CONTINUOUS BLOOD PRESSURE - estudogeral.sib.uc.pt³rio de Projecto - Ana...Ana Patrícia Coimbra de Matos RELATÓRIO DA DISCIPLINA DE PROJECTO R T | 2008 2009. 2 Quem não tem cão…

CONTINUOUS

FACULDADE DE CIÊNCIAS E TECNOLOGIA DA UNIVERSIDADE DE COIMBRA

CONTINUOUS BLOOD PRESSURE

A S S E S S M E N

MESTRADO INTEGRADO EM ENGENHARIA BIOMÉDICA


DEPARTAMENTO DE ENGENHARIA INFORMÁTICA

S U R R O G A T E S F O

BLOOD PRESSURE

A S S E S S M E N

Ana Patrícia Coimbra de MatosMESTRADO INTEGRADO EM ENGENHARIA BIOMÉDICA

RELATÓRIO DA DISCIPLINA DE PROJECTO


DEPARTAMENTO DE ENGENHARIA INFORMÁTICA

S U R R O G A T E S F O R

BLOOD PRESSURE

A S S E S S M E N T

Patrícia Coimbra de Matos

MESTRADO INTEGRADO EM ENGENHARIA BIOMÉDICA

RELATÓRIO DA DISCIPLINA DE PROJECTO | 2008 2009

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Quem não tem cão… Caça como o gato!

Portuguese proverb

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ACKNOWLEDGMENTS

I would be very glad to express my gratitude towards twelve people in particular.

Professor Paulo de Carvalho.

His remarkable skill, sagacity, enthusiasm and optimism made him a good mentor as well as

a fabulous team leader.

Engineer Mário Brito.

Patient, very helpful and wise, I did learn a lot from him. I also must highlight his friendly,

cheerful, positive personality.

Professors Jorge Henriques and Rui Pedro Paiva. Engineers Ricardo Couceiro, Pedro

Martins, Dinesh Kumar, Leandro Vale.

For the precious help and gentle cooperation.

Mother, Maria Eduarda. Sister, Vera. Friend, Elisabeth. Fellow, Magali.

For the support, concern and advising.

Furthermore, I cannot forget about Philips Research Laboratories Europe, for the kind

concession of data sets.

To all of you:

Many, many thanks!

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INDEX OF CONTENTS

AKNOWLEDGEMENTS…………………….………………………………………………………………………………………………….. 3

INDEX OF CONTENTS…………………………………………………………………………………….…………………………..………. 4

ACRONYMS………………………………………………………………………….…………….……………………………………………….. 7

ABSTRACT…………………………………………………………………………………………………………….……………………………… 8

RESUMO………………………………………………………………………………………………………………………………………………. 9

FIRST CHAPTER – INTRODUCTION………………………………………….…..………………………………………………. 10

1.1. CONTEXT…………………………………………………………………………………………………………………….…… 10

1.2. GROUNDINGS AND MOTIVATIONS……………………………………………………………….……………… 10

1.3. OBJECTIVES AND AIMS…………………………………………………………………………….…………………….. 11

1.3.1. HeartCycle Project………………………………………………………………………….…………………….. 11

1.3.2. The Academic Project…………………………………………………………………….…………………….. 11

1.4. STRUCTURE OF THE DOCUMENT…………………………………………………………….…………………… 12

SECOND CHAPTER - PRELIMINARY ACQUAINTANCE……………………………………………..………………… 13

OVERVIEW………………………………………………………………………………………………………………………….…………. 13

PART I. BIOMEDICAL CONTEXTUALIZATION………………………………………………………….………….... 13

2.1 .PHYSIOLOGICAL CONSIDERATIONS ON THE CARDIOVASCULAR SYSTEM………………… 13

2.1.1. Morpho-anatomical Aspects……………………………………………………………………………….. 13

2.1.1.1. The Heart……………………………………………………………………………………………………….. 13

2.1.1.2. The Vascular System…………………………………………………………………………………….. 14

2.1.2. Functional Aspects…………………………………………………………………………………………….….. 15

2.1.2.1. The Mechanisms of the Heart Cycle…………………………………………………………… 15

2.2. BIOMEDICAL CONSIDERATIONS ON BLOOD PRESSURE……………………………………………. 17

2.2.1. Arterial Pressure Pulse Wave……………………………………………………………………..………… 17

2.2.2. Blood Pressure and Cardiovascular Diseases……………………………………….……………. 19

2.2.2.1. Hypotension………………………………………………………………………………………………….. 19

2.2.2.2. Hypertension…………………………………………………………………………………………………. 19

2.2.2.3. Heart Failure………………………………………………………………………………………………….. 21

2.2.2.4. Coronary Artery Disease………………………………………………………………………………. 21

2.2.3. Circadian Profile of Blood Pressure……………………………………………………………………. 21

2.2.4. Mechanisms of Blood Pressure Regulation………………………………………………………. 22

PART II. STATE OF THE ART…………………………………………………………………………………….……………… 23

2.3. BLOOD PRESSURE MEASUREMENT:

A REVIEW ON THE METHODS AND INSTRUMENTS……………………………………………………. 23

2.3.1. Critical Circumstances: Invasive Methods…………………………………………………………… 23

2.3.1.1. Intra-arterial Catheter Systems…………………………………………………………………… 23

2.3.1.2 Swan-Ganz Catheterization………………………………………………………………………….. 24

2.3.2. Chronicle Circumstances: Non-invasive Methods……………………………………………… 25

2.3.2.1. Auscultatory Method……………………………………………………………………………………. 25

2.3.2.2. Ultrasonic Method………………………………………………………………………………………… 26

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2.3.2.3. Oscillometric Method…………………………………………………………………………………… 27

2.3.2.4. Tonometric Method……………………………………………………………………………………… 28

2.3.2.5. Vascular Unloading Method………………………………………………………………………… 29

2.4. TOWARDS THE PULSE TRANSIT TIME METHOD………………………………………………………….. 31

2.4.1. Theoretical Models………………………………………………………………….……………………………. 31

2.4.1.1 Modelling of the Cardiovascular System…………………………………………………….. 32

2.4.1.2 Modelling of Blood Pressure………………………………………………………………………… 33

2.4.2. Physiological Signals of Interest……………………………………………………………..……………. 34

2.4.2.1. The Electrocardiogram…………………………………………………………………………………. 35

A. General Characteristics……………………………………………………………………………………. 35

B. Segmentation and Signal Analysis ……………….………………………………………………….. 37

2.4.2.2. The Photoplethysmogram…………………………………………………….……………………… 38

A. General Characteristics………………………………………….………………………………………… 38

B. Segmentation and Signal Analysis…………………………………………….…………………….. 40

2.4.2.3. The Heart Sound …………………………………………………………………………………………… 43


B. Segmentation and Signal Analysis………………………………………………………….……….. 44

2.4.2.4. Impedance Cardiography…………………………………………………………………………….. 45


B. Segmentation and Signal Analysis…………………………………………………………………… 46

2.4.3. Upon Pulse Transit Time……………………………………………………………………………….………. 47

2.4.3.1 Clinical and Experimental Definitions………………………………………………………….. 47

2.4.3.2 An Income of Uncertainty…………………………………………………………………………….. 48

2.4.3.3 Pulse Arrival Time and Pre-ejection Period ………………………………………………… 48

2.4.4. Upon Pre-Ejection Period …………………………………………………………………………………….. 49

2.4.4.1. The Dynamic Nature…………………………………………………………………………………….. 49

2.4.4.2 Methods of Determination…………………………………………………………………………… 50

A. Echocardiography…………………………………………………………………………………………….. 51

B. Impedance Cardiography…………………………………………………………………………………. 51

C. Heart Sound Analysis………………………………………………………………………………………… 51

2.4.4.3 Considerations on Left Ventricular Ejection Time……………………………………. 52

2.4.5. Searching for Validation: Calibration Studies……………………………………………………… 53

2.4.5.1. Pulse Transit Time Approach……………………………………………………………………….. 54

2.4.5.2. Pulse Arrival Time Approach……………………………………………………………………….. 55

CONCLUSION…………………………………………………………………………………………………………………………………. 56

THIRD CHAPTER – METHODOLOGIES …………………………………………………………………………………………. 57

OVERVIEW……………………………………………………………………………………………………………………………………… 57

3.1. OVERALL DESIGN………………………………………………………………………………………………………….… 57

3.2. CLINICAL TRIALS……………………………………………………………………………………………………………... 58

3.2.1. Externally Provided Data…………………………………………………..…………………………….……. 58

3.2.2. In-house Acquired Data……………………………………………………..………………….……….…….. 60

3.3. DATA MANIPULATION: THE ALGORITHMIC IMPLEMENTATIONS…….……….………………. 63

3.3.1. Preliminary Operations………………….…………………………………………….…..…………………… 63

3.3.1.1. Synchronizing Operations…………………………………………….…….…….……………………. 63

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3.3.1.2. Data Storage …………………………………………………………………………………………….……… 66

3.3.2. Approaching Vascular and Systolic Time Intervals …………………………………….……… 66

3.3.2.1 PRE-EJECTION PERIOD…………………………………………………………….…………………….. 67

A. From Heart Sound and Electrocardiography………………….……………………………… 67

B. From Photoplethysmography, Heart Sound and Electrocardiography…..…. 68

C. From Impedance Cardiography ………………………………………………………………………. 70

3.3.2.2. PULSE ARRIVAL TIME……………………………………………………………………………………. 70

A. From Photoplethysmography and Electrocardiography……………………………… 70

3.3.2.3. PULSE TRANSIT TIME……………………………………………………………………………………. 73

A. From Pre-Ejection Period and Pulse Arrival Time…………….…………………………… 73

B. From Photoplethysmography and Heart Sound………….………………………………… 73

3.3.3. Blood Pressure Surrogates ………….………………………………………………………………………. 74

3.3.3.1. Pairing up Blood Pressure and Time Intervals…………………………………………… 74

A. Philips Data……………………………………………………………………………………………………….. 74

B. In-house Acquired Data……………………………………………………………………………………. 74

3.3.3.2. Model Validity: Tools for an Evaluation……………………………………………………… 76

A. Mutual Information………………………………………………………………………………………….. 76

B. Correlation Coefficient……………………………………………………………………………………… 76

C. Mean Squared Prediction Error………………………………………………………………………. 77

CONCLUSION…..…………………………………………………………………………………………………………………………….. 78

FOURTH CHAPTER - RESULTS AND DISCUSSION……………………..………………………………………………… 79

4.1. IN-HOUSE ACQUIRED DATA….………………………………………………………………………………………. 79

4.1.1. Systolic and Vascular Time Intervals Determination…….…………………………………… 79

4.1.2. Time Intervals and Blood Pressure Surrogates………………….………………………………. 83

4.2. PHILIPS DATA………………………………………………………………………………………….………………………. 89

4.2.1. Systolic and Vascular Time Intervals Determination…………….…………………………… 89

4.2.2. Time Intervals and Blood Pressure Surrogates………………….………………………………. 91

FIFTH CHAPTER – CONCLUSION………..…………………………………………………………………………………………. 96

5.1. FINAL CONCLUSIONS……………………………………………………………….…………………………………….. 96

5.2. SUGGESTIONS FOR FURTHER STUDIES………………………………….…………………………………….. 97

REFERENCES…………………………………………………………………………….………………………………………………………… 98

ANNEXES …………………………………………………………………………………………………………………………………………. 104

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ACRONYMS

AOV aortic valve

AVV atrioventricular valves

BMI body mass index

BP arterial blood pressure

CO cardiac output

CVD cardiovascular diseases

DBP diastolic (arterial) blood pressure

DN dicrotic notch

ECG electrocardiogram

ESH European society of hypertension

EU European Union

HR heart rate

HT hypertension

ICG impedance cardiogram

LVET left ventricular ejection time

MBP mean (arterial) blood pressure

MSPE mean squared prediction error

PAT pulse transit time

PEP pre-ejection period

PPG photoplethysmogram

PTT pulse transit time

PW (arterial pressure) pulse wave

PWV pulse wave velocity

S1 first heart sound

S2 second heart sound

SBP systolic (arterial) blood pressure

SD standard deviation

SR sample rate

SVR systemic vascular resistance

TPR total peripheral resistance

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ABSTR ACT

The frightful mortality and morbidity rates owing to cardiovascular diseases within the

occidental world have been triggering wide interest, not only of social but also of clinical and

economical orders, in developing solutions to promote patient vigilance and prevention.

The potential usefulness of an accurate, continuous, non-invasive, long-term evaluation

of the cardiovascular health status is immensely trusted; in such context, arterial blood

pressure (BP), in the quality of one of the most informative and dynamic cardiovascular

parameters, assumes a definite prominent role. Nevertheless, a clinically accredited non-

invasive method to measure BP in a beat-by-beat basis does not exist yet.

Being so, in this study one explored, the closest possible to the beat-by-beat regimen,

the dependency of BP with time intervals of vascular and systolic nature such as the pulse

transit time (PTT), the pulse arrival time (PAT) and the pre-ejection time (PEP), according to the

enunciations of Möens-Korteweg and Hughes. Additionally, in order to get directions on the

definition of the (controversial) experimental boundaries of PTT able to provide the highest

accuracy levels, one determined such time interval through seven distinct approaches, one of

them being of innovative nature.

In order to fulfil the designated purposes, one proceed to the acquisition of

electrocardiographic (ECG), photoplethysmographic (PPG), heart sound (HS) data in seven

subjects and determined the aimed time intervals. One also had access to a similar database

provided by Philips Research Europe, which was used as a complement. One subsequently

performed a statistical evaluation based on three tools (mutual information, correlation

coefficient and mean squared prediction error) between estimated and expected BP values,

the latter being measured resorting to a (merely discrete) oscillometric device.

However, due to experimental limitations combined with the scarcity of the available

data and eventual necessary algorithmic adjustments, one was not able to discern any clear

dependence tendencies or to draw any solid conclusions from the performed statistical

evaluation.

The reported studies have, thus, a prototypical nature to them. Their concept, involved

methods and strategies still justify, definitely, further attention and development.

Keywords: cardiovascular diseases, continuous arterial blood pressure, Möens-Korteweg,

Hughes, pulse transit time, pre-ejection time, pulse arrival time, left ventricular ejection time,

electrocardiogram, photoplethysmogram, heart sound, aortic valve, aorta artery.

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RESUMO

As avultadas taxas de mortalidade e morbilidade cardiovascular que assolam o mundo

ocidental têm vindo a despertar vasto interesse, tanto de ordem social como clínica e

económica, em desenvolver soluções que actuem ao nível da vigilância do paciente e da

prevenção.

A potencial utilidade de uma avaliação exacta, contínua, não-invasiva e de longo-termo

do estado de saúde cardiovascular é largamente acreditada; neste contexto, a pressão arterial

sanguínea, na qualidade de um dos parâmetros cardiovasculares mais informativos e

dinâmicos, assume um papel de suma importância. Contudo, ainda não existe nenhum método

não-invasivo clinicamente validado para determinar a pressão arterial de forma contínua.

Posto isto, no presente estudo explorou-se, do modo mais próximo possível ao nível do

batimento cardíaco, a dependência da pressão arterial com intervalos de tempo de natureza

vascular e sistólica tais como o PTT, o PAT e o PEP, de acordo com os pressupostos teóricos

estabelecidos por Möens-Korteweg e Hughes. Adicionalmente, com o intuito de obter

esclarecimentos acerca das (não consensuais) fronteiras experimentais do PTT capazes de lhe

proporcionar maiores níveis de exactidão, determinou-se este intervalo por intermédio de sete

abordagens distintas, uma das quais de natureza inédita, inclusive.

Foram adquiridos dados de ECG, PPG e HS para sete indivíduos e determinados os

intervalos de tempo pretendidos. Também se teve acesso a uma base de dados de constituição

semelhante, cedida pela Philips Research Europe. Subsequentemente, realizou-se uma

avaliação estatística baseada em três ferramentas (informação mútua, coeficiente de

correlação e erro de predição) estabelecida entre as pressões arteriais estimada e

experimentalmente aferida, esta última com recurso a um aparelho oscilométrico (regime

meramente discreto).

Contudo, devido às limitações experimentas, aliadas à escassez dos dados disponíveis e

a eventuais desajustes algorítmicos, não foi possível discernir nenhuma tendência ou tirar

conclusões sólidas com base na avaliação estatística efectuada.

Os estudos relatados apresentam, portanto, uma natureza prototípica, sem no entanto

se desvalorizar o seu conceito, métodos e estratégias – que justificam, sem dúvida, futuros

desenvolvimentos.

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FIRST CH APTER

INTRODUCTION

1.1 | CONTEXT

This document reports the studies and experiments realized within the ambit of the

discipline of Project, which integrates the curricular plan of the last year of the Integrated

Masters in Biomedical Engineering.

