Estimation of Respiration from Physiologic Pressure Signals S. Iamratanakul1, J. McNames1, B. Goldstein2 1

Biomedical Signal Processing Laboratory, Electrical and Computer Engineering, Portland State University, Portland, USA 3 Complex Systems Laboratory, Pediatrics, Oregon Health & Science University, Portland, USA

RSA [5]. Certain factors increase RSA such as age and being in the supine position [6]. Several methods exist to qualitatively and quantitatively assess RSA [7, 8], a recognized marker of cardiac autonomic function integrity [9]. Standard power spectral analysis has been used to provide an index of sympathovagal balance expressed as the ratio of low frequency (LF) and high frequency (HF) power components [10]. In the frequency domain, the common measures are energies in the power spectrum. The digitized data are mathematically transformed so that the entire waveform is represented as the sum of periodic (sine) waves of predefined frequency. The waveform is adjusted with respect to amplitude and phase so that the final sum replicates the original data [11]. This paper proposes a new estimator to estimate the respiration signal separate from the mixed signals (ABP, HR, and RESP). The first part of the estimator utilizes signal processing concepts and inputs the data into algorithms to achieve the results. The first part of the estimators is comprised of three sub-estimators: additive, amplitude modulation, and frequency modulation. We utilized the mixed signals as inputs of the three subestimators. The outputs of the three sub-estimators form the input of the linear estimator, which utilizes statistical concepts. The block diagram of three sub-estimators and the whole estimator are presented in the following section. We tested the estimator with data obtained from two patients and achieved a statistically significant result. The output of the estimator can estimate input consistently, while the estimator’s performance validates its output. Therefore, the estimator and its algorithm can provide a method for estimating the respiration signal from mixed signals.

Abstract—We created an algorithm to estimate the respiration signal, which consists of arterial blood pressure (ABP), and heart rate (HR) or RRI signals. Our goal is to create algorithmic models with which to estimate respiration by using signal processing and linear estimation. First, we created three algorithmic models: additive, amplitude modulation, and frequency modulation. Second, we used the output of those models as input for the linear estimator in order to estimate the original respiration input signal. The performance of the estimators was calculated to show their numeric results. Index Terms— Respiration (RESP), Arterial blood pressure (ABP), Heart rate (HR), R-R Interval (RRI), Additive, Amplitude Modulation (AM), Frequency Modulation (FM), Pulse Pressure Modulation, Linear Estimator. I.

INTRODUCTION

According to McNames, et al [1], three respiratory components in the arterial blood pressure (ABP) signal can be observed from the spectrogram. The first is an additive component, which is approximately 0.5 Hz [1]. The second is amplitude modulations (AM) of cardiac components, which is the mirror image of the respiratory signal, at approximately 1.6 Hz and 2.7 Hz [1]. The third is the frequency modulations (FM) of the heart rate (respiration sinus arrhythmia –RSA), which is the correlation between the respiratory rate and heart rate. Three components of respiration affect the ABP: additive effects, AM of the stroke volume (pulse pressure modulation -PPM), and FM of the heart rate (HR) or RSA. RSA is the cyclical variation in the instantaneous heart rate due to respiration [2]. Afonso, et al, [2] proposed that the RSA affects the body receptors that are simulated by changes in volume or respiratory blood pressure fluctuations. Additional components of heart rate modulation can also be related to other physiologic processes. Yli-hankala, et al, [3] proposed that respiration affects the heart rate at rest; in spontaneous respiration, the heart rate increases during the inspiration period and decreases during the expiration period. Sheridan [4] suggested that the parasympathetic nervous system conciliates the efferent control of RSA via the vagal nerve, and is responsible for rapid changes in the heart rate. We can claim that without a vagal mechanism, there can be no

0-7803-7789-3/03/$17.00 ©2003 IEEE

II. METHODOLOGY A. Data Acquisition Data, which was provided by Prof. McNames was acquired from Doernbecher Children’s Hospital. Patients in the Pediatric Intensive Care Unit (PICU) were connected to monitors to collect data on impedance between a pair of ECG-leads (RESP), arterial blood pressure (ABP), and heart rate (RRI). These data was sampled at a rate of 125

2734

EMBC 2003

Hz. Two patients’ data were utilized in the estimator and to calculate the heart rate, mean and standard deviation of the R_R interval were computed from the beat-to beat intervals. Unfortunately, the respiration data is poor due to the movement artifact and to indirect measurements in arbitrary units as result of clipping [12].

