Changes in the Spectral Characteristics of Plethysmographic Waveforms

Due to PAOD

Irina Mizeva

, Andrey Dumler

and Nikita Muraviev

2,3

Institute of Continues Media Mechanics, ak. Koroleva, 1, Perm, Russia

Perm State Medical Academy, Petropavlovskaya str. 26, Perm, Russia

The ﬁrst St. Petersburg State Medical University. named after Acad. Pavlov, Tolstova st., 17, St.Petersburg, Russia

Keywords:

Plethysmography, PAOD, Wavelets, Pulse Wave.

Abstract:

Peripheral arterial occlusive disease (PAOD) of increasing severity can lead progressively to disabling claudi-

cation, ischemic rest pain and gangrene. The blood supply of a limb with peripheral arterial disease is restored

by surgical operations, which treats the critical limb ischemia (CLI) only in 30% of the cases. CLI occurs

when the arterial lumen decreases signiﬁcantly and the nutritive requirements of the tissues, supplied by mi-

crocirculation, cannot be met. In the present paper, a simple, non-invasive and low-cost technique is proposed

for early screening diagnosis of PAOD. The approach is based on the investigation of the spectral character-

istics of pulse waves measured by photoplethysmography. Painless, versatility and simplicity are signiﬁcant

merits of the proposed methodology.

1 INTRODUCTION

Atherosclerosis is the most common cause of the

pathology of the major arteries of the lower extrem-

ities. The disease state is associated with the stenosis

of vessels in extremities and the formation of a com-

plex of clinical signs, designated as a chronic periph-

eral arterial obliterative disease. Progression of steno-

sis and (or) occlusion of major arteries results in the

gradual decompensation of the blood ﬂow in the ex-

tremity, increasing thus the rates of mortality and dis-

ability. In this stage of PAOD, critical limb ischemia

takes place, and surgery is recommended. The pur-

pose of vascular surgery is to restore a proper blood

ﬂow and to enlarge the lumen of a stenosed vessel.

However, the postoperative mortality within the ﬁrst

year after surgery reaches 20%, and approximately

half of the patients, who underwent surgery, need a

second operation (Norgren et al., 2007).

Diagnosis of PAOD includes anamnesis descrip-

tion, physical examination, and medical tests, of

which a Doppler ultrasound test of injured arteries

and ankle brachial pressure index (ABPI) measure-

ment are used most extensively. Doppler ultrasonog-

raphy of lower extremities provides visualization of

arterial injuries and the character of blood ﬂow within

the injured segments and a tentative estimation of the

amount of damage and the degree of stenosis.

X-ray contrast aortoarteriography is a reliable

imaging technique for optimal surgery planning. This

method includes evaluation of the abdominal aorta

with an intracardiac echocardiography probe, intro-

duction of X-ray contrast agents and x-ray imaging of

the vascular bed of the lower extremity. However, the

x-ray technique can only be used in operating rooms,

and is not suitable for fast preliminary diagnostic.

The optimal screening technique to examine

PAOD meets several requirements: noninvasiveness,

simplicity, reliability, reproducibility, and the possi-

bility of obtaining rapid results. The most common

method is based on the determination of the ankle

brachial pressure index ABPI, which is the ratio of

systolic leg blood pressure to systolic arm blood pres-

sure. The value of ABPI< 1 indicates the main blood

ﬂow disorders in lower extremities (Norgren et al.,

2007). For PAOD, the value of ABPI is asymmet-

ric, which is attributed to the various degrees of dam-

age in the extremities. The above method is nonin-

vasive and can be used for primary diagnosis of the

disease. The disadvantage of this method is that it is

prone to the subjectiveness of the practitioner. Be-

sides, blood pressure drifting, since measurements on

extremities are not performed simultaneously, limits

the technique.

Pulse wave is a high blood pressure wave prop-

agating through the aorta and arteries. It is caused

149

Mizeva I., Dumler A. and Muraviev N..

Changes in the Spectral Characteristics of Plethysmographic Waveforms Due to PAOD.

