Research Paper (APA STYLE)
J. Biomedical Science and Engineering, 2012, 5, 330-340 JBiSE http://dx.doi.org/ 10.4236/jbise.2012.56043 Published Online June 2012 ( http://www.SciRP.org/journal/jbise/ ) Sleep disorder detection and identification Dennis E. B. Tan, Wai Yie Leong Universiti Tunku Abdul Rahman (UTAR), Kuala Lumpur, Malaysia Email: [email protected] , [email protected] Received January 17 th, 2012; revised February 17 th, 2012; accepted March 2 nd, 2012 ABSTRACT Electroencephalogram (EEG) is one of the medical devices that used for sleep disorder detection. Sleep disorder such as Obstructive Sleep Apnea Syndrome (OSAS) often appears during sleep event. Since the OSAS patients have the difficulties to allow the air- flow into the lung while inspiration, the EEG is ap- plied to capture and record the brainwave of the pa- tient. In this work, the Empirical Mode Decomposi- tion (EMD) and Ensemble Empirical Mode Decom- position (EEMD) are used to process and analyze the accuracy and efficiency of the results. Both of these methods will decompose the EEG signal into a collec- tion of Intrinsic Mode Function (IMF). In this paper, index orthogonality has been calculated to indicate the completeness of the deco mposed signal with the original signal. The instantaneous frequency and Hil- bert Spectrum based on both methods also employed by IMF to analyze and present the results in fre- quency-time distribution to determine the character- istic of the inherent properties of signal. Besides, Hil- bert marginal spectrum has been applied to measure the total amplitude contribution from each frequency value. Finally, the results shown that the EEMD is better in solving mode mixing problem and better improvement over EMD method. Keywords: Empirical Mode Decomposition (EMD); Intrinsic Mode Function (IMF); Ensemble Empirical Mode Decomposition (EEM D); Hilbert Spectrum 1. INTRODUCTION Obstructive Sleep Apnea Syndrome (OSAS) is a com- mon sleep disorder problem that always happens among the general population nowadays. According to the [1], Wisconsin Sleep Cohort which is a comprehensive epi- demiologic study investigating of OSAS in middle-aged adults, found that 4% of men and 2% of women has OSAS.
The sleep disorder occurs when the collapse of throat’s tissue which leads to partially or completely blockage of airways flow into lung during inspiration. The OSAS will seriously affect the daily activities of the patients who suffer from sleep diso rder. Daytime sleepiness and the likelihood to sleep during driving are the most com- mon negative effects. Besides, their health will also be affected due to lack of sl eeping time which may cause high blood pressure, stroke, abnormal heart rhythms and even death due to myocardial infarction. From the observation on OSAS patients, the most common symptoms are choking or gasping at the termi- nation of obstructive apnea and this will cause self- arousal. From here, the el ectroencephalogram (EEG) can be used as a medical device to carry out the analysis. In order to carry out the diagnosis and interpretation pro- posed by the healthcare provider, the (EEG) has been used widely to capture and collect the human brainwave.
Although the signal has been captured by EEG, process- ing these data accurately and efficiently are always the key problem for most of the scientists. The signals which performed by EEG contains of noise from the environ- ment although the embedded system is established in EEG devices. Data analysis becomes necessary in re- search and practical applicati on in medical field. By en- suring the accuracy in signal processing and feature ex- traction, the analysis of data can be done well and also capable of providin g appropriate solutions. The EEG is a non-stationary and non-linear signal with amp litude, phase and frequency continuous changes [2]. The EEG signal can be analyzed by any kind of time-frequency analysis methods [2]. In this work, the recorded EEG signal will be pro- cessed into more useful information to analysis OSAS.