(Additive, AM, FM). The linear estimator equation is as follows: p −1 (3) yˆ = ω o + ∑ ω j x j j =1

B. Estimation 1) Estimation Overview: We estimated the respiration signal related to other signals in three perspectives,: additive estimator, amplitude modulation (AM) estimator, and frequency modulation (FM) estimator known as respiration sinus arrhythmia (RSA). We decimated the sampling frequency of the signal to five times less than the sample rate. The signal was passed through the elliptic band-pass filter and normalized the pass-band and stopband frequency to extract the additive components. The filtered signal was converted back to the original sample rate and achieved the estimated respiration signal. After the signal was passed through the ellipord band pass filter to extract the AM components, the Hilbert Transform was used to achieve the estimated respiration signal. The RSA or FM of the heart rate was extracted by using the ellipord band pass filter and passing through the RR interval process. The RR interval process is re-sampled RRI signals and sent the signal through the ellipord band pass filter. The estimated respiration signal was achieved after the up sample process. 2) Additive Estimator: The additive estimator is the estimator that uses the respiration summation with arterial blood pressure (ABP) as the input of it. The additive estimator divided into three components, as shown in Fig 1.

The goal is to estimate y given the data set. We can represent a linear estimator in terms of the matrix form as y = Aω + ε , where A is the data matrix and ω is the coefficient of the estimator [14]. To help clarify the complex links between respiration, HR, and ABP, we developed a linear estimator of respiration in Fig 4 shown below.

Respiration Signal ABP Signal

Ellipord Bandpass Filter

Down Sample

Up Sample

^

Respiration ABP

Down Sample

Ellipord Bandpass Filter

Hilbert Transform

Up Sample

Heart Rate Signal (RRI)

Process R-R Intervals

Estimated Respiration Signal

Modulate Frequency Signals

FREQUENCY MODULATION

LINEAR MODEL

^

r

Estimated respiration signal

r3

D. The measurement of estimator performance The measurement of performance between inputs and outputs of estimators shows how well they perform on the data. We utilized a coefficient of multiple determinations, namely R2 (R-square), to interpret the performance of estimators. R2 measures the proportional of total variance reduction associated with the estimator [14]. If R2 is equal to one, the estimator is perfect and all residuals are zero. Otherwise, it is the converse. The R2 can be calculated as follows: 2 SSR SSE ∑ ( rˆ − r ) 2 = 1− = R = (4) 2 SSTO SSTO ∑ ( r − r )

Respiration Signal

Process ABP and Respiration Signal

Respiration ABP Heart Rate

r 2

We utilized moving windows to form a data matrix of the estimator. The window length of the estimator was 50 samples over 10 seconds’ period of time. The spacing between samples is 25. The data matrix was utilized to find the coefficient of the estimator; these processed the output of the estimator, which is the estimated respiration signal.

Estimated Respiration Signal

4) Frequency Modulation (FM) Estimator: The frequency modulation (FM) estimator is divided into three components, as shown in Fig. 3. User specified Parameters

AMPLITUDE MODULATION

Fig 4. Block diagram of the Linear Estimator

Fig 2. Block diagram of the Amplitude Modulation (AM) Estimator

ABP Signal

Respiration ABP

^

3) Amplitude Modulation (AM) Estimator: The amplitude modulation (AM) estimator is divided into four components, as shown in Fig. 2. ABP Signal

ADDITIVE

^

Fig 1. Block diagram of the Additive Estimator

Respiration Signal

r 1

Estimated Respiration Signal

Fig 3. Block diagram of the Frequency Modulation (FM) Estimator

where SSR is Regression Sum of Squares, SSTO is Total Sum of Squares, SSE is Error Sum of Squares, r is the true data, r is the mean of the data, and rˆ is the estimated data output [14].

C. Linear Estimator We developed the linear estimator to estimate the respiration signal by using the input from the three signals

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III. RESULTS

TABLE I THE NUMERICAL MEASUREMENT OF PERFORMANCE IN THE MODELS

A. Additive estimator Figure 5 shows the results of the additive estimator in mmHg units and true respiration signal in mmHg units and plots them in the time range 110-120 sec. The first plot, shown in blue, is the true respiration-ECG. The second plot, shown in red, is the estimated respiration.

