n) = r(n)exp[jψ(n)]. Due to the narrow bandwidth of the filter and the properties of the Hilbert transformation, ψ(n) can be decomposed into a fast and a slowly varying part (Papoulis and Pillai 22) ψ(n) = ω n ϕ(n). (3) For epochs which are short compared to 1/ f, we can use the linear approximation ψ(n) = ω n ϕ, so that every single epoch, i, is characterized by a constant individual phase ϕ i, or, in terms of the centre frequency ω, by a latency n i = ϕ i /ω + n. (4)

3 A template-free approach for determining the latency of single events of auditory evoked M1 N45 x(n) Gaussian Filter 2b y re (n) y im (n) Conventional averaging 2c R(n) Ψ(n) 2a <x(n)> sin Ψ (n i ) = 2d <x(n-n i )> Latency adjusted averaging 3 n i Figure 1. Signal processing scheme. A single event, x(n), is filtered, real and imaginary parts of the filter output, y re (n) and y im (n), are decomposed into envelope and phase, R(n) and ψ(n), from sin ψ(n) the individual latencies, n i, are determined. After compensating the latency shift for each single event, the resulting average, x(n n i ), can be compared to its conventional counterpart, x(n). Encircled numbers refer to the other figures of this note, for y(n) and sin ψ(n), figures 2(b) and (c) do not reflect the single events, but the average over all samples. This defines the relative shift between the latencies of individual events, but leaves their absolute value open by the choice of n = ψ(n)/ω. Figure 1 summarizes the signal processing scheme. Results and discussion By averaging separately some 2 events for each stimulation frequency, the signal-to-noise ratio of the auditory evoked response is high enough to show a pronounced deflection of the MEG trace 1 2 ms after presenting the stimulus (figure 2(a)). As is known from earlier studies, the latency of this deflection decreases with the frequency of the stimulation tone (Jacobson et al 1992, Roberts et al 2). A quantitative measure of the latency can be defined as the time interval that has passed from stimulus onset to a somewhat arbitrarily chosen distinguished feature of the deflection, such as its peak or its maximum slope. Real and imaginary parts of the output of the complex 4th order Gaussian filter are much smoother, due to the suppression of contributions from outside the narrow band pass at 1 Hz (figure 2(b)). Within the chosen band pass, the intensity is the highest within an interval from 1 to 2 ms after stimulation, indicating that the signal energy in the selected frequency range concentrates on the duration of the studied evoked response. The maximum of the real part coincides approximately with the position of the peak of the unfiltered signal. In terms of the complex phase, this instant corresponds to the intersection of sin ψ(n) with the ψ = axis (figure 2(c)) and we define this instant as the fiducial point of the M1 latency. Note that this implicitly defines n = in equation (4). The smoothness of the trace in figure 2(c) indicates that a reduced number of averages may still provide meaningful results. The box plots of figure 3 show how latency information derived from the zero crossing of sin ψ(n)is successively broken down to averages of less and less events and even down to single responses. Average blocks of 36 responses unambiguously reflect the frequency dependence of the latency (figure 3(a)). A break down to blocks of six events still results in only a few overlapping latencies (figure 3(b)), and even the latencies

4 N46 M Burghoff et al (a) 25 (b) B(t)/fT -125 B(t)/fT (d) 25 (c) B(t)/fT B(t)/fT (e) sin ψ t/ms t/ms Figure 2. Evoked field response to binaural stimulation of 125 Hz recorded by the MEG channel above the position C3 according to the 1 2 system. Different stages of signal processing are presented: (a) average over some 2 events, (b) real (boldface) and imaginary (fine) parts of the output after applying a complex narrow band Gaussian filter to signal (a), (c) sine of the phase of the complex output, (d) reconstructed averaged unfiltered signal after adjusting the latency shift of each single event, (e) variance across the 2 events corresponding to the conventional average of (a) (fine) and to the latency adjusted average of (d) (boldface). determined for single events are fairly well clustered around distinct average values for the latency, so that most of the single responses to 125 Hz can be distinguished from the 1 Hz responses (figure 3(c)). This information on single-event latencies can be utilized to improve the conventional view of the unfiltered evoked response by latency adjusted averaging (LAA) (Brown et al 1998). Averaging unfiltered epochs, which are shifted in time according to their individual latency, results in a much sharper and two times higher peak than conventional averaging (figures 2(a) and (d)). But note that LAA is an appropriate procedure only if the observed fluctuations of the single latencies are generated mainly by the investigated physiological process itself rather than by noise of other sources. This condition is by no means justified apriori, nor should the resulting improvement of the signal-to-noise ratio be considered an

