NONINVASIVE CARDIOVASCULAR SYSTEM

IDENTIFICATION USING PULSE WAVE TRANSIT TIME

Sérgio Okida

1,2

, Pedro Giassi Júnior

, João Fernando Refosco Baggio

, Raimes Moraes

Maurício Gonçalves de Oliveira

and Gastão Fernandes Duval Neto

Electronics Coordination, Federal University of Technology of Paraná, Ponta Grossa, PR, Brazil

Electrical Engineering Department, Federal University of Santa Catarina, Florianópolis, SC, Brazil

Medical School Hospital, Federal University of Santa Catarina, Florianópolis, SC, Brazil

Faculty of Medicine, Federal University of Pelotas, Pelotas, RS, Brazil

Keywords: Heart Rate Variability, Autonomic Nervous System, System Identification, Autoregressive Moving Average

Model, Pulse Wave Transit Time.

Abstract: This work shows that it is possible to model the heart rate autonomic control from samples of ECG, PPG

and respiratory flow waveform (RFW). Usually, such modelling is carried out with physiological signals

that are more difficult to acquire during the clinical exams: ECG, arterial blood pressure and instantaneous

lung volume. In this work, the ECG, PPG and RFW were recorded with a portable system from volunteers

at two different postures: supine and standing. The ECG, PPG and RFW were processed off line in order to

obtain the RR, the inverse of the pulse wave transit time (IPWTT) and the RFW series. These series were

used as input for ARMA models and the obtained results were compared to the ones available in the

literature. The qualitative and quantitative comparisons of the results reveal very similar performance.

1 INTRODUCTION

The power spectral density (PSD) analysis of the

heart rate variability (HRV) is widely used for the

non-invasive assessment of the autonomic nervous

system (ANS). The higher frequency (HF)

components of the HRV (0.15 to 0.4 Hz) are related

to the breathing rate (Respiratory Sinus Arrhythmia -

RSA) and mediated by the parasympathetic system

(Pagani et al., 1986; Berntson et al., 1997). The

lower frequency components (LF: 0.04 to 0.15 Hz)

comprise the Mayer waves (around 0.1Hz) and

contain oscillations due to the interactions between

the heart rate (HR) and the blood pressure (BP). The

LF power is affected by both sympathetic and

parasympathetic systems. The LF/HF power ratio is

often used as an index of the sympathovagal balance

(Pagani et al., 1986; Task Force, 1996).

Although the spectral analysis contributes to the

understanding of the heart rate autonomic control, it

characterizes the output and not the system itself.

Modelling allows the system characterization, i.e., to

obtain the transfer functions between each input and

the output and their impulse responses (Xiao et al.,

2005).

The cardiovascular system neural control has

been modelled by a multi-input/single-output

(MISO) system, using as inputs, the arterial blood

pressure (ABP) and the instantaneous lung volume

(ILV) and, as output, the HRV (Perrott and Cohen,

1996). Systolic blood pressure (SBP) series obtained

from the ABP waveform has also been used as input

to discrete models instead of ABP samples (e.g.,

Baselli et al., 1997).

The instantaneous ABP is registered by a

catheter inserted into an artery or non-invasively,

using commercial systems such as the Finapress

(Ohmeda Inc). The ILV is usually measured using

chest-abdomen inductance plethysmography.

Research on the cardiovascular models has

provided useful data to characterize patients’ clinical

condition (Xiao et al., 2005; Faes et al., 2006).

Nevertheless, the acquisition of the ILV and ABP as

described above may hamper the broad use of

models to obtain diagnosis indexes. The chest-

abdomen inductance plethysmograph is cumbersome

in procedures during which cardiac arrest may

occur. The Finapress is not available in many

clinical facilities and it is susceptible to movement

artefacts. Besides, it is also difficult to synchronize

232

Okida S., Giassi Júnior P., Fernando Refosco Baggio J., Moraes R., Gonçalves de Oliveira M. and Duval Neto G..

NONINVASIVE CARDIOVASCULAR SYSTEM IDENTIFICATION USING PULSE WAVE TRANSIT TIME.

DOI: 10.5220/0003775402320237

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2012), pages 232-237

ISBN: 978-989-8425-89-8

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

signals acquired from different commercial systems

since no information is usually provided on their

processing (time delay).

As alternatives to the use of the SBP and ILV as

model inputs, the pulse wave transit time (PWTT)

and respiratory flow waveforms (RFW) are here

investigated.