The totality of the activities, which were carried over from October 2008 to July 2009,

took place at the Department of Informatics Engineering of the Faculty of Sciences and

Technology of the University of Coimbra. Everything was performed under the instructions and

main supervision of Professor Paulo Fernando Pereira de Carvalho.

1.2 | GROUNDINGS AND MOTIVATIONS

Cardiovascular diseases (CVD) were declared as the leading cause of death in 2004 [1],

essentially as the result of population ageing and adoption of improper lifestyles. In 2005, 17.5

millions of the worldwide deaths were claimed by CVD [1], 4.3 millions of which in registered

in Europe (and over 2 million only in the UE) [2]. Coronary heart disease (CHD) alone

represented the single most common cause of death in the later continent [2].

On another account, CVD have been entailing large amounts of costs. In 2006, EU’s

health care system spent a total of € 110 billion, 54% of which arising from hospitalizations and

28% from drugs. If one accounts for the effective deficit to EU’s economy, the total sum

ascended to € 192 billion [2].

There is, thus, a wide interest of social, clinical and economical orders in contradicting

the high rates of cardiovascular mortality and morbidity. Patient vigilance and preventive

measures – in essence, permanent patient monitoring – have been perceived as the most

effective strategies to implement. In that sense, the potential and usefulness of an accurate,

non-intrusive evaluation of the cardiovascular health status, based on a continuous analysis of

a variety of physiological signals and parameters, is consecrated.

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In such context, arterial blood pressure (BP), in the quality of one of the most

informative and dynamic cardiovascular parameters assumes a definite prominent role – it’s

enough to recall that hypertension either lies in the origin or appears as the result of various

CVD.

Nevertheless, a clinically validated non-invasive method able to continuously measure

BP – that is, in the beat-by-beat regimen – does not exist yet.

1.3 | OBJECTIVES AND AIMS

1.3.1 | HeartCycle Project

HeartCycle Project1 aims the development of autonomous systems equipped with

technology capable to ensure a continuous monitoring of the cardiovascular health pattern in

order to supply at-home health vigilance, assistance and support to the patient.

That way, patient stays updated on own health status, which can either be evaluated by

the software system itself or supervised by professionals at the hospital, to where information

can be communicated. It becomes possible, thus, to provide an assiduous feedback to the

patient. Such closed loop architecture attempts at stimulating the adherence to the treatment

(in terms of medication and lifestyle) – or, in other words, promote patient compliance.

Thereafter, the described capabilities and dynamics imply the development of specific

interface technology grounded in easy to use, wearable, low intrusive sensors, able to provide

daily long term and reliable2 measurements of several cardiovascular signals.

1.3.2 | The Academic Project

This Project, while proposed within the ambit of HeartCycle, aims to contribute to the

development of software capable of non-invasively assessing BP in a beat-by-beat basis,

feasible to be integrated in a robust, reliable, simple-to-calibrate, portable system.

First, given its relation with BP, it was aimed to inquire about an accurate, clear

experimental definition for the pulse transit time (PTT).

1 Further informations available at http://heartcycle.med.auth.gr/.

2 By reliability one means accuracy, endurance and output invariance.

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It was then intended to model BP the closest possible to the beat-by-beat regimen as a

function of the PTT and other related cardiovascular time intervals such as the pre-ejection

period (PEP) and pulse arrival time (PAT), all of them determined through the analysis of

convenient signals: the electrocardiogram (ECG), the finger photoplethysmogram (PPG) and

the heart sound (HS).

One last objective included to test the developed algorithms with real data.

1.4 | STRUCTURE OF THE DOCUMENT

This report is fundamentally organized into five main sections.

In the sequence of Introduction (First Chapter), one included:

� Preliminary Acquaintance, Second Chapter.

Brief considerations about human cardiovascular physiology. Biomedical contextualization

on BP. Inventory of most clinically adopted methods for BP measurements.

Exposition of the main theoretical cardiovascular models. Review of the scientific

Literature on the PTT method to determine BP.

� Methodologies, Third Chapter.

Detailed description on the experimental setup and data evaluation/analysis.

� Results: Presentation and Discussion, Fourth Chapter

Exhibition of the obtained results accompanied with suggestions for their interpretation.

� Conclusions, Fifth Chapter.

Discernment of general conclusions and proposal of further related approaches and

studies.

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SECOND CHAPTER

PRELIMINARY ACQUAINTANCE

OVERVIEW

Part I addresses the fundamental physiological concepts on the cardiovascular system

and BP necessary to the fully comprehension of the concepts involved in this study.

Part II, the State of the Art itself, starts by presenting and evaluating the principal

methods of BP measurement. Following, one treats, in mathematical and in experimental

terms, some of the concepts introduced in Part I to finally address the most relevant scientific

studies and methodologies on the pulse wave velocity/pulse transit time approach for

determining BP.

PART I . BIOMEDICAL CONTEXTUALIZATION

2.1 | PHYSIOLOGICAL CONSIDERATIONS ON THE CARDIOVASCULAR SYSTEM

2.1.1 | Morpho-anatomical Aspects

2.1.1.1. The Heart

In essence, the heart is a bilaterally symmetric muscular organ with the major function

of pumping blood, introducing it into the arterial circulation (Fig. 1). It is under the control of

the autonomic nervous system, more specifically the sympathetic and parasympathetic nerves.

The organ is constituted by muscular walls (myocardium), in which four inner chambers

are sculpted: two atria and two ventricles; two atrioventricular valves (AVV) separate the

former from the later. There also exist two semilunar valves: on the right side, the pulmonary

valve separates the ventricle from the pulmonary artery, while on the left side, the aortic valve

(AOV) limits between the ventricle and the (ascending) aorta.

One also counts

the ventricle from the pulmonary artery, while on the left side, the aortic valve (AOV) limits

between the ventricle and the ascending aorta.

2.1.1.2.

The diameter, morphology and histology of blood vessels are very diverse along the

vascular tree (Fig. 2).

Arteries are low resistance, elastic, muscular tubes that conduct blood with few losses in

(internal) pressure. They serve, thus, as a “pressure reservoir”, which guarantees blood

conduction along the

and veins are also low resistance vessels, whose walls contain remarkably less elastic and

muscular tissues than arterial, take blood back to the heart.

One also counts two semilunar valves: on the right side



Fig. 1. Aspect of the internal structures of the human heart. Adopted from [3].

2.1.1.2. The Vascular System


vascular tree (Fig. 2).



conduction along the tree [4]. Smaller in diameter, arterioles



two semilunar valves: on the right side, the pulmonary valve separates



Aspect of the internal structures of the human heart. Adopted from [3].




in diameter, arterioles offer resistance to flow. Venules



14

, the pulmonary valve separates


Aspect of the internal structures of the human heart. Adopted from [3].




nce to flow. Venules


15

On another account, there are two closed independent circuits: systemic and pulmonary

circulations. In the previous paragraph one just described the former. As for the latter,

deoxygenated blood, impregnated with diverse metabolic final products must be depurated in

pulmonary alveoli; then, it returns back to the heart to be ejected and directed to the various

body tissues.

Fig. 2. Cardiovascular system. Adopted from [5].

2.1.2 | Functional Aspects

2.1.2.1. The Mechanisms of the Heart Cycle

In systemic [pulmonary], circulation, blood enters the heart via cava [pulmonary] vein

and starts filling the left [right] atrium, which contracts a short while later. By the time the

pressure inside the ventricle is sufficiently elevated to open the AVV blood is directed to the

left [right] ventricle. Then, left [right] ventricle contracts until the pressure in its inside gets

higher than the pressure inside aorta [pulmonary] artery. (It’s important to note that AOV

offers little resistance to flow, unlike the atrioventricular valves.)

Heart beat coordination is assured by the cardiac conduction system (connected to the

autonomic nerves), which triggers myocardial electrical excitation (in essence, changing their

cellular transmembrane electrical potential

depolarizations and repolarizations, in the sequence of specific intracellular chain reactions,

myocardial muscle oscillates between states of contraction and relaxation: systole and diastole

respectively.

One heart cycle comprises, thus, a sequence of a diastole and a systole, which lasts a

total average duration of 0.8 seconds (by definition, 0.3 systolic and 0.5 diastolic

number of heart cycles during a minute defines the heart rate (HR), expressed in

minute (bpm).

Fig. 5 evidences the relationship between electrical and mechanical events in the cardiac

cycle, while Table I systematizes the main mechanic events of the heart cycle.

Fig. 3. Changes in blood pressure and volume of blood in the heart and aorta artery during a cardiac cycle.

3 In other words,



cellular transmembrane electrical potential3



art cycle comprises, thus, a sequence of a diastole and a systole, which lasts a



minute (bpm).



Changes in blood pressure and volume of blood in the heart and aorta artery during a cardiac cycle.

Adopted from [6].

In other words, the difference in voltage between the interior and exterior of the cell.



3). As the result of successive electrical









Adopted from [6].

between the interior and exterior of the cell.

16



). As the result of successive electrical




total average duration of 0.8 seconds (by definition, 0.3 systolic and 0.5 diastolic) [4]. The

number of heart cycles during a minute defines the heart rate (HR), expressed in beats per



17

Table 1. Systolic and diastolic heart events (PV = pulmonary valve). To note that ventricular phase alone defines the

global cardiac phase. Adapted from [4].

At this point, one shall emphasize the isovolumetric ventricular contraction time, which

represents the interval during which the myocardial contraction raises the intraventricular

pressure sufficiently enough to open the AOV and eject blood. Such systolic time interval is

commonly known as the pre-ejection time (PEP), and plays a prominent role in this study.

In its turn, another important systolic time interval is the left ejection ventricular time

(LVET). It consists in the period in which left ventricle is pumping blood into the aorta artery. In

other words, LVET corresponds to the period in which AOV remains open, that is, it starts

immediately after PEP ending. Further detail on these systolic time intervals will be resumed

later on, in 2.4.4.

2.2 | BIOMEDICAL CONSIDERATIONS ON BLOOD PRESSURE

2.2.1 | Arterial Pressure Pulse Wave

BP consists in the contact force exerted by blood on the inner arterial wall and is most

commonly expressed in millimetres of Mercury (mmHg).

One of the most relevant characteristics of BP consists in the fluctuations of its value

during the cardiac cycle. In the systolic phase a new bolus of blood is forced to enter the

arterial system; since the ejected volume of blood is always superior to the fraction that

leaves, such mechanism induces a rise in BP, its peak corresponding to systolic blood pressure

(SBP). On the other side, as a part of blood is conducted to the capillary system, BP will

gradually drop until a minimum value, the diastolic blood pressure (DBP), which is verified just

before the occurrence of a new systole. Another parameter worth mentioning is mean blood

D I A S T O L E S Y S T O L E

ISOVOLUMETRIC

VENTRICULAR RELAXATION

VENTRICULAR

FILLING

ISOVOLUMETRIC

VENTRICULAR CONTRACTION

VENTRICULAR

EJECTION

Events

blood flows into atria blood flows into

ventricles

blood is highly compressed

inside the ventricles blood flows out

of ventricles

AV closed open closed closed

AOV and PV closed closed closed open

Atria relaxed contracted relaxed relaxed

Ventricles relaxed relaxed contracted contracted

18

pressure (MBP), which takes into account the longer duration of the diastolic phase, according

to MBP = DBP + 1/3 (SBP-DBP).

Said differently, ventricles (left in particular) generate an increase in pressure that is

transmitted through the arterial tree, given, as [7] points out, “the exchange of energy

between the kinetic energy of blood flow and the potential energy of the elastic vascular wall”.

Such transmissible pressure is commonly designated by arterial pressure pulse wave (PW) and

shows up as a waveform through time, its amplitude being comprehended between SBP and

DBP values (Fig. 4).

Fig. 4. Typical PW of a systemic artery, fundamentally exhibiting an ejected (dominant) wave, an incisure

(indicated by the asterisk) and a dicrotic wave (on the blue area). Adapted from [8].

As PW propagates along the arterial tree, it faces numerous bifurcation points and,

consequently, experiences reflective phenomenons (in other words, a certain blood volume is

thrown back). The result is the secondary peak, which corresponds to the dicrotic wave. In its

turn, the incisure, known as dicrotic notch (DN), is defended to be caused by the reflections

suffered by the PW. On another account, DN shows an interesting property: while its

amplitude decreases as HR increases, its position is not affected when HR changes4 [9]. On a

final and very important note, the DN is still defended to signal the closure of the AOV [4].

Furthermore, PW contour is determined by a variety of factors such as age (Fig. 6),

height (arterial length), weight, physical condition, vascular health status, drug administration,

etc. [10, 11]. In the origin of a considerable part of these lies the arterial stiffness, understood

as a consequence of the degeneration of the elastic tissue layers of the arterial walls5

(arteriosclerosis) [10, 11]. On the other side, PW shape evolves as it travels along the arterial

tree. Due to the resistance offered by the vessels to the flow, PW amplitude attenuates as it

moves away from the heart; also, its the reflected component gains gradual expressivity,

contributing to the progressive disfiguration of the original (aortic) PW (Figs. 5, 6).

4 The DN is always perceptible, unless the HR becomes too elevated, which eventually causes the notch

to be “swallowed” by the dominant peak. 5 While a perfectly elastic artery absorbs all the ventricular PW, a stiffer artery reflects a portion of the

wave, which will sum up with the consecutive PW.

2.2.2 |

2.2.2.1.

People with lower BP values have a lower risk of contracting some specific

cardiovascular complications.

However, in case BP is insufficient to distribute blood within the organism, cellular

metabolic complications will promptly arrive, followed by eventual further organ damaging.

In the origin of hypotension may figure several and various factors and condit

(haemorrhages, organ inflammation, septicaemia), including some heart diseases, namely

cardiac muscle weakening, cardiac tissue inflammation, low or high

2.2.2.2.

Hypertension (HT)

6 One shall also remark that BP is modelled by agents such as environment and

Fig 6. Evolution of PW with age and arterial site. Since ageing

induces histological

stiffer), SBP and DBP undergo a chronic rise.

Blood Pressure and Cardiovascular Diseases

Hypotension


cardiovascular complications.





cardiac muscle weakening, cardiac tissue inflammation, low or high

.2.2. Hypertension

Hypertension (HT) refers to chronically elevated values of systemic BP (consult Table 2)

One shall also remark that BP is modelled by agents such as environment and

Evolution of PW with age and arterial site. Since ageing

induces histological alterations of arterial walls (which become

, SBP and DBP undergo a chronic rise.

Adapted from [10].

Blood Pressure and Cardiovascular Diseases






cardiac muscle weakening, cardiac tissue inflammation, low or high HR [13].

chronically elevated values of systemic BP (consult Table 2)

One shall also remark that BP is modelled by agents such as environment and ethnicity [15].

Fig. 5. Variations in BP along the systemic

vascular tree.

To note that the waveform is abolished in the

capillary tree. On the other side, the histology of

venules and veins (with little content in elastic

tissue and muscle) is not able to bring back any

of the anterior characteristics.

Adapted from [12].

Evolution of PW with age and arterial site. Since ageing

which become

Adapted from [10].

19




In the origin of hypotension may figure several and various factors and conditions


chronically elevated values of systemic BP (consult Table 2)6.

ethnicity [15].

Variations in BP along the systemic

To note that the waveform is abolished in the

capillary tree. On the other side, the histology of

content in elastic

is not able to bring back any

Adapted from [12].

20

In essence, such condition results from: a) elevated cardiac outputs (CO)7, that is, heart

pumps too much volume of blood (with too much vigour); b) high total peripheral resistance

(TPR)8, in consequence of arteriolar constriction (reduced diameters allow the exit of less

quantity of blood from the arterial tree); c) both conditions [4].

Category

Systolic range

(mm Hg)

Diastolic range

(mm Hg)

Optimal BP < 120 < 80

Normal BP 120 - 129 80 - 84

High-normal BP 130 - 139 85 - 89

Mild HT 140 - 159 90 - 99

Moderate HT 150 - 179 100 - 109

Severe HT ≥ 180 ≥ 110

Isolated systolic HT ≥ 140 < 90

Table 2. Classification of BP according to the European Society of Hypertension (ESH), in 2003.

The values refer to the resting condition. Adapted from [14].

In most HT cases, a specific cause isn’t identified; in such case, one speaks of primary HT

[15]. The hypotheses on its origin are mostly based in genetics, environment and personal

lifestyle; obesity, lack of physical activity, ageing, resistance to insulin and cigarette smoking

are HT inducers. In contrast, when it is possible to unequivocally establish the causes, one is

before a case of secondary HT. The main ones are related with the secretion of powerful

vasoconstrictor agents9, abnormalities in the system of regulation of BP, and various other

diseases, etc. [15].