DOI: 10.5220/0004747301490154

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2014), pages 149-154

ISBN: 978-989-758-011-6

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

by the ejection of blood from the left ventricle of

the heart during contraction of its muscles (systole

phase). The pressure wave propagates along the ar-

terial segment of the vascular system, and a short-

term expansion of the arterial wall can be palpated or

registered as an arterial pulse. The velocity of pulse

wave propagation in the vessels does not depend on

the blood ﬂow rate and is deﬁned by the elasticity and

diameter of the vessel, the thickness of vessel walls,

and the density of blood.

The shape of the volume pulse wave is produced

by the interaction between the left ventricle and the

blood vessels of the systemic circulation. The ﬁrst

peak of the pulse wave is formed due to the systolic

forward wave, and the second - due to the reﬂected

wave, which arises from the reﬂection of the volume

of blood circulating through the aorta and large arter-

ies to the lower extremities and moving back to the

ascending segment of the aorta. The available results

(O’Rourke and Kelly, 1993) have indicated that the

intensity of wave reﬂection is speciﬁed by the tone

of small muscular arteries in the main areas of reﬂec-

tion. That is why, the pulse waveform analysis can

adequately characterize the functional state and struc-

tural changes of a peripheral arterial bed.

There are different methods to register periph-

eral pulse waves: sphygmogram (Carter, 1968), PPG

(Allen et al., 2008), (Erts et al., 2005), (Lin, 2011),

impedance rheovasography (Schuhfried et al., 2003),

(Sherebrin and Sherebrin, 1990), and Doppler sonog-

raphy. It is known that the disorders of veins and ves-

sels cause qualitative changes in the peripheral pulse

waveform.

In this paper, we address photoplethysmography

(PPG), which is a simple and low-cost optical tech-

nique for blood ﬂow registration. The method is based

on the determination of the blood volume in the tissue

sample (see for the review (Allen, 2007)) placed be-

tween the receiver and the source of optical radiation.

Radiation frequency is chosen so that it can be maxi-

mally absorbed by blood red cells. Strictly speaking,

the signal is proportional to the number of red blood

cells entering the region between the source and the

receiver. Since the change in hematocrit (volume of

blood red cells per unit volume of blood) during a

single measurement is small, the intensity of the light

recorded by the receiver is inversely proportional to

the volume of blood in the lumen vessel area.

The registered signal, called a photoplethysmo-

gram (PPG), is a superposition of the variable compo-

nent (AC), associated with changes in the tissue blood

volume synchronous with a heartbeat, and the slowly

varying component (DC), associated with respiration,

sympathetic nervous system activity, and thermoreg-

ulation (Allen, 2007), (Holohan, 1996). Also, the ab-

sorption of light by bones, skin, tissues, and the blood

volume that remains unchanged in the venous and ar-

terial segments of the microvascular bed add a con-

stant level of PPG. Therefore, the absolute value of

PPG has no physiological meaning, and only the pul-

sations of different frequency bands or the changes in

the PPG level during the physiological tests can be

used in practice.

When a PPG probe is attached distally to the

artery stenosis, the waveform rises slowly, the peak

becomes more rounded, and the second peak (dicrotic

wave) is absent or attenuated. In (Allen et al., 2008),

the authors derived a parameter set for describing

pulse waveforms and performed the quantitative anal-

ysis of these parameters in healthy patients and pa-

tients with PAOD. Note that the spectral analysis of

peripheral pulse waves in patients with PAOD has not

been carried out previously, although the results pre-

sented in (F. Javed et al., 2010) have demonstrated the

effectiveness of the Fourier analysis for the study of

pulse waveforms in healthy volunteers.

Over the past two decades, the wavelet analy-

sis has been used extensively to study the signals of

various nature at different scales (Nesme-Ribes E.

et al., 1995). The method has been developed sig-

niﬁcantly in the analysis of astrophysical data, and in

the last decade introduced in the analysis of biophys-

ical signals, in particular, to assess the status of cen-

tral hemodynamics and peripheral circulation (Leon-

des, 2002), (Bernjak and Stefanovska, 2007). In the

wavelet decomposition procedure, the effects of mul-

tiple harmonics, noise and motion artifacts are essen-

tially weaker than in the case of Fourier decomposi-

tion (Nesme-Ribes E. et al., 1995).

