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Chemosensory Perception ISSN 1936-5802Volume 5Combined 3-4 Chem. Percept. (2012) 5:280-291DOI 10.1007/s12078-012-9134-8

Empirical Mode Decomposition-BasedApproach for Intertrial Analysis ofOlfactory Event-Related Potential Features

Chi-Hsun Wu, Po-Lei Lee, Chih-HungShu, Chia-Yen Yang, Men-Tzung Lo,Chun-Yen Chang & Jen-Chuen Hsieh

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Empirical Mode Decomposition-Based Approach for IntertrialAnalysis of Olfactory Event-Related Potential Features

Chi-Hsun Wu & Po-Lei Lee & Chih-Hung Shu &

Chia-Yen Yang & Men-Tzung Lo & Chun-Yen Chang &

Jen-Chuen Hsieh

Received: 27 March 2012 /Accepted: 27 August 2012 /Published online: 12 September 2012# Springer Science+Business Media, LLC 2012

Abstract This study presents an empirical mode decomposi-tion (EMD)-based method to study the intertrial variability ofolfactory event-related potential (OERP) features. The olfac-tory stimulus in this study was a mixture of 60 % humidity airand 40 % phenyl ethanol alcohol generated by a computer-controlled olfactometer with a constant flow rate of 8 L/min.A 32-channel whole-head EEG system was utilized to inves-tigate the olfactory responses in 12 healthy subjects. EachEEG epoch was segmented based on the olfactory stimulus

onset and subsequently decomposed into a set of intrinsicmode functions (IMFs) by using EMD. Only IMFs that metboth frequency and spatial dual criteria were chosen as OERP-related IMFs for reconstructing the noise-suppressed single-trial activity, and those significant trials with N1/P2 ampli-tudes lower/greater than the mean minus/plus two times thestandard deviations of baseline amplitudes were denoted assingle-trial OERP for intertrial variability analysis. The pres-ent approach enables the capability to study intertrial OERP

Chem. Percept. (2012) 5:280–291DOI 10.1007/s12078-012-9134-8

C.-H. Wu : P.-L. Lee (*)Department of Electrical Engineering, National Central University,No.300, Jhongda Rd.,Jhongli City, Taoyuan County 32001, Taiwan, Republic of Chinae-mail: pllee@ee.ncu.edu.tw

C.-H. Wue-mail: rexchwu@gmail.com

C.-H. Wu : P.-L. Lee : C.-H. Shu : J.-C. HsiehLaboratory of Integrated Brain Research, Department of MedicalResearch and Education, Taipei Veterans General Hospital,No.201, Sec. 2, Shipai Rd., Beitou District,Taipei City 11217( Taiwan, Republic of China

C.-H. Shue-mail: chshu@vghtpe.gov.tw

J.-C. Hsiehe-mail: jchsieh@vghtpe.gov.tw

P.-L. Lee : J.-C. HsiehInstitute of Brain Science, National Yang-Ming University,Taipei, Taiwan

P.-L. Lee :M.-T. LoCenter for Dynamical Biomarkers and Translational Medicine,National Central University,No.300, Jhongda Rd.,Jhongli City, Taoyuan County 32001, Taiwan, Republic of China

M.-T. Loe-mail: mzlo@ncu.edu.tw

C.-H. ShuDepartment of Otolaryngology, Taipei Veterans General Hospital,No.201, Sec. 2, Shipai Rd., Beitou District,Taipei City 11217( Taiwan, Republic of China

C.-Y. YangDepartment of Biomedical Engineering, Ming-Chuan University,No. 5 De Ming Rd., Gui Shan District,Taoyuan County 333( Taiwan, Republic of Chinae-mail: cyyang@mail.mcu.edu.tw

C.-Y. ChangScience Education Center and Graduate Institute of ScienceEducation, National Taiwan Normal University,No. 88, Sec. 4, Ting-Chou Road,Taipei City 11677, Taiwane-mail: changcy@ntnu.edu.tw

C.-Y. ChangDepartment of Earth Sciences,National Taiwan Normal University,Taipei, Taiwan

J.-C. HsiehSchool of Medicine, National Yang-Ming University,Taipei, Taiwan

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features, such as the latencies and amplitudes of N1 and P2peaks, on trial-by-trial basis, which may be helpful to shedlight on future olfactory dysfunction studies.

Keywords Electroencephalography . Empirical modedecomposition . Olfactory event-related potential

AbbreviationsANN Artificial neural networkA-N1 N1 peak amplitudeA-N1P2 Peak-to-peak N1P2 amplitudeA-P2 P2 peak amplitudeCOI Channel of interestDRS Dementia rating scaleECD Equivalent current dipoleECG ElectrocardiogramEMD Empirical mode decompositionEMG ElectromyographyEOG ElectrooculogramERP Event-related potentialFFT Fast Fourier transformGMM Gaussian mixture modelIMF Intrinsic mode functionISI Interstimulus intervalL-N1 N1 latencyL-P2 P2 latencyMS Multiple sclerosisOERP Olfactory event-related potentialPEA Phenyl ethyl alcoholPD Parkinson’s diseaseSSP Signal space projection

Introduction

Olfactory event-related potential (OERP) received little atten-tion prior to the 1980s due to the lack of an accurate method toproduce a selective and controlled odorant for inducing hu-man olfactory responses. Only after Kobal solved the majormethodological concern of controlling odorant stimulation atthe millisecond level did the measurement of OERP becomean objective tool for examining olfactory function (Kobal andHummel 1988). Compared to other psychophysical examina-tion tools for olfactory dysfunction assessment, OERPs aredirectly correlated to neuronal activities, are independent ofthe subject’s bias, and have high temporal resolution forsequentially investigating olfactory information. Researchershave used OERPs to explore neurophysiological mechanismsin normal brains and to probe pathophysiology in the dis-eased. The OERP technique has been used as a diagnosticindex (Lorig 2000) for investigating congenital anosmia (Cuiand Evans 1997), normal aging (Murphy et al. 2000), Parkin-son’s disease (Barz et al. 1997), multiple sclerosis (Doty et al.