On the other side, HT represents several and major threats to the integrity and proper

functioning of the organism. First, due to the extra effort required in pumping against higher

pressures, the walls of the left ventricle eventually grow thicker10

, which, in long-term, induces

the loose of elastic and contractile properties of the heart, which frequently leads to further

complications (heart failure and coronary heart disease). Brain is one of the organs most

placed at danger, given the increased risk of cerebrovascular accidents owed to the possible

rupture of larger blood vessels [15, 4].

7 CO is in the volume of blood ejected by the heart per minute.

8 TPR is the sum of the resistance of all the peripheral vascular systemic structures.

9 One refers to angiotensin II, whose releasing happens in certain kidney diseases.

10 Such condition is termed as left ventricular hypertrophy.

21

In what concerns to the treatment of HT, there are essentially medication (capable of

reduce CO and/or TPR) and the adoption of healthier lifestyles [15, 4].

2.2.2.3. Heart Failure

One faces a case of heart failure ever since heart isn’t capable of pumping an adequate

volume of blood (low CO). Two factors use to dictate the disease [4]: HT itself, as previously

stated and coronary heart disease.

2.2.2.4. Coronary Artery Disease

Alterations in coronary arteries11

may determine the reduction of blood flow to the

cardiac muscle, which would affect of its metabolism. Tissue damage (or even death) may

occur: what one commonly calls by a heart attack. HT increases the risk for a heart attack by

up to five times – moderate or severe HT is diagnosed in about half of people who suffer their

first heart attack [15].

2.2.3 | Circadian Profile of Blood Pressure

BP has physiological propensity12

to undergo appreciable changes throughout the 24

hours of the day. These fundamentally arise as a combined consequence of hormonal changes

and physical, emotional and intellectual activity levels.

BP is usually at its highest when the subject is at work and slightly tumbles down at

home, fact clearly related with the involved stressing level. During sleep BP decreases to its

lowest values13

14

; as morning approaches, BP increases gradually, often showing a peak just

before patient’s awakening [15] (Fig. 7). Eating also exerts influence: a few minutes after

having a meal, BP increases. Keeping urine inside the bladder makes BP to climb as well. Stress

and anxiety are also able to significantly modulate BP; a good classical example is the “White

Coat Syndrome”, which translates into a systematic rise in BP once the patient is getting

examined at the medical office.

11

Coronary arteries are bifurcations of the aortic arch that irrigate cardiac tissues themselves. 12

That is, out of disease context. 13

As a complementary note, BP decreasing is the result of sleeping: not the cause, as originally thought. 14

Even the dreaming process itself exerts influence: the inclusion of physical activity in a dream raises

BP to values close to its real life correspondent!

To finish the list, corporal posture exerts a wide influence on BP: it’s highest at the

reclining subject, reducing to the sitting position and further to the standing position. These

changes also present a wide inter

[16]. Corporal

thematic in more detail.)

Fig. 7. Circadian profile of SBP and DBP. Each curve refers

Samples were acquired

2.2.4 |

MBP, the force responsible for the circulation of blood on the systemic arterial tree,

must be kept within a proper, physiological range of values.

Given its dependence on CO and TPR

induce changes in the fo

inspiration, vasoconstriction/vasodilatation, blood viscosity, etc. are able to modulate systemic

MBP [4].

Being so, any drift in MBP triggers specific homeostatic reflexes

of a few seconds to some hours, effect on CO and/or TPR so that the alteration registered in

MBP is minimized. These reflexes, usually called

hormonal secretion or neural cardiac autonomic activity

15

Systemic MBP can be expressed as the product of CO by TPR.16

Homeostasis is the

environment in order to assure its stability/constancy through time.



changes also present a wide inter-subject variation and are most pronoun

Corporal movements also represent changes in BP.

thematic in more detail.)

Circadian profile of SBP and DBP. Each curve refers

Samples were acquired from hour to hour, throughout the day. Ad

Mechanisms of Blood Pressure Regulation



Given its dependence on CO and TPR15

, any alteration on the later will consequently

induce changes in the former. This way, various factors such as systemic blood volume, air


Being so, any drift in MBP triggers specific homeostatic reflexes


MBP is minimized. These reflexes, usually called

hormonal secretion or neural cardiac autonomic activity

MBP can be expressed as the product of CO by TPR.

Homeostasis is the ability of a system (typically a living organism)

ronment in order to assure its stability/constancy through time.



subject variation and are most pronounced in obese people

movements also represent changes in BP. (Sub-section 2.4.5 will

Circadian profile of SBP and DBP. Each curve refers to a different age group

from hour to hour, throughout the day. Adopted from [17].

Mechanisms of Blood Pressure Regulation




rmer. This way, various factors such as systemic blood volume, air


Being so, any drift in MBP triggers specific homeostatic reflexes16

that exert, in


MBP is minimized. These reflexes, usually called baroreceptor reflexes, consist, for example, in

hormonal secretion or neural cardiac autonomic activity.

MBP can be expressed as the product of CO by TPR.

of a system (typically a living organism) to regulates own

ronment in order to assure its stability/constancy through time.

22



ced in obese people

will treat this

(males).

pted from [17].



rmer. This way, various factors such as systemic blood volume, air


that exert, in a matter


, consist, for example, in

tes own internal

23

Furthermore, while baroreceptor reflexes are short term MBP regulators, blood volume

itself works as the long term stabilizer of this hemodynamic parameter.

PART II . STATE OF THE ART

2.3 | BLOOD PRESSURE MEASUREMENT:

A REVIEW ON THE METHODS AND INSTRUMENTS

Within the clinical scenario, one can delineate two groups of methods, attending to the

type of medical assistance required by the patient.

2.3.1 | Critical Circumstances: Invasive Methods

Due to the highly accurate, continuous monitoring of BP, invasive methods are

specifically used, besides biomedical researching, under critical clinical circumstances, when a

dynamic evaluation of the parameter is crucial (surgical operations and intensive care

medicine).

Invasive methods aim to assess the actual BP, not any intermediate parameter,

justifying the designation of “direct” often attributed to the category. These methods imply,

thus, intrusiveness, i.e. the actual contact with the interior of the body.

2.3.1.1. Intra-arterial Catheter Systems

Intra-arterial catheterization systems provide high accurate beat-by-beat BP readings,

holding, by that reason, the actual gold-standard title [18]. On the other hand, since

calibrations can be constantly performed (thus correcting eventual baseline drifts and changes

in sensitivity) for a static/mean BP, this parameter can be assessed for relatively long periods

of time, enabling, thus, the monitoring of its dynamics approximately in real time – that is,

what one calls a continuous, beat-by-beat continuous measurement [19].

24

These methods demand a catheter, connected to an electronic pressure transducer17

(Fig. 8) to be introduced into the cardiovascular system. In case of BP measurements, the

invaded vessels are mainly the femoral, brachial and radial arteries.

However, besides discomfort and pain, direct methods represent some potential danger

to the patient, since the risk of the following increases [20]: a) air embolism (small portions of

air may enter the vascular system through the catheter insertion site); b) thrombosis (blood

clots can be formed due to the contact with the air); c) bacterial infection; d)

contamination/disease transmission; e) haemorrhage.

2.3.1.2 Swan-Ganz Catheterization

While not as accurate as intra-arterial, Swan-Ganz catheterization represents another

method for assessing BP in a continuous basis. The involved procedure is extremely invasive: a

flexible catheter is introduced in a central vein of appreciable caliber (femoral, subclavian,

jugular) and reaches pulmonary artery/capillary vessels after going through the right atrium

and ventricle [22]. There is a variety of models of Swan-Ganz catheters, making use of

thermodilution and optical fibres, among other technologies.

The counterparts associated with Swan-Ganz technique will be quite close to the already

presented, cumulatively with its purpose being the pulmonary BP (not central) [22].

17

Among the sensor types more commonly used are strain gage, piezoelectric, optoelectronical, variable

indutance, and variable capacitance.

Fig. 8. Example of equipment for

vascular catheterization, composed by

a pressure transducer catheter and a

pressure control unit (Millar

Instruments, USA).

Adapted from [21].

25

2.3.2 | Chronicle Circumstances: Non-invasive Methods

Non-invasive, indirect methods concern about assessing other quantities besides BP

itself, which serve as tracers of the latter. Less accurate than the previous ones, such methods

are, thus, more established for non-critical/chronic clinical situations.

2.3.2.1. Auscultatory Method

This method involves the identification of a characteristic sequence of vessel murmurs,

known as Korotkoff sounds, produced as the result of the gradual opening of occluded arterial

segments18

.

To perform a measurement, one needs a stethoscope and a sphygmomanometer (Fig.

9). One insufflates the arm cuff until the externally applied pressure collapses brachial artery;

afterwards, the air is gradually released. At such point one is ready to hear to hear the

Korotkoff sounds (stethoscope). In the moment first ones are sensed, the applied pressure is

read in the manometer, since it shall equal SBP19

. Analogously, DBP is the pressure at which

the sounds are barely audible (Phase IV). MBP can be also determined [23].

One must emphasize that mercurial manometer, providing the reading of absolute

pressure values, i.e., already scaled in units of mmHg (millimetres of mercury), dispenses a

calibration process (therefore not never affected by errors arising there from). Such property

makes the mercurial manometer the gold standard in BP measurement20

.

In fact, auscultatory methods are the most frequently adopted within the actual clinical

environment [25] when it comes to chronic circumstances as routine clinical checking. Besides

non-invasive, this methodology: a) provides accurate results; b) is quite simple (and relatively

brief) to perform; c) requires little equipment, less expensive than the one for direct methods.

18

A full sequence of Korotkoff sounds comprises five distinguishable stages. Phase I is defined by a

"tapping" sound, Phase II, by a subtle "swishing" sound, Phase III, by a "crisp" sound, Phase IV, by a

"blowing" sound and finally there is silence in Phase V [4]. 19

In a more rigorous analysis, an externally applied pressure force is not equal to BP in magnitude; in

fact, supposing the hydrostatic effect is null (cuff and heart aligned in height), BP is the sum of both

externally applied and transmural (through the wall itself) pressures [24]. 20

As a side note, one calls the attention to the distinction between a gold standard method

(catheterization external systems) and a gold standard transducer (the mercurial manometer).

Fig.9. Equipment used for auscultatory BP measurements (Spirit Medical Diagnostic, Australia).

On the right: aneroid sphygmomanometer (composed by an inflatable air cuff and an air manometer).

On the other hand, disadvantages associated with the method include, first of all, the

various sources of error. Th

Korotkoff sounds not being perceived [27]. One shall also address the subjectivi

with sound perception and resultant dispersion of results between different operators.

Electronic sphygmomanometers haven’t been very commonly used due to the difficulty of

detecting the Korotkoff sounds, since the frequency spectrum of the d

close to that of heart beats [28].

Afterwards, only a discrete, poor BP evaluation is possible, due to the time required to

obtain a single measurement and the discomfort experienced by the patient. Also, the

ambulatory implementati

extra power consumption,

pollutant power) of Mercury and the difficulty of applying the method to specific groups of

patients (children, hypotensive, obese).

2.3.2.2.

Ultrasonic method deals with the movement of vessel walls, perceived through the

recording of ultrasound echo patterns of the structures.

A Doppler transcutaneous sensor is used in conjunction with an inflatable cuff. The

former emits high frequency sound waves to the skin, which penetrate in depth, and, once

reflected by the internal structures (at interfacial sites), return to the sensor,

collected and converted into electrical impulses.

of the transmitted and received ultrasound signals is proportional to the velocity of wall

movements (also to the velocity of the blood), one is able t

occluded - fully closed

Equipment used for auscultatory BP measurements (Spirit Medical Diagnostic, Australia).


On the left: mercurial sphygmomanometer. Adapted from [26].

e other hand, disadvantages associated with the method include, first of all, the

various sources of error. These may relate to: a) inappropriate cuff size and positioning; b)




detecting the Korotkoff sounds, since the frequency spectrum of the d

close to that of heart beats [28].



ambulatory implementation of the method is possible, but not viable (using a cuff represents

extra power consumption, size and weight). Finally, one shall add the high toxicity (and


nts (children, hypotensive, obese).

2.3.2.2. Ultrasonic Method




high frequency sound waves to the skin, which penetrate in depth, and, once


collected and converted into electrical impulses.


movements (also to the velocity of the blood), one is able t

fully closed - or not [29]. In practice, as one increases the externally applied



On the left: mercurial sphygmomanometer. Adapted from [26].


ese may relate to: a) inappropriate cuff size and positioning; b)




detecting the Korotkoff sounds, since the frequency spectrum of the different phases is very



on of the method is possible, but not viable (using a cuff represents

). Finally, one shall add the high toxicity (and







collected and converted into electrical impulses. Since the difference between the frequencies


movements (also to the velocity of the blood), one is able to determine when the artery is

practice, as one increases the externally applied

26




ese may relate to: a) inappropriate cuff size and positioning; b)

Korotkoff sounds not being perceived [27]. One shall also address the subjectivity associated



ifferent phases is very



on of the method is possible, but not viable (using a cuff represents

). Finally, one shall add the high toxicity (and





reflected by the internal structures (at interfacial sites), return to the sensor, where are

Since the difference between the frequencies


o determine when the artery is

practice, as one increases the externally applied

27

pressure, the time interval between the opening and closure of the artery gradually decreases;

in the instant it becomes null, cuff pressure shall equal SBP. During the deflation process, at

the time the closure of the vessel coincides with the consecutive opening, DBP equals the cuff

pressure.

Ultrasonic methods allow for a semi-continuous measurement of BP. The method,

however, is not validated for the clinical use [29]. All the disadvantages associated with the

usage of an arm cuff still persist. Additionally, the actual equipments are heavy and

cumbersome, what impossibilities them to be integrated in viable ambulatory monitoring

system of BP; patient movements alter the trajectory between sensor and vessel, which

consequently translate in the erroneous nature of the readings.

2.3.2.3. Oscillometric Method

Oscillometric devices are still used in clinical practice, although the at-home use is being

democratized; it is, in fact, the most used method in automatic measurements.

Once again, the principle (that is, the relationship between cuff pressure, blood flow and

BP) and procedures are the same as in auscultatory method, the stethoscope and the human

hear being replaced by a pressure transducer.

As long as the pressure exerted by the cuff remains superior to DBP and inferior to SBP,

intra-arterial pulsation generates small oscillations in the BP, which are transmitted to the air-

filled cuff and detected by piezoelectric sensors21

. The maximum amplitude of these

oscillations is used to estimate DBP and SBP values [28]. MBP can also be determined

accurately as the cuff pressure correspondent to the maximum amplitude of the mentioned

oscillations.

This being said, advantages inherent to oscillometric methodology mainly comprise the

accuracy of the readings, the simplicity of execution and the low cost of the required

equipment.

Relatively to the other side of the coin, besides the whole problematic associated with

the cuff usage, one must emphasize the rigidity of the implemented mathematical algorithms,

as they don’t account for inter-subject variability [28]. In fact, SBP and DBP are computed as

immutable ratios of the maximum amplitude of the sensed BP oscillations, neglecting their

variations according to specific characteristics of arterial walls (flexibility, compliance, etc.).

21

Piezoelectric sensors are able to measure acceleration, pressure or strain forces by converting them to

electrical signals. These devices contain piezoelectric materials, which have the ability of

generating electric potentials in response to applied mechanical stress.

28

Results are, thus, distorted to a certain extent. Moreover, it is demonstrated that the arteries

are able to adapt to external pressures - tissue properties are altered with successive cuff

inflations and deflations, which means the accuracy returned results get progressively weak

(underestimation) [28].

2.3.2.4. Tonometric Method

Tonometric methods22

allow continuous non-invasive measurements of MBP and PW. In

spite of not being clinically validated, the method has been important in researching on HT,

arterial compliance and PW velocity.

The basic principle behind tonometry is the Imbert-Flick Law principle: the pressure

within a spherical body of dry, elastic and thin walls equals the pressure exerted on such body

divided by the surface of applanation. Accordingly, tonometric methods suppose the flattening

of a superficial artery with bony support, usually the radial. The sensory element of an arterial

tonometer (Fig. 10) usually consists in a linear array of miniature23

independent pressure

transducers24

, less than a millimetre spaced away from each other. The latter idea is to ensure

that at least one of them will be correctly positioned, i.e., right over the artery, which provides

a good quality signal. In its turn, the flattening process is executed by means of an inflatable

cuff, which traps the sensory element, pressing it against the wrist. The sensor will detect

forces which are perpendicular to its surface. Thus, as long as stress forces exerted by arterial

walls remain parallel to the surface of the sensor, the contact pressure shall equal BP.