Since the low-frequency ﬂuctuations of the heart

rate is mediated mainly by the sympathetic nervous

system, it is also reasonable to attribute the low-

frequency ﬂuctuations in the baseline and amplitude

of the PPG signal to the same nervous system. Fur-

thermore, the ﬂuctuations in the ﬁnger blood volume

are due to the constriction and relaxation of the tissue

blood vessels which are predominantlyaffected by the

sympathetic nervous system (Nitzan et al., 1998).

The purpose of the paper is to investigate the spec-

tral characteristics of PPG signal in LF and HF bands

in the distal parts of lower extremities of patients with

PAOD.

2 MATERIALS AND METHODS

The investigation were conducted for 59 male volun-

teers - 25 healthy (age 55 ±9, ABPI 1.2 ±0.6) and

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150

34 (age 60 ±11) with CLI, treated at the Department

of Cardiovascular Surgery, Perm’s Clinical Hospital

No 4. In the investigation, we did not include patients

with diabetes and autoimmune diseases of blood ves-

sels. The main clinical manifestation, which occurred

in patients selected for the study, was the presence

of intermittent claudication. In this case, the diagno-

sis was made according to the recommendations of

the TASC II in the presence of typical clinical symp-

toms for at least 2 weeks. The clinical examination,

ABPI measurements and radionuclide aortoaretriog-

raphy were used to verify the tentative diagnosis.

In the majority of cases critical limb ischemia pro-

duces different effects on the lower extremities of the

person. In group B (34 records) we included PPG col-

lected from the lower extremities seriously affected

by arterial disease (ABPI= 0.7 ±0.2); the invasive

methods supported the necessity of surgical revas-

cularization. The contralateral extremities were less

amenable to this disease, and PPG were included in

group A (34 records). It should be noted that PAOD

is a manifestation of generalized atherosclerosis, and

so the measurements of the contralateral limb (group

A, ABPI=1.0±0.2) correspond to the atherosclerotic

lesions of major arteries, which do not lead, at the

time of the survey, to peripheral circulatory decom-

pensation. Figure1 presents data corresponding to the

control group and groups A and B.

Figure 1: Characteristic form of pulse waves in the distal

parts of the lower extremities measured in different groups:

control group (top plot), group A (middle plot), and group

B (bottom plot).

To investigate the inﬂuence of surgery on the low

frequency pulsations we used in the study long-time

(10 minutes) PPG records collected from 5 healthy

subjects, 5 diseased persons before (B1 group) and 3

days after (the inﬂuence of operation anesthesia was

excluded) the revascularization surgery (B2 group).

Registration of the PPG signal was carried out

at controlled temperature (24±1

◦

C ) after a ﬁfteen-

minute adaptation of the patient to the measurement

system. Data were collected from the distal phalnax

of second toe of the subject lying in the supine po-

sition. A standard patient monitor Microlux (Russia)

designed to record the PPG signal in the transparent

mode was used. The Nellcor PPG probe was held

comfortably in place, and the interference from the

external light sources was reduced.

The software was adapted for the purposes of the

study, all signal pre-processing functions were dis-

abled, sampling frequency was 50 Hz. Measurements

were performed for 10 minutes in series with the two

extremities. We did not consider the PPG, which

could not be processed due to poor tissue perfusion

or due to movement artifacts caused by the tremors of

the extremities.

3 CALCULATION

Usually, by the spectral analysis the decomposition

of the signal into a Fourier series of harmonic func-

tions is meant. The harmonic functions are deﬁned

from −∞ to +∞, and in the analysis of real signals

we are dealing with ﬁnite realizations. Choosing an

analyzing function in the limited space, yields a gen-

eralization of the Fourier analysis - the wavelet anal-

ysis. This method gives better results in the analy-

sis of short nonstationary data with a low signal to

noise ratio. Since the PPG signal for extremities with

CLI is rather weak and the signal to noise ratio is

low, it seems reasonable to use wavelets. The discrete

wavelet transform of the function f (t) is

W(ν,τ) =

√

∞

∑

t=−∞

f(t)ψ(t −τ,ν). (1)

In (1) t is the time, τ is the time shift, ν (∼ 1/a,

where a - is time scale) is the frequency, and ψ(t,ν) is

the function called an analyzing wavelet, the form of

which depends on the signal of interest and the pur-

pose of the study.