Numeric Numeric Coefficient of Multiple Results of the Results of the Determination training data separate data R2 (ALL) R2 (Additive) R2 (AM) R2 (FM) R2 (Additive&AM) R2 (AM&FM) R2 (Additive&FM)

0.681 0.534 0.445 0.599 0.583 0.653 0.602

0.818 0.642 0.535 0.719 0.700 0.784 0.723

R2 range is between 0 and 1. Names in brackets are names of models.

C. Frequency Modulation (RSA) Estimator Figure 7 shows the Frequency Modulation Estimator (FM) known as RSA. The plot is in the time range of 110 – 120 sec. The first part of the figure plots the respiration signal in mmHg units and time (sec). The second part of the figure plots the instantaneous heart rate (IHR) in frequency (HZ) and time (sec).

Figure 5. The Additive Estimator

The range of amplitude in additive components is between –4 and 4 mmHg and little variability along the time range. The estimated respiration has a greater time delay than the true respiration-ECG signal. B. Amplitude Modulation Estimator (AM) Figure 6 shows the amplitude modulation estimator. The plot is in the time range 110 – 120 sec and displays the respiration-ECG signal and the AM estimator’s output, which is the estimated-respiration.

Figure 7. The Frequency Modulation (RSA) Estimator

From the plot, the estimated respiration signal of the output of the estimator varies in frequency along the time line. The heart rate is modulated to a respiration-ECG signal as a result of changes in the frequency of the instantaneous heart rate (IHR). D. Linear Estimator The output of Additive, AM, and FM, are inputs of the linear estimator we utilized to develop the algorithm to estimate the input signal (respiration signal). The objective of the estimator is to achieve the best estimate of the output, one which is as close to the input as possible. Figure 8 shows the result of the linear estimator in the time range between 60 – 80 seconds; the respiration is in mmHg units.

Figure 6. The Amplitude Modulation Estimator

The amplitude of the signal varies along the time range because we modulated the respiration data with the ABP data according to the AM procedure in order to generate the data output.

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perform other estimators that we have created since it traces the input more precisely. The result proves that the estimator algorithms are a valuable tool in estimating the input respiration signal. The quantification measurement of performance in the estimators also indicates positive numerical results. REFERENCES [1] [2] [3]

Figure 8. The Linear Estimator

E. The performance of the estimators Table I presents the performance measurement of the estimators. For the interpretation of the numeric result, the number “one” indicates the perfect estimator, while zero is the worst. The measures of performance listed in Table I include the R2 values on the training data used to find the solutions for the estimator coefficients and on separate data. R2 (ALL) also presents the coefficient of multiple determination of the total estimator [14]. The results shown in Table I conclude that the output of the linear estimator is the best estimate of the respiration signal because it has the highest numeric value.

[4] [5] [6] [7] [8] [9]

IV. DISCUSSION [10]

The purpose of this work was to create an algorithmic model to estimate the output of a respiratory signal. Four estimators were utilized to achieve this: (1) an additive estimator, which extracted the additive components from the mixed signal input, the respiratory signal, and the ABP signal; (2) an amplitude modulation estimator, which used a parameter of a respiratory signal to process amplitude variation in proportion to the amplitude of an ABP signal; (3) a frequency modulation estimator, which used a respiratory signal to modulate a frequency variation in proportion to the amplitude of an ABP signal; and (4) an overall estimator, which combined all three previous estimators with the linear estimator. The result was that we were able to accurately trace the original input and create a waveform that was similar in shape to the input.

[11] [12] [13] [14]

[15] [16] [17]

V. CONCLUSION In this paper, we have developed new algorithmic models to estimate the respiration signal. These models out-

