Photoplethysmogram Fits Finger Blood Pressure Waveform for

non-Invasive and minimally-Intrusive Technologies

Evaluation of Derivative Approaches

Gonzalo Tapia

1

, Mat

´

ıas Salinas

1

, Jaime Plaza

1

, Diego Mellado

1

, Rodrigo Salas

1

, Carolina Saavedra

1

,

Alejandro Veloz

1

, Alexis Arriola

1

, Juan Idiaquez

2

and Antonio Glar

´

ıa

1

1

Escuela de Ingenier

´

ıa Civil Biom

´

edica, U. de Valpara

´

ıso, General Cruz 222, Valpara

´

ıso, Chile

2

Escuela de Medicina, U. de Valpara

´

ıso, Campus de la Salud, Angamos 655, Re

˜

naca, Vi

˜

na del Mar, Chile

Keywords:

VPG, nImI, Arterial Hypertension, Fractional Derivatives, Finapres, Photoplethysmography Derivatives.

Abstract:

The purpose of this work is to ﬁt Photoplethysmography (PPG) to ﬁnger Arterial Pressure (ﬁAP) waveform

using derivative approaches. Derivative approaches consider using Linear Combination of Derivatives (LCD)

and Fractional Derivatives (FDP

α

). Four informed healthy subjects, aging 35.8 ± 11.0 years old, agreed to

perform Handgrip maneuvers. Signals are recorded continually; a Finapres NOVA device is used for ﬁAP,

while a BIOPAC System is used for PPG and ECG. PPG is smoothed and segmented by heartbeat; recording

sections interfered with spiky blocking noise, are eliminated. Finally, PPG is processed using LCD and FDP

α

and their results are enriched using Lasso technique. Twenty records per subject at rest and twenty at raised

BP are analyzed. Results show PPG to ﬁAP ﬁtting errors 5.38% ± 0.91 at resting ﬁAP and 5.86% ± 1.21 at

raised ﬁAP, being always lower than 15%, suggesting that derivative approaches could be suitable for medical

applications.

1 INTRODUCTION

Invasive methods are used for Blood Pressure (BP)

monitoring in critically ill patients, because measure-

ment is more accurate introducing a cannula in the

arterial system. Non-invasive procedures to mea-

sure Blood Pressure (BP) are perceived by patients

as intrusive, the procedure is frequently abandoned,

and the detection, monitoring and control of Ar-

teria Hypertension (AHT) remains elusive (Kaplan,

2004). The acronym nImI stands for non-Invasive and

minimally- Intrusive and it is proposed to summarize

a concept that could be applied to medical devices

(Tapia and Glar

´

ıa, 2015).

In the literature, (Payne et al., 2006) established

an empiric relation between Systolic Blood Pressure

(SBP) and Pulse Transit Time (PTT) when an im-

planted BP sensor was used. (Wong et al., 2009)

found new empirical relations between BP and PTT

before and after subjects performed controlled run-

ning routine. (Gesche et al., 2012) has proposed a

mathematical model relating the Pulse Wave Velocity

and PTT according with two anthropometric param-

eters. (Liu et al., 2014) measured Pulse Waves with

which produced PPT hysteresis. The Pulse Wave Ve-

locity (PWV) was found in the work of (Galli et al.,

2004) for vascular evaluations in patients.

In a review of Photoplethysmography (PPG) clin-

ical applications, (Allen, 2007) alerts on artifacts that

interfere its normal use, nevertheless they envisions

new clinical applications supported by computational

solutions (Zheng et al., 2008). (Tapia and Glar

´

ıa,

2015) tried to reduce intrusiveness in detecting phys-

ical stress caused by exercise associated with ris-

ing BP, they have used an Artiﬁcial Neural Network

to analyze the phase plane of two PPGs. (Baruch

et al., 2011) and (Salinas, 2016) developed method-

ologies to decompose ﬁnger PPG components that

reﬂect cardio-vascular characteristics. Finally, previ-

ous derivative approaches using PPG ﬁrst derivative,

named VPG and PPG second derivative, named APG,

are reported (see (Zahedi et al., 2007) and (Elgendi,

2012)).

In this paper we propose the development of a

methodology to ﬁt PPG to the ﬁAP, using either a lin-

ear combination of two subsequent derivatives or us-

ing fractional derivatives (Loverro, 2004; Herrmann,

2014).