1999), dementia (Morgan and Murphy 2002), brain tumors(Daniels et al. 2001), head trauma (Geisler et al. 1999), andepilepsy (Hummel et al. 1995).

The aforementioned OERP studies required an average ofolfactory responses over many trials, which may mask theintertrial variability and smear the OERP amplitudes. SinceEEG responses can vary from trial to trial depending on thesubject’s performance and state and since they carry importantinformation on cognitive and physiological states such asexpectation, attention, and arousal (Jung et al. 2001; Lee etal. 2003, 2009), the average of many trials may obscure theintertrial OERP variability during olfactory experiments. Pre-vious researches show that OERP responses are affected bythe intensity of odorized air (Rombaux et al. 2006), flow rateof odorant stimulus (Rothe 2003), interstimulus interval (ISI)(Hummel and Kobal 1999; Wang et al. 2002; Wetter andMurphy 2003), subject vigilance (Geisler and Murphy 2000;Nordin et al. 2005), age of participant (Evans et al. 1993;Hummel et al. 1998, 2003; Covington et al. 1999), gender(Evans et al. 1993; Morgan et al. 1997, 1999; Lundstromet al. 2005), hormonal cycle (Pause et al. 1996), pregnan-cy (Olofsson et al. 2005), attention loss (Masago et al.2001), olfaction fatigue (Caccappolo et al. 2000), andtraining effect (Livermore and Hummel 2004). According-ly, an effective method for studying OERP on single-trialbasis can greatly reduce experimental time and enable thetrial by trial examination of brain olfactory functions.

Trial-wise EEG analysis has been developed for time-locked and phase-locked, evoked brain activities. Previ-ous methods include blind source separation algorithms(Belouchrani et al. 1997; Jung et al. 2001; Tang et al. 2002;Barbati et al. 2006), differentially variable component analysis(Knuth et al. 2006), Kalman filter methods (Georgiadis et al.2005), and wavelet decomposition and time-frequency-basedmethods (Quian Quiroga and Garcia 2003; Wang et al. 2007).However, signal extraction in the aforementioned trial-wisemethods requires prespecified basis functions or predefinedstatistical models. This might cause difficulties in adaptivelydetermining the requisite prior information due to the complextemporal and spectral changes in stochastic signals. For ex-ample, the ICA-based method premises no more than onenormal Gaussian source existing in the extracted componentsunder the assumption of either a super-Gaussian or sub-Gaussian probability distribution (Bingham and Hyvarinen2000). Other methods, such as wavelet or short-time Fouriertransform, decompose signals using a predefined basis, whichmay be too stringent for stochastic signal interpretations(Huang et al. 1998a).

This study presents an empirical mode decomposition(EMD)-based approach to study intertrial variability ofOERP signals. Huang et al. firstly proposed the EMD pro-cess as an efficient method for analyzing nonlinear andnonstationary data (Huang et al. 1998a; Flandrin et al.

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2004; Wu et al. 2007). The EMD is a useful data-driven toolfor extracting meaningful stochastically modulated signalsin many applications, such as measuring blood pressure(Huang et al. 1998b), heart-rate variability in electrocardio-gram (ECG) (Balocchi et al. 2004), and pulmonary hyper-tension (Huang et al. 1998b). With the merit of EMD, trial-by-trial examination of OERP quality is allowed whichmakes it possible to exclude trials with poor-performanceOERPs.

Materials and Methods

EEG Recordings

A 32-channel whole-head EEG system (Quick Amplifier,Brain Product Co., Munich, Germany) was used to measureEEG signals. Interelectrode impedance was monitored atbelow 10 kΩ during EEG recordings to ensure EEG signalquality. One electrooculogram (EOG) channel was moni-tored with an electrode pair placed at the outer canthi below/above the left eye and above/below the right eye in obliquedirection, providing eye-blinking information, and an EOGthreshold at 150 μV was used to define artifact-suppressedEEG epochs. EEG activities and EOG signals were bothdigitized at 2 kHz without applying any digital filter, sub-jected to the following EMD-based approach and conven-tional event-related potential (ERP) processes.

Odorant Preparation

Olfactory stimuli were given by an olfactometer (OM6b,Burghart,Wedel, Germany) (Kobal and Hummel 1988) whichis capable of generating rectangular-shaped chemosensorystimuli with rise time less than 20 ms. Every olfactory stimu-lus had a 300-ms stimulus duration. One odorant as olfactorystimuli and odorless air were used for the experiment. Humid-ified air was controlled at 36.5 °C, and 80 % humidity wasused for the airstream during the nonstimulation period andfor odorant dilution during the olfactory stimulation period.The odorant was 40 % concentration of phenyl ethanol alco-hol (PEA) (40 % volume fraction of pure PEAmixed with the60% volume fraction of humidified air), while the odorless airwas pure humidified air. The airstream and olfactory stimuliwere delivered to each subject’s right nostril by using a Teflontubing (1.6 mm inner diameter) and computer-controlled at8 L/min to avoid inducing mechanosensory responses.