2737

McNames, J., et al., Techniques for visualization of Non-Stationary Biomedical Signals. BIOSIGNAL, 2002. Saul, J.P., et al., Transfer function analysis of the circulation: unique insights into cardio vascular regulation. American Journal of Physiology, 1991. 261: p. 1231-1245. Afonso, V.X., W.J. Tompkins, and J.G. Webster, Quantitative Measures of Respiratory Sinus Arrhythmia for Apnea Detection. 1994: p. 129-130. Yli-hankala, A., et al., Respiratory sinus arrhythmia is reversed during positive pressure ventilation. Acta Physiol Scand, 1991. 141: p. 399-407. Sheridan, D.J., Autonomic regulation of heart rate, in Autonomic failure, R. Bannister, Editor. 1989, Oxford University Press: Oxford. p. 113-128. Kero, P., et al., Decreased heart rate variation in decerebration syndrome: quantitative clinical criterion of brain death? Pediatrics, 1978. 62: p. 307-311. Bennett, T., et al., Assessment of methods for estimating autonomic nervous control of the heart in patients with diabetes mellitus. Diabetes, 1978. 22: p. 1167-1174. Eckberg, D., Respiratory sinus arrhythmia and other human cardiovascular neural periodicities, in Regulation of Breathing. 1995, Marcel Dekker: New York. p. 669-740. Grossman, P., V.J. Beek, and C. Wientjes, A Comparison of three quantification methods for estimation of respiratory sinus arrhythmia. Psychophysiology, 1990. 27: p. 702-713. Dinh, T.P., et al., New Statistical Method for Detection and Quantification of Respiratory Sinus Arrhythmia. IEEE Transactions on Biomedical Engineering, 1999. 46(9): p. 1161-1165. Almasi, J. and O. Schmitt, Basic technology of voluntary cardio respiratory synchronization in electro cardiology. IEEE Transactions on Biomedical Engineering, 1974. 21: p. 264-273. Buchman, T.G., P.K. Stein, and B. Goldstein, Heart rate variability in critical illness and critical care. Current Opinion in Critical Care, 2002. McDonald, A.B., et al., A real-time, continuous physiologic data acquisition system for the study of dynamical disease in the intensive care unit. Critical Care Medicine, 1999. 27(12): p. 227. Shannon, T.T., et al., Estimatoring Respiration from Blood Pressure Waveform Signals: An Independent Component Approach. EMBS, 2001. Mitra, S.J., Digital Signal Processing: A Computer-Based Approach. 2 ed. 2001: McGraw-Hill. McNames, J., Linear Estimator, in Learning From Data. 2002, Portland State University. Anderson, T.R., Productivity Measurement Using Data Envelopment Analysis. 1999: Portland. p. 1-93.

Biomedical Signal Processing Laboratory, Electrical and Computer Engineering, Portland State University, Portland, USA 3 Complex Systems Laboratory, Pediatrics, Oregon Health & Science University, Portland, USA

RSA [5]. Certain factors increase RSA such as age and being in the supine position [6]. Several methods exist to qualitatively and quantitatively assess RSA [7, 8], a recognized marker of cardiac autonomic function integrity [9]. Standard power spectral analysis has been used to provide an index of sympathovagal balance expressed as the ratio of low frequency (LF) and high frequency (HF) power components [10]. In the frequency domain, the common measures are energies in the power spectrum. The digitized data are mathematically transformed so that the entire waveform is represented as the sum of periodic (sine) waves of predefined frequency. The waveform is adjusted with respect to amplitude and phase so that the final sum replicates the original data [11]. This paper proposes a new estimator to estimate the respiration signal separate from the mixed signals (ABP, HR, and RESP). The first part of the estimator utilizes signal processing concepts and inputs the data into algorithms to achieve the results. The first part of the estimators is comprised of three sub-estimators: additive, amplitude modulation, and frequency modulation. We utilized the mixed signals as inputs of the three subestimators. The outputs of the three sub-estimators form the input of the linear estimator, which utilizes statistical concepts. The block diagram of three sub-estimators and the whole estimator are presented in the following section. We tested the estimator with data obtained from two patients and achieved a statistically significant result. The output of the estimator can estimate input consistently, while the estimator’s performance validates its output. Therefore, the estimator and its algorithm can provide a method for estimating the respiration signal from mixed signals.

Abstract—We created an algorithm to estimate the respiration signal, which consists of arterial blood pressure (ABP), and heart rate (HR) or RRI signals. Our goal is to create algorithmic models with which to estimate respiration by using signal processing and linear estimation. First, we created three algorithmic models: additive, amplitude modulation, and frequency modulation. Second, we used the output of those models as input for the linear estimator in order to estimate the original respiration input signal. The performance of the estimators was calculated to show their numeric results. Index Terms— Respiration (RESP), Arterial blood pressure (ABP), Heart rate (HR), R-R Interval (RRI), Additive, Amplitude Modulation (AM), Frequency Modulation (FM), Pulse Pressure Modulation, Linear Estimator. I.