Under the required conditions, previous studies on tonometric BP measurements have

demonstrated accuracy with standard deviations of about 5 mmHg (comparatively to the

highly accurate intra-arterial readings) [31].

Although, in spite of the potentialities tonometric method has to offer, some doctors

and investigators remain apprehensive about its validity.

22

First arterial tonometer theoretical modeling is authored by G. Pressman and P. Newgard (1983). 23

The size of each sensor must be clearly inferior to arterial radius. 24

Usually LVDT, linear variable displacement transducers (based in electromagnetism).

Fig. 10.

Two tonometers are used to detect PW in distinct sites, which enables to compute PTT not the

A first counterpart keeps up with the complexity of the procedure its

positioning of the sensor can be difficult to set, being required a specialized hand.

Furthermore, in spite of minimized by the use of a set of sensors, the introduction of motions

artefacts by the subject is another worry incoming. Then,

uncomfortable to the patient, since the wrist is squeezed during the totality of the operation

not to mention the relative heaviness of the instrumentation. The reasons listed so far

represent, consequently, a major drawback if on

ambulatory, long

issue. A device grounded in tonometry requires it to be performed in a regular basis by an

independent BP measurement

2.3.2.5.

Vascular unloading method

monitoring of SBP, DBP and PW.

Overall, the strategy consists in applying a

finger so as to ensure that blood flow in the arteries is maintained. Cuff pressure shall, in each

instant, equalize (intra

The required instrumentation includes a finger cuff, an inflatable bladd

infrared plethysmograph

blood capillaries (consult

pressure control, it’s required to provide the system with a feedback mechanism, played by

25

One must also focus as well that new developments have been made in implantable arterial

tonometry [31].26

The idea behind the method was first presented by the physiologist J. Peñáz (1973).

Equipment based on arterial tonometry, the

Two tonometers are used to detect PW in distinct sites, which enables to compute PTT not the

addressed later on). Adapted from [30].

A first counterpart keeps up with the complexity of the procedure its



artefacts by the subject is another worry incoming. Then,



represent, consequently, a major drawback if on

ambulatory, long-term monitoring instrument25


independent BP measurement, usually auscultatory or oscillometric methods.

2.3.2.5. Vascular Unloading Method

Vascular unloading method26

allows for non

monitoring of SBP, DBP and PW.

Overall, the strategy consists in applying a


instant, equalize (intra-arterial) BP.


infrared plethysmographic device, which assess beat

blood capillaries (consult 2.4.2.3 for further development on this subject). To perform cuff



tonometry [31].


Equipment based on arterial tonometry, the SphygmoCor Technology (AtCor Medical, Australia).

Two tonometers are used to detect PW in distinct sites, which enables to compute PTT not the true

addressed later on). Adapted from [30].

A first counterpart keeps up with the complexity of the procedure itself. The correct



artefacts by the subject is another worry incoming. Then, the process is somewhat



represent, consequently, a major drawback if one thinks in integrating tonometric method in

25. Finally, calibration constitutes another actual


, usually auscultatory or oscillometric methods.

non-invasive, long-term, real-time, beat

Overall, the strategy consists in applying a dynamically adjustable external pressure on a



device, which assess beat-by-beat oxygen content within superficial

for further development on this subject). To perform cuff




29

(AtCor Medical, Australia).

true PTT, as it will be

elf. The correct



the process is somewhat

uncomfortable to the patient, since the wrist is squeezed during the totality of the operation –


e thinks in integrating tonometric method in

. Finally, calibration constitutes another actual


time, beat-by-beat

dynamically adjustable external pressure on a


The required instrumentation includes a finger cuff, an inflatable bladder and an

beat oxygen content within superficial

for further development on this subject). To perform cuff



means of a hydraulic servo system

electronic, automati

In first place, one must determine the proper unloaded diameter of the finger arteries,

i.e. the point at which finger cuff pressure and intra

transmural pressure across the finger arterial walls. Unde

kept at such unloaded

managed by the control system [32]. That said, any changes in vascular flow, coordinated with

heart beating and BP, are written

control system and promptly compensated, if necessary, by implementing inflation or

deflation of the finger cuff. It’s important to underline that blood flow is never completely

blocked.

First instrument to concretize such idea was FINAPRES (Finapres Medical Systems, The

Netherlands), in 1987. These devices had the advantage of allowing the usage for a few hours

and a small size, suitable for ambulatory measurements. Since then, various other instr

have been developed, essentially by the same company

Fig. 11.

Given to the pair of finger cuffs, used alternatively for 30 minutes, monitoring

Several studies have been made to evaluate the reliability of vascular unloading

technology. Some obtained good correlations with direct measurements. Other, however,

proved otherwise [28].

diastolic and systolic signals in the lower frequency ranges [28].

Furthermore, one has the introduction of artefacts mainly derived from hydrostatic

errors (since the sensor is not posit

measurements on the upper arm). Also, since the photoplethysmographic signal is obtained at

27

To set it clear, a hydraulic servo system is a type of fluid p

that uses feedback to maintain consistency in its input and output.

means of a hydraulic servo system27

with valve (pressure adjustments have a mechanical,

electronic, automatic nature).


i.e. the point at which finger cuff pressure and intra

transmural pressure across the finger arterial walls. Unde

kept at such unloaded diameter by varying the pressure exerted by the finger cuff, which is


heart beating and BP, are written in the photoplethysmograph signal, which is analysed by the



trument to concretize such idea was FINAPRES (Finapres Medical Systems, The



have been developed, essentially by the same company

Fig. 11. Ambulatory setting of PORTAPRES (Finapres Medical Systems, The Netherlands).

Given to the pair of finger cuffs, used alternatively for 30 minutes, monitoring

allowed. Adapted from [33, 34].



proved otherwise [28]. Recent studies involving FINAPRES® and FINOMETER® accused errors in



errors (since the sensor is not positioned at the level of


To set it clear, a hydraulic servo system is a type of fluid p




i.e. the point at which finger cuff pressure and intra-arterial pressure are equal, being null the

transmural pressure across the finger arterial walls. Under such conditions, the arteries are

diameter by varying the pressure exerted by the finger cuff, which is


in the photoplethysmograph signal, which is analysed by the






have been developed, essentially by the same company (Fig. 11).

Ambulatory setting of PORTAPRES (Finapres Medical Systems, The Netherlands).

Given to the pair of finger cuffs, used alternatively for 30 minutes, monitoring periods of about 24 hours are

allowed. Adapted from [33, 34].



Recent studies involving FINAPRES® and FINOMETER® accused errors in



ioned at the level of the heart, like it happens in the


To set it clear, a hydraulic servo system is a type of fluid power system in closed loop management i.e.


30



arterial pressure are equal, being null the

r such conditions, the arteries are

diameter by varying the pressure exerted by the finger cuff, which is


in the photoplethysmograph signal, which is analysed by the





and a small size, suitable for ambulatory measurements. Since then, various other instruments

Ambulatory setting of PORTAPRES (Finapres Medical Systems, The Netherlands).

periods of about 24 hours are



Recent studies involving FINAPRES® and FINOMETER® accused errors in


the heart, like it happens in the


ower system in closed loop management i.e.

31

a peripheral site, the reflected component of PW is significative, fact that can compromise

results given the role of this signal in the control of cuff pressure.

Another issue consists in circulation becoming minimal or non-existent in the distal

arterial portions (that is, after the cuff). To end the subject, one shall emphasize the most

worrying problem, definitely being the nature of BP measurements, which have a very

peripheral nature, while central circulation (at the level of the largest vases, like aorta) is the

most relevant to evaluate one’s cardiovascular status.

Despite the narrow usage in patient care, vascular unloading method has been

particularly useful in psycho-physiological researching, (study BP variation in response to

physical and emotional stress [35]). In any case, the method represents one of the most viable

strategies to monitor continuously in long term.

2.4 | TOWARDS THE PULSE TRANSIT TIME METHOD

Keeping the objectives defined for this Project in mind, the present sub-chapter is

devoted to a review of the Literature on subject-matters related with and useful to this

method of assessing BP.

2.4.1 | Theoretical Models

In empirical terms, one can state that BP, as any other pressure force exerted by a fluid

on elastic, distensible walls (as are arterial), essentially depends on two factors [4]. The first

one refers to the intervenient volume of fluid – the greater the volume, the higher the

pressure. Second factor holds up with the ease of stretching, i.e., the compliance (ratio

between the change in volume and the change in pressure) of the walls – the higher the

compliance, the lower the pressure. If one still considers a tubular system, the effect of the

resistance offered by the tubular walls to the passage of the fluid must be accounted,

especially if there are variations in their diameter.

This sub-chapter treats these concepts in a more rigorous, quantitative perspective.

2.4.1.1 Modelling of the Cardiovascular System

One of the most established approaches in the modelling of the cardiovascular system is

the Windkessel model. It compares the cardio

fitted with a water

hydraulic system is shown in Fig. 12.

Fig. 12. Schematization of the electrical analog circuit for

R represent resistors, C, a capacitor, P(t), a time

Such RRC circuit is described by the differential equation

in which

in the aorta artery,

blood offered by the AOV

also R2 represent, thus, the drop in PW amplitude as t

system.

Moreover, one can establish an equation for aortic BP from (1) if we assume heart’s

diastolic phase, according to (

28

Or pulmonary artery, if we considers the pulmonary circulation.29

Or pulmonary valve, if we considers the pulmonary circulation.

Modelling of the Cardiovascular System


the Windkessel model. It compares the cardio-circulatory system to a closed hydraulic system

fitted with a water pump [36]. On the other hand, a possible electrical ana

hydraulic system is shown in Fig. 12.

Schematization of the electrical analog circuit for

R represent resistors, C, a capacitor, P(t), a time-varying electrical potential and

currents. Adopted from [36].


in which I(t) represents the flow of blood from the heart to the aorta

in the aorta artery, C corresponds to the compliance of aorta artery,

blood offered by the AOV29

and R2 represents the peripheral resistance. To note that R

represent, thus, the drop in PW amplitude as t


diastolic phase, according to (td marking its initial instant

Or pulmonary artery, if we considers the pulmonary circulation.


Modelling of the Cardiovascular System


circulatory system to a closed hydraulic system

On the other hand, a possible electrical analogue circuit for such

Schematization of the electrical analog circuit for the three-element Windkessel model.

varying electrical potential and I(t), I2, I

currents. Adopted from [36].


represents the flow of blood from the heart to the aorta28

P(t)

corresponds to the compliance of aorta artery, R1, the resistance to the

represents the peripheral resistance. To note that R

represent, thus, the drop in PW amplitude as the latter moves along the arterial


marking its initial instant):

Or pulmonary artery, if we considers the pulmonary circulation.


32


circulatory system to a closed hydraulic system

logue circuit for such

element Windkessel model.

, I3, electrical

P(t) models BP

, the resistance to the

represents the peripheral resistance. To note that R1 and

he latter moves along the arterial


33

More sophisticated Windkessel models can be, however, defined – for example,

considering an inductance in the branch parallel to R1, in order to simulate the inertia of the

fluid in the hydrodynamic model (4-element Windkessel model).

2.4.1.2 Modelling of Blood Pressure

Pulse wave velocity (PWV) is defined as the velocity (expressed in meters per second) at

which PW is transmitted through a certain arterial segment. It is a particularly informative

hemodynamic parameter since it is closely related with the constitution of arterial walls,

particularly arterial stiffness, or, in other words, their elasticity, or compliance. Being so, a

higher PWV value accuses a stiffer arterial wall [7] and therefore a higher value of BP.

As early as in 1878, Möens and Korteweg established the relationship between the

elasticity of an arterial segment and the velocity of the PW (PWV) propagating through it,

according to

�� 2 �3�,

in which L is the length of the mentioned arterial segment and E is the Young elasticity

modulus of the arterial wall, h the wall thickness, ρ the blood density, r the arterial radius [37].

By its turn, pulse transit time (PTT) defines as the lapse required by PW to propagate between

two distinct sites of the arterial tree. As it is intimately related with PWV, this approach is

often referred to as PTT method.

Furthermore, as long as the variations of r, � and h are negligible, the Young elasticity

modulus, by its turn, will depend on BP, as Hughes equation implies:

� � �� 4�,

being E0 the elastic modulus at zero pressure. In its turn, α is a coefficient ranging from

0.016 to 0.018 (unit is the mmHg-1

), dependant on the characteristics of the particular vessel.

By replacing (4) in (3), one testifies a relationship between BP and PWV (or PTT):

34

�� 2 �5�.

Responding to a BP variation, the change in the arterial wall elasticity overshadows any

changes in wall thickness and vessel diameter: this fact constitutes the reason why an increase

in BP is followed by an increase in PWV (in other words, a decrease in PTT) [38].

However, given the nature of the constants in (5), which are subject-specific and difficult

to measure directly, it becomes crucial to build a bridge between BP and PTT values, that is, to

establish a valid scaling between them (from now on, one will be taking only PTT into account).

To serve such purpose, calibration functions have been derived from the combination of

(3) and (4), in the form of a logarithmic and quadratic expression. Respectively [37, 39]:

�� !"�� # � �6�; �� %& # � �7�.

Once again, A and B are representing subject-specific constants [39], which involve

complex experimental determinations.

The simplistic and restrictive nature of the exposed theoretical model shall not be,

however, forgotten.

On the other hand, these models don’t suppose any clear distinction between SBP and

DBP. C. Poon et al. [40] proposed, by exploring the concept of MBP, two distinct expressions to

estimate those parameters, both as a function of PTT measurements.

2.4.2 | Physiological Signals of Interest

In what concerns to PTT method, investigators have chosen to essentially work with two

signals: the electrocardiogram (ECG) and the photoplethysmogram (PPG). Since the first one

relates to the heart and the second one relates to body peripheral sites, a significative part of

the arterial path can be evaluated, from central aorta to epidermic capillary beds (regional

assessment, in opposition to a local one).

Furthermore, both signals are methods feasible to implement in a portable device to

continuously assess BP, due to the beat-by-beat, non-invasive nature of the recordings. On the

35

other hand, the economical convenience, the required equipment is minimal, the hardware set

up is easy and their usage, simple. The same can be said relatively to Impedance Cardiography

(ICG) and the Heart Sound (HS), which have been used more recently.

2.4.2.1. The Electrocardiogram

A. General Characteristics

Electrocardiography consists in a quite powerful tool when it comes to monitor the

myocardial electrical events through the heart cycle.

The ECG is generated by the accumulation of electrical potentials of the stimulated

cardiac cells generates an electrical current, which is detected and recorded at skin surface by

special electrodes30

strategically positioned [37]. The morphological and temporal set of

characteristics of an ECG carries great parcels of information, carrying a strong force in the

evaluation of the neuro-cardiac health condition. Heart attack, conduction disorders and

valvular disease are some examples of disorders possible to diagnose through ECG analysis.

The typical ECG (Fig. 13) exhibits three sub-waveforms and two neutrality intervals [4,

41]:

i. PR Interval

This segment coincides with the end of atrial depolarization (even though atria are still

contracting) and the onset of ventricular depolarization is the expression of the delay in the

conduction in atrioventricular node.

Since no relevant polarities are present, no currents are flowing and no wave can be

viewed. This segment usually lasts 0.1 seconds.

ii. QRS Complex

This component shows a short downward portion (Q wave) adjacent to a very

pronounced peak (R wave) followed by a second downward portion (S wave). Q and S waves

may not be detected, though.

QRS-complex monitors ventricular electrical stimulation, which is followed by muscular

contraction. Its normal duration lies between 0.06 and 0.10 seconds.

30

In fact, the electrical current that is recorded in the ECG refers to the extracellular medium. The ECG

is, thus, an indirect measurement of the electrical activity within cardiac cells [4].

36

iii. ST Interval

It marks the end of ventricular end contracting, before their diastole period arrives.

There is no noticeable formation of polarities, similarly to what occurred in PR-Segment.

iv. T wave

T-wave, similar in shape to P-wave but slightly more pronounced, reports the ventricular

repolarization, right before the onset of ventricular diastole. Atrial repolarization occurs at

almost the same, although generally not perceived.

Fig. 13. Typical ECG waveform (voltage through time) obtained with the Lead II configuration (Fig. 14).

It’s remarked that the baseline represents the resting potential of the membrane of the myocardial

cells. Being so, any drifting from the baseline level denotes movement of charged particles across the

membranes; upward and downward drifts accuse opposite directions of the electrical flows. Adopted

from [41].

On another account, the contour and characteristics of the ECG will vary according to

the positioning of the electrodes, or, in other words, with the adopted configuration (Fig. 14).

B. Segmentation and Signal Analysis

Segmentation consists in the process of identifying and isolating distinct/characteristic

sections of a signal.

each heart cycle/beat.