5 A template-free approach for determining the latency of single events of auditory evoked M1 N47 2 Latency/ms (a) Latency/ms 15 (b) 1 2 Latency/ms 15 (c) Frequency/Hz Figure 3. Distribution of the latencies of M1 for 125 Hz, 25 Hz and 1 Hz determined for blocks of 36 averages (a), 6 averages (b) and single events (c). In this presentation, the median value is represented by the horizontal dash in the middle of the distribution, the notches indicate its confidence interval, upper and lower border of the box indicate the 25% and 75% percentiles, the outer two dashes the 1% and 9% percentiles of the distribution. In addition, outliers beyond these limits are indicated by single crosses. a posteriori justification. If the latency fluctuations in the repetitively recorded signals were solely caused by external noise, LAA would also increase the peak amplitude, but this peak would be an overestimation of the signal due to the inclusion of deliberately collected noise contributions which do not add further information. A little more insight into what happens during LAA is given by looking at the temporal development of the variances across the epochs of the underlying single-event recordings (figure 2(e)). Without latency adjustment, the variance level between 1 ms and 2 ms is slightly higher than outside of this interval, indicating that there are indeed fluctuations of the evoked response which contribute to the noise during this interval. By adjusting the latency of the epochs, the variance level around 15 ms decreases significantly. This is exactly what we expect from a reduction of the latency fluctuations of the signal and it can be taken for evidence that LAA indeed compensated for the inherent instability of the evoked response and improved the signal-to-noise ratio. Conclusion By narrow band complex Gaussian filtering, noise in the MEG of the M1 evoked response is dramatically reduced, leaving the information relevant for its latency untouched. This

6 N48 M Burghoff et al is illustrated by evoked responses to tones of different frequencies which preserve the well-known latency shift in small blocks of averages and even in signals of single events. This tool could be particularly helpful for studying event related responses reflecting higher cognitive function for which the number of repetitions may be limited. On the condition that latency fluctuations are caused mainly by the temporal instability of the response itself and not by noise, knowledge on individual latencies can be used by LAA to improve the signal-to-noise ratio of averaged responses. Note that a similar assumption is the background for the well-established template approach for studying single events. Inspecting the variance of the individual responses with and without latency adjustment may help us to identify situations where this condition is not met and LAA would generate more heat than light for MEG or EEG recordings of evoked responses. Acknowledgments The study was performed within the framework of the Berlin NeuroImaging Center (BMBF 1 GO 28). The study was in part supported by NIH DC566 to DP. References Brown W S, Bjerke M D and Galbraith G C 1998 Interhemispheric transfer in normals and acallosals: latency adjusted evoked potential averaging Cortex Heinrich H, Dickhaus H, Rothenberger A, Heinrich V and Moll G H 1999 Single-sweep analysis of event-related potentials by wavelet networks methodological basis and clinical application IEEE Trans. Biomed. Eng Jacobson G P, Lombardi D M, Gibbens N D, Ahmad B K and Newman C W 1992 The effects of stimulus frequency and recording site on the amplitude and latency of multichannel cortical auditory evoked potential (CAEP) component N1 Ear Hear Jaskowski P and Verleger R August 1999 Amplitudes and latencies of single-trial ERPs estimated by a maximumlikelihood method IEEE Trans. Biomed. Eng Jung T-P, Makeig S, Westerfield M, Townsend J, Courchesne E and Sejnowski T J 21 Analysis and visualization of single-trial event-related potentials Hum. Brain Mapp Kado H, Higuchi M, Shimogawara M, Haruta Y, Adachi Y, Kawai J, Ogata H and Uehara G 1999 Magnetoencephalogram systems developed at KIT IEEE Trans. Appl. Supercond Karjalainen P A, Kaipio J P, Koistinen A S and Vauhkonen M 1999 Subspace regularization method fort he single-trial estimation of evoked potentials IEEE Trans. Biomed. Eng Kisley M A and Gerstein G L 1999 Trial-to-trial variability and state-dependent modulation of auditory-evoked responses in cortex J. Neurosci Link A, Endt P, Oeff M and Trahms L 21 Variability of the QRS signal in high-resolution electrocardiograms and magnetocardiograms IEEE Trans. Biomed. Eng Liu L and Ioannides A 1996 A correlation study of averaged and single trial MEG signals: the average describes multiple histories each in a different set of single trials Brain Topogr Papoulis A and Pillai S U 22 Probability, Random Variables and Stochastic Processes (New York: McGraw-Hill) Roberts T P L R, Ferrari P, Stufflebeam S and Poeppel D 2 Latency of the auditory evoked neuromagnetic field components: stimulus dependence and insights towards perception J. Clin. Neurophysiol Salajegheh A, Link A, Elster C, Burghoff M, Sander T, Trahms L and Poeppel D 24 Systematic latency variation of the auditory evoked M1: from average to single-trial data NeuroImage TuanPD,Möcks J, Köhler W and Gasser T 1987 Variable latencies of noisy signals: estimation and testing in brain potential data Biometrika von Spreckelsen M and Bromm B 1988 Estimation of single-evoked cerebral potentials by means of parametric modeling and Kalman filtering IEEE Trans. Biomed. Eng Woody C D 1967 Characterization of an adaptive filter for the analysis of variable latency neuroelectric signals Med. Biol. Eng

19 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, 2-7 SEPTEMBER 2007 AUDITORY EVOKED MAGNETIC FIELDS AND LOUDNESS IN RELATION TO BANDPASS NOISES

19 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, 2-7 SEPTEMBER 2007 AUDITORY EVOKED MAGNETIC FIELDS AND LOUDNESS IN RELATION TO BANDPASS NOISES PACS: 43.64.Ri Yoshiharu Soeta; Seiji Nakagawa 1 National