A PULSE WAVEFORM DATA DECOMPOSITION BASED ON

MULTI COMPONENT CURVE FIT COMPARED WITH SECOND

DERIVATIVE PHOTOPLETHYSMOGRAPHY AND PHASE

PLANE PLOT

M. Huotari

1

, K. Maatta

2

and J. Kostamovaara

2,3

Department of Electrical and Information Engineering,

1

Microelectronics and Materials Physics Laboratories

2

Electronics

Laboratory, University of Oulu, Pentti Kaiteran tie 1, FIN-90014 Oulu, Finland

3

Academy of Finland, PO Box 99, FIN-00501 Helsinki, Finland

Keywords: Pulse wave analysis, Photoplethysmography, Arterial stiffness, Lognormal function, Second derivative,

Phase plane plot.

Abstract: With a new photoplethysmographic (PPG) device we have been attending to photoplethysmographic signals

of different ages for signal decomposition purpose. Because PPG is a non-invasive, and easily attachable

measurement technique both suitable in health care applications we concentrated on its comprehensive

signal analysis and waveform interpretation. By means of PPG it is easy to capture data for further analysis.

In the world cardiovascular diseases are the frequent cause of death that’s why we are concern on

cardiovascular diseases. The main cause of incidents can be high arterial stiffness which is symptomless and

increases the risk as a function of age causing cardiovascular diseases. Arteries stiffen normally as a

consequence of age, but also because of insalubrious mores and many diseases. Normal age related stiffness

occurs when the elastic fibers within the arterial walls begin to weaken due to age, but diseases as

arteriosclerosis accelerate this process. However, we believe that it is possible to prevent arterial stiffening

if detected early enough. For this reason we have derived indexes to indicate a possible arterial stiffness

value..

1 INTRODUCTION

Many photoplethysmographic (PPG) devices exist,

but they are not practical and not accurate enough

for the purpose of the recent study. Infra red light

emitting diode (LED) is used as the light source as it

is cheap, small, secure to human eye and energy-

friendly.

Cardiovascular diseases or even arterial stiffness

does not cause any symptoms, but after the person

exercises the symptoms appear. During the first

symptoms 60% of the affected persons die. These

persons are and have been in danger for long time.

But measuring blood pressure is not enough,

because it do not see the arterial stiffness at all.

That’s why we have been developing an optical

device for arterial stiffness measurement and

software for analysis of the measurement results.

The extracted PPG pulse wave was evaluated by

a pulse waveform analysis for 10-20 s every single

pulse of the finger and toe records.

2 MATERIALS AND METHODS

The new PPG system consists of two optical

measurement probes, one for a finger and the other

for a toe, and a compound electronics unit for

handling the optically measured signals based on

phase sensitive detection (PSD). The measurement

head consists of two LEDs and one large area

semiconductor photo detector for collecting light

emitted by the LEDs through the finger or toe. The

compound electronic unit contains electronics for

driving the LEDs (940 nm), two preamplifiers for

signals, four PSD channels, an analog-to-digital

converter and an USB-interface for transferring the

digitized results onto a laptop. In addition, parallel

methods of electrocardiogram (ECG) and

phonocardiogram (PCG) have been measured

simultaneously to support the later PPG analyses.

The subjects were measured a.m. in supine position

without coffee or tobacco in the morning. Each

measurement took about five minutes to obtain

477

Huotari M., Maatta K. and Kostamovaara J..

A PULSE WAVEFORM DATA DECOMPOSITION BASED ON MULTI COMPONENT CURVE FIT COMPARED WITH SECOND DERIVATIVE

PHOTOPLETHYSMOGRAPHY AND PHASE PLANE PLOT.

DOI: 10.5220/0003163804770480

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2011), pages 477-480

ISBN: 978-989-8425-35-5

Copyright

c

2011 SCITEPRESS (Science and Technology Publications, Lda.)

consecutive 300 pulses, of which parallel 10 to 20

most stable were selected for pulse wave

decomposition analysis.