Two algorithms have been representing a visibl

of the fiducial ECG waves. The first one, proposed by J. Pans and W. Tompkins is able to detect

the QRS complex with remarkable accuracy (99.3% of correct detections

point out, the major issues i

them and the interference of noise originated from various sources

muscular tissue, baseline drifts, etc.

proposed to combine the analysis of a set of QRS characteristics such

slope and energy

The algorithm starts by giving special attenti

suppress large quantities of noise, filtering is performed by

Then, they applied a five

slope of the R peak to afterwards square the amplitude of the signal, with the intention of

amplifying the slope and eliminat

filtering routine consisted in

waveform characteristics. The last steps consist

T waves and adaptive thresholding. The

dynamics of the ECG as well as

Segmentation and Signal Analysis


sections of a signal. In the case of hemodynamic

each heart cycle/beat.

Two algorithms have been representing a visibl


the QRS complex with remarkable accuracy (99.3% of correct detections

point out, the major issues in QRS complex identification are the physiological variability to

the interference of noise originated from various sources

muscular tissue, baseline drifts, etc.). For an unequivocal identification of this ECG wave they

ed to combine the analysis of a set of QRS characteristics such

energy.

The algorithm starts by giving special attenti

suppress large quantities of noise, filtering is performed by

Then, they applied a five-point derivative to the ECG in order to obtain information on the


amplifying the slope and eliminate eventual false R peaks (higher amplitude T waves). A last

filtering routine consisted in a moving window integration, used to extract information on the

waveform characteristics. The last steps consist

and adaptive thresholding. The described approach

dynamics of the ECG as well as to operate in real


In the case of hemodynamic signals, the aim is to slice ECG according to

Two algorithms have been representing a visible reference in the automated detection


the QRS complex with remarkable accuracy (99.3% of correct detections) [43]. As the

n QRS complex identification are the physiological variability to

the interference of noise originated from various sources (electrodes motion,

For an unequivocal identification of this ECG wave they

ed to combine the analysis of a set of QRS characteristics such as width

The algorithm starts by giving special attention to the signal pre-processing. I

suppress large quantities of noise, filtering is performed by a special band-pass filter (

point derivative to the ECG in order to obtain information on the


e eventual false R peaks (higher amplitude T waves). A last

window integration, used to extract information on the

waveform characteristics. The last steps consisted in decision rule algorithms: identification

described approach was able to auto

to operate in real-time.

Fig. 14. Examples of distinct

configurations of the ECG

electrodes.

The most commonly used

are Lead I and Lead II

clinical ECG exam it’s usual

to record with different

configurations and in various

sites in order to gather more

information.

Adapted from [42].

37


G according to

e reference in the automated detection


) [43]. As the authors

n QRS complex identification are the physiological variability to

electrodes motion,

For an unequivocal identification of this ECG wave they

width, amplitude,

processing. In order to

pass filter (Fig. 15).

point derivative to the ECG in order to obtain information on the


e eventual false R peaks (higher amplitude T waves). A last

window integration, used to extract information on the

in decision rule algorithms: identification of

was able to auto-adapt to the

Examples of distinct

configurations of the ECG

The most commonly used

Lead II. In a

clinical ECG exam it’s usual

to record with different

configurations and in various

sites in order to gather more

Adapted from [42].

38

Fig. 15. Illustration of the stages of Pans and Tompkins-based signal processing for two ECG cycles.

From top to bottom: Raw signal, band-pass filter output, derivative output, amplitude squaring

output and moving window integration output. Adapted from [44].

In its turn, Y. Sun et al. [45] defended that the traditional filtering-based approach is not

always efficient since the variations in frequency of the waves can either turn the task

particularly hard or even be confused with noise. On the other side, the efficiency of threshold

methods drops when dealing with not-so-expected (while still physiological) odder shapes. In

such context, they proposed a multiscale morphological derivative transform to replace the

traditional derivative, based on signal dilation and erosion.

The method proved to be able to accurately detect not only the QRS complex but also

the onsets of P and T waves (the comparison with annotated data returned correlations of

0.93 for PR interval, 0.95 for QRS complex, and 0.93 for QT interval).

2.4.2.2. The Photoplethysmogram


Photoplethysmography has been vastly used in the clinical context, especially in

anesthesiology and at the intensive care unit [9].

The fundament behind the method is based on the characteristics of red and infrared

light absorption by

absorbs more infrared light and allows

latter [46]. The pulse oximeter (Fig. 16) is a device used to obtain photoplethysmographic

readings, being pla

lobes.

In other words, the amplitude of the acquired signal will be proportional to the oxygen

content within arteriolar and capillary trees; the PPG illustrates, thus, the vol

of arterial blood.

Fig. 16. Left: Schematic representation

emits at two different wavelengths and the photosensor detects the intensity of the reflected light.

Rigth: Schematic representation of the electronics of a pulse oximeter.

That being said, one promptly thinks in the PPG waveform as

peripheral PW. In fact, per heart beat, the characteristic PPG waveform

from the arterial PW

a secondary peak (Fig. 17).

related to the underlying BP. However

these two circulatory signals.”

The PPG is able to gather important information relative to the cardiovascular status and

even to the autonomic nervous

and low frequency components to the PPG. They affirm that the first ones

on BP control, venous return to the heart, ventilation and thermoregulation, while the higher

components include the PW itself which contains information about BP, peripheral resistance

and vessel compliance. The later descending part

to not carry relevant information [9].

31

When haemoglobin, a protein found in blood red cells, is bounded to oxygen

otherwise, deoxyhemoglobin.


light absorption by the oxygenated and deoxygenated variants of haemoglobin

absorbs more infrared light and allows for more red light to pass through, in opposition to the

[46]. The pulse oximeter (Fig. 16) is a device used to obtain photoplethysmographic

readings, being placed on the skin of the thinnest body extremities, such as fingers, toes or ear


content within arteriolar and capillary trees; the PPG illustrates, thus, the vol

of arterial blood.

Schematic representation of a reflectance pulse oximeter. The LED (


Rigth: Schematic representation of the electronics of a pulse oximeter.

That being said, one promptly thinks in the PPG waveform as

peripheral PW. In fact, per heart beat, the characteristic PPG waveform

from the arterial PW: it exhibits a dominant peak emerging from an onset/foot point, a DN and

a secondary peak (Fig. 17). As P. Shaltis et al. [48] point out, “it is well known that the PPG is

related to the underlying BP. However, there is ambiguity regarding the precise relationship of

these two circulatory signals.”


even to the autonomic nervous system. As J. Allen

and low frequency components to the PPG. They affirm that the first ones



and vessel compliance. The later descending part

to not carry relevant information [9].

When haemoglobin, a protein found in blood red cells, is bounded to oxygen

otherwise, deoxyhemoglobin.


deoxygenated variants of haemoglobin31

more red light to pass through, in opposition to the


ced on the skin of the thinnest body extremities, such as fingers, toes or ear


content within arteriolar and capillary trees; the PPG illustrates, thus, the volumetric

of a reflectance pulse oximeter. The LED (light emission diode


Rigth: Schematic representation of the electronics of a pulse oximeter. Adopted from [47].

That being said, one promptly thinks in the PPG waveform as an indirect measure of the

peripheral PW. In fact, per heart beat, the characteristic PPG waveform does seem modelled

: it exhibits a dominant peak emerging from an onset/foot point, a DN and

[48] point out, “it is well known that the PPG is

, there is ambiguity regarding the precise relationship of


As J. Allen et al. [49] address, there are

and low frequency components to the PPG. They affirm that the first ones include information



and vessel compliance. The later descending part (portion after the DN), however, is believed

When haemoglobin, a protein found in blood red cells, is bounded to oxygen is called oxyhemoglobin;

39


31: the former

more red light to pass through, in opposition to the


ced on the skin of the thinnest body extremities, such as fingers, toes or ear


umetric variations

light emission diode)


Adopted from [47].

an indirect measure of the

seem modelled

: it exhibits a dominant peak emerging from an onset/foot point, a DN and

[48] point out, “it is well known that the PPG is

, there is ambiguity regarding the precise relationship of


] address, there are several high

include information



(portion after the DN), however, is believed

is called oxyhemoglobin;

Fig. 17.

resulting from light absorption by: a) residual


In what concern

on the PPG waveform: the foot, the peak

Contrarily to the peak,

out, due to the little variations exhibited by the signal in such area, the i

may be completely overshadowing, making its determination to be quite challenging.

The two metho

derivative maximum

determined as the maximum of the second derivative of the PPG signal, which must be

previously filtered (

second method,

intersection point of the two represented straight lines.

In each cycle, the pre

through the PPG samples comprehended between the position of the R

located at a distance of 2/5 of the RR interval. In its turn, the straight line located after the foot

is defined again by the least squares fitting to the PPG samples comprehended between the

maximum of PPG’s first derivative (b) and five sample

Typical aspect of the PPG, giving emphasis to pulsatile and basal components (the later

resulting from light absorption by: a) residual oxyhaemoglobin in the arterial blood; b) skin and bone; c)

venous blood). The amplitude of PPG is usually expressed in percentage.

Adapted from [9].


In what concerns to PPG segmentation, one considers, at least,

n the PPG waveform: the foot, the peak and the DN (Fig. 17).

Contrarily to the peak, the foot is particularly problematic to determine. As

out, due to the little variations exhibited by the signal in such area, the i


The two methods traditionally more used for the

derivative maximum and the tangent intersection foot


previously filtered (in the frequency domain and

second method, illustrated in Fig. 18, assumes that t

point of the two represented straight lines.

In each cycle, the pre-foot straight line is drawn following the least squares method

through the PPG samples comprehended between the position of the R



maximum of PPG’s first derivative (b) and five sample


oxyhaemoglobin in the arterial blood; b) skin and bone; c)

The amplitude of PPG is usually expressed in percentage.

Adapted from [9].

s to PPG segmentation, one considers, at least, three points of interest

and the DN (Fig. 17).

he foot is particularly problematic to determine. As

out, due to the little variations exhibited by the signal in such area, the interference of noise


ds traditionally more used for the previous finality are the

tangent intersection foot-to-foot. In the first method the foot is


and also through triangular moving average). The

illustrated in Fig. 18, assumes that the PPG foot is coincident with the

point of the two represented straight lines.

foot straight line is drawn following the least squares method

through the PPG samples comprehended between the position of the R-peak and



maximum of PPG’s first derivative (b) and five samples below it.

40


oxyhaemoglobin in the arterial blood; b) skin and bone; c)

points of interest

he foot is particularly problematic to determine. As [50] points

nterference of noise


are the second

first method the foot is


g average). The

he PPG foot is coincident with the

foot straight line is drawn following the least squares method

peak and the point



Fig. 18. Schematic representation of the

More recently two innovative methods have been proposed by E. Kazanavicius et

[50]. The first one goes by the designation of

Fig. 19 reports

of the first derivative was parted into ten sub

drawn through to least squares fitting method.

calculated; the combination of all of these was fit with the cubic polynomial. Finally, the foot of

the PPG was assumed to coincide with the

Fig. 19. Schematic representation of the

Schematic representation of the tangent intersection foot


[50]. The first one goes by the designation of pulse wave foot polynomial approximation

Fig. 19 reports, the interval of PPG samples comprehended from the R peak to the maximum

of the first derivative was parted into ten sub

drawn through to least squares fitting method.


the PPG was assumed to coincide with the smallest value of the fitting curve.

Schematic representation of the pulse wave foot polynomial approximation

Adopted from [

tangent intersection foot-to-foot method. Adopted from [


pulse wave foot polynomial approximation

, the interval of PPG samples comprehended from the R peak to the maximum

-intervals; in each of them a straight line was

drawn through to least squares fitting method. Per straight-line an average abscissa value was


smallest value of the fitting curve.

pulse wave foot polynomial approximation

Adopted from [50].

41

Adopted from [50].

More recently two innovative methods have been proposed by E. Kazanavicius et al.

pulse wave foot polynomial approximation. As

, the interval of PPG samples comprehended from the R peak to the maximum

a straight line was

line an average abscissa value was


method.

Finally, the second innovative purpose reported by these authors consisted in the

bottom straight

determined as the intersection point of the straight

Still in the same study, the authors added noise

described methods, having observed that the tangent intersection was associated with the

lowest accuracy level (error between estimated and referential PPG foot of 5 ± 11

milliseconds), while the polynomial approximation method provid

foot estimation.

Fig. 20. Schematic representation of

Relatively to the DN, the main inflection point of the PW, it can be determined through

the analysis of the derivative of the PPG waveform, as “the first negative

crossing of the fourth derivative of the pressure

generates a noisier waveform. P. Tsui

method, which was based in the probability distribution function of PW (or PPG

fundament was that the PW exhibits lower variation in t

other segment.

Moreover, J.

which proved to be capable of overcoming the problematic entailed by HR variability and

motion artefacts. After PPG segmentation (performed through the fist derivative of the signal)

the authors trunca

extrapolation method, they reconstructed the segment until it fulfils the mean segment


bottom straight-line and forefront intersection

determined as the intersection point of the straight

Still in the same study, the authors added noise



milliseconds), while the polynomial approximation method provid

foot estimation.

Schematic representation of bottom straight

Adopted from [50].


the analysis of the derivative of the PPG waveform, as “the first negative

crossing of the fourth derivative of the pressure

generates a noisier waveform. P. Tsui et al. proposed the pulse wave probability analysis


fundament was that the PW exhibits lower variation in t

other segment.

Moreover, J. Weng et al. [9] proposed an algorithm to extract a mean PPG waveform,



the authors truncated the later descending part if it is longer than the mean segment. By the



line and forefront intersection method, illustrated in Fig. 20; the PPG foot is

determined as the intersection point of the straight-line with the bottom line of the PPG signal.

Still in the same study, the authors added noise to PPG signal and applied the four



milliseconds), while the polynomial approximation method provided the more accurate PPG

bottom straight-line and forefront intersection

Adopted from [50].


the analysis of the derivative of the PPG waveform, as “the first negative-to-

crossing of the fourth derivative of the pressure signal” [11]. A derivative operation, however,

proposed the pulse wave probability analysis


fundament was that the PW exhibits lower variation in the immediacies of the DN than in any

proposed an algorithm to extract a mean PPG waveform,



ted the later descending part if it is longer than the mean segment. By the


42


method, illustrated in Fig. 20; the PPG foot is

line with the bottom line of the PPG signal.

and applied the four



ed the more accurate PPG

method.


-positive zero

operation, however,

proposed the pulse wave probability analysis

method, which was based in the probability distribution function of PW (or PPG) [11]. The

he immediacies of the DN than in any

proposed an algorithm to extract a mean PPG waveform,



ted the later descending part if it is longer than the mean segment. By the


43

length. Finally, they computed the mean pulse waveform, and, by applying a correlation

detection algorithm, the distorted pulses (affected by noise) were eliminated.

Finally, G. Chan et al. [51] proposed an algorithm capable of detecting specific fiducial

points designated to determine LVET, as it will be addressed later (2.4.4.3).

2.4.2.3. The Heart Sound


As P. Carvalho et al. [52] point out, “the recent developments in digital signal processing

and analysis are leading to a renewed interest in heart sound. It has emerged as a powerful

(easy to use, low intrusive, repeatable and accurate) and inexpensive bio-signal to develop

monitoring systems”. As these authors underlined, HS alone carries important information,

since “the timings between its main components, its morphology as well as its spectral content

can be applied to directly estimate relevant cardiac parameters”. In fact, HS were proved to

relate with certain conditions such as valvular malfunctioning and heart failure, among others.

If one uses a stethoscope in specific points on the chest, right above or near the heart,

four characteristic sounds can be perceived as the heart cycle follows, discernible between

them in terms of intensity, frequency and temporal duration. The most relevant and clinically

informative are the first and second sounds; in fact, the third and fourth sounds are not always

heard (Fig. 21).

The first heart sound to be heard (S1) is composed of several high-frequency

components, in spite of only the first two are normally audible. These, in turn, are

distinguishable from each other in terms of frequency and amplitude – the first component

has higher amplitude and frequency. On the other hand, the second heart sound (S2) is a “short

burst of auditory vibrations of varying intensity, frequency, quality, and duration” [53]. S2 has

two audible components, which may not overlap in time.

On another account, in spite of distinct theories on the genesis of heart sounds are still

coexisting [53], one of the most accepted is the valvular theory [4]. As P. Carvalho et al. [52]

state, there is “the hypothesis that heart sounds encode clear makers that enable the

detection of the opening and the closing of the aortic valve”. Accordingly, the first S1

component is believed to relate with the closure of the atrioventricular valves (mitral and the

tricuspid), which may not overlap in time [53]. The second component is suspected to be

mainly related with the vibration induced by the aortic valve opening [52]. Relatively to S2, its

first component corresponds to AOV closing sound, while the second refe

pulmonary valve.