INTRODUCTION

According to McNames, et al [1], three respiratory components in the arterial blood pressure (ABP) signal can be observed from the spectrogram. The first is an additive component, which is approximately 0.5 Hz [1]. The second is amplitude modulations (AM) of cardiac components, which is the mirror image of the respiratory signal, at approximately 1.6 Hz and 2.7 Hz [1]. The third is the frequency modulations (FM) of the heart rate (respiration sinus arrhythmia –RSA), which is the correlation between the respiratory rate and heart rate. Three components of respiration affect the ABP: additive effects, AM of the stroke volume (pulse pressure modulation -PPM), and FM of the heart rate (HR) or RSA. RSA is the cyclical variation in the instantaneous heart rate due to respiration [2]. Afonso, et al, [2] proposed that the RSA affects the body receptors that are simulated by changes in volume or respiratory blood pressure fluctuations. Additional components of heart rate modulation can also be related to other physiologic processes. Yli-hankala, et al, [3] proposed that respiration affects the heart rate at rest; in spontaneous respiration, the heart rate increases during the inspiration period and decreases during the expiration period. Sheridan [4] suggested that the parasympathetic nervous system conciliates the efferent control of RSA via the vagal nerve, and is responsible for rapid changes in the heart rate. We can claim that without a vagal mechanism, there can be no

0-7803-7789-3/03/$17.00 ©2003 IEEE

II. METHODOLOGY A. Data Acquisition Data, which was provided by Prof. McNames was acquired from Doernbecher Children’s Hospital. Patients in the Pediatric Intensive Care Unit (PICU) were connected to monitors to collect data on impedance between a pair of ECG-leads (RESP), arterial blood pressure (ABP), and heart rate (RRI). These data was sampled at a rate of 125

2734

EMBC 2003

Hz. Two patients’ data were utilized in the estimator and to calculate the heart rate, mean and standard deviation of the R_R interval were computed from the beat-to beat intervals. Unfortunately, the respiration data is poor due to the movement artifact and to indirect measurements in arbitrary units as result of clipping [12].

(Additive, AM, FM). The linear estimator equation is as follows: p −1 (3) yˆ = ω o + ∑ ω j x j j =1

B. Estimation 1) Estimation Overview: We estimated the respiration signal related to other signals in three perspectives,: additive estimator, amplitude modulation (AM) estimator, and frequency modulation (FM) estimator known as respiration sinus arrhythmia (RSA). We decimated the sampling frequency of the signal to five times less than the sample rate. The signal was passed through the elliptic band-pass filter and normalized the pass-band and stopband frequency to extract the additive components. The filtered signal was converted back to the original sample rate and achieved the estimated respiration signal. After the signal was passed through the ellipord band pass filter to extract the AM components, the Hilbert Transform was used to achieve the estimated respiration signal. The RSA or FM of the heart rate was extracted by using the ellipord band pass filter and passing through the RR interval process. The RR interval process is re-sampled RRI signals and sent the signal through the ellipord band pass filter. The estimated respiration signal was achieved after the up sample process. 2) Additive Estimator: The additive estimator is the estimator that uses the respiration summation with arterial blood pressure (ABP) as the input of it. The additive estimator divided into three components, as shown in Fig 1.

The goal is to estimate y given the data set. We can represent a linear estimator in terms of the matrix form as y = Aω + ε , where A is the data matrix and ω is the coefficient of the estimator [14]. To help clarify the complex links between respiration, HR, and ABP, we developed a linear estimator of respiration in Fig 4 shown below.