Tapia G., Salinas M., Plaza J., Mellado D., Salas R., Saavedra C., Veloz A., Arriola A., Idiaquez J. and GlarÃ a A.

Photoplethysmogram Fits Finger Blood Pressure Waveform for non-Invasive and minimally-Intrusive Technologies - Evaluation of Derivative Approaches.

DOI: 10.5220/0006143901550162

In Proceedings of the 10th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2017), pages 155-162

ISBN: 978-989-758-212-7

Copyright

c

2017 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

155

2 MATERIALS AND METHODS

The required cardiovascular signal acquisition is per-

formed in four healthy subjects (see Table 1), they

were asked to answer a questionnaire, adapted from

Arterial Hypertension Clinical Guide of the Chilean

Ministry of Health. Twenty records per subject at rest

(before Handgrip maneuver) and twenty at raised BP

are analyzed (Handgrip maneuver).

Table 1: Characteristics of the subjects (S) participating in

the essay. It shows their Age, Sex, Body Mass Index (BMI)

and Level of Physical Activity (LPA)(Ser

´

on et al., 2010).

Subjects Characteristics

S AGE SEX BMI LPA

1 26.2 M 18.5 Moderate

2 28.8 M 22.7 High

3 49.6 M 22.2 High

4 39.6 F 21.6 Moderate

2.1 Data Acquisition

Three non-invasive cardiovascular signals are

recorded per subject at a rate of 200 Hz. For the

non-deft hand, it was measured the Arterial Pressure

waveform at the middle phalanx of the middle ﬁnger

(ﬁAP) and the PPG at the tip of index ﬁnger. The

electrocardiogram (ECG) is recorded in Einthoven

Lead I. The ﬁAP signal is recorded continuously and

non-invasively using the “volume-clamp” method

developed by (Pe

ˇ

naz, 1973). This work is the base

for (Finapres, 2015) and is currently implemented

and improved in the Finapres new NOVA model.

Directly from ﬁAP, the ﬁnger Systolic (ﬁSYS),

Diastolic (ﬁDIA) and Mean Arterial Pressure

(ﬁMAP) together with Heart Rate (HR AP), and

Inter-beat interval (IBI) are evaluated. After brachial

oscillometric calibration, the Brachial Arterial

Pressure waveform is reconstructed (reBAP) from

ﬁAP, and brachial Systolic BP (reSYS) Diastolic BP

(reDIA) and Mean BP (reMAP) are estimated from it.

Oscillometric BP device Model BM 35s from Beurer

is used to calibrate reSYS and reDIA. This calibration

method may be inaccurate, however our proposal

should also work if we use the sphygmomanometer

or a cannula in a further clinical validation.

PPG and ECG are detected using a BIOPAC Sys-

tem conﬁgured with a MP-150 Unit and three Biono-

madix Dual Biopotential Pairs. Two pairs are BN-

PPGED which are connected to PPG sensors BN-

PULSE-XCDR which is connected to ECG electrodes

BN-EL30-Lead. PPG and ECG signals are in the

bandwidths from DC to 10 Hz and from 0.3 to 35

Figure 1: Data acquisition set-up.

Hz, respectively. The MP-150 unit concentrates these

signal together with selected NOVA waveforms and

cardiovascular trends, which are transferred to a note-

book via an Ethernet cable. BIOPAC System uses

proprietary signal acquisition and processing Acq-

Knowledge software which is installed in the note-

book.

The data acquisition set-up is shown in Figure 1.

The subject of the illustrated session has, in his left

hand, a PPG BN-PULSE-XCDR sensor at the tip of

the index ﬁnger, and the cuff to measure ﬁAP from

NOVA device, at the middle phalanx of the main ﬁn-

ger. In his wrist, he has the transmitter of the Biono-

madix pair. Behind the transmitter, in his forearm, he

has the Finapres actuator/sensor for the cuff.

The receivers of Bionomadix pairs are at the

Biopac System. The central unit of Finapres NOVA

device, on one hand, sends a selected set of cardio-

vascular signals to Biopac MP-150 Unit; on the other

hand it sends pneumatic commands to the cuff and

receives the ﬁAP sensor signals from the Finapres ac-

tuator/sensor. Below the photograph, in the left side,

it is shown the negative image of Nova device display;

and in the right side, it is the display produced by the

software AcqKnowledge.