One well-established information fusion model, namely the waterfall model is shown in Figure 1. There are se- veral processing stages, starting from the raw data acqui- sition to situation assessment and decision making stages [3]. Decision making stage can be achieved by inspection or by post-processing in the form of machine learning algorithms such as Support Vector Machines (SVM) which proposed by [4]. In this paper, signal processing and feature extraction will be the main focus in order to enhance the accuracy of data analysis. There are plenty of methods to analyze signals such as Fourier analysis, Wavelet analysis, Independent Component Analysis (ICA), etc. In general, the data which need to be analyzed have OPEN ACCES S Figure 1. The “waterfall model” of information fusion. several problems. For example, lack of total data span; data are non-stationary and non-linear processes. How- ever, two solutions which are the Empirical Mode De- composition (EMD) and the modified original EMD so called Ensemble Empirical Mode Decomposition (EEMD) will be emphasized in this paper. Hilbert Spectral Analy- sis also will be applied onto the Intrinsic Mode Functions (IMFs) to analyze the useful information. The EEG sig- nal processing based on EEMD has been proposed by [5] which provides new bases for feature extraction and pat- tern recognition of EEG signals.
EMD has been proposed by [6] as an adaptive time- frequency data analysis method. This method has been proven high capability for extracting signals in a broad range of applications. EMD decomposes the data into a set of Intrinsic Mode Function (IMF) components, which become basis representing the data. These data can be further presented through Hilbert Spectral Analysis. The obtained IMF components can be used in applying Hilbert transform onto each of them. Si nce the basis is adaptive, there is no need for harmonics [7]. Therefore, EMD is a method for analyzing nonlinear and non-stationary and it is an alternative to the wavelet analysis and the short- time Fourier Transform [8]. However, there is still re- maining deficiency in the decomposed data. The major drawback of EMD is the frequent appear- ance of mode mixing. This is the consequence of signal intermittency and affects th e physical meaning of IMF components. The intermittence will cause serious alias- ing in the time-frequency distribution [6]. To improve the efficiency of original EM D, the application of noise- assisted data analysis (N ADA) method, so called En- semble Empirical Mode Decomposition (EEMD) which discussed before by [9] is necessary. EEMD is applied to solve the mode mixing problem through the decomposi- tion of EEG signal into IMF components. Hilbert spec- trum can act as a tool to observe and analysis the com- parison between IMFs of these two EMD and EEMD. 2. METHODOLOGY In this paper, the data set was created and contributed by the developers of the BCI2000 instrument system and downloaded from the PhysioNet. These data was used as the simulation object. These data whose sampling fre- quency is 100 Hz had been collected by EEG from a se- vere OSAS patient. The EEG electrodes have been used to collect brain signal, the other medical devices are used to derive extra information and conditions from patient during sleep. For example, electrooculogram (EOG) to measure resting potential of retina; electromyogram (EMG) to evaluate and record the electrical activity produced by skeletal muscles; electrocardiogram (ECG) to measure the electrical activity of heart, etc. Since there are a lot of data from various medical devices, only the EEG data will be chosen and focused in our simulation and discus- sion. These EEG data will be processed and analyzed through EMD method and EEMD method by decom- posing the data into IMF that admit well-behaved Hilbert transform. Hilbert Spectrum w ill aid to apply for general purpose in energy-frequency -time distribution such as identify the basic frequency and their range variation.
2.1. Empirical Mode Decomposition (EMD) Any complicated data set can be adaptively decomposed into IMF components through EMD method. The term IMFs, are the functions that need to satisfy two condi- tions [6]: 1) In the whole time series , the number of extrema and the number of zero crossings must be either equal or dif- fer at most by one. 2) At any point in the time series, the mean value of the envelopes which is defined by local maxima (upper envelope) and local minima (lower envelope) is equal to zero. EMD method is a sifting process that estimates IMFs.