The wavelet transform (1) of one-dimensional

signal gives a two-dimensional image on the time-

frequency plane. This kind of presentation allows us

to study the variation of the oscillation characteristics

of different scales in time. Since we are dealing here

with the stationary signal investigation, we consider a

global power spectrum, which is obtained by integrat-

ing the power over time:

ChangesintheSpectralCharacteristicsofPlethysmographicWaveformsDuetoPAOD

151

M(ν) =

∑

t=0

|W(ν,τ)|

. (2)

Normalization

√

ν in (1)allows us to compare the

Fourier scalogram and wavelet global spectrum. We

use the complex Morlet wavelet ψ(t) = e

2πit

−t

/(2σ

)

(Goupillaud et al., 1984) and the damping parameter

σ = 2. This analyzing function has enough spectral

resolution and is well localized in time.

The wavelet global spectrum (2) of each recording

was performed in the frequency range 0.01-5 Hz by

100 harmonics with logarithmic frequency decompo-

sition. Fig.2 shows a comparison of the Fourier scalo-

gram and wavelet spectra for one PPG from the group

of healthy patients. It is seen that the wavelet spec-

trum reproduces fairly well the main features of the

Fourier spectrum.

Both, the power spectral density (called also the

Fourier spectrum) and the wavelet spectrum demon-

strate the presence of frequency pulsation. Although

the spectra coincide in the frequency range under con-

sideration, it is easier to analyze the wavelet spectrum.

The limitation of the observation time leads to a very

indented Fourier spectrum. The smooth power spec-

tral density can be observed in the case when T → ∞,

but under real conditions the time interval is rather

short. As we intend to create a time-saving method of

screening diagnostics, which will last a few minutes,

we cannot increase signiﬁcantly the observation time.

We suggest to use the spectral characteristics of

high frequency band for description of the pulse

waveform, namely we use the energy, which is local-

ized in the vicinity of 2ν

frequency. In this fre-

quency band the difference in the spectra of healthy

and diseased people is very strong.

0.05

0.10

0.50

1.00

100

1000

Ν,Hz

E, a.u.

Figure 2: Fourier (black thick line) and wavelet (gray thin

line) spectra of PPG signal.

To compare the energy of pulsation at cardiac fre-

quency ν

and at 2ν

, we deﬁne the dimensionless

frequency (

ν) and energy

ν), which is maximum in

the range from 0.3 to 5 Hz.

ν) = E(ν)/Max[E(ν)]

ν = ν/ν|

Max[E(ν)]

(3)

Figure 3: Normalized wavelets in the control group (top

panel), subgroup A (middle panel), and subgroup B (bottom

planel).

The observed spectra, which were normalized us-

ing

E and

ν, are shown in Fig.3. In the spectra of sig-

nals obtained in the control group (top panel in Fig.3),

the secondary peak is observed in the frequencyrange

1.7-2.2 Hz. In the group A (middle panel in Fig. 3)

the energy of oscillations within this frequency range

is smaller, which is shown by the peak that is less pro-

nounced at these frequencies. In group B the reﬂected

wave due to the so called ”early reﬂection” coincides

with the main peak producingno visible dicrotic wave

(Nichols et al., 2011) (bottom panel in Fig.1). It is

accompanied by a decrease in the energy spectra, as

shown in the bottom panel of Fig.3.

We did not examine the spectra, within which we

could not identify accurately the ﬁrst harmonic be-

cause of severe arrhythmias and/or poor perfusion of

tissues with blood. So we excluded 5 persons from

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152

Figure 4: Distribution of I for different groups: dots denote

mean values, straight line - medians, and upper and lower

boundaries of boxes correspond to distribution percentiles

(25% - lower, 75% - upper). Hatching indicates different

limits of integration (open rectangles ν

= 1.8, ν

= 2.2;

gray rectangles ν

= 1.7, ν

= 2.3; hatched rectangles ν

1.6, ν

= 2.4.