Subjects and Experimental Paradigm

Twelve healthy subjects (eight males and four females; agedbetween 22 and 42 years old, mean age 26.2±5.5 years old)were recruited in this study. All subjects had no history of

olfaction disorder. Each subject was asked to sit comfortablyin a dimly lit, well-ventilated EEG room. A pair of earplugswas provided to each subject to block out ambient noise. AnLCD screen located at 50 cm in front of the subject was usedto present experimental instructions. Each trial was 40 slong, including an experimental period (0–30 s) and a re-laxation period (30–40 s). A red marker appeared on thelower side of the LCD screen at the beginning of each trialto maintain subject’s vigilance. The olfactory stimulus onsetwas randomly administered, with equal presence probabilitybetween 10 and 20 s anchored to the onset timing of the redmarker, to avoid subject’s expectation effect. A green mark-er appeared on the LCD screen at 30 s to instruct the subjectto relax (Fig. 1). During the whole experimental period,subjects were asked to keep their eyes focused on a fixationcross in the center of the LCD to reduce eye motion artifacts.Before EEG recording, five odorless-air trials were given foreach subject to familiarize with the experimental paradigm.In the olfactory experiment, each subject completed 100trials (50 odorant trials and 50 odorless-air trials) in arandom order. To prevent subjects from olfactory fatigue,subjects were forced to take a 5-min break after every 20trials. All subjects gave an informed consent after a fullexplanation of the experimental protocol. This study wasapproved by the Ethics Committee of the Institutional Re-view Board at Taipei Veterans General Hospital, Taiwan.

Determination of Subject-Specific OERP-Laden FrequencyBand and Creation of Spatial Template for Frequencyand Spatial Dual Criteria

To optimize the procedure of EMD-based approach forOERP-related single-trial activity extraction, the frequency

Visual cue

Eventduration 10 s

Olfactory stimulus onset (stimulus duration = 0.3 s)

Subject’saction velopharyngeal breathing Relaxation

ISI: 40 s

eyefixation

Experimental period

10 s 10 s

Relaxationperiod

10 s

Time

Fig. 1 Experimental paradigm for the EMD-based OERP study. Eachtrial was 40 s long and included an experimental period (0–30 s) and arelaxation period (30–40 s). A red marker was presented as an instruc-tion for subject’s vigilance. The olfactory stimulus onset was randomlyadministered, with equal presence probability between 10 and 20 sanchored to the onset timing of red marker, to avoid subject’s expec-tation effect. A green marker appeared at 30 s to instruct the subject torelax

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and spatial dual criteria were designed for each subjectto select OERP-related intrinsic mode functions (IMFs)in the EMD-based approach (see below). For each sub-ject, the continuous EEG data were first filtered within0.1–100 Hz and then segmented into epochs, from −300to 1,000 ms, anchored to the olfactory stimulus onset.The epochs that passed the EOG examination (EOG<150 μV) were designated as artifact-suppressedepochs. In this study, the survival rates of the EOGexaminations were 84, 80, 96, 94, 90, 80, 82, 92, 86,90, 98, and 86 % for subject I to subject XII, respec-tively. All artifact-suppressed epochs were baseline-corrected (−300 to 0 ms) and averaged to obtain theaveraged activity in each EEG channel, and the aver-aged activity at Cz was defined as the averaged OERP.The fast Fourier transform (FFT) was applied to theaveraged OERP, and the subject-specific OERP-ladenfrequency band was determined by finding the frequen-cy band with power greater than the mean plus twotimes the standard deviation (i.e., mean+2×std.) throughthe averaged OERP spectrum. Figure 2 shows the de-termination of the OERP-laden frequency band in sub-ject I. The averaged OERP obtained from subject I isshown in Fig. 2a. In Fig. 2b, the Fourier spectrum ofthe averaged OERP is computed, and the frequenciesfrom 0.5 to 11.5 Hz which have values higher than themean plus two times the standard deviation (i.e., mean+2 × std.) were defined as the subject-specific OERP-laden frequency band.

The spatial template was created by finding the latency ofthe P2 peak, denoted as tP2, which was identified by search-ing the maximum value within a time window between 450and 700 ms in the averaged OERP. The amplitudes in theaveraged activity of all EEG channels at tP2 were detectedand integrated to define a spatial template as

~St ¼ ½AP2ð1ÞAP2ð2Þ � � �AP2ðMÞ�; ð1Þ

where AP2(j) is the amplitude of the jth EEG channel at tP2 andM is the total number of EEG channels. The signal flowchartfor the generation of subject-specific OERP-laden frequencyband and spatial template was shown in Fig. 3.