The PWTT, usually defined as the interval

between the ECG R-wave

and the base of the

leading photoplethysmography (PPG) deflection

within a same cardiac cycle (Figure 1), has been

shown to be significantly correlated to the systolic

blood pressure (SBP). The SBP is inversely

proportional to the PWTT (Lass et al., 2004; Teng

and Zhang, 2006).

Figure 1: The PWTT is the interval between the ECG R-

wave peak and the base of the leading edge of the PPG.

The RR series is a measurements set of the time interval

between consecutive ECG R-waves.

Eckberg (2003) suggests that the mechanical

stretch of pulmonary and thoracic receptors has

small contribution to the RSA, pointing out that the

RSA is mainly generated by the central respiratory

motoneurone activity. Therefore, the breathing rate

obtained from the inspired and expired flow

waveform (acquired by nasal thermometry) may

convey information on the respiratory motoneurone

discharges that affect the HRV.

This work investigates the feasibility of using the

PWTT series and the RFW samples as inputs for the

cardiovascular system neural control modelling.

These signals can be acquired with a simple system,

barely disturbing the usual clinical exams.

Therefore, their use circumvents practical

difficulties to obtain useful indexes from models in

order to help assessing patients’ health.

2 MATERIALS AND METHODS

This section describes the acquisition of the

physiological signals from healthy volunteers and

the methods used to model the HRV.

2.1 Subjects

Five volunteers (4 males; 1 female; age: 22-46

years; ASA1) took part of the study. The protocol

(Project 529/10) was approved by the Research

Ethics Committee of the Federal University of Santa

Catarina (UFSC). These subjects were informed

about the protocol and gave their written consent.

The experiments were carried out at the Medical

School Hospital of the UFSC.

2.2 Protocol

The experimental data were recorded from

volunteers at two different postures: supine and

standing. After changing the posture, five minutes

were waited for hemodynamic stabilization before

the data acquisition.

At each position, the subjects breathed according

to two different patterns guided by a metronome.

The first pattern corresponds to a broadband

respiratory signal (Poisson distribution) necessary as

input to generate a reliable autonomic heart rate

control model (Berger et al., 1989). This pattern

consists of breathing cycles ranging from 1 to 15s

(mean=5s) during 6 minutes.

The second pattern is paced breathing at the rate

of 12 breaths/min. This pattern was recorded for

each subject during 2 minutes.

2.3 Signal Acquisition and

Discrete–time Signal Processing

A portable device developed in our laboratory was

employed to acquire the required waveforms: RFW

by nasal thermometry, EGC and PPG. The RFW,

ECG and PPG were filtered by band-pass second

order Butterworth filters to limit their bandwidths to

0-6Hz, 0.5-100Hz and 0.8-10Hz, respectively. The

filtered waveforms were sampled at the rate of 1

kSPS and converted to 12-bit words. The sampled

waveforms were transmitted via Bluetooth to a

laptop computer where they were stored into

separated files (16 bits Intel PCM format). More

information on the developed system can be found

elsewhere (Giassi Jr. et al., 2011).

The sampled waveforms were processed off line

in order to obtain the inputs series for the models.

NONINVASIVE CARDIOVASCULAR SYSTEM IDENTIFICATION USING PULSE WAVE TRANSIT TIME

233

The ECG, PPG and RFW were further filtered by

digital FIR filters in order to attenuate interfering

signals. The ECG, PPG and RFW bandwidths were

limited to 0.5-40Hz, 0.26-15Hz and 0-0.75Hz,

respectively.

The R-wave peaks of the ECG were detected

using continuous wavelet transform (CWT) as

proposed by Ghaffari et al. [9]. According to these

authors, the algorithm achieved a sensitivity of

99.91% and a predictivity of 99.72% when applied

to signals of the MIT/BIH database. The RR series is

the measurements set of the time interval between

consecutive R-waves of the ECG. As it corresponds

to an irregularly sampled waveform, the RR series

was linearly interpolated to achieve the sampling

rate of 1.5 SPS. The HR consists of the inverse

interpolated RR series.

The ECG and the PPG are used to obtain the

PWTT series. The Figure 1 shows a PWTT

measurement for a cardiac cycle. The PWTT is the

time interval between the R-wave peak and the base

point within the same cardiac cycle. Following Chiu

et al. (1991), the base marker corresponds to the

intersection of the tangent through the steepest part

of the slope (determined by the maximum first

derivative point) with its baseline. The PWTT series

is the set of these consecutive measurements. The

IPWTT series corresponds to 1/PWTT. The IPWTT

series was also interpolated to achieve 1.5 SPS.

The RFW was decimated to 1.5 SPS in order to

have all the input signals sampled at the same rate.

