Applications of Infrared Plethysmograph Waveform Time-Frequency Analysis

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1 Applications of Infrared Plethysmograph Waveform Time-Frequency Analysis Tsu-Hsun Fu 1 and Te-Shun Wang 2 1 Department of Biomedical Engineering, Yuanpei University, No.306, Yuanpei St., Hsinchu, Taiwan fcs58@mail.ypu.edu.tw 2 Department of Computer Science and Information Engineering, Yuanpei University No.306, Yuanpei St., Hsinchu, Taiwan wangts@seed.net.tw Abstract. In the past, when patients were taking computed tomography (CT) scan, the physician usually monitored the patients on-site as a passive way; however, the entire physiological conditions of the patients couldn t be fully comprehended this way. According to many clinical reports, the heart rates of the patients under tomography may fluctuate because of the injection of contrast medium. A standard pulse oximeter is usually used to measure the variation of heart rates. The problem is, the measured signal waveform could be distorted if the patients move their fingers or toes, or the connections of probes are loose. In this dissertation, several different time-frequency analysis methods will be used to explore the instantaneous frequency fluctuation of infrared plythysmograph waveform. We hope to find a feasible and direct time-frequency analysis to apply to monitoring patients physiological conditions. Keywords: Computed tomography, heart rate, Standard pulse oximeters, infrared plethysmograph waveform, time-frequency analysis. 1 Introduction The radiography image generated from computed tomography (CT) scan has been a powerful clinical diagnostic tool. In order to improve the quality of the radiography, physicians usually use iodinated contrast medium (ICM) to increase the intensity of tissue image in order to enhance the contrast capability. An automatic auxiliary injector may be used for ICM intravenous injection to shorten the radiography time of Multi-Detector-Row CT [1]. Nevertheless, injecting iodinated contrast medium may result in many uncomfortable reactions or allergy symptoms, such as nausea, vomiting, itchy skin, hives, short of breath, and tightness in chest. Patients with severe allergy symptoms could have a seizure [2-5]. At present there are two kinds of contrast media: ionized contrast medium with high osmosis pressure, intrigues more side-effects than the non- ionized one; and one-ionized contrast medium with similar osmosis pressure as human blood, intrigues less side-effects, and causes less pain and burn after injection. Therefore, most patients are keen to take non-ionized contrast medium. However, only ionized contrast medium is covered by Taiwan S. Lin and X. Huang (Eds.): CSEE 2011, Part IV, CCIS 217, pp , Springer-Verlag Berlin Heidelberg 2011

2 596 T.-H. Fu and T.-S. Wang Health Insurance policy except special cases. And that leads to the importance of understanding instant physical conditions of the patients when they are going through CT scan with injecting ionized contrast medium. Most patients were isolated in a separate room for CT scan, and the physicians can only observe the reactions of patients through lead glasses. Once a problem happens, it is difficult to find out instantly and handle it in a short time. Many reports show that the variation of heart rate may explain the physical changes of patients [6-7]. In order to monitor the physical reactions while the ionized contrast medium is injected into patients bodies, Standard pulse oximeters would be used to measure the heart rates of patients. If the patients move their fingers or toes, or the connections of probes are loose, distorted waveform would be generated, and the heart rates would be hard to detect. In order to solve these problems, we adopted several methods and achieved pretty good result [8-9]. In this dissertation, we hope to find a direct and appropriate analysis method for detecting heart rates by using different time frequency analysis methods for the waveform of Potoplethysmography (PPG). 2 The Time-Frequency Analysis of Signals Traditionally people use Fourier Analysis for signals or time sequence analysis. By this method, we get the characteristics of signals, and furthermore, find out the hidden physical sense of them. Here we introduce Fourier Analysis as the way to use j t complex number sinewave signal e ω as the basis function to accomplish its Fourier Transfer. Usually we define the transfer as the following: jωt jωt F( ω ) =< f ( t), e >= f ( t) e dt (1) We factorize one signal into a linear combination of many fixed frequency harmonic functions. The magnitude of each harmonic function represents its energy level under a certain frequency. Therefore, we are able to obtain the distribution of frequency and energy. Among many applications for non-stationary signal analysis, we often hope to acquire the representing status of the signal within one certain period of time or frequency, which is impossible to be fulfilled by Fourier Transfer. However, most signals in our nature are non-linear and non-stationary. We had no choice but to pay attention to some physical limits when we work on Fourier analysis. In order to analyze a non-stationary signal efficiently, the Time-Frequency Analysis concept is derived for it. Which is to say, we consider the time variable when we do energy frequency distribution. Therefore, analyzing a non-stationary signal is possible by analyzing energy frequency response versus time coordinate. j t Short-Time Fourier Transform (STFT). Since e ω is a unlimited extending basis function of time coordinate, the information of any time-local would be expanded to the whole frequency coordinate. Therefore, it s very difficult to distinguish the information of F (ω ). In order to clearly describe the information of signal shown on frequency and time-local, Short-time Fourier transform was used for analyzing time-frequency representations technique, which is defined as the following:

3 Applications of Infrared Plethysmograph Waveform Time-Frequency Analysis 597 jωt F( τ, ω) = f ( t) w( t τ ) e dt (2) Where w ( ) is a certain applicable window function (such as Gauss function). The basis function of STFT was generated due to different frequency modulation and time shift to w ( ). However, there s a resolution limit problem in STFT. Since the same time support width window function has been used for each frequency modulation for the basis function, the time-frequency resolution on time-frequency plane at each different time became the same. Other than this, according to uncertainty principle, we know that 1 Δ tδω (3) 2 Where Δ t is the time support width of basis function, and Δ ω is the frequency width of the basis function. This theory prevented random resolution from basis function in any frequency or time, which means that we have no choice but to choose either better resolution for time or for frequency: with one time support narrower basis, we obtain better time resolution but lower frequency resolution, and vise versa. Wavelet Transform. Wavelet Transform theory has been a very popular topic in computational science and engineering field in the recent years. It is also a very effective tool for time-frequency analysis. The feature of Wavelet Transform provides fine analysis specialty for various regions on both time domain and frequency domain, which are difficult to be obtained with any other signal process tools such as Fourier Transform. Therefore, Wavelet Transform has been applied to computer vision, image or verbal signal analysis. In order to acquire short-time instantaneous signal, we are looking for some kind of base that provides a narrower time support during a high-frequency analysis, and better time resolution. Regarding the other low-frequency signal, it also provides sufficient time support and better frequency resolution. These seem impossible features from STFT are found in Wavelet Transform. The Wavelet Transform base possesses flexible time-frequency characteristic, which becomes narrow within high-frequency situation, and wide within lowfrequency situation. Certain conditions must be fulfilled. The first one is reversibility, with the original data y(t) and the square integrable function φ(t). Wavelet Transform becomes the following: 1 t W a * τ (, τ ) = y( t) ϕ ( ) dt (4) a a where φ * is the conjugate complex number of φ, a is the scaling parameter of mother wavelet, τ is the translation parameter. Morlet Transform. According to the conditions described above, Morlet Transform was developed by Morlet: 1 * t τ W ( a, τ ) = y( t) ψ ( ) dt (5) a a

4 598 T.-H. Fu and T.-S. Wang and 2 t τ t τ ( t τ) ψ = exp i6 exp (6) 2 a a 2a where 6 appears in admissible conditions [10-11]. However, inevitably the 2- dimentional Morlet Transform cannot be used for analyzing a waveform in a very small range of a. Therefore, when there re many waveforms with affiliated wavelengths and similar amplitudes in the original data, it is difficult to identify the characteristics of the data from the transform outcome. Enhanced Morlet Transform (EMT). The defect of Morlet Transform is located in the high-frequency portion. High frequency signal scatters because of the decrease of frequency resolution. Enhanced Morlet Transform proceeds with the signal with Gaussian function in advance to avoid high-frequency energy scattering problem. Before Wavelet transform, a Gaussian function is multiplied to the signal, and then some marginal and low-amplitude signals are also removed. Hence the high frequency resolution increases. The transform function is as the following: 1 t τ X ( a, τ ) = x( t) ψ ( ) G( σ, τ, t) dt (7) a a where G(σ,τ,t) is the Gaussian function ( t τ ) 4σ 4π σ e (8) Since the scaling parameter a decreases and high frequency resolution becomes lower, we multiply a Gaussian Window G(σ,τ,t) to Morlet Wavelet before Wavelet Transform to increase the frequency resolution. 3 Analysis Result of Measured Signals In this dissertation, waveforms measured from Infrared Plethysmograph were used for analyzing time-frequency variation. The sampling rate is 250Hz. The measured waveform signals were sent to the computer through serial interface. By using Infrared Plethysmograph, we recorded signals during the ionized contrast medium injection to the patient and captured the heart rate variation. The information was used to understand the patient s physical reaction before and after ICM. However, since the Infrared Plethysmograph signals include two or more peaks within a cycle, which were caused by the movement of patients or bad connections of probes, certain persecution and errors may occur while obtaining heart rate. Therefore, we hope to use time-frequency analysis method directly in order to understand the heart rate variation of patients before and after ICM, and apply it to monitoring patients physical situation. Fig. 1 shows the instantaneous waveform of a patient s PPG 350 seconds before and after the injection of ICM. It is apparent that the patient s fingers moved during second. Fig. 2 shows the time-frequency diagram with Short-Time Fourier

Applications of Infrared Plethysmograph Waveform Time-Frequency Analysis 599 Transform (STFT). Different colors represent different intensity of energy.

into time-frequency 2-dimension matrix x(t,ω) we obtain the distribution x(ω) operated integral transform of time domain. It is called Marginal Frequency, as the left-side curve shown in the diagram.

According to the diagram, the heart rate is slightly higher than 1Hz before the injection. Then it starts to rise around the 120 th second with injection and goes up to 2Hz.