B group and 8 from A group. To quantify the energy

ﬂuctuations in some frequency band, we introduce an

index I deﬁned by

I = log

νd

ν), (4)

where ν

and ν

are the boundary frequencies for the

chosen interval. To compare the reﬂected wave en-

ergy, we take the integral with the limits in the vicin-

ity of ν = 2. Fig.4 illustrates the distribution I for

different combinations of the boundary frequencies

and ν

. The variation of the frequencies within

certain limits does not cause changes in the statisti-

cally signiﬁcant properties of the quantities of inter-

est, namely, the differences between the group data

remain reliable even though the integration interval

becomes twice as much.

Table 1 summarizes the mean values of the index

I and ABPI measured in the examined groups. The

obtained results are presented as a M±SD (M - mean

values, SD - standard deviation). The mean values for

different groups were compared in the analysis of re-

liability by applying the Mann-Whitney test. The reli-

ability p < 0.05 is considered statistically signiﬁcant.

From Table 1 it follows that in the examined groups

the values of index I differ signiﬁcantly, and the dif-

ference is more reliable for index I than for ABPI.

4 LOW FREQUENCY

PULSATIONS

Fig.5 presents the averaged spectra of long PPG

records. The subjects with PAOD have the higher

low-frequency energy, which can be attributed to

Table 1: Comparison of the ankle-brachial index (ABPI)

with the index (I) for different groups.

groups A B Control

ABPI 1.0±0.2 0.7±0.2 1.2±0.6

=0.005 p

= 0.04

I −4.1±0.5 −4.6±0.4 −2.9±0.4

=0.02 p

< 0.00

< 0.001

Figure 5: Averaged spectra of control group, PAOD with

CLI subjects (B1 group) and the same PAOD subjects 3

days after revascularization surgery (B2 group).

the fact that compensatory mechanisms increase

the blood ﬂow supply. After the revascularization

surgery, the low-frequency pulsations associated with

the sympathetic nervous system are depressed. Since

the PPG were collected 3 day after surgery, the effect

of anesthesia should be negligible.

5 SUMMARY

In this study, the spectral method has been applied

for a quantitative description of the characteristics of

pulse waves in the lower extremities of patients with

PAOD.

It is shown that index I determined as the ratio of

energy of the heart beat frequency νHR and on the

2νHR, obtained by integrating the normalized spectra

in a deﬁned frequency band is signiﬁcantly different

in the examined subgroups. The experiments have in-

dicated that the proposed technique has high sensitiv-

ity and can be used as the traditional tool (ABPI de-

terming) in screening diagnostics. It has been found

that the ratio of secondary and primary waves in the

limb with CLI is several times smaller than the same

ratio in the healthy limb.

Obtained results may favor further development

of research in this area. The merits of the proposed

methodology such as painless, versatility and simplic-

ChangesintheSpectralCharacteristicsofPlethysmographicWaveformsDuetoPAOD

153

ity, as well as an ever increasing use photoplethysmo-

graphic monitors in clinical practice create conditions

that promote implementation of the proposed method

for screening diagnosis of PAOD.

Restrictions imposed in connection with the use

of PPG are associated with weak signals generated by

motion artifacts or with the limited peripheral blood

ﬂow (F. Javed et al., 2010). The numerical analysis

of the PPG signals proposed in this paper can be ap-

plied to pulse waveforms obtained by other registra-

tion techniques.

The results obtained in the study of LF waves as-

sociated with sympathetic nervous system are also

presented. The spectral analysis of the PPG signal

shows, that LF pulsations of blood ﬂow of subjects

with PAOD are higher then of healthy ones. The

cause of it can be microcirculation adaptation to the

decreased blood ﬂow in the limb. The amplitude of

LF oscillations becomes smaller after surgery. This

can be explained by suppressing active mechanisms,

induced by peripheral nervous ﬁbers trauma.

ACKNOWLEDGEMENTS

The work is undertaken under ﬁnancial support of

RFBR-Ural 11-01-96018.

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