A clinical essay on this work consists on a vol-

unteer that had to lie down and stay at rest during

10 minutes after connecting all the sensors, mean-

while the NOVA is calibrated with two consecutive

BP measures with the oscillometric BP device. After

the complete resting time, the subject must perform

two Handgrip isometric maneuvers, where he/she

must press a device in a sustained manner during a

standardized time (Chatterjee, 1999). The maneu-

BIOSIGNALS 2017 - 10th International Conference on Bio-inspired Systems and Signal Processing

156

ver is used to induce a controlled rise of the blood

pressure. Both maneuvers are separated by a ten

minute resting period. During the maneuver, the sub-

ject grips steadily, with his deft hand, a cuff during

three minutes; the pressing is performed with one

third of subjects maximal strength. Once the Hand-

grip is ﬁnished, the volunteer had to stay at rest dur-

ing, at least, three additional minutes, and the second

Handgrip, the essay is over. Essays were conducted

at the School of Biomedical Engineering (EICB),

Faculty of Engineering, Universidad de Valpara

´

ıso

(Chile). The data set is available in Physionet Works

https://physionet.org/ as a part of the project called

”Non invasive and minimally intrusive blood pressure

estimates.

2.2 PPG Signal Processing

Because PPG is sensitive to thermal changes, move-

ments or respiration (Allen, 2007), and due to quanti-

zation errors, the raw PPG is processed with two FIR

ﬁlters. Later, PPG ﬁrst derivative, known as VPG,

and second derivative, known as the APG, are evalu-

ated using Five Point Stencils (FPS) algorithms. Then

PPG is segmented by heartbeat. Finally and the PPG

is processed to extract sections interfered with spiky

blocking.

2.2.1 Pre-processing of the PPG

The derivative approaches used in this paper requires

differentiating PPG once or twice. Considering that

derivatives are increasingly sensitive to quantization

noise as the differentiation order increases, two off-

line cascade preprocessing are used. First, symmetric

Finite Impulse Response (FIR) ﬁlters, with Transition

Bands order 19 and 399 are applied to the PPG. Low

order FIR smooths the PPG by decreasing energy in

quantization error frequency band. High order FIR

stabilizes the DC component of the PPG.

Figure 2 illustrates the effects of smoothing the

PPG and getting its baseline, differentiating the

smoothed PPG using, both conventional L’H

ˆ

opital

rule and Five Point Stencil (FPS) algorithm, getting

VPG estimation, and differentiate the FPS processed

VPG using, both conventional L’H

ˆ

opital rule and FPS

algorithm, getting the APG and its baseline. The sen-

sitivity of L’H

ˆ

opital rule to quantiﬁcation error can be

observed.

In the ﬁgure, the ﬁrst three black signals are as-

sociated with the PPG; from top to bottom, the raw

PPG, the smoothed PPG and its baseline. Next three

red signals are the scaled, VPG*0.15 evaluated us-

ing both, the L’H

ˆ

opital rule, VPG*0.025, and the FPS

algorithm and VPG baseline. Finally, the next three

blue signals are the scaled APG*.001 using L’H

ˆ

opital

rule, and FPS, APG*0.002, and its APG baseline. The

illustrated signals are from a subject recorded during

minute 3.07 to 3.23 of a Handgrip maneuver. PPG is

FIR Low Pass ﬁltered at 10.5 Hz and FIR High Pass

Filtered at 0.25 Hz.

Figure 2: It is shown, from top to bottom. Black

Traces: PPG raw, smoothed and PPG Baseline. Red

Traces: VPG*0.15 (L’H

ˆ

opital rule), VPG*0.25 (FPS) and

VPG Baseline. Blue Traces: APG*0.001 (L’H

ˆ

opital rule),

APG*0.002 (FPS) and APG Baseline. Subject VE01.

Recording between minutes 3.07 and 3.23. FIR: Low pass

ﬁlter at 10.5 Hz; High pass ﬁlter at 0.25 Hz.

2.2.2 PPG Signal Segmentation

In order to obtain ﬁAP and PPG during each heart-

beat, the continuous records must be segmented. A

modiﬁed Pan-Tompkins (PTA) algorithm (Pan and

Tompkins, 1985) is used to detect ECG R wave to

segment PPG in the cardiac cycle, which is the unit

of study in this work. PTA processing begins with

a Band-Bass Filter, formed by a cascade of a low-

pass ﬁlter (LPF), which attenuates high frequencies

noises, and a High-Pass Filter (HPF), which atten-

uates the ECG waves P and T. The ﬁltered signal

is then derived to sharp the QRS waves with pro-

nounced slopes. In this stage, PTA is modiﬁed, intro-

ducing Continuous Wavelet Transform (CWT) using

a Mexican- Hat wavelet to detect R waves.