Fig. 21. Temporal representation of the main heart sounds and respective physiological synchronization


Segmenting the HS means in the fist instance to detect the signal sections corresponding

to S1 and S2. D. Kumar

to the ECG. First

extracted from each HS cycle by the fast wavelet decomposition”. The existence of such high

frequency characteristic pattern

the heart valves.

that of S1 (therefore, more accurately determined), given the higher difference

across the AOV than across the AVVs.

Once verified the presence of high frequency signatures in at least one type of

Shannon energy operator is used to identify HS cycles. Finally, S1 and S2 are estimated within

each cycle by identifying the closest interval between them to the estimated value. The

authors proved the accuracy and reliability of the described algo

sensibilities and specificities superior to 95% (subjects with prosthetic valves were also tested).

Still the same authors

physiological complications (namely valvular dysfunction and heart diseases

first component corresponds to AOV closing sound, while the second refe

pulmonary valve.

Temporal representation of the main heart sounds and respective physiological synchronization

with ECG and the PW (PCG Ξ phonocardiogram). Ado



D. Kumar et al. [55] recently presented an algorithm that dispenses any reference

to the ECG. Firstly, it estimates “the instantaneous HR through a high


frequency characteristic pattern is substantiated by the elevated differences in pressure across

heart valves. It’s important to note that the


across the AOV than across the AVVs.




authors proved the accuracy and reliability of the described algo


Still the same authors adapted the algorithm to

physiological complications (namely valvular dysfunction and heart diseases

first component corresponds to AOV closing sound, while the second refers to the closure


phonocardiogram). Adopted from [54].


presented an algorithm that dispenses any reference

, it estimates “the instantaneous HR through a high frequency marker


is substantiated by the elevated differences in pressure across

that the high frequency pattern of S2 is more evident





authors proved the accuracy and reliability of the described algorithm with results whose


adapted the algorithm to function even in the context of

physiological complications (namely valvular dysfunction and heart diseases) [56].

44

rs to the closure



presented an algorithm that dispenses any reference

frequency marker


is substantiated by the elevated differences in pressure across

high frequency pattern of S2 is more evident

that of S1 (therefore, more accurately determined), given the higher differences in pressure

Once verified the presence of high frequency signatures in at least one type of HS, the



rithm with results whose


in the context of

) [56]. As they

45

explain, they made use of the wavelet decomposition-simplicity filter to decompose the HS

signal, which was then adaptively thresholded in order to allow the discrimination of S1 and S2

sounds from murmurs (i.e., noise introduced by the anomalous physiological conditions).

On the other hand, the interest of identifying the AOV movements (i.e., opening and

closure) through HS is emerging.

P. Carvalho et al. leaded a study which implied the determination of AOV opening and

closing times from HS [52]. The authors modelled HS by an amplitude modulated chirp signal

and utilized it to identify, through spectral and energy analysis, clear markers in S1 able to

define the AOV opening moments. Also, through the detection and analysis of specific high

frequency components in the second heart sound (S2) (utilizing the algorithm described

above), they identified the closing times of the AOV. Results collected from 17 (healthy)

subjects demonstrated strong correlations with those obtained from echocardiography (in

which one can see the movement of cardiac structures).

The authors concluded that AOV movements can be, thus, discerned from HS.

Moreover, given the fact that AOV opening and closure were early detected (3.7 and 15.48

milliseconds, respectively) the authors suggested that this algorithm determines the very

beginning of the two movement processes.

2.4.2.4. Impedance Cardiography


As [57] explains, the impedance cardiography signal (ICG) results from the first time

derivative of the impedance signal, hence the designation of dZ/dt often attributed to former.

ICG is acquired in a non-invasive process that involves the application of electrical impedance32

to the subject’s chest in order to detect and measure alterations in blood volume, in particular,

inside the thoracic aorta artery and cava vein. This technique is mainly used to monitor stroke

volume and determine LVET.

32

Impedance is the electrical resistance of an alternating current circuit.

B. Segmentation

The ICG (usually) exhibits a set of characteristic points, each one associated with a

distinct event of the heart cycle (Fig

Fig. 22.

Contraction of atrium; B

The most important are the B

of the ICG is

upstroke of dZ/dt

peak in the dZ/dt signal”

difference between the B

ejection” [57].

As X. Wang

differentiation, process that did not

by these operations

improvements in the clinical hardware set

se), these authors prop

through the time

On the other side

characteristic points based in the wavelet transform. For example, L. S

approach exclusively used

condition while performing the Valsalva manoeuvre [57]. As the

transform decomposes the signal into components at di



distinct event of the heart cycle (Fig. 22).

Fig. 22. ICG signal’s typical form. Each marked point contains information related to: A

Contraction of atrium; B – opening of AOV; C- maximum flow from left ventricle into aorta; X

AOV; O – widest open of mitral valve. Adapted from [58].

The most important are the B-point and X

is defined to mark the opening of AOV and “occurs at the onset of the rapid

upstroke of dZ/dt”. In its turn, “the X point is defined as the minimum following the major

peak in the dZ/dt signal” [57]. On the other hand, “dZ/dt

difference between the B-point and the maximum of dZ/dt [i.e., C

As X. Wang et al. clear up, such points were traditionally determined through

fferentiation, process that did not reveal effective due to noise interference (

operations and related with the acquisition process

improvements in the clinical hardware set-up (which reduced noise and motion artefacts

), these authors proposed an algorithm capable of reliably determine B, X and C points

through the time-frequency analysis method.

On the other side, other investigators proposed a determination of the ICG

characteristic points based in the wavelet transform. For example, L. S

exclusively used in the ECG so far to ICG data

condition while performing the Valsalva manoeuvre [57]. As the

transform decomposes the signal into components at di


ICG signal’s typical form. Each marked point contains information related to: A

maximum flow from left ventricle into aorta; X

widest open of mitral valve. Adapted from [58].

point and X-point (used to determine LVET).

defined to mark the opening of AOV and “occurs at the onset of the rapid

he X point is defined as the minimum following the major

. On the other hand, “dZ/dtmax is defined as the amplitude

point and the maximum of dZ/dt [i.e., C-point] after the onset of the

, such points were traditionally determined through

effective due to noise interference (both

and related with the acquisition process) [58]. Besides some

up (which reduced noise and motion artefacts

osed an algorithm capable of reliably determine B, X and C points

, other investigators proposed a determination of the ICG

characteristic points based in the wavelet transform. For example, L. Shyua et al.

to ICG data, which was collected at the resting

condition while performing the Valsalva manoeuvre [57]. As the authors affirm, “

transform decomposes the signal into components at different frequency scales (…) and

46


ICG signal’s typical form. Each marked point contains information related to: A -

maximum flow from left ventricle into aorta; X – closing of

used to determine LVET). The B-point

defined to mark the opening of AOV and “occurs at the onset of the rapid

he X point is defined as the minimum following the major

ed as the amplitude

point] after the onset of the

, such points were traditionally determined through the time

both introduced

Besides some

up (which reduced noise and motion artefacts per

osed an algorithm capable of reliably determine B, X and C points

, other investigators proposed a determination of the ICG

et al. applied an

collected at the resting

authors affirm, “wavelet

fferent frequency scales (…) and

47

characterizes the local regularities of signal in those scales”, what avoids many of the noise-

derived issues of the conventional methods. X and B points were calculated with more

accuracy than by the conventional methods, even with artificially added noise (comparatively

to echocardiography).

Furthermore, some controversy associated with the reliability and accuracy of the

determination of B-point still persists. Such distrust grounds in two main reasons; firstly, the

closure of AOV is not an instantaneous process: it is a physiological event that requires time –

in the order of the milliseconds – to be fully performed. Second, the event is only detectable

by the impedance exam once a reasonable volume of blood had already passed through the

(opened) valve. In fact, as reported by Ermishkin et al. [59], the referred method introduced a

delay of 3 to 20 milliseconds relatively to the onset of blood flow in the Doppler

echocardiography.

2.4.3 | Upon Pulse Transit Time

2.4.3.1 Clinical and Experimental Definitions

As equation (5) set clear, PTT is a hemodynamic parameter that depends on specific

factors such as blood viscosity and reflection coefficient, arterial diameter and stiffness,

physical activity status. Furthermore, a relatively short PTT is observed with ageing and in

disease context (hypertension, arteriosclerosis33

and diabetes mellitus [38], etc.).

Originally PTT was measured by recording the time interval as the PW travels between

two arterial sites at a known distance apart. Most of the used methods in such approaches

(tonometry, Doppler echography, etc.) are, however, weighty, complex to operate and

expensive. More recently investigators started to recur to the ECG and to the PPG for two

main reasons: ease of measurement and to account for central/aortic BP, which is, as

expected, the most relevant in physiological terms.

In theory, PTT is clear to define. Being a merely vascular parameter, it corresponds to

the time took by the ejected blood volume to go from the ascending aorta (right after the

AOV) to the arterioles and capillaries at a specific body zone (usually peripheral). However, in

the practice the situation is different.

33

To note the difference between arteriosclerosis and atherosclerosis; while the former refers to the

histological degradation of arterial walls, the later consists in the deposition of fatty plaques in the

luminal arterial wall surface.

48

First, although Q waves consist in the clinically recognized starting point for measuring

systolic and vascular time intervals, R-peaks also have been used as such [60]. However, both

signal the opening of the AOV with some anticipation (see section 2.1.2.1) [4]. In fact, the

processes of contraction and blood ejection, in spite of instantaneous, still take place in

between ventricular depolarization and AOV opening.

However, the uncertainty is amplified in the definition of the terminal reference for PTT,

which remains a matter of researching: “conventionally the point on the PPG waveform which

is either 25% or 50% (depending on which equipment is used) of the height of the maximum

value is taken to indicate the arrival of the PW” [60]. Moreover, other studies comprehended

the time interval until between 70 to 80% of the maximum PPG amplitude. On the other side,

M. Wong et al. [61] reported higher correlations between BP and PTT measured until the onset

of the PPG comparatively to the peak (in post-physical exercise conditions).

2.4.3.2 An Income of Uncertainty

In fact, while no study denies the correlation existent between PTT and BP, the

legitimacy of measuring PW delays from the ECG and PPG has long been called into question.

Several studies have been proving the unreliability of such approach as an accurate BP

assessment method [38]. Even in algorithms and instruments that measure an absolute, local

PTT – that is, defined between two points a known distance apart (e.g., [62], Complior (Colson,

France), the Sphygmocor by AtCor) –, one isn’t able to measure anything but changes in BP, or,

in other words, a local BP: not central, not omnibus.

PTT is, thus, currently trusted as a mere reliable assessor of changes in BP.

2.4.3.3 Pulse Arrival Time and Pre-ejection Period

Actually, if counted from the ventricular electrical stimulation, the pulse detected at the

periphery is not the true PTT, because it also includes the systolic time interval that lasts until

the opening of the AOV: the already introduced PEP.

That said, the time interval actually measurable is known as pulse arrival time (PAT) and

consists, consequently, in the summation of PTT and PEP:

PAT � PTT # PEP �8�.

Besides its consecrated expression on PAT, PEP is proved to not be a mere addictive

constant, but rather exhibits its own dynamics and changes (subject explored in 2.4.4.1).

49

To finish this discussion, one shall add that, in practice, the setting of PAT remains,

obviously, controversial and uncertain as well. X. Aubert et al. [37], for example, considered it

to be defined between the ECG’s R wave and the foot of the PPG volume pulse of the same

cycle, while others defend that the ending reference should be the peak of the latter signal.

Thus, only PEP can be experimentally well known.

2.4.4 | Upon Pre-Ejection Period

2.4.4.1. The Dynamic Nature

Some studies have been proving that PEP is not a mere constant under some specific

circumstances.

The dynamic nature of PEP associated with physical exercise was demonstrated by J.

Muehlsteff et al. [37]. By subjecting 18 volunteers to short effort bicycle tests, the authors

reported PEP to exhibit appreciable fluctuations. Moreover, this systolic time interval was

verified to vary in synchrony with PAT (the latter defined from ECG’s R wave to the foot of the

PPG), in a beat-by-beat basis, both during physical activity phases and subsequent resting

periods. Moreover, the authors also reported that PEP values fulfilled a significant parcel of

PAT, thus, clearly not negligible. Such observations have proved to be more accurate if subjects

included physical exercise in their routines. Also, this group of subjects also exhibited a linear

relationship between SBP and PAT, unlike the subjects who did not perform any sports.

Furthermore, the same authors refer that psychological stress (emotional, intellectual, etc.)

also promotes PEP variation.

Another interesting characteristic relative to the behaviour of PEP was testified already

in 1981 by H. Mertens et al. [63], which also described changes in this systolic time interval

once subjects were submitted to physical exercise: it shortened significantly. However, if only

HR alone was varied (by artificial atrial stimulation), the value of PEP did not accuse changes.

As the authors point out, the experiment suggested that PEP only undergoes changes if the

dynamic state of the heart – as a whole piece – is altered.

Later on, J. Muehlsteff et al. [64] investigated the effect of vaso-active drugs on pulse

delays measured from the ECG. As they elucidated, this type of drug, often administered to

cardiovascular patients, exert influence on the resistance offered by the systemic vasculature

(systemic vascular resistance, SVR), without, in general, alter HR and the intensity of cardiac

50

contractions. Thus, the higher the SVR, the higher BP becomes (unless CO decreases). They

also intended to study the effect of ventricular contractility34

.

Since no closed equation – i.e., in which all the variables are well known – to compute

PEP is defined so far, these authors decided to implement a lumped analog model of arterial

circulation in order to analyse the relationship of PEP with BP. They followed a three-element

Windkessel model, simulating the left ventricle (AOV included) and arterial system (aortic

impedance, vascular compliance and peripheral resistance took into account) according to

their analogous electrical circuits. They established two differential equations, one relating

aortic pressure and vascular resistance and the other one relating ventricular pressure and

contractility. They observed that ever since the peripheral resistance parameter was varied, an

approximately linear correlation between PEP and both SBP and DBP was verified. In addiction,

negative – but almost linear – correlations were found by varying the left ventricular

contractility parameter. Such observations guide towards the relationship between PEP and

left ventricular contractility. In fact, in addiction to its important role in BP assessments, PEP is

recognized as a measure of the performance and health of the left ventricle.

On a final account, pulmonary ventilation35

consists in another modulating agent of PEP.

As Ermishkin et al. observed, PEP was slightly modulated by ventilation at rest [59].

2.4.4.2 Methods of Determination

PEP has been defined as the time interval comprised from the starting of ventricular

depolarization (QRS complex, Q wave in particular, according to the clinical convention) to the

AOV opening moment [59]. In order to reliably define PEP, one has, thus, to assess the opening

of the AOV.

However, due to the fact that the opening (or closing) of the AOV is a dynamical

physiological process, distinct detection methods usually happen to return slightly diverted

results.

34

Left ventricular contractility evaluates the performance of the muscle of the former, or, in other

words, the capacity of a muscle fibre to contract at a given fibre length. 35

In physiologically accurate terms, respiration refers to the cellular processes involved in the

generation of energy (ATP) with the intervention of oxygen.

51

A. Echocardiography

Presently the clinical gold standard method for determining PEP uses the

echocardiography, providing an overestimating of 12 milliseconds [65]. As every ultrasound-

based clinical procedure, cardiac echocardiography allows for a monitoring in almost real time,

similarly to a movie of an internal structure (M-mode imaging) or blood flow velocity (Doppler

mode imaging). It is, thus, possible to visually confirm and to mark the opening of the AOV.

However, it is not viable to integrate such exam in ambulatory, patient home-monitoring

systems, for a variety of reasons: the requirement of clinical knowledge to perform the

measurement and the appreciable volume, weight and discomfort implied by the

instrumentation.

B. Impedance Cardiography

One of the most popular actual alternatives to assess PEP is based in the ICG processing.

PEP is conventionally set, per heart beat, from the Q wave of the ECG to the B-point of the ICG

[59], the latter representing, as already acquainted, the AOV opening.

Recently, innovative algorithms to determine PEP through ICG have been proposed; a

good example is presented by Ermishkin et al. [59]. These authors defined PEP as the time

interval between the R-wave of the ECG and the maximum point of the second time derivative

of the impedance signal per heart beat (that is, the first derivative of the ICG signal). They

tested the algorithm with 18 subjects, using different protocols (Valsalva manoeuvre,

handgrip) and reported the achieved PEP values to show consistency with echocardiography.