Extraction of Single-Trial Activity Using EMD-BasedApproach and Frequency and Spatial Dual Criteria

Empirical mode decomposition is a time-series dataanalysis method. The EMD method is based on theassumption that any data set can be constructed by aseries of IMFs. These bases are analytic, self-constructed,well-defined, data-driven function whose amplitudesand frequencies can vary with time (Huang et al.1998a). In signal processing, the construction of IMF

is especially helpful to present the local characteristicsof nonlinear and nonstationary signals, e.g., brain signal.In this study, raw Cz EEG (no filter being applied) wassegmented into epochs, from −300 to 1,000 ms, basedon the timing of olfactory stimulus onsets. Each epoch~xwas a 1×N (N02,600) data vector and then decomposedinto a finite number of IMFs using EMD through asifting process. The EMD sifting process contains thefollowing steps:

(a) Identifying all the local extrema in ~x , including localmaxima and local minima; connecting all the localmaxima/minima by a cubic spline to generate the up-per/lower envelope;

(b) Calculating the pre-IMF, ~h, by subtracting the localmean, ~m, from the upper and lower envelop, i.e.,~h ¼~x� ~m;

(c) Continuing steps of (b) for k iterations until the differ-ence of two continuing pre-IMFs, SD(k), reaches auser-defined stopping criterion, ε, i.e.,

0

0

0

0

0

0.5Hz-11.5Hz

Sp

ectr

al m

agn

itu

de

(a.u

.)

Frequency (Hz)

-300 1000 Time (ms)

5

-5

Am

plit

ud

e (

µV

)

300 ms PEA stimulus

0 35

2300

0

(a)

(b)

Fig. 2 Determination of the OERP-laden frequency band for subject I.a An averaged OERP was obtained by averaging artifact-suppressedEEG epochs under odorant stimulation. b The spectrum of the aver-aged OERP was computed using FFT. A threshold, defined as themean plus two times the standard deviation (i.e., mean+2 × std.)through the spectrum, was used to determine significant frequencies.The frequency range, including significant frequencies, was defined asthe subject-specific OERP-laden frequency band

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SDðkÞ ¼~hðkþ1Þ �~h

ðkÞ������2

~hðkÞ������2 < "; ð2Þ

where || . || denotes the Euclidean distance;(d) Setting~c1 ¼~hk as the first IMF; calculating~r ¼~x�~c1

as residue;(e) Replacing in step (a) with and repeating steps from (a)

to (d) (sifting process) to find other IMFs,~c2;~c3; � � � ; and~cJ .

The procedure continues until the residue functionbecomes a monotonic function from which no more IMFscan be extracted. After applying the EMD sifting process to anEEG epoch, ~x can be represented by a monotonic residuefunction, , plus a set of posteriori-defined IMF basis,~c1;~c2;� � � ; and~cJ , where J is the number of IMFs extracted from~xand each~ck , 1 � k � J , is a 1� N vector.

Calculation of Mean Frequency and Creation of a SpatialTemplate for Each IMF

The selection of OERP-related IMFs can be achieved viatemporal, spectral, or spatial approaches; this study tookonly the frequency and spatial information for selectingOERP-related IMFs, based on the assumption that OERP

latencies could vary temporally across trials. Therefore, themean frequency and the spatial distribution of each IMFwere calculated to facilitate the selection of OERP-relatedIMFs. The mean frequency of each IMF was computed by

fmean ¼Pn

i¼0Ii � fi

Pn

i¼0Ii

; ð3Þ

where fmean is the mean frequency, n is the number of frequen-cy bins in the spectrum, fi is the frequency of the ith bin, and Iiis intensity of the ith bin in the spectrum.

In addition, a spatial map was created for each IMF bycomputing the correlation between the measured EEG ep-och and each IMF (Lee et al. 2009). The correlation between

the ith EEG channel ( ) and the jth IMF ( ), denoted as ρ(i,

j), was calculated as

ð4Þ

where and are the mean values of and ,

respectively. The correlations between all EEG channelsand the jth IMF are normalized and arranged into a vector

, represented as

ð5Þ

in which �k k is the L2-norm operator and~Sj is the normalizedvector, denoted as the spatial map for the jth IMF.

Selection of OERP-Related IMFs for ReconstructingSingle-Trial Activity Using Frequency and Spatial DualCriteria

The OERP-related IMFs were selected by examining theirfrequency and spatial information. First, the IMFs withmean frequencies within the subject-specific OERP-ladenfrequency band were identified as candidate IMFs. Second,

the correlation coefficient between the spatial template ~Stand spatial map of each candidate IMF ~Sj was expressed as

ρð S!j; S!

tÞ ¼ ð S!j � E½ S!j�Þð S!t � E½ S!t�ÞT

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiS!

j � E½ S!j����

���2� S

!t � E½ S!t�

������2

r ; ð6Þ

whereE½ð S!jÞ� andE½ð S!iÞ� are the mean values of S!

j and S!

i,respectively.

The correlation coefficients obtained from all candidateIMFs were categorized into highly and lowly correlated

Applying FFT to the averaged OERP and determining the subject-specific OERP-laden frequency band by finding the frequency band with power greater than mean+2 std. through the whole averaged OERP spectrum

Finding the latency of P2 peak in the averaged OERP, denoted as tP2. Detecting the amplitudes of averaged activities at tP2 in all channels and defining a spatial template as

Where AP2(j) is the amplitude of the averaged activity at tP2 at jth channel. D

eter

min

e th

e su

bjec

t-sp

ecif

ic

freq

uenc

y ba

nd a

nd s

pati

al te

mpl

ate

Filtering the continuous EEG data within 0.1 –100 Hz and segmenting the EEG data into epochs, from -300 ms to 1000 ms, anchored to the olfactory stimulus onset.

Selecting the artifact-suppressed epochswith EOG < 150 µV.

Averaging the artifact-suppressed epochs toobtain the averaged activity in each EEG channel, and the averaged activity at Cz is defined as the averaged OERP.