In this research, the index

finger and index toe were always under

measurement. After measurements we depict the toe

PPG as a function of the finger PPG which describe

complex non-harmonic motion in all cases. The

phase shifts were apparent that delay semantics can

be difficult to define and used with a causal system

relations.

In the pulse wave decomposition analysis, each

pulse wave was divided into four lognormal wave

components. The compound decomposed

waveforms were after computation and fitting

visually compared to the original waves to make

sure the best fitting. This comparison and the four

lognormal functions can be used to obtain a residual

error curve and its chi-square value will describe the

goodness of the fit. The verification of multi-

lognormal functions can be justified as they well

represent the vascular network with many

asymmetric arterial double-branching and lognormal

distribution of the length of capillary arteries and

also the blood flow velocities in these capillaries

(Qian et al. 2000).

The Origin 7.5 (OriginLab

®) lognormal

procedure was utilized for analyzing the pulse waves

in time domain to obtain best mathematical fitting

with minimal residual error. In this procedure, the

Levenberg-Marquart algorithm (LMA) is a very

popular curve-fitting algorithm used in many

applications for solving non-linear curve-fitting

problems, e.g., logarithmic normal function curves.

LMA provides a numerical solution to the problem

of minimizing a function which can be nonlinear,

over a space of parameters of the function. In our

case we have selected four similar lognormal

components which have 4x3 parameters and the

requirement for the correlation coefficients (R

2

) to

be 0.995 or over. We used the peak time values of

the 1

st

and the 2

nd

lognormal function, called

percussion and tidal component to find out arterial

stiffness values for the population measurements.

We also determined the 2

nd

derivative function of the

PPG wave which contains the parameters a, b, c, d,

and e, respectively in each pulse wave. The second

derivative of the finger photoplethysmography

(SDPPG) has been applided as a rapid and

convenient method for pulse-wave inspection. The

determination of vascular aging is possible

throughout the SDPPG, but especially effective it is

through the third derivative of the finger PPG

(TDPPG). In the case of typical SDPPG waveform

were characteristic waves are missing, the TDPPG

can still more uncover the characteristic waves. PPG

waveforms are varied by very little with each

subject. Therefore there are some cases when

characteristic wave of PPG was not found by one

technique we selected another one. The derivatives

of waveforms are changed by the area, width and the

function’s peak value.

3 RESULTS AND DISCUSSION

In Figure 1 it is shown as an example consecutive

PPG waveforms of the pulse wave signal at 940 nm

(IR) measured through the index finger tip pulse

wave (PPG1, straight) and the second toe tip (PPG2,

dash). Signals are normalized for the amplitude.

012345678

0,0

0,2

0,4

0,6

0,8

1,0

PPG

relative

t[s]

BTTL72_PPG1

D PPG2

Figure 1: The finger (straight) and toe (dash) PPG of a 72

years male person.

Figure 2 shows the causal relation between the

PPG1 and PPG2 in a phase plane, the PPG2 as a

function of the PPG1. When the PPG1 increases the

PPG2 still decreases, but after a certain value of the

PPG1 the PPG2 begins to increase. After the peak

value, the both signals decreases almost linearly to

the end of each pulse wave.

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

PPG2

rel

PPG1

rel

F TTLL72 PPG2 vs PPG1

Figure 2: PPG2 vs. PPG1 of the pulse waves in Figure 1.

BIOSIGNALS 2011 - International Conference on Bio-inspired Systems and Signal Processing

478

In Figure 3 it is illustrated an analyzed

compound finger PPG waveform. It contains the

typical PPG components. In this case the PPG

waveform analyses are covering the following four

pulse components in each pulse wave: percussion,

tidal, dichrotic, and peripheral reflection component.

Percussion is caused by the contraction of the heart

left ventricular muscle. The second component is the

tidal wave, occurring during the later part of the

systole, caused by the elastic properties of aorta. The

dichtrotic component is the reflected pulse from

lower periphery elasticity and vessel branching (A G

Scandurra et al. 2007).