The use of this sampling rate allows the comparison

of the obtained impulse responses to those of Perrott

and Cohen (1996).

The smoothness priors approach (Tarvainen et

al., 2001) was used to detrend the HR, IPWTT and

RFW. For that, the lambda value used was 50 that

makes the detrending to correspond to a high-pass

filter with a cut-off frequency of 0.0375 Hz.

The HR, RFW and the IPWTT series were then

normalized by their respective standard deviation.

2.4 The Model

Closed-loop systems have been proposed to model the

cardiovascular system neural control to take into

account the SBP and heart rate (HR) interactions

(Appel et al., 1989). Nevertheless, Takalo et al.

(2004) showed that the transfer functions obtained

from the open-loop model proposed by Perrott and

Cohen (1996) were not significantly different from

those obtained by the closed-loop model. In order to

assess the adequacy of the IPWTT and RFW as model

inputs, this work employs the open-loop model.

Briefly, the open-loop model is described by the

Eq. 1 where the usual ILV and SBP inputs are

replaced by RFW and IPWTT, respectively.



[



]

=−

∑

[



]

[ − ]





+

∑

[

]





RFW

[

n−j

]

+

(1)

∑

[]







[

−

]

+[]

where n, i, j and k are discrete time indexes; a

[

]

are

the autoregressive (AR) coefficients; b[j] and c[k]

are the moving average (MA) coefficients and e[n]

is the estimation error of the model. N, M and Q

define the order of the model. m and q stand for

delays between each input and the output.

Due to the non-causal coupling between the

breathing and the HR (RFW→HR) (Mullen et al.,

1997), m was made equal to -4.

The interactions of the SPB and HR are mediated

by their autonomic coupling (IPWTT→HR) and

also, by the mechanical effects of the HR on the SBP

(HR→IPWTT). To disentangle that, it is necessary

to impose causality (Mullen et al., 1997) that is

achieved by making q equal to 1.

The coefficients estimates are calculated using

the least square method. The multivariate model

order was determined by means of the

autoregressive moving average (ARMA) parameter

reduction method: APR (Perrot and Cohen, 1996).

Applying the Z transform to the Eq. 1, the

transfer functions between each input and the output

are given by:



,

(



)

()



()

∑

b(j)







∑

(

)







(2)



,

(



)

()



()

∑

c(k)







∑

(

)









(3)

From these equations, each impulse response

(RFW→HR and IPWTT→HR) can be obtained by

applying the inverse Z transform for RFW(z)=1 and

IPWTT(z)=1.

2.5 Statistical Analysis

The Student’s t-test was used to compare the power

of the LF and HF bands between the PSD curves

obtained from the measured (LF

measured

and

measured

) HR and from the modelled (LF

model

and

model

) HR. This was repeated for the different

postures and breathing patterns. A p-value below

BIOSIGNALS 2012 - International Conference on Bio-inspired Systems and Signal Processing

234

0.05 was chosen as threshold for statistical

significance.

3 RESULTS

From the data recorded during the broadband

respiratory protocol, the ARMA model order and its

coefficients were estimated for each volunteer.

With the estimated ARMA model parameters of

each subject, HR output series were generated from

the IPWTT and RFW series obtained for irregular

(broadband) and paced breathing patterns at the

supine and standing postures.

Figures 2 and 3 show the typical impulse

responses (RFW→HR and IPWTT→HR,

respectively) obtained from the ARMA model for a

subject at supine posture breathing according to the

broadband pattern.

Figure 2: Typical RFW→HR impulse response of the

ARMA model obtained from a subject at supine position,

breathing according to the broadband pattern.

Figure 3: Typical IPWTT→HR impulse response of the

ARMA model obtained from a subject at supine position,

breathing according to the broadband pattern.

The fitness of the models could be verified by

observing their responses to the RFW and IPWTT

series that were acquired from the same subjects

during the paced breathing. As illustrated by the

Figure 4, the models outputs were able to follow up

the measured HR, showing their suitability.

In order to compare the model output (HR

model

)

to the measured HR (HR

measured

) in the frequency

domain, each of these two series were segmented in

three non-overlapping 40s segments and Hamming

window was applied to all them. For each series, the

DFT of the three segments were averaged. Next, the

PSD curves of the HR

measured

and HR

model

obtained

from all five subjects were averaged. Figures 5 and 6

show the averaged PSD curves obtained from the

subjects at supine and standing postures,

respectively, breathing at irregular pace. These

averaged PSD curves were also obtained for the

subjects breathing at 12 breaths/min during supine

(Figures 7) and standing (Figures 8) positions.