)]()2()1([ 222 MAAAS PPPt

Acquired EEG data

Fig. 3 Flowchart of the generation of subject-specific OERP-ladenfrequency band and spatial template

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groups using a K-means approach. Only the candidate IMFsbelonging to the highly correlated group were taken asOERP-related IMFs and were subjected to reconstructsingle-trial activity, represented as (Lee et al. 2009)

~xrecon ¼X

j2S1~cj; ð7Þ

where S1 is a group that contains the index number of thecandidate IMFs belonged to the highly correlated group and~xrecon is the reconstructed single-trial activity.

Determination of Significant Trials for Statistical Analysis

The EEG epochs obtained from the presence of an olfactorystimulus were decomposed into a set of IMFs using EMD.IMFs that met both frequency and spatial dual criteria weresubsequently chosen as OERP-related IMFs for reconstructingsingle-trial activities. Since the N1 and P2 components are themost prominent features in OERPs, the amplitudes and laten-cies of these two components were used to evaluate the activ-ities of single-trial OERPs (Wetter and Murphy 2003;Rombaux et al. 2006; Boesveldt et al. 2007). Only those trialswhich had single-trial activities with N1/P2 amplitudes lower/greater than the mean minus/plus two times the standard devi-ations of baseline amplitudes (−300 to 0 ms) were identified assignificant trials for subsequent statistical analyses. The single-trial activities of significant trials were denoted as single-trialOERPs. The analysis procedure of the proposed EMD-basedapproach is described by a flowchart as depicted in Fig. 4.

Results

Figure 5 shows one example of a single-trial OERP extractionin subject I. The significant trial was decomposed into tenIMFs using EMD sifting process. The temporal waveforms,Fourier spectra, and spatial maps of the ten IMFs appear in thefirst, second, and third columns of Fig. 5, respectively. Themean frequencies were 523.49, 256.01, 112.51, 53.50, 22.42,11.30, 5.55, 3.31, 1.77, and 0.94 Hz from IMF 1 to IMF 10,respectively. Themean frequencies from IMF6 to IMF10werewithin subject-specific OERP-laden frequency band (0.5–11.5 Hz) (see Fig. 2b) and were designated as candidate IMFs.The correlation coefficients between the spatial maps of can-didate IMFs and the spatial template were 0.32, 0.25, 0.76,−0.50, and −0.33 for IMF6, IMF7, IMF8, IMF9, and IMF10,respectively. After K-means clustering, the IMF6, IMF7, andIMF8 were categorized in the highly correlated group andsubsequently used to reconstruct the single-trial activity.

To demonstrate the effectiveness of the present EMD-based approach, single-trial extraction of OERP activitieswas applied to Fz, Cz, and Pz channels in subject I to test its

feasibility. Figure 6 depicts the temporal waveforms of thesingle-trial activities on Fz, Cz, and Pz channels for subjectI. Solid lines represent the single-trial activities induced byodorant, while dashed lines present the epoch-averagedEEG responses under the condition of odorless-air stimula-tion. The P2 peak amplitudes (A-P2) of the single-trialOERPs were 3.86, 5.55, and 6.86 μV, and the P2 latencies(L-P2) were 495, 545, and 574 ms on Fz, Cz, and Pz,respectively. The N1 peak amplitudes (A-N1) were −2.78,−8.02, and −5.05 corresponding to the N1 latencies (L-N1)at 352, 430, and 448 ms, respectively. No significant fea-tures were found in the epoch-averaged EEG responses ofodorless-air stimulation. Since the EMD-based approach hasbeen featured in its ability to preserve phase and amplitudewhile empirically separating signal from noise (Battista etal. 2007), the Fz channel which is away from OERP sourceis not suitable for OERP extraction in the proposed EMD-based approach. In this paper, the Cz channel, presenting themost prominent OERP response, was chosen for the follow-ing statistical analysis in all subjects.

This study investigates the intertrial variability of OERPfeatures in trial-by-trial manner. To represent the latencyvariability, the ERP image (Jung et al. 2001) of single-trialOERPs for subject I is shown in Fig. 7 for illustration, andsimilar findings were observed in all subjects. The magni-tudes of single-trial OERPs in Fig. 7a, b were normalized tothe amplitudes of their P2 peaks. Figure 7a shows the sorted

Empirical mode decomposition (EMD): sifting process

Dual criteria based on

frequency and spatial template

Calculating the mean frequency and creating a spatial map for each IMF: The mean frequency of each IMF was computed by and the spatial map was

represented as

Selecting OERP-related IMFs using the frequency and spatial dual criteria: 1. The IMFs with mean frequencies within the subject-

specific OERP-laden frequency band were identified as candidate IMFs;

2. The correlation coefficient between the spatial template of each candidate IMF was calculated and categorized by k-means. Only candidate IMFs belonged to highly-correlated group were chosen as OERP-related IMFs for subsequent sing-trial activity reconstruction

Single epoch of the artifact-suppressed EEG

Identifying significant trials for those trials with N1/P2 amplitudes lower/greater than the mean minus/plus 2 times the standard deviations of baseline amplitudes. The single-trial activities for those significant trials are denoted as single-trial OERP.