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

0,0

0,2

0,4

0,6

0,8

1,0

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

-0,050

-0,025

0,000

0,025

0,050

0,16221

0,27575

0,4704

0,71372

t

2

PPG1

rel

Residual error

t[s]

t´= t

2

-t

1

=0.05354s ; t´-t

1

= Δt= -0.10867s ; t

2

/t

1

=1.7000

Data: Data8_B

Model: LogNormal

Equation:

y = y0 + A/(sqrt(2*PI)*w*x)*exp(-(ln(x/xc))^2/(2*w^2))

Weighting:

y No weighting

Chi^2/DoF = 0.00037

R^2 = 0.99595

y0 0 ±0

xc1 0.27539 ±0.00779

w1 0.7163 ±0.0101

A1 0.29007 ±0.00777

xc2 0.28766 ±0.00337

w2 0.21826 ±0

A2 0.05006 ±0.00246

xc3 0.5124 ±0.00606

w3 0.26652 ±0.01688

A3 0.15757 ±0.00531

xc4 0.72135 ±0

w4 0.12946 ±0.01189

A4 0.02792 ±0.00522

t[s]

t

1

Figure 3: An analyzed finger PPG waveform which

contains the percussion component (green), the tidal

component (blue), the dicrotic component (magneta), and

the peripheral reflection component (navy). The lower part

of the figure shows the residual error and R

2

=0.99595.

5 101520253035404550556065707580

1,00

1,25

1,50

1,75

2,00

2,25

2,50

2,75

Linear Regression for Data2_B:

Y = A + B * X

Parameter Value Error

--------------------------------------------

A 2,341 0,09292

B -0,0123 0,00197

---------------------------------------------

RSDNP

-0,813 0,1797 22 <0.0001

B

Linear Fit of Data2_B

t

T

/t

P

age [years]

Figure 4: The tidal peak time divided by the percussion

peak time as a function of the age for 22 persons of

different ages (R=-0.813).

Figure 4 shows the tidal peak time divided by the

percussion peak time of each PPG waveform R=-

0.813 which is rather good correlation coefficient.

012345678

-0,5

-0,4

-0,3

-0,2

-0,1

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

1,1

0,14063

0,74805

0,92969

1,08398

1,70313

1,88281

2,04102

2,65625

2,81836

2,98633

3,61133

3,78906

3,94531

4,55469

4,73047

4,90625

5,51758

5,69531

5,85547

6,48242

6,6543

6,83008

7,4394

7,61914

7,77344

0,06055

0,82031

1,01367

1,77734

1,95898

2,73438

2,9043

3,68555

3,86133

4,63086

4,81836

5,59375

5,78125

6,55273

6,74219

7,51563

7,68945

e

d

c

b

d

2

PPG1/dt

2

t[s]

B TTLL72; d

2

PPG1/dt

2

a

Figure 5: The SDPPG waveform for the PPG1 in Figure 4.

The 2

nd

derivative of PPG1 contains the parameters a, b, c,

d, and e for each consecutive pulse wave. All peaks were

completely found in this case, but only marked for the first

pulse wave.

In Figure 5 it is shown a 2

nd

derivative of the

finger PPG waveform. They well hit into the search

window and all the peaks were found. However,

their biophysical meaning is open. It is known that

the components a, b c, and d belong to the first part

of systole, and e belongs to the late part of the

systole (J Hashimoto et al. 2002).

The characteristic points of the finger PPG can

be also extracted using the 3

rd

derivative PPG

(TDPPG) as shown in the Figure 6. The positions of

the peak of the percussion wave and the dicrotic

wave can be evaluated also from the inflection

points, where the third derivative of the PPG

changes sign, such as the zero crossing points.