The “stopping criterion” actua lly determines the number of sifting steps to produce IMF [10]. The envelopes are defined by local maxima and local minima. When these extrema are identified, all the local maxima and local minima will be connected by spline line as upper enve- lope and lower envelope which should cover all the data between them respectively. The mean is designated as m 1 and the difference between original data, x(t) and m 1 is the first component, h 1 as shown: 1hxtm 1 (1) The purposes of sifting process are eliminating the riding wave and produce more symmetrical wave-profile [3]. Therefore, the sifting pr ocess is required to repeat several times. For the second sifting process, h 1 is treated as the data: 11 1 11hhm (2) Sifting process will be continued up to k times when h 1k is fulfilling the two conditions of IMF to become the first IMF component, c 1:
1 11 k khh m 1k (3) where (4) 11 kch Determ ination of stopping criterion for the sifting process is necessary to ensu re the IMF components con- tain enough physical sense of both amplitude and fre- quency modulations. Hence, the standard deviation, SD, criteria is applied by limiting its size: 2 1 11 2 0 11 T k k t k htht SD ht (5) The typical value of SD can be set between 0.2 and 0.3.
The original signal, x (t) is then separated with the first IMF component, c 1 through 11 xtcr (6) Residue r 1 is taking as new data since it still contains information of longer period components. The process will be repeated: 11 2 1 nnrc r rc nr (7) Finally, Eq.6 and Eq.7 are summed up and expressed as the summation of all the IMF components and the resi- due signal: 1 n in i X tc r (8) 2.2. Ensemble Empirical Mode Decomposition (EEMD) As mentioned before, the major drawback of EMD is the effect of mode mixing. To overcome this problem, the EEMD which is the improved EMD method has been applied in this work. When the signal is intermittent, means not continuous, will result as affecting the cha- racteristic component of di fferent time scales, an IMF component can increase their physical meaning of the original signal since the interruption of signal is occurred to perturb the time-frequency distribution. The EEMD defines the true IMF components as the mean of an en- semble of trials, each consisting of the signal plus a white noise of finite amplitude. The added white noise would populate the whole time-frequency space uni- formly, facilitating a natural separation of the frequency scales that alleviate the exis t of mode mixing [4]. The collection of white noise w ill cancel each other in a time space ensemble mean, so only the signal can survive in the final noise-added signal ensemble mean [9]. Accord- ing to [5], two situations will be shown as the mode mixing exists, which are:
1) A single IMF component of the signal contains various components of scales; 2) Same components exist in different scales of IMF.
This NADA method, so called EEMD is developed as follows [5,9]: 1) A white noise series is added into the signal, iiX txtwt (9) where w i(t) is i th copies of white noise.
2) The added white noise’s signal is processed to de- compose into IMF components. 3) Step 1 and step 2 are repeated with different white noise series each time. 4) Obtain the (ensemble) means of corresponding IMFs of the decomposition as the final result.
1 1 lim N j N k ct C t N j k (10) 2.3. Index Orthogonality Theoretically, all of the decomposed IMF components should reconstruct the original data set to indicate that they are orthogonal to each ot her [11]. It is used to en- sure the completeness and orthogonality of this decom- position. According to the [6], they define an index based on the most intuitive way to check the orthogonality of the IMFs from EMD and EEMD as following: 1) Rewrite Eq.8 as 1 1n j j X tc t k (11) In which the r n is included as an additional element.
2) Form the square of the signal 11 1 22 11 1 2 nnn jj jj k X tct ctc t (12) 3) With this expression, the overall index of orthogo- nality, IO, is defined as 11 2 011 IO Tnn jk tjk ctct X t (13) However, the EMD method which proposed by [6] is not fully fulfilling the theory of the orthogonality toward these IMF. The index of or thogonality is depending on the amount of leakage when decomposing the signal. The leakage which will affect th e index of orthogonality of the decomposed data from the original data should be as low as possible to enhance th e analysis result. The IMFs of EEMD method will be compared with EMD method to show their performance later. D. E. B. Tan, W. Y. Leong / J. Biomedical Science and Engineering 5 (2012) 330-340 Copyright © 2012 SciRes. 333 2.4. Hilbert Spectral Analysis where T is the total dat a length.
Hilbert marginal spectrum is the time integration of Hilbert spectrum, , H wt which is a reduced frequency-energy representation [10].