A threshold function is used to detect QRS com-

plexes. For this reason the ECG is separated in 10

seconds windows to eliminate large amplitude arti-

facts over the whole signal. CWT is applied using

a scale of 3, that is ﬁxed during the process after an

exploratory analysis ﬁnding QRS complexes. From

the coefﬁcients obtained on the 10 seconds windows,

the one that have the higher amplitude is chosen to

establish a searching threshold for the rest of the win-

Photoplethysmogram Fits Finger Blood Pressure Waveform for non-Invasive and minimally-Intrusive Technologies - Evaluation of

Derivative Approaches

157

dow. Threshold is established at the 30% of this max-

imum amplitude. Furthermore, a refractory time of

0.3 seconds is established (Guyton and Hall, 2011),

representing the minimal period before the next QRS

complex.

After R wave detection, a searching for possible

missing waves is made differentiating twice the time

interval from two consecutive complexes. After the

detection of windows with missing R waves, a new

threshold is calculated from the two QRS complexes

that contain this window. The searching process is

repeated until the missing R is founded, or a number

of iterations is completed.

Finally, to compensate for the phase change with

respect to the original ECG that the ﬁltering process

produces, a searching of a local maximum on the orig-

inal signal is made to 20 ms rearwards from the po-

sitions already founded. This local maximum corre-

sponds to the R wave on the original ECG signal.

2.2.3 Noisy PPG Extraction

While PPG is transmitted from sensor module to

Biopac system, spiky communication interruption oc-

curs and the signal is blocked. An algorithm is imple-

mented to detect and remove the PPG segments inter-

fered by blocking noise. The unaffected segments are

isolated and saved. Furthermore, it is considered that

unaffected PPG sections with less than ten segments

are useless, the reasons are given below.

The local minimum of PPG wave within the 500

ms after an R wave is considered as the PPG wave be-

ginning. To improve PPG wave discrimination from

interruption artifacts, the ﬁrst derivative of the seg-

mented PPG named the VPG- is calculated using FPS

algorithm. Maximum VPG is normally near the ﬁrst

third of cardiac cycle, while interruption artifact is not

synchronized, happening at any instant within the seg-

ment.

To detect artifacts in the ﬁrst third of the heart-

beat, a Mexican Hat Wavelet Transform is used at

scale of 15 which correlates better with artifacts than

with VPG. Nevertheless, higher correlation is at arti-

facts minimum values, while VPG higher correlation

is at its maximum values. The interruption artifacts

are well detected when both parts of the algorithm are

combined.

2.3 Derivative Approaches

VPG and APG have been extensively used in PPG

analysis. See for example (Zahedi et al., 2007), where

the effect of aging on its velocity rising edge is stud-

ied, and (Elgendi, 2012) proposes standardizing PPG

terminology.

Figure 3: Temporal diagram of ﬁAP, PPG, VPG and APG.

During a private visit to Paul Bourgine in Paris,

last February, and while talking about complex adap-

tive systems and large interactive networks, conver-

sation suddently switched towards the textbook on

Fractional Calculus (Herrmann, 2014). By that time,

fruitless initial efforts, trying to ﬁt PPG with ﬁAP,

were tested in Valpara

´

ıso. Both events triggered the

idea that Fractional Derivatives (FD) would deserve

a chance. During last June, Mat

´

ıas Salinas got sur-

prising preliminary results, in Valpara

´

ıso, using Frac-

tional Derivative (FD) to ﬁt PPG to ﬁAP. In addition,

while, trying to ﬁnd an intuitive meaning of FD, Gon-

zalo Tapia tested with a Linear Combination of the

PPG with its ﬁrst Derivative (LCD). Results of ﬁtting

PPG to ﬁAP with LCD were again as surprising as

those of Mat

´

ıas, although it is clearer that FD is not

equivalent to LCD. The results obtained by Mat

´

ıas

and Gonzalo are at the center of this paper.

A non explicit hypothesis, can now be formulated

after these results, it could be phrased: ”the blood ﬂow

through the digital artery of the index ﬁnger can be

modeled using both derivative approaches.

Subsequently, LCD and FD are enriched using

Lasso method for linear regression that combines

multiple values of parameter α, either LCD and FD.