Collecting the single-trial OERPs for inter-trial variability analysis

x

),(),2(),1(

]),(),2(),1([

jMjj

jMjjS

T

j

n

ii

n

iiimean IfIf

00

meanf

Fig. 4 Flowchart of the EMD-based approach for single-trial OERPextraction

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single-trial OERPs obtained from 26 significant trials. Adashed line marks the onset of the olfactory stimulus. La-tency jitter cross trials were observed in the ERP image. Theintertrial latency jitter in P2 peaks was 566±53 ms (mean ±std.). The latency jitter may attenuate and smear the ampli-tudes of OERP features when applying simple averagingtechnique, such as conventional ERP method. Figure 7bshows the ERP image of single-trial OERPs with latenciesaligned to the mean latency of P2 peaks. Figure 7c, d plots

the averaged OERPs without and with P2 latency alignment.The values of A-P2 are 5.43 and 8.45 μV in Fig. 7c, d,respectively.

The EMD-based approach enables the studies of latencyjitter and intertrial variability throughout the whole mea-surement process. Figure 8 demonstrates the smearing ofN1 and P2 features caused by latency jitter through thecross-trial averaging process. The peak-to-peak N1P2amplitudes (A-N1P2) were 10.16, 9.25, 8.23, 8.15, 7.79,

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p. (n

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p. (n

orm

alized)

Am

p. (n

orm

alized)

Am

p. (n

orm

alized)

0.4064

-0.3812

0.2169

-0.4846

0.2793

-0.8569

0.5014

-0.8175

0.9443

-0.154

Am

p. (n

orm

alized)

0.2985

-0.4509

0.1557

-0.5780

Am

p. (n

orm

alized)

Am

p. (n

orm

alized)

Am

p. (n

orm

alized)

Am

p. (n

orm

alized)

Am

p. (n

orm

alized)

0.3577

-0.3970

0.3566

-0.4521

Corr. Coef. = 0.32

Corr. Coef. = 0.25

Corr. Coef. = 0.76

Corr. Coef. = -0.50

Corr. Coef. = -0.33

IMF 10

Am

plit

ud

e (u

V)

1

-1

2000

00 2.5

0 8

(a.u

.)

(a.u

.)(a

.u.)

(a.u

.)

(a.u

.)

(a.u

.)

(a.u

.)

(a.u

.)

(a.u

.)

Mean freq. = 523.49 Hz

Mean freq. = 256.01 Hz

Mean freq. = 112.51 Hz

Mean freq. = 53.50 Hz

Mean freq. = 22.42 Hz

Mean freq. = 11.30 Hz

Mean freq. = 5.55 Hz

Mean freq. = 3.31 Hz

Mean freq. = 1.77 Hz

Mean freq. = 0.94 Hz

0.3123

-0.3809

9

-7

Am

plit

ud

e (u

V)

Am

plit

ud

e (u

V)

Fig. 5 One example of single-trial OERP extraction using the EMD-based approach. A single EEG epoch recorded at the Cz position forsubject I was decomposed into ten IMFs using EMD. The temporalwaveforms, Fourier spectra, and spatial maps of the ten IMFs appear inthe first, second, and third columns, respectively. The mean

frequencies were 523.49, 256.01, 112.51, 53.50, 22.42, 11.30, 5.55,3.31, 1.77, and 0.94 Hz for IMF 1 through IMF 10, respectively. IMF6,IMF7, and IMF8, which met both spatial and frequency criteria, wereselected for reconstructing a single-trial activity

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and 7.55 μV after averaging over 1, 5, 10, 15, 20, and 25significant trials, respectively. This demonstrates that boththe latency jitter and intertrial variability could attenuate andsmear OERP features.

Table 1 lists the results of single-trial OERPsobtained from significant trials in 12 subjects. In thisstudy, the percentage of the number of significant trialsover the number of total trials is 52, 70, 58, 72, 44, 50,44, 78, 62, 70, 76, and 82 % for subject I to subjectXII, respectively. The subject-specific OERP-laden fre-quency bands were 0.5–11.5, 0.5–16, 0.5–18.5, 0.5–21.5, 0.5–21.5, 0.5–9.5, 0.5–10.5, 0.5–14, 0.5–15, 0.5–21.5, 0.5–13, and 0.5–13.5 Hz for subjects I throughXII, respectively. The mean A-N1, A-P2, and A-N1P2were −4.52 ± 0.74, 5.7 ± 1.15, and 10.13 ± 1.61 μV,respectively. The mean L-N1 and L-P2 were 401 ± 43and 549 ± 40 ms, respectively. To illustrate the superi-ority of the EMD-based approach, the significant trialswere also processed by the conventional ERP methodfor comparison purposes. In the conventional ERPmethod, the raw Cz EEG signals were filtered within0.1–100 Hz (zero phase, fourth order, IIR Butterworthfilter) on continuous data and segmented into epochs(from −300 to 1000 ms anchored to the olfactory stim-ulus onset), and the epochs corresponding to thosesignificant trials in the EMD-based approach were aver-aged across trials. Table 2 shows the OERP featuresobtained from conventional ERP method; average A-N1, A-P2, and A-N1P2 were −2.96 ± 1.36, 3.51 ±1.91, and 6.46 ± 2.95 μV, respectively. The amplitudesA-N1, A-P2, and A-N1P2 of the OERP features inTable 1 were significantly larger than those extractedfrom conventional ERP method in Table 2 (p<0.05,Wilcoxon signed-rank test), highlighting the effective-ness of trial-wise OERP analysis using the proposedEMD-based approach.