Hilbert Transform w ill be applied onto each of the IMF components after decomposition had been done. Through Hilbert transform, obtaining the instantaneous frequency of each IMF will have no difficult to analysis the result on Hilbert Spectrum. The instantaneous frequency of the original signal is defined as [12]. 3. SIMULATION RESULTS AND DISCUSSION The complete set of the original EEG data are collected from severe OSAS patient which is called as objects contain of 120,000 samples for each of the channels and sampling frequency is 100 Hz for 20 minutes. These EEG data in Figure 2 corresponds to channels C3, C4, P2, Pz, O1, O2 and reference point (mastoid area) ac- cording to the 10 - 20 EEG electrodes placement. Since there are several channels of EEG signals, the electrode which is placed on the C3 channel will be chosen for analysis based on EMD, EEMD and Hilbert transform.
The C3 location is related to the electrical activity in somato-sensoric and motoric brain areas [13]. Due to the amount of time samples of C3 is large, the time samples between 91,500 th and 93,000 th, which is totally 1500 samples as in Figure 3 will be observed and analyzed. d d j jt wt t (14) where Ѳj( t) is instantaneous phase.
After performing the Hilber t-Huang transform (HHT), we can express the data in the following form [12]: 1 exp d n ej j i X tRat iwtt (15) where a j(t) is the instantaneous amplitude.
Since the Hilbert spectrum ha s been defined, the Hil- bert marginal spectrum is shown as following: 0 ,d T hw H wt t (16) Figure 2. The original EEG data from severe OSAS patient.
Figure 3. The original 1500 samples EEG data from C3 channel of severe OSAS patient.
OPEN ACCESS The original C3 channel EEG signal in Figure 3 has been decomposed by EMD and EEMD respectively.
These IMFs are based on EMD in Figure 4 and EEMD in Figure 5 have been arranged from low to high order.
The EEMD is implemented with the added noise having amplitude of 0.1 standard deviation in C3 channel. With the observation onto these IMFs, the frequency of each individual IMF decreases as the order of IMF increases.
Overall, the decomposition of EEMD is more precise and accurate and the waveform presented is regular com- pared to EMD. We can observe that the EEMD method still retains more useful info rmation. This happens signifi- cantly by comparing the third IMF of EMD and EEMD methods. Obviously, from samples 600 th to 1000 th, the third IMF based EMD contains less physical meanings compared to the EEMD method. From the decomposed signals through observation, how can we ensure that these IMFs whether had estab- lished the completeness of the decomposition or the dif- ference between the reconstructed data from the sum of all IMFs and the original data were exists? One of the methods to solve this question is to check the orthogo- nality of IMF components whic h had been proposed by [14]. The index of orthogonality can be calculated and the interpolation techniques can be evaluated from the According to the [6], the orthogonality is required in linear decomposition systems; it might not make physical sense for nonlinear decomposition as in EMD and EEMD. But, in most cases, th e leakage is still considered small. However, we still can compare the index of or- thogonality (IO) in both meth ods since the data is the same from C3 channel. Table 1 shows the IO of EMD Table 1. Comparison of IO values between EMD and EEMD methods. Decomposition method Index of orthogonality (IO) EMD 0.2579 EEMD 0.1989 Figure 4. EMD method.