The Lasso technique (Tibshirani, 1996), which con-

sists in a penalized least squares method imposing a

L

1

penalty on the regression coefﬁcients. Let (x

i

, y

i

),

i = 1, 2, ..., N be some data, where x

i

= (x

i1

, ..., x

ip

)

T

are the predictor variables and y

i

are the responses.

As in the usual regression set-up, it is assumed either

that the observations are independent or that the y

i

are

conditionally independent given the x

i j

. It is assumed

that the x

i j

are standardized so that:

∑

i

x

i j

N

= 0 and

BIOSIGNALS 2017 - 10th International Conference on Bio-inspired Systems and Signal Processing

158

∑

i

x

2

i j

N

= 1. Let

ˆ

β = (

ˆ

β

1

, ...,

ˆ

β

p

)

T

, then the parameters

(

ˆ

β

0

,

ˆ

β) are obtained with the Lasso technique :

(

ˆ

β

0

,

ˆ

β) = argmin(

N

∑

i=1

(y

i

− β

0

−

∑

j

β

j

x

i j

)

2

+ λ

∑

j

|β

j

|)

where N is the number of observations, y

i

is the re-

sponse at observation i, x

i

is data at observation i and

λ is a positive regularization parameter. The parame-

ters β

0

and β are scalar parameter. As λ increases, the

number of nonzero components of β decreases.

2.3.1 Linear Combination of Derivatives

For a ﬁrst approach, let LCD

(i)

, be deﬁne as:

LCD

(i)

= (1 − α)PPG

(i)

+ αPPG

(i+1)

(1)

where PPG

(k)

is the k

th

order temporal derivative of

the PPG, and α is a single parameter to ﬁt PPG to

ﬁBP. Notice that, if LCD=LCD

(0)

, given (1), then:

LCD = (1 − α)PPG + αV PG (2)

Figure 4: LCD PPG to ﬁAP before Handgrip maneuver.

2.3.2 Fractional Derivatives

For the second approach, Fractional Derivatives is

used. The α

th

FD of PPG (FDP

α

) is given by:

FDP

α

=

dPPG

α

dt

α

(3)

According to (Loverro, 2004), if f (t) = PPG and

f

α

(t)=FDP

α

dt

α

, then :

f

α

= lim

h→0

1

h

n

t−a

h

∑

m=0

(−1)

m

Γ(∝ +1)

m!Γ(∝ −m + 1)

f (x − mh) (4)

In FD, two possible criteria are given to evaluate

the derivative of a constant; Riemann-Liouville and

Caputo criterium. It is decided to use the ﬁrst criteria

because of “physiological plausibility” (Glar

´

ıa et al.,

2010). In such a case, α

th

FD of DC component of

PPG, DCP

α

, is given by

DCP

α

=

d

α

dt

α

t

0

=

1

Γ(1 − α)

t

−α

(5)

Figure 5: FD PPG to ﬁAP before Handgrip maneuver.

3 RESULTS

Table 2 shows the mean of ﬁSYS and ﬁDIA mea-

sured in the ﬁAP on each subject, at resting ﬁAP

and at raised ﬁAP. There is a consistent increase

in the average over the four cases, and in rest and

raised ﬁAP; ﬁSYS raised, 32.5±5.9 mmHg and ﬁDIA

raised, 26±3.1 mmHg.

Table 2: Mean ﬁSYS and ﬁDIA from ﬁAP before and at the

end of Handgrip maneuver.

S RESTING ﬁAP RAISED ﬁAP

ﬁSYS ﬁDIA ﬁSYS ﬁDIA

1 122 82 162 109

2 109 59 143 89

3 127 73 153 96

4 104 64 134 88

Table 3 is a summary for each subject comparing

Root Mean Square Distance (RMSD) and the Relative

Distance (R DIST) between raw PPG and ﬁAP.

The average over the four subjects of RMSD is

26.8±7.6 mmHg and of R DIST is 30±8.4%. On

the contrary, at raised ﬁAP, the average of RMSD is

31.6±5.6 mmHg and the R DIST is 27.1±5.7%.

Table 4 shows the mean and standard deviation of

optimal α values from the twenty resting ﬁAP and the

Photoplethysmogram Fits Finger Blood Pressure Waveform for non-Invasive and minimally-Intrusive Technologies - Evaluation of

Derivative Approaches

159

Table 3: Fitting distances: from raw PPG to ﬁAP wave-

forms before and at the end of Handgrip.

