RESPIRATORY INFORMATION IN ARTERIAL OXYGEN

SATURATION MEASUREMENT

Yue-Der Lin

Department of Automatic Control Engineering

Master Program of Biomedical Informatics and Biomedical Engineering

Feng Chia University, 100 Wenhwa Road, Seatwen, Taichung 406, Taiwan

Keywords: Pulse oximeter, Photoplethysmography (PPG), Arterial oxygen saturation (SpO

), Multi-channel

autoregressive (AR) spectral estimation, Coherence analysis.

Abstract: Pulse oximeter has become a standard in intensive and critical care units for the monitoring of oxygen

support from respiratory system since 1990’s. The multi-wavelength photoplethysmography (PPG)

technique is now utilized for the measurement of arterial oxygen saturation by pulse oximeter (SpO

). This

research utilized multi-channel autoregressive (AR) spectral estimation method for the coherence analysis

between the respiratory signal and the PPG signal derived from pulse oximeter. Five healthy male subjects

participated in this research with signals being measured at different respiratory status. The results

demonstrate high coherence between respiration and the PPG signal from pulse oximeter, and the coherence

disappears in breath-holding experiments. The results demonstrate that the respiratory status can also be

acquired from the measurement of arterial oxygen saturation. This implies the possibility to acquire the

physiological parameters other than arterial oxygen saturation form pulse oximeters.

1 INTRODUCTION

Pulse oximetry is a non-invasive method widely

used in clinical environments for the analysis of

oxygen delivery. Two-wavelength (660 nm and 940

nm) photoplethysmography (PPG) technology is

utilized for the measurement of arterial oxygen

saturation (SpO

) in most commercial pulse

oximeters (Webster, 1997). In addition to the

reading of arterial oxygen saturation, pulse

oximeters also provide PPG signal (940-nm wave-

length in general) for pulse rate or heart rate

monitoring.

PPG signal represents the volumetric changes in

blood vessels. Such blood volume change occurs

mainly in the arteries and arterioles. The principle of

PPG is that the light (mainly red, infrared or green

light) traveling through biological tissue (e.g. the

fingertip or earlobe) will be absorbed by different

absorbing substances, including skin pigmentation,

bone, and arterial and venous blood. The arteries

contain more blood during systole than during

diastole, and their diameter increases due to the

increased blood pressure. The detected light

reflected from or transmitted through the vessels will

thus fluctuate according to the pulsatile blood flow

during the circulation. Therefore, the PPG signals

are composed of two components, the alternating

part of total absorbance due to the pulsatile

component of the arterial blood (AC component)

and the absorbance due to venous blood, the part of

the constant amount of arterial blood, and other non-

pulsatile components such as skin pigmentation (DC

component) (Hertzman and Spielman, 1937).

As the AC component of PPG signal is

synchronous with the heart beat and thus can be

identified as a source of heart rate information. In

addition, the PPG signal is claimed to contain

respiratory-induced intensity variations (RIIV)

(Johansson et al., 1999; Nilsson et al., 2000). The

so-called RIIV is a kind of modulation arises from

the respiratory-induced variations in venous return

to the heart. Such variation is primarily caused by

the alterations in intrathoracic pressure during

respiration. A part of the respiratory-related drift in

perfusion also originates from the autonomous

control of the peripheral vessels and is also

synchronous with respiration. RIIV signal can be

extracted from PPG by a bandpass filter (0.13-0.48

Hz). High coherence has been shown to exist

168

Lin Y. (2010).

RESPIRATORY INFORMATION IN ARTERIAL OXYGEN SATURATION MEASUREMENT.

In Proceedings of the Third International Conference on Bio-inspired Systems and Signal Processing, pages 168-173

DOI: 10.5220/0002693501680173

 SciTePress

between RIIV and the changes in tidal volume and

respiratory rate (Johhansson et al., 1999a and 1999b;

Nilsson et al., 2003). As some commercial pulse

oximeters also provide PPG signal, these results

imply that the pulse oximeters can be a potential tool

for the acquisition of arterial oxygen saturation,

heart rate and respiration at the same time.