Respiration Signal ABP Signal

Ellipord Bandpass Filter

Down Sample

Up Sample

^

Respiration ABP

Down Sample

Ellipord Bandpass Filter

Hilbert Transform

Up Sample

Heart Rate Signal (RRI)

Process R-R Intervals

Estimated Respiration Signal

Modulate Frequency Signals

FREQUENCY MODULATION

LINEAR MODEL

^

r

Estimated respiration signal

r3

D. The measurement of estimator performance The measurement of performance between inputs and outputs of estimators shows how well they perform on the data. We utilized a coefficient of multiple determinations, namely R2 (R-square), to interpret the performance of estimators. R2 measures the proportional of total variance reduction associated with the estimator [14]. If R2 is equal to one, the estimator is perfect and all residuals are zero. Otherwise, it is the converse. The R2 can be calculated as follows: 2 SSR SSE ∑ ( rˆ − r ) 2 = 1− = R = (4) 2 SSTO SSTO ∑ ( r − r )

Respiration Signal

Process ABP and Respiration Signal

Respiration ABP Heart Rate

r 2

We utilized moving windows to form a data matrix of the estimator. The window length of the estimator was 50 samples over 10 seconds’ period of time. The spacing between samples is 25. The data matrix was utilized to find the coefficient of the estimator; these processed the output of the estimator, which is the estimated respiration signal.

Estimated Respiration Signal

4) Frequency Modulation (FM) Estimator: The frequency modulation (FM) estimator is divided into three components, as shown in Fig. 3. User specified Parameters

AMPLITUDE MODULATION

Fig 4. Block diagram of the Linear Estimator

Fig 2. Block diagram of the Amplitude Modulation (AM) Estimator

ABP Signal

Respiration ABP

^

3) Amplitude Modulation (AM) Estimator: The amplitude modulation (AM) estimator is divided into four components, as shown in Fig. 2. ABP Signal

ADDITIVE

^

Fig 1. Block diagram of the Additive Estimator

Respiration Signal

r 1

Estimated Respiration Signal

Fig 3. Block diagram of the Frequency Modulation (FM) Estimator

where SSR is Regression Sum of Squares, SSTO is Total Sum of Squares, SSE is Error Sum of Squares, r is the true data, r is the mean of the data, and rˆ is the estimated data output [14].

C. Linear Estimator We developed the linear estimator to estimate the respiration signal by using the input from the three signals

2735

III. RESULTS

TABLE I THE NUMERICAL MEASUREMENT OF PERFORMANCE IN THE MODELS

A. Additive estimator Figure 5 shows the results of the additive estimator in mmHg units and true respiration signal in mmHg units and plots them in the time range 110-120 sec. The first plot, shown in blue, is the true respiration-ECG. The second plot, shown in red, is the estimated respiration.

Numeric Numeric Coefficient of Multiple Results of the Results of the Determination training data separate data R2 (ALL) R2 (Additive) R2 (AM) R2 (FM) R2 (Additive&AM) R2 (AM&FM) R2 (Additive&FM)

0.681 0.534 0.445 0.599 0.583 0.653 0.602

0.818 0.642 0.535 0.719 0.700 0.784 0.723

R2 range is between 0 and 1. Names in brackets are names of models.

C. Frequency Modulation (RSA) Estimator Figure 7 shows the Frequency Modulation Estimator (FM) known as RSA. The plot is in the time range of 110 – 120 sec. The first part of the figure plots the respiration signal in mmHg units and time (sec). The second part of the figure plots the instantaneous heart rate (IHR) in frequency (HZ) and time (sec).

Figure 5. The Additive Estimator

The range of amplitude in additive components is between –4 and 4 mmHg and little variability along the time range. The estimated respiration has a greater time delay than the true respiration-ECG signal. B. Amplitude Modulation Estimator (AM) Figure 6 shows the amplitude modulation estimator. The plot is in the time range 110 – 120 sec and displays the respiration-ECG signal and the AM estimator’s output, which is the estimated-respiration.

Figure 7. The Frequency Modulation (RSA) Estimator

From the plot, the estimated respiration signal of the output of the estimator varies in frequency along the time line. The heart rate is modulated to a respiration-ECG signal as a result of changes in the frequency of the instantaneous heart rate (IHR). D. Linear Estimator The output of Additive, AM, and FM, are inputs of the linear estimator we utilized to develop the algorithm to estimate the input signal (respiration signal). The objective of the estimator is to achieve the best estimate of the output, one which is as close to the input as possible. Figure 8 shows the result of the linear estimator in the time range between 60 – 80 seconds; the respiration is in mmHg units.

Figure 6. The Amplitude Modulation Estimator

The amplitude of the signal varies along the time range because we modulated the respiration data with the ABP data according to the AM procedure in order to generate the data output.