C. Heart Sound Analysis

P. Carvalho et al. demonstrated the feasibility of determining PEP through HS analysis

[52]. This systolic time interval was “measured indirectly by subtracting LVET from R:S2, where

R:S2 is the time interval from the ECG R-peak to S2”. LVET was calculated as the difference

between AOV closing and opening times, these latter determined according to the described in

2.4.2.3. Comparatively to echocardiography, the error was 5.81 ± 4.91 milliseconds, which

deposited trust in the followed approach.

Furthermore, in parallel to the previously work, R. Paiva et al. [65] determined PEP (and

also LVET) using HS and ECG. To assess PEP, these authors relied on a Bayesian probabilistic

approach, regarding the instantaneous amplitude of the HS signal and the typical/estimated

52

values of the time interval comprised from the closure of atrioventricular valve to the opening

of AOV.

Relatively to the echocardiography, the achieved results for PEP showed promising small

errors (Table 3), pointing towards the viability of the method.

Parameter Annotated Range

(milliseconds)

Estimation Error

(milliseconds)

Correlation

Coefficient

PEP 47.55 ± 12.72 10.54 ± 7.88 0.45

LVET (HS) 265.97 ± 24.20 32.62 ± 38.00 0.32

LVET (PPG) 254.92 ± 20.10 27.50 ± 25.00 N.A.

Table 3. Results achieved by [65] (mean ± standard deviation).

The annotated data was visually extracted from echocardiographic data.

2.4.4.3 Considerations on Left Ventricular Ejection Time

While not directly related with the Möens-Korteweg/Hughes theories, this sub-chapter

is justified by the clinical and experimental definitions of LVET being entirely related with PEP’s

(consult 2.1.2.1).

Likewise PEP, the actual golden standard method for determining LVET is the

echocardiography (Fig. 23).

One way of determining LVET is, as already pointed out, through ICG analysis, seeing

that this signal encodes information on both the opening and closure of the AOV. LVET can

thus be determined as the difference between the X-point and B-point times.

Furthermore, besides the reported in 2.4.4.2.C [52], two other approaches for

determining LVET recently emerged [65].

One of them consisted in directly calculate the difference between AOV opening

(through the PEP values obtained from HS) and closing times (through the high frequency

signature of S2).

The other one followed the algorithm presented by G. Chan et al. [51] (consult Table 3

for results), which promises the continuous LVET monitoring using finger

photoplethismography. The authors established an algorithm based in the analysis of the

mathematical derivatives of the PPG up to the fourth order, combined with waveform

averaging and rule-based logic so that some fiducial points could be determined.

Fig. 23. Annotation

This way, per cycle, the onset of ventricular systolic ejection was

maximum of the third derivative of PPG, while its ending was marked by the local maximum of

the same signal which was “typically followed by a sharp falling edge”. A referential, averaged

LVET served as reference to help locating the referred

Results obtained for 13 (healthy) subjects during gradual head

correlations with the LVET derived from Doppler echocardiography. Although not enough to

guarantee a clinical validation

investigations.

2.4.5 |

By calibration one means the process of determining the relationship between the

output of a sensor or system and its input.

Given everything that was discussed so far, one concludes that some main obstacles are

associated with the PTT method in the assessment of BP.

Systematizing the most pertinent ones, one lists:

i. The statics of the theoretical models

Möens-Korteweg and

ambulatory, at

Annotation of aortic valve timings using Doppler (top) and M

(bottom). Adopted from [52].

This way, per cycle, the onset of ventricular systolic ejection was



LVET served as reference to help locating the referred

Results obtained for 13 (healthy) subjects during gradual head


guarantee a clinical validation per se, the proposed algorithm proved to be

investigations.

Searching for Validation: Calibration Studies


output of a sensor or system and its input.




The statics of the theoretical models

Korteweg and derived equations do not account for situations often found in

bulatory, at-home measurements. Therefore,

of aortic valve timings using Doppler (top) and M-mode mode echocardiography

(bottom). Adopted from [52].

This way, per cycle, the onset of ventricular systolic ejection was marked by the



LVET served as reference to help locating the referred points.

Results obtained for 13 (healthy) subjects during gradual head-up tilt shown high


, the proposed algorithm proved to be deserver of further

Searching for Validation: Calibration Studies





derived equations do not account for situations often found in

Therefore, special experimental protocols, involving

53

mode mode echocardiography

marked by the



up tilt shown high


deserver of further



derived equations do not account for situations often found in

experimental protocols, involving

54

changes in posture, movement of body parts physical exercise, etc. must be explored, since

they introduce diverse artefacts – hydrostatic36

and of movement.

ii. Subject-specific constants implied in the theoretical models

Those need to be determined experimentally.

iii. Theoretical models only account for vascular time delays

With the ECG and the PPG, one only is able to extract PAT. One needs, thus, the

intervention of PEP to determine PTT.

iv. Experimental definition of PTT (and PAT)

What point on the PPG waveform marks their ending limit?

Thus, it can be said it lacks a convenient, absolute calibration method, in spite of some

studies have already resulted in interesting, useful contributes.

2.4.5.1. Pulse Transit Time Approach

Y. Liu et al. [66] analysed PTT (defined from the peak of the ECG’s R wave to the

upstroke of the PPG pulse) and radial MBP changes at discrete vertical wrist positions above

heart level. In the moving arm, PTT was testified to increase with the height, while (estimated)

radial MBP decreased. High correlation coefficients between these parameters were observed

during the hand elevation process.

Yan et al. [67] suggested a linear model to describe the effects of radial BP change on

PTT during subject’s hand elevation, at rest. They derived an equation that relates radial BP at

a given height to PTT (experimentally measured from ECG’s R peak to the foot of the PPG), arm

length and two subject-specific constants. They measured radial BP with an oscillometric

device as well. High correlations were verified between estimated and measured DBP and SBP

values in the majority of the results. The number of tested subjects was solely 11, though.

(Authors didn’t account for PEP either.)

36

In a closed fluid-filled recipient, two points at different levels will be acted by pressure forces of

different intensity, according to P = ρ g h, where P is the pressure exerted on a given point, ρ is the

density of the fluid, g, the acceleration of gravity and h the distance measured from the base of the

recipient.

55

C. Poon et al. [24] leaded a quite similar study to Yan et al. These authors found

significative correlations between estimated radial BP and PTT and their experimentally

measured correspondents.

J. Yong et al. [68] studied, on the other side, the variation induced on PTT by the

adoption of different corporal postures (sitting and supine position) on 23 subjects. This way,

they established a model, grounded in Bernoulli’s equation (from the physics of fluids), able to

estimate the changes in PTT at a given posture. In practice, PTT was treated as the time

interval comprising ECG’s R peak and the point of PPG corresponding to 90% of its maximum

amplitude (this latter signal was acquired at the toe). Significative correlations between

estimated and measured changes in PTT were reported.

2.4.5.2. Pulse Arrival Time Approach

In the sequence of proving the important contribution of PEP in PAT, J. Muehlsteff et al.

[37] derived heuristic (that is, empirical, semi-intuitive) calibration models from equations (6,

7), that consider PAT instead of PTT. Those provided acceptable estimations of SBP (measured

at the fingertip). This calibration algorithm only required a single initial BP measurement for

each subject.

The same authors still evaluated [69] the impact of body posture on PAT (again, defined

between the R-peak of the ECG and the pulse-foot of the PPG), LVET, PEP and finger BP, under

protocols of posture changing and angle dependency in posture changing, both in rest. They

concluded that one must provide the measurement system with background information on

the subject specific posture. They also suggested the eventual implementation of

accelerometers to automatically detect changes on body posture.

By other side, D. McCombie et al. [70] presented a novel algorithm, designated by

adaptive PTT calibration, which allows for a complete calibration of PTT to MBP while

dispensing the use of any external devices. The calibration was performed by subject motions

themselves, these being understood as height variations of the sensor relatively to the heart,

so that hydrostatic pressure is altered at the measurement site. PTT was extracted from the

PPG measured in two in-line finger pulse oximeters (no ECG was used). Acceptable correlations

were found with Finapres® measurements.

W. Chen et al. [71], in their turn, focused in spectral analysis approaches. These

authors merely used the higher frequency component of PAT (defined as the time interval

from ECG’s R peak to the onset of the finger PPG) to continuously companion changes in SBP.

56

The estimated values for the latter parameter (collected from 20 patients) were compared to

those invasively measured using a radial intra-arterial catheter; high correlations were verified.

CONCLUSION

For a genuine, integrate understanding and evaluation of the cardiovascular status, it

becomes essential to assess BP with high accuracy – in real time and for relatively long periods.

Although portable wrist/finger devices and intra-arterial catheterization constitute a

fairly good approximation to the sought, there isn’t any non-invasive, continuous method with

clinical validation.

One of the most promising candidates to bridging the gap is the PWV/PTT approach

that, due to present limitations and uncertainties, still cannot be trusted as a clinical tool per

se. A definitive, fully reliable calibration strategy needs to be established.

57

THIRD CH APTER

METHODOLOGIES

OVERVIEW

The current section provides an enlightening general view the detailed description on

every approach and strategy developed in the context of this study – in essence, data

acquisition and data processing.

3.1 | OVERALL DESIGN

The purpose was to explore, the closest possible to the beat-by-beat regimen, the

relationship between SBP/DBP and PEP, PAT, PTT in order to investigate which parameters

would eventually exhibit a more evident, strong relationship. A statistical evaluation based on

mutual information, correlation coefficient and mean squared prediction error was carried out

for such end.

The time intervals of interest were supposed to be determined through the analysis of

convenient signals such as ECG, PPG and HS, which were recorded. A patient monitor and a

stethoscope acquired PPG and HS respectively. Both equipments acquired ECG, responsible for

the (temporal) synchronization of the other two signals.

To achieve a more complete analysis, one invested in the variety of results,

implementing distinct ways to define and compute the same time interval. The programming

job, carried out with MATLAB software (Release 2008a, The MathWorks, USA) consisted in the

adaptation and integration of pre-existent algorithms, complemented with some originals.

PEP, the only time interval likely to be unequivocally defined in experimental terms

(same applying to LVET), was determined by two different methods: direct (using a HS-based

routine previously developed within the research team37

) and indirect (using HS, ECG and

LVET). PAT, in its turn, was defined in three distinct modes, ranging from ECG’s R-peak and

different points along the peripheral PW (which is assessed by the PPG signal). Finally, PTT was

both defined accordingly to the classic approach (as the difference between the determined

37

Adaptive Computation Group, part of the Centre for Informatics and Systems of the University of

Coimbra (CISUC).

58

PATs and PEPs) and an innovative approach. With the exception of innovative PTT, all the time

intervals were referenced to ECG’s R-peak.

One also worked with a second database, supplied by Philips Research, whose analysis

was quite similar, with the main exception of PEP being determined from ICG.

3.2 | CLINICAL TRIALS

3.2.1 | Externally Provided Data

The data sets provided by Philips Research Laboratories Europe (Aachen, Germany)

constituted the starting point in this study.

Each file (54 in total) contained non-clinical, individual data recorded for a period of

approximately 17 minutes38

.

Moreover, data files were divided into three categories according to the adopted

protocol, specifically designed for inducing alterations in the cardiovascular dynamics – and,

consequently, also in BP and in the systolic/vascular time intervals. Such protocols assumed: a)

ergometric exercising; b) Valsalva’s manoeuvre39

performing; c) postural changing.

Among the several available cardio-thoracic signals and parameters, the suitable for

further analysis were:

� ECG and PPG, recorded at a sample rate (SR) of 200 Hz with a NICCOMO patient

monitor (Medis®, Germany). These signals had been temporally synchronized (Fig. 1).

� PEP, obtained with the equipment mentioned above, at 1 Hz, which signifies that one

disposed of less than a measurement per cardiac cycle. Also, each PEP sample was temporally

referenced to the beginning of the data recording (Fig. 1).

Moreover, the NICCOMO-implemented algorithmic routines involved in PEP

computation were not known, and still, the results were rounded to multiples of 5 – hence the

step-shaped contour of its plot (Fig 2).

38

One will colloquially be using the term “acquisition” to refer to a single data file. 39

The execution of the Valsalva’s manoeuvre implies holding breath for some moments, keeping

abdominal and pectoral muscles contacted. Consequently, the intra-thoracic pressure increases, leading

to a rising in BP.

59

408 409 410 411 412 413 414 415 416 417

1

2

3

4

5

6

7

x 104

Time (s)

ICG signal wasn’t took into account40

whereas the algorithms which were been

developed at the time (by the research team) weren’t foreseeing reliable/stable results. On

the other hand, as pointed in section 2, ICG doesn’t provide a precise detection of the onset of

the AOV movements.

� SBP and DBP, determined by oscillometric methods, with Intellivue MP50 patient

monitor (Philips®, Germany). Only 4, 5 or 6 samples were available per acquisition, which

means that these were spaced minutes away from each other (Fig. 2).

Given the reduced number of BP measurements performed per acquisition, one readily

concludes about the non-feasibility of any proper intra-subject analysis involving SBP or DBP.

On the other hand, the uncertainty towards PEP values, while definitely undesirable in a study

of this nature, accented the need to own a different database.

Fig. 1. ECG (red) and PPG (blue) signals (for the ergometric exercise protocol).

Cyan lines signalize PEP measurements.

40

To remember that PEP can be determined from ICG, since the analysis of the latter allows the

detection of AOV opening and closure times.

60

0 100 200 300 400 500 600 700 800 900

50

100

150

200

250

300

350

400

Fig. 2. HR (red) and PEP (blue) samples (ergonometric exercise) (to note their negative relation).

Magenta lines signalize the available DBP and SBP measurements (took at the same time).

3.2.2 | In-house Acquired Data

It was intended to collect an appreciable number of BP measurements: the closest

possible to the beat-by-beat basis. Plus, it would be necessary to impose changes in the

cardiovascular dynamics in order to obtain changes in BP (and eventually on the various time-

intervals under analysis).

i. Experimental Protocol

Keeping previous requirements in mind, one defined a protocol based in several (twelve

or more) data acquisitions per subject, at different levels of physical stress.

At this point, it is highly recommended to consult Annex I (as well as Fig.3), which

reveals a complete description on the defined experimental protocol. It’s important to reassert

that the described procedures weren’t performed in any controlled conditions nor counted on

any clinical supervision.

Originally one also intended to study the eventual impact of adopting a specific corporal

posture on the relation of BP with the time intervals under analysis. One even came to

elaborate and test a quit more complex and tardy experimental protocol, which aimed to

record data at three different body postures: supine, standing upright and sitting up. However,

such procedures proved to be impracticable, mainly due to hardware limitations and to the

Time (s)

61

complexity of execution itself (the stress level progressively fading away as one was getting

ready to acquire).

ii. Subjects

Seven healthy subjects (three females, four males) were submitted to the established

protocol.

One of the subjects assumed to have gone through one cardiac incident in the past,

while four affirmed to practise physical exercise with regularity. An approximation to the

length of the arterial path comprised from the aortic cross to finger capillaries was also

measured (corresponding to the parameter L in sub-section 2.4.1.2). Table 1 displays this and

other biometric parameters relative to the group of subjects.

Age

BMI

L

29.4 ± 6.0 years old 25.0 ± 3.0 Kg m-2

97.3 ± 3.6 cm

Table 1. Biometric parameters of the population (mean ± SD).

.

iii. Acquired Data

� PPG and ECG

These signals were acquired at 500 and 125 Hz respectively (the disparity being justified

by the higher complexity of the electrocardiographic contour).

The pair of signals was acquired with S54 M1165A patient monitor (Hewlett Packard,

USA). In the origin of the preference for such relatively old equipment is a more trustful

temporal synchronization between the various data channels, when compared to that of

newer models.

A software application developed within the research group, Vital, was utilized as the

interface to transmit data to a personal computer and to later export each channel as a csv file

(Fig. 3). As one never interrupted the acquisition of these signals, the exported data refer to

the integrity of the protocol (totalizing around 30-40 minutes).

62

3.5 4 4.5 5 5.5 6 6.5

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Time (s)

� SBP and DBP

The measurements were also acquired with S54 M1165A® patient monitor, which

integrated oscillometric equipment.

Unfortunately it wasn’t possible to perform continuous BP measurements due to the

lack of adequate instrumentation – as specified in Annex I, the best approach one could

achieve was to take one BP measurement per each short recording period (20 seconds).

� HS and ECG

HS and ECG signals were acquired with The Meditron Stethoscope System (Meditron,

USA), both at 44100 Hz.

The data from both channels was logged in the computer and further exported by

means of a software interface developed by the manufacturer, as wav files (Fig. 4). With the

intention of minimizing noise interferences, the recording was manually started as soon as the

cuff filling process (of the oscillometric device) stopped.