0,0918

0,72656

0,84766

1,0332

1,68164

1,80859

2,00586

2,64063

2,75781

2,94922

3,59375

3,71094

3,91016

4,5332

4,65625

4,85352

5,49609

5,61914

5,8125

6,45898

6,58203

6,7793

7,4277

3

7,54102

7,72656

0,03906

0,77539

0,98242

1,72852

1,93945

2,67969

2,88477

3,63867

3,8418

4,58398

4,78711

5,54492

5,75

6,50977

6,7168

7,45898

7,66992

012345678

-30

-20

-10

0

10

20

30

TDPPG1

rel

t[s]

21 point S-G Derivative Smoothing of Data1_B TTLL72_TDPPG1

Figure 6: The TDPPG waveform for the PPG1 in Figure 1.

The 3

rd

derivative of PPG1 contains more clearly that the

SDPPG the similar parameters a, b, c, d, and e for each

consecutive pulse wave.

Figure 7 shows that the tidal peak times divided

by the percussion peak times of each PPG waveform

have clearly concentrated on the value 0.5 and the

A PULSE WAVEFORM DATA DECOMPOSITION BASED ON MULTI COMPONENT CURVE FIT COMPARED

WITH SECOND DERIVATIVE PHOTOPLETHYSMOGRAPHY AND PHASE PLANE PLOT

479

0,30 0,35 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80

0

5

10

15

20

25

30

35

40

45

0.7143

0.46666

0.41666

0.53333

0.5625

0.62497

0.66668

Count

t

1

/t

2

Count 293 events of t

1

/t

2

as a functio of value t

1

/t

2

0.5

Figure 7: The percussion peak time divided by the tidal

peak time count as a function of the percussion peak time

divided by the tidal peak time for 293 events in 83 persons

of different ages. (see also Figure 3).

on some discrete values in 83 persons for 293 PPG

pulses.

This research studies the potential of PPG for

early diagnosis of arterial stiffness. PPG technology

is widely available at the pulse oxygen saturation

measurements and is relatively cheap and does not

require special expertise. PPG can be utilized for

detecting pulse waveforms. In the blood circulatory

system, the arterial pulse wave reflections depend on

the arterial wall stiffness. This study includes

creating a mathematical model for pulse wave-forms

for analyzing the four wave components of the

human pulse. This information based on the second

derivative photoplethysmogram can be further used

for estimating arterial stiffness which is normally

determined based on pulse wave velocity (A Qasem,

A Avolio 2008).

4 CONCLUSIONS

The location of a tidal wave seems to drift earlier by

the age, while the percussion wave drifts to the

opposite direction. By analyzing the four

components, one may be able to make conclusions

relating to arterial stiffness. It might be beneficial to

measure pulse waves instead of blood pressure due

to more information being available on the condition

of veins.The use of lagged gamma function might

also prove interesting (Qian et al. 2000).

Because the tidal peak time divided by the

percussion peak time of each PPG waveform (R=-

0.813) which is rather good correlation coefficient as

a function of age, this could be used as a measure of

arterial aging. The further investigation would be

warranted to see if a predictive index of blood

pressure changes might be obtained from pulse wave

analysis of PPG waveforms. The determination of

age-related changes in the arterial pulse wave by the

high fidelity PPG device, thus, provides important

supplementary information to that obtained by use of

the blood pressure measurements.

ACKNOWLEDGEMENTS

The research grant from the Finnish Cultural

Foundation is acknowledged for MH.

REFERENCES

H Qian, J. B. Bassingthwaighte (2000) A Class of Flow

Bifurcation Models with Lognormal Distribution and

Fractal Dispersion, Journal of theoretical Biology 205,

261-268.

A. G. Scandurra, G. J. Meschino, L. I. Passoni, A. L. Dai

Pra, A. R. Introzzi and F. M. Clara (2007)

Optimization of arterial age prediction models based

in pulse wave, Journal of Physics: Conference Series

90 012080.

J. Hashimoto et al. (2002) Pulse wave velocity and the

second derivative of the finger photoplethysmogram in

treated hypertensive patients: their relationship and

associating factors Journal of Hypertension, Vol 20

12; 2415-2422.

A. Qasem, A. Avolio (2008) Determination of aortic pulse

wave velocity from waveform decomposition of the

central aortic pressure pulse, Hypertension 51;188-

195.

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