The relationship between RIIV and respiratory

signal has been examined extensively in the past

decades (Johhansson et al., 1999a and 1999b;

Nilsson et al., 2003). However, little research has

been done concerning the coherence between the

raw PPG signal acquired from pulse oximeter and

respiratory signal. As the RIIV may deviate with the

varying respiratory rate, the fixed bandpass filter for

PPG signal filtration may limit the accuracy of

analysis in practical conditions, especially in slow

and fast breathing cases. The objective of the present

study was to investigate whether such coherence

exists between raw PPG signal and respiratory signal.

The multi-channel autoregressive (AR) spectral

estimation method proposed by Morf et al. (1978),

was utilized for the coherence analysis under

different breathing rates and the breath-holding state

for five healthy male subjects. The two-channel AR-

based cross-spectral analysis demonstrated that raw

PPG signal and respiration were coherent

(magnitude-squared coherence greater than 0.5) at

the respiratory frequency in the subjects studied,

with changes in respiration leading to changes in

PPG. No coherence was found in breath-holding

cases for the subjects participated. The results of this

research verify that there exists the corresponding

respiratory component in spectrum of raw PPG

signal. The results may provide another attractive

approach to acquire the respiratory information from

PPG without the need of filtering. The results also

imply the possibility to acquire the physiological

parameters other than arterial oxygen saturation

form pulse oximeters.

2 METHODS AND MATERIALS

2.1 Subjects and Experiments

Five healthy male subjects (non-smoker and with no

prior history of cardiovascular disease) aged

between 22 and 24 took part in the experiments after

giving the informed consent. All subjects were asked

to refrain from caffeine and alcoholic drink at least 4

hours before the experiments. All of the experiments

were performed at the same university laboratory

with the room temperature being maintained at about

25 degrees centigrade during the night time (from 9

to 11 pm). The subjects were required of having a

resting period of at least 5 minutes under relaxation

status before the experiment.

0 5 10 15 20 25 30

-0.15

-0.1

-0.05

0.05

0.1

Respiration

Time (second)

0 5 10 15 20 25 30

0.5

1.5

2.5

3.5

Time (second)

PPG from Pulse Oximeter

Figure 1: Typical signals acquired. Upper: respiratory

signal (natural respiration); lower: PPG signal derived

form pulse oximeter.

Each experiment included two stages classified

by different respiratory rate (natural respiration and

holding the breath in order). Each stage was

maintained at least one minute, and the intervals

between stages were three minutes. Throughout the

experiment, the subjects were seated in a

comfortable chair with their right upper arm kept at

the height of heart level.

2.2 Signal Measurement

The physiological data acquisition system MP150

(Biopac Inc.) was utilized for signal measurement.

Pulse oximetry signal (by pulse oximeter module

OXY100C) and respiratory signal (by temperature

amplifier module SKT100C with fast response

thermistor sensor TSD202A) were collected

simultaneously during each experimental stage. The

Pulse oximetry probe (TSD123A, with infrared

wavelength 910 nm) was attached to the right index

finger, whereas the respiratory signal was acquired

at the nostril during the measurement. The analysis

package Biopac AcqKnowledge

(version 3.9.1)

was used for signal management, including the

signal quality pre-screening, data storage and

retrieval. The signals were verified visually by a

well-trained technician. A typical respiratory signal

and PPG signal acquired form pulse oximeter are

shown in Figure 1. If the signal quality was poor, the

signal would be excluded from further analysis and

the subject was asked to repeat the experiment once

again.

As the dominant components of the processed

signals primarily locate around the frequencies

below 6 Hz, a sampling frequency of 60 Hz is

RESPIRATORY INFORMATION IN ARTERIAL OXYGEN SATURATION MEASUREMENT

169

enough. However, the ECG (electrocardiogram)

measurement is sometime needed in the experiments

for timing reference. A sampling frequency of 250

Hz was selected in this research to assure all the

signals could be acquired without aliasing. Before

the signal analysis, both respiration and PPG signal

were down-sampled by a factor of 4.