PPG EVALUATION

RESTING ﬁAP RAISED ﬁAP

S RMSD R DIST RMSD R DIST

(%) (%)

1 18.6 18.8 27.3 21.1

2 34.3 37.5 36.1 39.1

3 32.3 35.6 36.9 34.2

4 22.3 28.2 26.1 24.0

twenty raised ﬁAP, in the four subjects, using both

LCD and FD. The average of α over four subjects, for

both at resting ﬁAP, LCD is 0.74 and for FD is 0.73.

In raised ﬁAP for LCD is 0.70 and for FD it is 0.76,

suggesting that VPG clearly outweighs the PPG when

ﬁtting PPG to ﬁAP.

Table 5 summarize, for each subject, the Root

Mean Square Error (RMSE) and the relative error (R

ERR) between LCD, FD, LCD + Lasso and FD +

Lasso processing with PPG. At resting ﬁAP, RMSE

average over the four subjects, for LCD is 5.2 mmHg

and R ERR is 5.4%; for FD is 6.0 mmHg and R ERR

is 6.0%; for LCD + Lasso is 5.7 mmHg and R ERR is

6.1%; and, ﬁnally, for FD + Lasso is 3.9 mmHg and

R ERR is 4,1%. At raised ﬁAP, RMSE average, over

the four subjects, for LCD is 7.6 mmHg and R ERR

is 6.0%; for FD is 8.3 mmHg and R ERR is 6.4%; for

LCD + Lasso is 8.4 mmHg and R ERR is 6.9%; and,

ﬁnally, for FD + Lasso is 5.2 mmHg and R ERR is

Table 4: Comparison of the mean of α and its standard de-

viation on each subject estimated with the two methods on

20 waves before and 20 waves at the end of Handgrip.

α EVALUATION

RESTING ﬁAP RAISED ﬁAP

S LCD FD LCD FD

1 .71±.14 .74±.04 .53±.07 .67±.06

2 .72±.06 .62±.07 .74±.04 .72±.09

3 .80±.08 .84±.09 .81±.09 .90±.06

4 .71±.04 .71±.08 .72±.03 .73±.05

4,1%.

Figure 6 illustrates a comparison between the two

derivative approaches, with and without Lasso, in

each subject at resting ﬁAP.

Figure 7 shows a comparison of ﬁtting errors rel-

ative to the initial raw PPG to ﬁAP distance (Blue

bars), when using LCD (red bars), without and with

Lasso, and FD (green bars), without and with Lasso.

Errors are Evaluated using average of Relative errors

plus or minus the standard deviation. It can be ap-

preciate that the FD with Lasso outperforms with sta-

tistical signiﬁcance the other models and reduce the

distance between the raw PPG and ﬁAP from approx-

imately 30% to 5%.

Finally, we have extended the results for a total of

15 subjects with 250 heartbeats for each subject. Due

to the limit space available, we summarize the results

in the total adjusting error of 5.7% ± 1.8. Moreover

the α is subject dependent and the value obtained was

Figure 6: Four subjects, single heartbeat, before Handgrip; ﬁtting PPG to ﬁAP. Top row, left to right: subject 1 ﬁt using LCD

and FD; subject 2 ﬁt using LCD and FD. Bottom row, left to right: subject 3 ﬁt using LCD and FD; subject 4 ﬁt using LCD

and FD. Color codes: ﬁAP (Black), PPG (Blue), Derivative approaches (Red), and Derivative approaches with Lasso (Green).

BIOSIGNALS 2017 - 10th International Conference on Bio-inspired Systems and Signal Processing

160

Table 5: Fitting errors. Top: at resting ﬁAP and Bottom: at Raised ﬁAP. From left to right: LCD ﬁtting, FD ﬁtting, LCD +

Lasso Fitting and FD + Lasso Fitting.