10

-10

P2

N1

Cz(b)

-300 1000 Time (ms)

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(a)Fz Odorant stimulus (PEA)

Odorless Air 300 ms Stimulus interval

Am

plit

ud

e(µ

V)

Am

plit

ud

e(µ

V)

Fig. 6 A reconstructed single-trial OERPs on Fz, Cz, and Pz channelsfor subject I. The solid lines represent the single-trial OERPs inducedby odorant stimulus (PEA), while the dashed lines represent the epoch-averaged EEG responses under the condition of odorless-air stimula-tion. The P2 peak amplitudes (A-P2s) of the single-trial OERPs were3.86, 5.55, and 6.86 μV, and the P2 peak latencies (L-P2s) were 495,545, and 574 ms on Fz, Cz, and Pz, respectively. The N1 peakamplitudes (A-N1) were −2.78, −8.02, and −5.05 μV correspondingto the N1 latencies (L-N1) at 352, 430, and 448 ms, respectively

26

1

So

rted

tri

al o

rder

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-300 0 566 1000

7

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µV

)

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(c) (d)

5.43 µV 8.45 µV

Stimulusonset

9

0

-5

Time (ms)

Am

p. (

µV

)

Fig. 7 ERP image of thenormalized single-trial OERPssorted by the latencies of P2peaks. The ERP image demon-strated the intertrial latency jit-ter; the amplitudes of the single-trial OERPs were normalized totheir P2 peak amplitudes. a TheL-P2s over 26 trials were 566±53 ms (mean±std.). A dashedline marks the onset of the ol-factory stimulus. b The ERPimage single-trial OERPs withlatencies aligned to the meanlatency (566 ms) of P2 peaks. cThe amplitude of averagedsingle-trial OERP without P2latency alignment was 5.43 μV.d With P2 latency alignment,the averaged single-trial OERPwas 8.45 μV

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Discussion

This study develops an EMD-based approach to study theintertrial variability of single-trial OERPs. In comparisonwith other signal processing methods, the EMD methoddoes not require a prior knowledge or a predefined statisticalmodel for data decomposition. The EMD method is anefficient tool, especially beneficial to present the local char-acteristics of nonstationary signals (Huang et al. 1998a;

Liang et al. 2005). Since the amplitudes and latencies ofthe OERP features are usually influenced by the parametersof olfactory stimuli (e.g., odor intensity, duration, flow rate,ISI, types of odors, etc.) (Tateyama et al. 1998; Wang et al.2002; Rothe 2003) and intersubject variability (e.g., trainingeffect, hormonal conditions, etc.) (Pause et al. 1996, 1999;Wang et al. 2002; Livermore and Hummel 2004), the pro-posed EMD-based approach could serve as a tool to inves-tigate intertrial differences. As shown in Fig. 7, the cross-

-300 1000 Time (ms)

Am

p. (

µV

)

10

-8

Time (ms)

Am

p. (

µV

)

10

-8-300 1000 Time (ms)

Am

p. (

µV

)

10

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µV

)

10

-8-300 1000 Time (ms)

Am

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µV

)

-300 1000 Time (ms)

Am

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µV

)

10

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-300 1000

(a)

(b)

(c)

(d)

(e)

(f)

Single-trial

5-trial averaged

10-trial averaged

15-trial averaged

20-trial averaged

25-trial averaged

10

-8

Fig. 8 Smearing of N1 and P2features due to latency jitter.The A-N1P2s of averagedsingle-trial OERPs were 10.16,9.25, 8.23, 8.15, 7.79, and7.55 μV after being averagedover 1, 5, 10, 15, 20, and 25trials. The smearing averagedsingle-trial OERP profiles werecaused by latency jitter crosstrials

Table 1 Descriptive statistics of investigated parameters for the response to odorant stimulus obtained at recording site Cz

Subject A-N1 (μV) A-P2 (μV) A-N1P2 (μV) L-N1 (ms) L-P2 (ms) Subject-specific OERP-ladenfrequency band (Hz)

I −4.50±2.70 5.43±2.47 10.29±3.37 367±73 566±53 0.5–11.5

II −5.37±3.59 8.67±2.57 13.35±3.31 345±47 506±58 0.5–16

III −4.35±2.05 5.37±1.80 9.72±3.30 366±74 520±57 0.5–18.5

IV −6.12±2.59 6.63±2.23 12.75±3.42 356±55 536±54 0.5–21.5

V −4.70±1.48 5.83±1.91 10.53±2.48 431±80 549±57 0.5–21.5

VI −3.85±2.08 4.50±1.77 8.35±2.90 461±42 599±107 0.5–9.5

VII −5.19±1.99 5.37±2.31 10.55±2.34 463±38 631±76 0.5–10.5

VIII −3.42±1.83 5.81±3.21 8.46±3.16 462±77 568±55 0.5–14

IX −4.21±1.7 4.69±2.36 8.9±3.02 383±67 531±69 0.5–15

X −3.87±1.89 5.13±2.08 9.0±2.54 379±65 486±68 0.5–21.5

XI −4.31±1.86 4.61±2.18 8.91±2.57 395±57 557±80 0.5–13

XII −4.38±1.69 6.4±2.36 10.78±3.06 407±52 540±65 0.5–13.5

Average −4.52±0.74 5.7±1.15 10.13±1.61 401±43 549±40

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trial realignment enhanced the averaged P2 peaks, instead ofbeing smeared by the intertrial latency jitter.