2.3 Signal Analysis

The source code for multi-channel AR spectral

estimation was developed in MATLAB

version

7.3.0 (MathWorks Inc.). The estimation method was

originally developed by Morf et al. (1978). It is an

expansion of single-channel Levinson recursion

algorithm (Levinson, 1947). Two-channel case is

introduced as below. The same procedure can be

easily expanded to the cases which are more than

two channels.

Let x[n] denote the vector of samples from two-

channel process at sample index n

nxnxn ]][ ][[][

, (1)

where the superscript

represent the transpose

operation. In this research, x

[⋅] and x

[⋅] represent

the acquired respiratory signal and the PPG signal

from pulse oximeter respectively. The two-channel

AR(p) model, assumed to be wide-sense stationary,

can be represented as

∑

+−−=

nknkn

][][)(][ exAx , (2)

in which the A

(k) are the 2×2 AR(p) forward

prediction parameter matrices and

][n

e is a 2×1

vector representing the forward linear prediction

error or the AR(p) driving noise process. With the

property that the driving noise process is

uncorrelated with past values of the AR process, the

multichannel Yule-Walker normal equations of

forward linear prediction version can be derived as

] [ 00PRa "

ppp

= , (3)

with

)]( )1( [ p

ppp

AAIa "= , (4)

]}[][{ nnE

ppp

xxR = , (5)

and

pnnnn ]][ ]1[ ][[][ −−= xxxx " . (6)

In the above equations, 0 are 2×2 null matrices and I

denotes a 2×2 identity matrix. The symbol E

represents the expectation operator, and

]}[][{ nnE

eeP = is the covariance matrix of

the driving noise process for the forward AR(p)

process.

The corresponding multichannel Yule-Walker

equations for the backward parameter B

(⋅) can also

be derived in a similar way as

] [

ppp

P00Rb "= , (7)

in which

] )1( )([ IBBb

ppp

p "

. (8)

The matrix

]}1[]1[{ −−= nnE

eeP is the

covariance matrix of the driving noise process for

the backward AR(p) process.

The matrix R

has a Hermitian and a block-

Toeplitz structure. On a matrix element-by-element

basis, the prediction parameter matrices possess the

recursion relationships

)1()1()()(

kppkk

pppp

−++

BAAA

(9)

)1()1()()(

kppkk

pppp

−++

ABBB (10)

for k=1 to p. Define

]}1[][{ −= nnE

eeP , i.e.

P is the cross correlation between the forward and

backward linear prediction residuals at one unit of

delay. Then the normalized partial correlation, a

counterpart to the single-channel reflection

coefficient in multichannel case, can be derived as

−−

⎟

⎠

⎞

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

PPPΛ

, (11)

in which the superscript

1/2

denotes the lower

triangular matrix obtained by the Cholesky

decomposition of the Hermitian matrix, and the

superscript

−H

represents the matrix Hermitian of its

inverse. And then, A

p+1

(p+1) and B

p+1

(p+1) can be

expressed in terms of

1+p

Λ as

)1(

−

⎟

⎠

⎞

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

−=+

p PΛPA (12)

and

)1(

−

⎟

⎠

⎞

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

−=+

p PΛPB

(13)

respectively. In addition, the order update for the

covariance matrix of the driving noise process can

also be derived by

ppp

pp PBAIP )]1()1([

111

++−=

+++

(14)

and

ppp

pp PABIP )]1()1([

111

++−=

+++

. (15)

Finally, the relationships of the driving noise

process between AR(p) and AP(p+1)can be obtained

]1[)1(][][

−++=

npnn

eAee (16)

and

][)1(]1[][

npnn

eBee ++−=

. (17)

BIOSIGNALS 2010 - International Conference on Bio-inspired Systems and Signal Processing

170

The above procedure is summarized in Table 1. It

is assumed that there are N samples in each channel

and the order of two-channel AR process is P.