Figure 5. EEMD method. and EEMD respectively. These values indicate the leak- age level of the decomposed signal. Observed that the IO values are “less orthogonal” to EMD and EEMD, but these will still prov ide us a result to determine a better method. From table 1, it shows that IO value based on EMD method which is 0.2579 is quite higher much compare with the EEMD meth od which is 0.1989. As low as the IO value, the difference between the recon- structed data from sum of all IMFs component and the original data is very smal l. Another word, the leakage while decomposition of signals is less as the IO value is very low. From here, we can confirm that the EEMD method can retain more physical meaning and less leak- age of information will be loss on the decomposed sig- nals, which are IMF components. Next, we can do some comparison of the details of IMF components for each method by observation. Before analyzed these decomposed signals, there are a few properties of original EMD is presented according to the [9]. The main properties are the dyadic property always compromised in the original EMD while the data is in- termittent. Therefore, the pur pose of adding noise is to provide a uniformly distributed reference scale. This will enable EMD to solve the problem of compromised dy- adic property. Since the different series of noise which corresponding to th e IMFs have no correlation with each other, the mean of different white noise series will cancel each other. The comparison be tween original signal with IMF components based on EMD and EEMD had been carried out to show their difference in containing the useful information in decomposed data. In this paper, the fifth IMF component (for EMD is Figure 6 , EEMD is Figure 7 ) and sixth IMF component (for EMD is Figure 8, EEMD is Figure 9 ) were selected to analyze and compare to the original C3 channel EEG data which shows in Figure 3 .
Figure 6. IMF5 of EMD.
Figure 7. IMF5 of EEMD.
Figure 8. IMF6 of EMD. Through the observation of C3 channel EEG signal, we can briefly know that between the 200 th to 300 th sam- ples, the event of sleep apnea was occurred. From Fig- ures 6 to 9, the spike within thes e hundred samples range is still remained after appl ying EMD and EEMD process.
So, we can ensure that the expectation is realistic. Com- pare with the C3 EEG data, the fifth IMF of EEMD in red column is obviously co ntaining more information compare to the EMD as shows in the figure. Same condition appears in the sixth IMF of EEMD and EMD. As the decompositi on process go along to the higher order, the EMD is unable to avoid the mode mix- ing problem since the dyadic property is comprised which it had loss the physical meaning of the data. Con- versely, EEMD still able to retain more information since the added white noise had solved this problem. The de- composition of EEMD had proved that it can present well the inherent physical pr operties of the original sig- nal. Therefore, the EEMD is enabling EMD to repair the compromised dyadic property which can regulate the mode mixing problem effectively. After obtaining the IMF components of EMD and EEMD, the Hilbert transform can be applied to construct the time-frequency-energy distribution, designated as Hilbert Spectrum [15]. Hilbert spectra analysis can be used in exploring the full physical m eanings of the complicated data such as EEG data we analyzed here. Hilbert spec- trum can perform the high time-frequency resolution; the signal can characterize the local features of the signal effectively by combining th e instantaneous spectrum of each IMF component [5]. The Hilbert-Huang spectrum is shown in Figures 10 and 11 .
According to [9], Hilbert spectra can be used to iden- tify the basis frequency and ranges of variation but not in quantitative measurement. Although it is realistic, we still know that EEMD method shows good improvement in Hilbert spectrum. As we can see in Figures 10 and 11 , we can observe that the comprehensible and unmistak- able were appeared on the characteristics of Hilbert spectrum based on EEMD compare to the EMD. From here, we can confirm that th e accuracy and efficiency of the EEMD method are better compare with the EMD.
For Figure 10 , the time-frequency distribution has been affected and the trace was separated from one scale to another in certain distance due to the mode mixing effect in EMD method. Conversely, in Figure 11 , EEMD me- thod has alleviated the problem of mode mixing since there are less or almost no transitional gap occur. The continuous basis frequency also indicated that the inher- ent physical information can be retained and handled so that the problem of mode mixing can be ameliorated.
Figure 9. IMF6 of EEMD.
Figure 10. Hilbert spectrum of EMD method. Figure 11. Hilbert spectrum of EEMD method. According to [16], the instantaneous frequency is em- ployed to understand the detailed mechanisms of nonlin- ear and non-stationary signal. Through the Hilbert trans- form, the instantaneous frequency also can derive to compare the accuracy of the result based on these two methods. Instantaneous freque ncy can be calculated by Equation (14) where it is mentioned before. The instan- taneous frequency of EEG signals based on EMD and EEMD methods has been shown in Figures 12 and 13 .