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perform other estimators that we have created since it traces the input more precisely. The result proves that the estimator algorithms are a valuable tool in estimating the input respiration signal. The quantification measurement of performance in the estimators also indicates positive numerical results. REFERENCES [1] [2] [3]

Figure 8. The Linear Estimator

E. The performance of the estimators Table I presents the performance measurement of the estimators. For the interpretation of the numeric result, the number “one” indicates the perfect estimator, while zero is the worst. The measures of performance listed in Table I include the R2 values on the training data used to find the solutions for the estimator coefficients and on separate data. R2 (ALL) also presents the coefficient of multiple determination of the total estimator [14]. The results shown in Table I conclude that the output of the linear estimator is the best estimate of the respiration signal because it has the highest numeric value.

[4] [5] [6] [7] [8] [9]

IV. DISCUSSION [10]

The purpose of this work was to create an algorithmic model to estimate the output of a respiratory signal. Four estimators were utilized to achieve this: (1) an additive estimator, which extracted the additive components from the mixed signal input, the respiratory signal, and the ABP signal; (2) an amplitude modulation estimator, which used a parameter of a respiratory signal to process amplitude variation in proportion to the amplitude of an ABP signal; (3) a frequency modulation estimator, which used a respiratory signal to modulate a frequency variation in proportion to the amplitude of an ABP signal; and (4) an overall estimator, which combined all three previous estimators with the linear estimator. The result was that we were able to accurately trace the original input and create a waveform that was similar in shape to the input.

[11] [12] [13] [14]

[15] [16] [17]

V. CONCLUSION In this paper, we have developed new algorithmic models to estimate the respiration signal. These models out-

2737

McNames, J., et al., Techniques for visualization of Non-Stationary Biomedical Signals. BIOSIGNAL, 2002. Saul, J.P., et al., Transfer function analysis of the circulation: unique insights into cardio vascular regulation. American Journal of Physiology, 1991. 261: p. 1231-1245. Afonso, V.X., W.J. Tompkins, and J.G. Webster, Quantitative Measures of Respiratory Sinus Arrhythmia for Apnea Detection. 1994: p. 129-130. Yli-hankala, A., et al., Respiratory sinus arrhythmia is reversed during positive pressure ventilation. Acta Physiol Scand, 1991. 141: p. 399-407. Sheridan, D.J., Autonomic regulation of heart rate, in Autonomic failure, R. Bannister, Editor. 1989, Oxford University Press: Oxford. p. 113-128. Kero, P., et al., Decreased heart rate variation in decerebration syndrome: quantitative clinical criterion of brain death? Pediatrics, 1978. 62: p. 307-311. Bennett, T., et al., Assessment of methods for estimating autonomic nervous control of the heart in patients with diabetes mellitus. Diabetes, 1978. 22: p. 1167-1174. Eckberg, D., Respiratory sinus arrhythmia and other human cardiovascular neural periodicities, in Regulation of Breathing. 1995, Marcel Dekker: New York. p. 669-740. Grossman, P., V.J. Beek, and C. Wientjes, A Comparison of three quantification methods for estimation of respiratory sinus arrhythmia. Psychophysiology, 1990. 27: p. 702-713. Dinh, T.P., et al., New Statistical Method for Detection and Quantification of Respiratory Sinus Arrhythmia. IEEE Transactions on Biomedical Engineering, 1999. 46(9): p. 1161-1165. Almasi, J. and O. Schmitt, Basic technology of voluntary cardio respiratory synchronization in electro cardiology. IEEE Transactions on Biomedical Engineering, 1974. 21: p. 264-273. Buchman, T.G., P.K. Stein, and B. Goldstein, Heart rate variability in critical illness and critical care. Current Opinion in Critical Care, 2002. McDonald, A.B., et al., A real-time, continuous physiologic data acquisition system for the study of dynamical disease in the intensive care unit. Critical Care Medicine, 1999. 27(12): p. 227. Shannon, T.T., et al., Estimatoring Respiration from Blood Pressure Waveform Signals: An Independent Component Approach. EMBS, 2001. Mitra, S.J., Digital Signal Processing: A Computer-Based Approach. 2 ed. 2001: McGraw-Hill. McNames, J., Linear Estimator, in Learning From Data. 2002, Portland State University. Anderson, T.R., Productivity Measurement Using Data Envelopment Analysis. 1999: Portland. p. 1-93.