The proposed approach took the intersubject and intertri-al difference into account. It customizes the OERP detectionby defining the subject-specific OERP-laden frequencyband. As shown in Table 1, the single-trial OERPs showvaried frequency bands among different subjects. Therefore,the conventional ERP method which uses predeterminedfrequency range for data filtering (Table 2) may not opti-mize the signal extraction. Besides, the selection of OERP-related IMFs was achieved based on the frequency andspatial dual criteria. Since neural activities evoked by par-ticular external stimuli usually express themselves withspecific patterns (Tesche et al. 1995), the correlation withthe spatial template is helpful to ensure the fidelity andreliability of each IMF in reconstructing a single-trial activ-ity. The extraction of single-trial activity across differentartifact-suppressed trials (EOG <150 μV) allows the possi-bility to exclude poor-performance OERP trials. In thispaper, only those single-trial activities with N1/P2 ampli-tudes lower/greater than the mean minus/plus two times thestandard deviations of baseline amplitudes (−300 to 0 ms)were taken into the statistical analyses in Tables 1 and 2.Though the proposed EMD-based approach was only ap-plied to OERPs induced by PEA stimulations, further inves-tigations of OERPs induced by other odorants might bepossible with adequate modifications.

The proposed EMD-based approach preserves the salientfeatures of multichannel signal processing on event-relatedevoked potential (ERP) data. In contrast to other EMD appli-cations, which provide only the temporal-frequency informa-tion of IMFs in one single channel (Solis-Escalante et al.2006; Cong et al. 2009; Williams et al. 2011), this studyidentifies olfactory-related IMFs by creating spatial mapsand examining their topographic distributions (Lee et al.2009). As a consequence, the proposed EMD-based approach

separated IMFs into olfactory-related and olfactory-unrelatedcomponents based on their spatial maps; hence, the olfactory-related components could be extracted for single-trial OERPreconstruction. In this study, the K-means classifier methodhas been applied to demonstrate the efficacy of single-trialOERP reconstruction by grouping the highly correlated spatialmaps in the OERP-related IMFs selection process. The pres-ent selecting process could also be performed by using anadvanced classifier technique, e.g., artificial neural network,Gaussian mixture model, etc.

The EMD-based approach is an effective method for theremoval of OERP-unrelated components that can be imple-mented on an EEG system with fewer channels. This studydemonstrated the EMD-based approach on a whole-headEEG system; nevertheless, applications to a few-channelsystem or a sparse montage EEG system are also possible.This is because the IMFs were decomposed from one des-ignated channel, so-called channel of interest, and the otherrecording channel obtained was used to establish a spatialmap. For a few-channel EEG system, the spatial map couldbe simplified as a reference pattern which was created byfew representative channels, such as Fz, Cz, Pz, C3, and C4.It is distinct from other multivariate methods, such as ICA,that usually require a sufficient number of EEG channels toachieve better estimation of task-related signals.

Conclusions

This study proposes an EMD-based approach to study theintertrial variability of OERP features. Dual criteria on fre-quency and spatial template were adopted to facilitate theselection of OERP-related IMFs. The subject-specificOERP-laden frequency band was determined for each sub-ject to prescreen the IMF candidates, and the spatial tem-plate provides a priori spatial information for targeting

Table 2 The results of OERPfeatures obtained by the con-ventional ensemble averageapproach

Subject A-N1 (μV) A-P2 (μV) A-N1P2 (μV) L-N1 (ms) L-P2 (ms)

I −3.19 4.36 7.54 376 565

II −5.42 5.91 11.33 345 494

III −4.62 4.23 8.85 354 513

IV −2.83 6.94 9.77 340 524

V −4.65 5.03 9.65 429 542

VI −0.82 1.74 2.56 435 569

VII −2.14 2.27 4.40 449 612

VIII −2.02 4.65 6.67 375 591

IX −2.31 1.93 4.24 437 610

X −2.54 1.43 3.97 375 447

XI −3.28 2.3 5.58 415 558

XII −1.64 1.29 2.93 371 507

Average −2.96±1.36 3.51±1.91 6.46±2.95 392±39 544±50

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OERP-related IMFs. The OERP-related IMFs were subse-quently used to reconstruct single-trial activities, and onlythose single-trial activities with prominent N1 and P2 OERPfeatures were recognized as significant trials. This studytakes the trial-by-trial dynamics into account which enablestrial-wise examination of OERP quality and makes it possi-ble to exclude trials with poor-performance OERPs, whichmight be degraded by olfactory fatigue, lower attentionlevel, or artifact (e.g., EMG, EOG, ECG, etc.) contamina-tion. The proposed method retains the temporal and phaseinformation of OERP on trial-wise base.

Acknowledgments This study was funded by the National CentralUniversity, the Center for Dynamical Biomarkers and TranslationalMedicine, National Science Council (99-2628-E-008-003, 99-2628-E-008-012, 100-2628-E-008-001, 100-2221-E-008-006, 100-2623-E-008-006-D); Center for Dynamical Biomarkers and Translational Med-icine, National Central University, Taiwan (NSC 100-2911-I-008-001);Veterans General Hospital University System of Taiwan Joint ResearchProgram (VGHUST 99-P3-13); Taoyuan General Hospital IntramuralProject (PTH-9819); Cheng Hsin General Hospital Intramural Project((298)101-06); Cheng Hsin and Yang-Ming University Program(100F117CY30); and National Taiwan Normal University (NSC 98-2511-S-003-050-MY3).

Conflict of interest The authors declare that they have no conflict ofinterest.

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