Observed that the red colour line which is IMF 3, the mode mixing was appeared obviously from the time samples 500 th to 1000 th based on EMD compared to the EEMD. The instantaneous frequency based EEMD, at the same ranges of time samples provided more informa- tion to analyze the EEG signal.
Lastly, Hilbert marginal spec trum will be presented to describe the total amplitude (or energy) contribution of OSAS signal from each frequency value. Figures 14 and 15 shown the Hilbert marginal spectrum obtained by EMD and EEMD methods. Through the graphs, we can observe that the characteris tics of OSAS’s EEG signal are more obvious in marginal spectrum by EEMD com- pared to the EMD. Therefore, the severity and condition of OSAS event can be determined.
Figure 12. Instantaneous frequency of EMD method.
Figure 13. Instantaneous frequency of EEMD method. Figure 14. Hilbert marginal spectrum by EMD method.
Figure 15. Hilbert marginal spectrum by EEMD method.
4. LIMITATIONS AND CHALLENGES In this paper, the limitati on of EMD method has been resolved using the improved EEMD method. The sepa- ration of signals of different scales by EEMD has suc- cessfully improved the result by reducing the effect of mixing mode. The most important thing is, the EEMD has cancelled off the backgr ound noise since it is zero mean of noise after these no ise acts as the provider to distribute uniformly frame of scales. With this technique, the physical meaning of the inherent properties of sig- nals can be retained for analysis purpose. Although the EEMD has been proven a good im- provement of the EMD method, there are still remaining drawbacks [9]. Handling the multi-mode distribution of the IMF components is the main drawback of EEMD.
Referring to [9], the problem appeared due to the over- lapping of scales in dyadic filter which is based on [7].
Two different modes will occu r due to the signals where having a scale located in overlapping region. For bi- modal, one of the alternative ways is the number of sift- ing times must be low to derive these IMF components.
Another one is the noise leve l which has been adjusted and increased the number of trials to decrease root-mean- square deviation. However, handling of multi-mode dis- tribution is still remained problem although these me- thods have been carried out. Recently, multivariate EMD has been proposed [17] by Rehman & Mandic to alleviate the problem in origin- nal EMD algorithm which is the computation of the local mean of the original signal. The standard EMD method lacks of capability to pro cess the complex signals. Mul- tivariate extensions of EM D show the improvement over EMD for bivariate [3] and trivariate [18] processing.
Since the original EMD has the limitation in analyzing the bivariate data, the rota tion-invariant EMD (RI-EMD) is first proposed by Altaf et al. [19] to obtain the local mean of bivariate signal by using component-wise spline interpolation and then averag ing the local extrema. For the extension EMD for trivaria te signal, the equi-longi- tudinal lines is used to pr oduce a set of multiple direc- tion vectors in 3D to project onto the trivariate signal for estimation of local mean and envelopes. Similarly, the multivariate EMD algorithm employed the concept of bivariate and trivariate as it also taking signal projections along different directions in n-dimensional spaces to produce multiple n-dimensional envelopes and the fur- ther averaged them to derive the local mean. Further study will be carried out in this field later.
5. CONCLUSION This paper investigated the EMD and EEMD methods for EEG signal from OSAS patients. The EEMD applied NADA method, the added noise provided uniform dis- tribution onto the signal. The zero-mean characteristics has resulted the noise cancelling out each other. Finally, the mean value of IMF will be taken as a result. These results were presented thro ugh Hilbert spectrum and Hilbert marginal spectrum in frequency-time distribution and amplitude (or energy)-frequency distribution. Both of them show that the EEMD has better performance compared to the EMD. It can be concluded that the EEMD method has the capability to eliminate the mode mixing problem from the original EMD method. It is important to avoid data losing features during the de- composition process and ensure the physical meaning of inherent properties of the signals was retained. This use- ful information provides an idea to extract the feature and recognize the pattern of OSAS’s EEG signal for diagnosis and treatment purposes. REFERENCES [1] Lee, E.-K. and Jerri, R.H. (2001) Sleep disorder. Sacra- mento, Greenville.
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