Figure 4: Typical result of HR series generated by the

model (continuous red line) that follows up the HR

(dashed black line) measured from a subject at supine

posture breathing at 12 breaths/min.

Figure 5: Averaged PSD of the HR

measured

(dashed black

line) and the HR

model

(continuous red line) for all subjects

at supine posture, breathing at irregular pace.

Figure 6: Averaged PSD of the HR

measured

(dashed black

line) and the HR

model

(continuous red line) for all subjects

at standing posture, breathing at irregular pace.

Measurements of LF and HF power were carried

out in normalized units (Task Force, 1996).

NONINVASIVE CARDIOVASCULAR SYSTEM IDENTIFICATION USING PULSE WAVE TRANSIT TIME

235

Table 1 contains the HR power values within the

LF and HF bands that were obtained from the

averaged PSD curves of all subjects breathing at

irregular breathing pattern in the different postures.

Table 2 shows the same for the subjects breathing at

12 breaths/min.

The Student’s t-test does not show significant

differences between LF

measured

and LF

model

and neither

between HF

measured

and HF

model

for the two different

postures and for the two different breathing patterns.

Figure 7: Averaged PSD of the HR

measured

(dashed black

line) and HR

model

(continuous red line) for all subjects at

supine posture, breathing at 12 breaths/min.

Figure 8: Averaged PSD of the HR

measured

(dashed black

line) and the HR

model

(continuous red line) for all subjects

at standing posture, breathing at 12 breaths/min.

4 DISCUSSION

According to Payne et al. (2006), the variable

cardiac pre-ejection period constrains the use of the

IPWTT as a reliable estimate of the SBP; however,

these authors point out that it may be useful for

assessing the SBP variability.

When compared to non-invasive SBP

measurements carried out with an arterial tonometer,

the IPWTT has lower cost and does not offer risk of

interrupting the perfusion due to the application of

excessive pressure to the finger-cuff (Teng and

Zhang, 2006).

Using the IPWTT and RFW as inputs, the model

parameters were generated for each volunteer from

data recorded when they were breathing according to

an irregular pattern (Berger et al, 1989). The APR

method was used to define the model orders (Perrott

and Cohen, 1996).

Table 1: LF and HF powers (nu) measured from the

averaged PSD curves for subjects breathing at irregular

pace (Mean±SD).

measured

model

Supine

70.42

±10.36

29.58

±10.36

58.74

±11.60

41.25

±11.60

Standing

84.71

±6.02

15.29

±6.02

73,24

±10.74

26.76

±10.74

Table 2: LF and HF powers (nu) measured from the

averaged PSD curves for subjects breathing at 12

breaths/min (Mean±SD).

measured

model

Supine

46.8

±27.14

53.82

±27.14

27.59

±22.35

72.41

±22.35

Standing

66.46

±11.52

33.54

±11.52

60.00

±24.70

40.04

±24.70

As can be seen in Figure 4, the generated models

were able to follow the measured HR when the

subjects were breathing at a constant rate.

It is possible to note in the Figures 2 and 3 that

the model impulse responses are, respectively, very

similar to the ILV→HR and SBP→HR impulse

responses obtained, for instance, by Perrott and

Cohen (1996) and by Chen and Mukkamala (2008).

The averaged PSD obtained for the HR

measured

and HR

model

from the different volunteers breathing

at irregular pace (Figures 5 and 6) and at 12

breaths/min (Figures 7 and 8) presented similar

trends.

The statistics results do not point significant

differences between the LF powers and HF powers

calculated for the HR

measured

and HR

model

5 CONCLUSIONS

This work investigated the use of the IPWTT and

RFW as inputs to generate ARMA models of the

heart rate autonomic control.

The assessment of the presented results allows us

to conclude that the generated models are able to

follow up the HR of subjects not submitted to

nervous blockade.

It is much safer and easier to get these two series

to model the autonomic control during routine

clinical exams as alternatives to ILV and SPB.

Therefore, they can be recorded from a larger

BIOSIGNALS 2012 - International Conference on Bio-inspired Systems and Signal Processing

236

number of patients under different clinical

conditions, speeding up the investigation of

parameters obtained from the models that may be

useful to assist diagnosis.

Additional experiments using the RFW and

IPWTT series as inputs are going to be carried out

under sympathetic, vagal and double blockade to

evaluate the model output generated in these

scenarios. Furthermore, the effect of the IPWTT on

the causal analysis as proposed by Faes et al. (2006)

will be also investigated.

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