FITTING ERRORS: RESTING ﬁAP

LCD FD LCD + Lasso FD + Lasso

S RMSE R ERR RMSE R ERR RMSE R ERR RMSE R ERR

(%) (%) (%) (%)

1 6.3±1.4 6.8±1.7 5.2±0.5 5.4±0.5 7.5±1.7 8.2±1.9 3.5±0.5 3.7±0.6

2 3.5±0.8 3.7±0.8 5.9±1.2 5.4±1.0 3.7±1.1 4.0±1.2 3.5±0.7 3.7±0.6

3 9.1±0.8 8.5±1.2 10.1±0.7 9.9±0.9 9.5±0.9 9.3±1.2 6.7±2.2 6.5±2.0

4 1.9±0.8 2.4±1.0 2.8±0.7 3.3±0.8 2.0±0.8 2.7±1.1 2.0±0.5 2.5±0.6

FITTING ERRORS: RAISED ﬁAP

LCD FD LCD + Lasso FD + Lasso

Sub RMSE R ERR RMSE R ERR RMSE R ERR RMSE R ERR

(%) (%) (%) (%)

1 10.5±4.0 8.6±3.4 9.3±1.0 7.0±0.9 12.9±5.4 11.1±4.8 5.0±0.5 3.8±0.5

2 6.2±1.1 4.6±0.7 8.1±1.1 5.7±0.9 6.4±1.2 4.8±0.8 4.9±0.7 3.6±0.5

3 9.8±2.1 7.6±1.8 10.9±1.6 8.6±1.3 10.1±2.2 8.0±2.0 7.7±1.9 6.2±1.5

4 3.7±0.5 3.1±0.4 5.0±1.5 4.4±1.3 4.2±0.7 3.7±0.6 3.1±0.8 2.9±0.8

Figure 7: Relative Distances between raw PPG (Blue); LCD

/ LCD + Lasso (Red); and FD / FD + Lasso (Green) with

the ﬁAP waveform.

0.73 ± 0.1.

4 CONCLUSIONS

The analysis of the results, considering that the to-

tal average ﬁtting error is 5.7% for 15 subjects, al-

lows to conclude that it is possible to reconstruct ﬁAP

waveforms from the PPG using LCD and FDP

α

ap-

proaches. Due to the high variability of the ﬁtting

errors per subject at resting and raised ﬁAP, these re-

sults suggest that the method should be customized

for each subject.

Although not shown, the worst ﬁtting error is

15%. In all cases, the ﬁtted waveform keeps the pat-

tern. This result suggests that derivative approaches

could be suitable for medical applications. However

further work must be done in order to be used for es-

timation purposes. On the other hand, the Fitting pre-

cision on each subject has relative low variability be-

cause it is performed in every segmented PPG wave.

When the total average of mean ﬁtting errors, over

the four subjects is ordered by performance, at rest

and raised ﬁAP, results are, for FD + Lasso process-

ing, 4.1 and 4.2%, for LCD processing, 5.4 and 6.0%,

for FD, 6.0 and 6.4% and for LCD + Lasso, 6.1 and

6.9%. In addition, the Variation Coefﬁcient, at rest

and raised ﬁAP results are, for FD 15.3% and 18.3%,

for LCD 25.6% and 23.4%, for LCD + Lasso, 26.7%

and 24.3% and FD + Lasso 24.8% and 19.7%. Fitting

PPG to ﬁAP at rest is always more precise (error =

5.38%±0, 91) than during raised ﬁAP (5.86%±1.21)

Finally, it should be noted that although FD algo-

rithm requires much more complex algorithms than

LCD, both approaches produce similar results. How-

ever, it is surprising that results obtained using LCD

are better than those obtained with LCD + Lasso. A

possible explication would be that LCD + Lasso could

be penalizing twice the weights.

COMPLIANCE WITH ETHICAL

REQUIREMENTS

The authors declare that they have no conﬂict of in-

terest. In addition, Informed Consents were obtained

and discussed with the subjects for the acquisition of

ﬁAP, PPG and ECG from 2015 up to date. Clini-

cal Essays have been approved by the Universidad de

Valpara

´

ıso, Bioethics Institutional Committee for Hu-

man Beings Research (CIBI-SH UV for its acronym).

Photoplethysmogram Fits Finger Blood Pressure Waveform for non-Invasive and minimally-Intrusive Technologies - Evaluation of

Derivative Approaches

161

ACKNOWLEDGEMENTS

The authors acknowledge the support by Chilean

Grants FONDEF IT13I20060 from Conicyt, CONI-

CYT + PAI/CONCURSO NACIONAL INSERCI

´

ON

EN LA ACADEMIA, CONVOCATORIA 2014 + Fo-

lio (79140057) and PMI UV1402 from the Ministry

of Education. Thanks to anonymous subjects, ei-

ther healthy volunteers or patients, who participate in

Clinical Essays.

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