5 Applications of Infrared Plethysmograph Waveform Time-Frequency Analysis 599 Transform (STFT). Different colors represent different intensity of energy. In order to further realize the time/frequency domain distribution, which is the integral transform of time-frequency curve by frequency axis/time axis, by transforming the time domain signal x(t) into time-frequency 2-dimension matrix x(t,ω) we obtain the distribution x(ω) operated integral transform of time domain. It is called Marginal Frequency, as the left-side curve shown in the diagram. After the integral of frequency axis, the distribution x(t) with time as the parameter is then obtained, which is called Marginal Time, as the below curve shown in the diagram. According to the diagram, the heart rate is slightly higher than 1Hz before the injection. Then it starts to rise around the 120 th second with injection and goes up to 2Hz. Then it decreases after the 260 th second. After the 300 th second, it slows down gradually. There re two apparent low-frequency energy signals around the 220 th and the 250 th seconds, which are the fluctuation shown in the transient diagram. We can also find it from Marginal Time curve on the bottom of the diagram. Fig. 3 shows the time-frequency analysis result using Morlet Transform. Even then the frequency variation can be observed in different time, the poor high-frequency resolution is still an obvious problem. The result is not good enough with a wide frequency range. Fig. 1. The instantaneous waveform of a patient s PPG before and after the injection of ICM Fig. 2. The time-frequency diagram of measured data with Short-Time Fourier Transform (STFT) Fig. 3. The time-frequency diagram of measured data with Morlet Transform

6 600 T.-H. Fu and T.-S. Wang Fig. 4. The time-frequency diagram of measured data with Enhanced Morlet Transform Fig. 4 shows the time-frequency analysis result using Enhanced Morlet Transform. It shows an improved high-frequency resolution for a clear frequency variation within different time frame. It s definition is better than the result from STFT, which can be found from the two fluctuation signals around the 220 th and 250 th seconds. The frequency appears in a dotted form after EMT, which means that the fluctuation frequency is located between 0.1 and 0.2Hz. 4 Conclusion During the tomography period of time for patients, we usually inject Iodinated contrast medium (ICM) with intravenous injection method in order to increase imaging quality. However, it always leads to certain physiological reaction and heart rate variation. There are many researches about how to improve the accurate heart rate sampling methods nowadays. Most of them adopt the R-R interval of ECG signal as the foundation of heart rate sampling. However, it is very difficult and infeasible to measure ECG signal during the tomography process. There is a feasible and effective method for monitoring a patient s physiological situation during intravenous injection of ICM by measuring PPG signal. In this dissertation, we use PPG signal timefrequency analysis method to understand the transient frequency variation. According to the results of measured data, we successfully analyzed the heart-rate variation. It can be applied to the instant physiological monitoring of a patient under tomography. By comparing the three time-frequency transform methods mentioned above, the result of Morlet transform is the worst of all. And the results of Enhanced Morlet Tranform and Short-Time Fourier Trasform provide pretty satisfactory outcome, especially the EMT. References 1. Fishman, E.K., Jeffery, R.J.: Multidetector CT Principles, Techniques & Clinical Applications, pp Lippincott Williams & Wilkins (2004) 2. Dahnert, W.: Radiology Review Manual. Lippincott Williams & Wilkins (2003) 3. Webb, A.W., Stacul, F., Thomsen, H.S., Morcos, S.K.: Late adverse reactions to intravascular iodinated contrast media. European Radiology 13, (2003) 4. Morcos, S.K., Thomsen, H.S.: Adverse reaction to iodinated contrast media. European Radiology 11, (2001)

7 Applications of Infrared Plethysmograph Waveform Time-Frequency Analysis Arias, M.A., Peinado, R., Sanchez, A.M., Merino, J.L.: Incessant ventricular tachycardia acutely controlled with intracoronary injection of radiographic contrast media. Am. J. Emerg. Med. 24, (2006) 6. Merati, G., Rienzo, M., Parati, G., Veicsteinas, A., Castiglioni, P.: Assessment of the autonomic control of heart rate variability in healthy and spinal-cord injured subjects: contribution of different complexity-based estimators. IEEE Trans. Biomed. Eng. 53, (2006) 7. Nakamura, T., Horio, H., Miyashita, S., Chiba, Y., Sato, S.: Identification of development and autonomic nerve activity from heart rate variability in preterm infants. Biosystems 79, (2005) 8. Fu, T.-H., Liu, S.-H., Tang, K.-T.: Heart Rate Extraction from the Photoplethysmogram Waveform Using Wavelet Multi-Resolution Analysis. Journal of Medical and Biological Engineering 28(4), (2008) 9. Fu, T.-H., Liu, S.-H., Yang, S.-C.: Wavelet Filter Evaluation for extract Heart Rate of infrared plethysmograph waveform. In: The 2nd International Conference on Bioinformatics and Biomedical Engineering, vol. 5, pp (2008), doi: / ICBBE Boashash, B.: Time-Frequnecy Signal Analysis, Methods and Applictions. Longman Cheshire, Australia (1992)

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