For two-channel AR spectral estimation, define

the complex exponential vector E

(f) of P+1 block

elements as

] [)(

IIIE

TPfjTfj

eef

⋅⋅⋅⋅⋅

ππ

" , (18)

in which T is the evenly sampled interval (sec) of the

signals x[

⋅

]. After the computation of the related

coefficients, the power spectrum density (PSD) can

be calculated by

])([)]([)(

−−

PPAR

ffTf aEPEaP (19)

⎥

⎦

⎤

⎢

⎣

⎡

)()(

2221

1211

fPfP

, (20)

where a

is defined in (4).

The magnitude squared coherence (MSC)

)()(

)(

2211

fPfP

fC =

(21)

and the coherence phase

)}(Re{

)}(Im{

tan)(

−

(22)

versus frequency f are utilized for the coherence

analysis between respiration and the PPG signal

acquired from pulse oximeter in this research. From

equation (20), P

(f) and P

(f) versus f are the PSD

of respiration and PPG signal respectively.

3 RESULTS AND DISCUSSION

The coherence between the respiratory signal and

the PPG signal acquired from pulse oximeter at

different breathing status for five subjects was

analyzed to evaluate their relationships in frequency

domain. Though only the results for one subject are

demonstrated in this paper, similar results are

derived for all subjects.

Figure 2 shows the coherence analysis results for

one subject in the condition of natural frequency. As

seen in Figure 2(a), there exists a peak of MSC

greater than 0.5 near 0.2 Hz (the respiratory

frequency, see Figure 2(b)). Also, the coherence

phase is smaller than zero (see Figure 2(a)), which

imply that the changes due to respiration in PPG lags

the respiratory signal. It also can be appreciated that

there is one corresponding component near the

respiratory frequency in the spectrum of PPG signal,

as depicted in the lower trace of Figure 2(b). This

component is relatively smaller in magnitude

compared with the dominant peaks which relate

directly to the heart beats.

0 0.5 1 1.5 2 2.5

0.2

0.4

0.6

0.8

Frequency (Hz)

Magnitude Squared Coherence

0 0.5 1 1.5 2 2.5

-4

-2

Frequency (Hz)

Coher en ce P hase

(a)

0 0.5 1 1.5 2 2.5

Frequency (Hz)

PSD (Respiration)

0 0.5 1 1.5 2 2.5

Frequency (Hz)

PSD (PPG)

(b)

Figure 2: Coherence analysis results for the case of natural

respiration: (a) MSC (upper) and coherence phase (lower),

(b) PSD of respiratory signal (upper) and PPG signal

(lower).

0 0.5 1 1.5 2 2.5

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Frequency (Hz)

Magni t ude Sq ua r e d C oh e r en ce

0 0.5 1 1.5 2 2.5

-4

-2

Frequency (Hz)

Coherence Phase

(a)

0 0. 5 1 1.5 2 2.5

0.5

1.5

2.5

Frequency (Hz)

PSD (Respiration)

0 0. 5 1 1.5 2 2.5

Frequency (Hz)

PSD (PPG)

(b)

Figure 3: Coherence analysis results at the breath-holding

condition: (a) MSC (upper) and coherence phase (lower),

(b) PSD of respiratory signal (upper) and PPG signal

(lower).

RESPIRATORY INFORMATION IN ARTERIAL OXYGEN SATURATION MEASUREMENT

171

0 0.5 1 1.5 2 2.5

0.1

0.2

0.3

0.4

Frequency (Hz)

Magnitude Squared Coherence

0 0.5 1 1.5 2 2.5

-1

Frequency (Hz)

Coher en ce P hase

(a)

0 0.5 1 1.5 2 2.5

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Frequency (Hz)

PSD (Respiration)

0 0.5 1 1.5 2 2.5

Frequency (Hz)

PSD (PPG)

(b)

Figure 4: The results by FFT-based cross-spectrum

analysis for the case of natural respiration: (a) MSC (upper)

and coherence phase (lower), (b) PSD of respiratory signal

(upper) and PPG signal (lower).

The results in the breath-holding condition for the

same subject are demonstrated in Figure 3 with the

same order arranged in Figure 2. As all of the MSC

values are less than 0.5 (see Figure 3(a)), it is

appreciated that no coherence is found in such case.

The results derived by FFT-based cross-spectrum

analysis are demonstrated in Figure 4 (natural

respiration case for the same subject). The utilized

method is Welch’s estimate of periodogram (Welch,

1970) with Hanning window of length 128, 256-

point FFT and 64-point overlapping. It can be

appreciated that the coherence is not evident as

using Fourier-based techniques. One primary reason

may arise from the limited frequency resolution of

FFT-based techniques.

4 CONCLUSIONS

This study utilized multi-channel AR spectral

estimation method to investigate the coherence

between the respiratory signal and PPG signal

acquired from pulse oximeter under different

respiratory status. The Morf’s algorithm (Morf et al.,

1978) was used for the computation of two-channel

AR parameters. The algorithm is summarized in

Table 1. The AR-based coherence analysis results

Table 1: Morf’s Algorithm.

model. AR bivariate oforder the and

]][ ][ ]2[ ]1[[Let

Nn xxxxX

⎩

⎨

⎧

===

,2,1 ][][][

Nn fornnn

Hbf

XXPP

xee

tionInitializa

]1[][

]1[]1[

][][

⎪

⎩

⎪

⎨

⎧

−=

−−=

≤

∑

Ppwhile

eeP

nComputatio

()

()()

⎪

⎩

⎪

⎨

⎧

−=+

−

)1(

PPB

PPA

⎪

⎩

⎪

⎨

⎧

++−=

+++

ppp

PABIP

PBAIP

)]1()1([

111

end for

kppkk

pkfor

pppp

)1()1()()(

1,2,1

⎩

⎨

⎧

−+++=

−

ABBB

BAAA

le end whi

end for

npnn

Nppnfor

][)1(]1[][

]1[)1(][][

,2,1

⎪

⎩

⎪

⎨

⎧

++−=

−++=

eBee

eAee

are demonstrated in Figure 2(a) and Figure 3(a). The

results show that they are coherent (MSC greater

than 0.5) at the respiratory frequency. In addition,

the response delay in PPG induced by respiration is

also implied in the negative coherence phase (see

Figure 2(a)). The respiration induced component is

evident in the AR-based PSD of PPG signal, as

shown in Figure 2(b). The coherence analysis is also

specific to respiration. As the breath is in holding

status, no coherent peak was found (see Figure 3).

The coherent phenomenon cannot be observed by

the FFT-based cross-spectrum method (as shown in

Figure 4).

The existence of coherent peak is determined by

whether the corresponding pole inside the unit circle

is prominent or not. It has been shown that the

coherence spectrum is sensitive and specific to the

BIOSIGNALS 2010 - International Conference on Bio-inspired Systems and Signal Processing

172

respiration in this research, it may be possible to

acquire the respiratory information from the PPG

signal by single-channel AR method with the

consideration of poles around the respiratory

frequency. It may provide another attractive

approach to acquire the respiratory information from

PPG signal without the need of filtering. It also

implies the possibility to acquire the other

physiological parameters other than arterial oxygen

saturation form pulse oximeters. Besides, the two-

channel AR method introduced in section 2 can be

easily expanded to more than three channels. Such

multi-channel AR method may be an alternative

attractive tool for the coherent analysis among

respiration, central venous pressure (CVP), arterial

blood pressure (ABP) and PPG signal in the related

research, e.g. for the cases in intensive care unit

(ICU) or during surgical operation.

ACKNOWLEDGEMENTS

The author wishes to express the gratitude to the

National Science Council, Taiwan, for the financial

support on this research (under contract number

NSC 97-2221-E-035-001-MY3 and NSC 97-2221-

E- 035-053).

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