On a parallel note, one chose to use HS instead of ICG; it was originally intended to use

the later signal to determine AOV opening and closing times. However, the equipment wasn’t

available at the time.

Fig. 3. ECG (red) and PPG (blue), acquired with the patient monitor.

63

2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Time (s)

Fig. 4. ECG (red) and HS (blue), acquired with the stethoscope system.

3.3 | DATA MANIPULATION: THE ALGORITHMIC IMPLEMENTATIONS

3.3.1 | Preliminary Operations

Current sub-section focuses on the processes required to leave the newly-acquired data

ready to use in further operations. It is, therefore, dedicated to own database.

So, after putting the experimental protocol into practice, one had, for each subject: a) two

csv lengthy files acquired with the patient monitor, one with PPG data and another with ECG data

(labelled as mECG from now on); b) twelve41

brief wav files acquired with the stethoscope with

two data channels, HS and ECG (labelled as sECG).

3.3.1.1. Synchronizing Operations

First and foremost, it was essential to align the signals obtained with each acquisition

system42

- or, in other words, PPG and HS had to be temporally synchronized. ECG signals are

fundamental since they serve as elements of connection between the two used acquisition

systems.

41

Or a few more, in the case of some subjects. 42

One shall emphasize that the signals acquired by the each system are already synchronized.

64

2800 3000 3200 3400 3600 3800 4000

-0.2

0

0.2

0.4

0.6

0.8

To accomplish such operation, one made use of pre-existent routines within the research

group. These considered two ECG segments, one of which being clearly (temporally) lengthier –

mECG in this case.

The first step was to segment each ECG signal.

The utilized segmentation algorithms (also previously developed by the research team)

were based in the Pan-Tompkins algorithm [43], in conjunction with the multi-

scale morphological derivative method. They were capable of identifying Q, R and S waves,

after applying an adequate pre-processing (Fig. 5).

For synchronization effects, the referential features were the R-peaks (or, more

precisely, the RR intervals), given the higher accuracy rates of their detection (Fig. 6).

Then, as the shorter segment (that is, sECG) was sliding along the other, the mean square

error established between the positions of the R-peaks of each signal was being computed.

Once probed the entirety of the lengthier signal, the pairing sECG-mECG in which the error

was smaller was assumed to refer to the “same” portion of the signal, i.e., contemporaneously

acquired.

Fig. 5. Original (red) and pre-processed (blue) mECG. The horizontal axis refers samples.

Pre-processing consisted of noise suppression, elimination of the drift-line and normalization.

65

-5 0 5 10 15 20 25 30

-0.5

0

0.5

Time (s)

2500 3000 3500 4000 4500 5000 5500 6000 6500

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Fig. 6. Detection of R-peaks in mECG (indicated by the blue spots).

The final product consisted, per wav file, in a cell array containing all the unaltered four

signals – with changes in the temporal indexes associated with each sample of the monitor

signals. Being so, once the matching pair was determined, the correspondent PPG/mECG

indexes started counting from zero, what permitted to situate the 20 seconds segment along

them (Fig. 7).

Fig. 7. Matching of one sECG (brown) with the mECG (blue).

As one can see, the R-peaks of both appear properly aligned.

66

5.5 6 6.5 7 7.5

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Time (s)

3.3.1.2. Data Storage

Following synchronization, for a single subject one loaded the output files and extracted the

portion of interest from each (that is, 20 seconds of synchronized PPG, HS, mECG and also sECG;

see Fig. 8).

Finally, one exported it to a new data structure (that also contained the respective SBP and

DBP measurements pair). This way, one obtained (at least) twelve data files per subject.

The described process was applied to each subject.

Fig. 8. Synchronized ECG (red), PPG (blue) and HS (green) signals (sECG and mECG showed a very similar plot).

Note that the two components of S1 (distinct in amplitude and frequency) are clearly noticeable.

Note that the time coupling between the three signals is physiologically correct (compare with Fig. 21 of Chapter 2).

3.3.2 | Approaching Vascular and Systolic Time Intervals

In the current chapter one details and clarifies the strategies behind the determination of

PEP, PAT and PTT, which must be computed in parallel per heart cycle for a valid analysis. The

synchronization of ECG, PPG and HS signals reveals, thus, as being fundamental to the credence of

the following approaches.

One opted for not treating in-house acquired and Philips-provided data bases in

separate sub-sections inasmuch as the essence of the analysis was very similar.

67

One chose to compute the various time intervals with reference to the R-peaks of the

respective heart cycles. Nevertheless, Q waves integrate the actual clinical conventions and

are often adopted as the reference in the definition and computation of PTT, PAT and systolic

time intervals.

One’s preference towards the R peaks was based in the higher accuracy on their

detection when compared to any other ECG component. On the other hand, as previously

discussed in 2.1.2.1, some instants are still separating the beginning of myocardial

depolarization and the actual contraction of these cells. Accordingly, the fact remains that

settling R-peaks as the starting reference will eliminate some of the excessive time otherwise

introduced by Q waves.

3.3.2.1 PRE-EJECTION PERIOD

As previously discussed, unlike PTT and PAT, PEP and LVET are bordered by well defined

events, also able to be determined in practical/experimental terms by different methods.

A. From Heart Sound and Electrocardiography

The HS-ECG approach consisted in a direct method for determining PEP (labelled as

PEP.HS from now on), since one made use of pre-existent algorithms43

(from now on referred

to as HS toolbox for simplicity’s sake), which were able of return the value of this systolic time

interval per heart beat (in milliseconds). One had to introduce some minor alterations, like

setting R-peaks as the timing reference instead of Q waves.

Furthermore, ever since S2 wasn’t detected or the value achieved for PEP was too

deviated from the expected44

, the respective cardiac cycle was considered unvalued. There

was information available, thus, only for valid cycles.

43

The referred algorithms were addressed in sub-section 2.4.4.2.C ([65]). 44

One recalls that the algorithm compared the computed value for PEP with the “typical time intervals

between AV closing and AOV opening”.

68

B. From Photoplethysmography, Heart Sound and Electrocardiography

In its turn, PPG-HS-ECG approach proposed an indirect method for determining

alternative PEP values per heart cycle. The strategy was about to explore the concepts of PEP

and LVET accordingly to AOV movements.

Being so, PEP was defined, per cardiac cycle, as the time interval comprehended from

the R-peak to AOV opening. LVET, in its turn, was defined from AOV opening to AOV closure.

On the other side, as [51] proposed, LVET could be directly derived from PPG. For that

purpose, algorithms were being developed at the time within the research group (referred to

as PPG toolbox).

That said the premise was that the value of PEP could be calculated as the difference

between the time of closure of AOV and the time of the correspondent R-peak once

subtracted the value of LVET. So, given a heart beat, one established that

PEP.PPG � [time �AOV closing� – time �R peak�]*1000 – LVET �9�,

where events are measured in seconds and LVET, in milliseconds.

Further detailing on the steps involved in PEP.PPG calculation follow up:

i. Calculation of AOV closing times

One made use of the already mentioned HS toolbox, which was able to detach AOV

opening and closing times45

.

Moreover, it is important to keep in mind the transitory nature of AOV movements,

which are dynamic processes that last for some moments – rather than a mere instant.

Although HS toolbox achieved to isolate both the beginning and ending times of each AOV

movement, one solely considered the former to proceed with this study (Fig. 9).

45

By AOV opening/closing times (or simply AOV closing), one mean absolute time i.e. counted from the

very beginning of the acquisition.

69

3.1 3.15 3.2 3.25 3.3

x 105

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6

x 105

-0.6

-0.4

-0.2

0

0.2

0.4

Fig.9. On the top: Detection of the onsets of AOV opening (green) and closing (red). At bottom: In more detail.

Magenta lines are signalizing the R-peaks. The horizontal axis is in sample units.

To remark that the AOV opening wasn’t obtained directly from the HS (unlike it happens with AOV closing), but

rather from PEP.HS itself, which is calculated before.

ii. Selection of the valid heart beats

In a comparative analysis it only makes sense to have both PEP.HS and PEP.PPG values

per cycle. It was necessary, thus, to know in which PPG cycles46

PEP.HS was available. Since

LVET was going to be derived solely from PPG, one still had to distinguish the cycles

corresponding to the valid R-peaks.

PPG toolbox was also of use for such purpose. One of the output items was a vector

containing the sampling index of various fiduciary points localized per cycle, along the entire

46

By a PPG cycle one is meaning the portion of PPG signal comprehended between two R-peaks.

70

PPG signal. One chose the point marked near the foot, that is, the nearest possible to the

respective (implying precedent) R-peak. Then, one selected the index of the chosen fiduciary

point which was the closest located to each valid R-peak time.

At this point, one had indications on which PPG cycles LVET was supposed to be

calculated.

iii. Calculation of the intervals between R-peak and AOV closure

R peaks were detected according to the segmentation routines addressed in 3.3.1.1.

Furthermore, it only remained to subtract it only remained to subtract the times of the

valid R-peaks from the AOV closure times.

iv. Determination of LVET

Per valid cycle, LVET was determined directly using PPG toolbox.

C. From Impedance Cardiography

ICG approach was the only applicable to the data provided by Philips.

As was clarified in 3.2.1, one had less than a PEP value per cardiac cycle and disposed of

a very small set of BP samples.

Given such circumstances, the adopted solution simply consisted in getting the

temporally closest PEP measurement to each BP sample (let it be labelled as PEP.IGC).

3.3.2.2 PULSE ARRIVAL TIME

A. From Photoplethysmography and Electrocardiography

This approach was applied to both databases.

Per heart cycle, one defined PAT in three different ways (Fig. 10); as comprehended

between the R-peak and: a) the peak of PPG (PATmax); b) the point at which PPG reaches 75%

of its maximum amplitude47

(PAT75); c) the foot of PPG (PATmin).

47

To note that in the Literature the ending reference usually goes to 70-90% of the maximum PPG

amplitude.

71

Fig. 10. Schematic representation of PATmax, PAT75 and PATmin.

i. Determination of PATmax and PATmin

One had to determine the indexes of both the peak and the foot of the PPG segment

established between two consecutive R-peaks: a valid one and its subsequent.

Nevertheless, for simplicity’s sake, one limited the segment to the portion defined

between valid R-peaks and their respective chosen fiduciary point (one picked the point placed

right before the DN). This way, it was necessary, first, to determine the fiduciary point

corresponding to each valid R-peak (Fig. 10). One made sure to be locating the right point,

immediately after each valid R-peak (in terms of samples).

Whereas the signal didn’t exhibit major sudden artefacts (given its relative stability and

applied pre-processing48

) the easiest way to accomplish the aimed was to directly get the

maximum and minimum values, which are accompanied by their respective indexes49

.

In the performed tests it was verified that the indexes of the peaks and foots of the PPG

were being correctly settled and in the intended cycle (Fig. 11).

48

Normalization, low-pass filtering (with a cutoff frequency of 125 Hz) and base-line removal. 49

That is, using max and min functions included in Matlab®. To underline that the considered indexes

are counted from the R-peak – they’re, thus, not absolute, counted from the beginning.

72

900 1000 1100 1200 1300 1400 1500 1600 1700

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

150 200 250 300 350 400 450 500 550 600 650-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Fig. 10. Segmentation of PPG. The red lines mark the R-peaks and the spot, the selected fiduciary points.

Horizontal axis reads in samples.

ii. Determination of PAT75

One obtained the index (counted from R-peak as before) of the closest PPG sample to ¾

of the difference between the amplitudes of peak and the foot.

Fig. 11. Detection of peak (red spot), foot (green spot) and point at 75% of the maximum amplitude

(magenta spot) per PPG segment. The horizontal axis refers to samples.

73

3.3.2.3 PULSE TRANSIT TIME

A. From Pre-Ejection Period and Pulse Arrival Time

The current approach relies on the differential (classical) definition of PTT.

At this point, one was able to establish various distinct combinations of PEPs and PATs in

order to design distinct PTTs.

Being so, for the in-house acquired data one was able to propose six distinct equations

describing PTT, and three other ones for Philips data, which are collected in Table 2.

Table 2. Different equations for PTT. One tried to use the most adequate/suggestive nomenclatures possible.

B. From Photoplethysmography and Heart Sound

This approach represents an innovation in the practical concept of PTT, which is

currently being investigated by the research group.

As previously addressed (in section 2.2.2), the closure of the AOV is distinguishable on

the contour of the PW50

, being flagged by the DN. Being so, the premise is that one could use

AOV closure as a tracer of a complete transit of the PW, which is established from the very

beginning of aorta artery to the peripheral arteries. Thus, PTT would be determined, per cycle,

as the time interval elapsed from AOV closure and the DN, according to

PTT.DN � [ time �DN� – time �AOV closing� ] �10�.

50

Don’t forget that PPG assesses peripheral PW.

PATmax PAT75 PATmin

IN-HOUSE ACQUIRED DATA

PEP.HS PTT.HSmax = PATmax – PEP.HS PT.HS75 = PAT75 – PEP.HS PTT.HSmin = PATmin – PEP.HS

PEP.PPG PTT.PPGmax = PATmax – PEP.PPG PTT.PPG75 = PAT75 – PEP.PPG PTT.PPGmin = PATmin – PEP.PPG

PHILIPS DATA

PEP.ICG PTT.ICGmax = PATmax – PEP.ICG PTT.ICG75 = PAT75 – PEP.ICG PTT.ICGmin = PATmin – PEP.ICG

74

At this point, one highlights that the position of the DN on the PW isn’t influenced by HR

variations [9].

AOV closing times were obtained with HS toolbox while DN approximate times could be

obtained with the PPG toolbox.

3.3.3 | Blood Pressure Surrogates

One’s purpose was to compare experimentally measured and theoretically estimated

values of BP. The evaluation of the relationship between these was made by means of three

statistical tools: mutual information, correlation coefficient and prediction error.

3.3.3.1. Pairing up Blood Pressure and Time Intervals

A. Philips Data

As previously pointed out, one disposed of very little BP measurements per acquisition.

In order to obtain an admissible quantity of data, one agglomerated various subjects in

the same analysis. Accordingly, for each experimental protocol one were able to count on

around 90 sets composed of SBP/DBP and PEP.ICG, PATmax, PATmin, PAT75, PTT.ICGmax,

PTT.ICGmin and PTT.ICG75 samples.

B. In-house Acquired Data

As anteriorly clarified, one carried out a single BP measurement during the 20 seconds

that each data recording took. As the result, one disposed of a single BP sample for several

(clearly more than 20) heart beats.

It was necessary, thereafter, to perform a sifting operation, other than simply

considering the average beat, which represented the coarser solution in terms of accuracy.

This stage of work proved to be the most challenging.

75

The ideal would be to isolate the exact heart beat corresponding to the measurement of

SBP and DBP51

.

One attempted to get the closest possible to such approach.

Initially, it was intended to perform a series of practical timed tests in order to enquire

how long the equipment took to return the result of a BP measurement with reference to the

beginning of air deflation (the occasion in which one started the data recording). Nevertheless,

along with other problems52

, by the time one wanted to put the described idea into practice,

the equipment was no longer available to use53

.

Under such circumstances, the most reasonable/feasible, less complex alternative was

to find a zone of cardiac stability along the 20 seconds of acquisition; the premise was

grounded in the constancy of the correspondent time intervals so that one could average and

pair them up with the BP measurement with alleged less loss of information.

The chosen indicator was HR variability54

. One implemented a window function with

(manually) adjustable radius, able to slide through the HR signal (that is, HR value per beat,

determined from R-peaks times). Ever since the difference between the maximum and

minimum values covered by the window was equal or inferior to 5 beats per minute (one of

the input parameters), a “stable zone” was identified. Finally, one calculated the mean of the

time intervals correspondent to the stable zone (same applied to a mean value of HR).

Moreover, one still performed a series of practical tests with another oscillometric

device in order to confine where to search for HR stability if necessary. Since all the timed

values were above 20 seconds, one expressed preference for the final part of the HR signal in

case more than one zone was detected.

At the end, per subject one gathered at least twelve pairs of SBP/DBP and PEP.HS,

PEP.PPG, PATmax, PATmin, PAT75, PTT.HSmax, PTT.PPGmax, PTT.HS75, PTT.PPG75, PTT.HSmin,

PTT.PPGmin as well as PTT.DN samples (that is, one per 20-second acquisition).

51

As left clear in 2.3.2.4, SBP and DBP are actually assessed in distinct moments, presumably in distinct

heart beats. 52

The determined time interval would be, however, overvalued, due to a whole set of machine-related

processes posthumous to sensor reading, such as algorithmic calculations, exportation and display on

the screen, which one named by latency period. On another note, one would have to check time

“manually”. Finally, the (total) interval in question would depend on the BP value itself (and eventually

on the subject as well). 53

The arm cuff and respective connective cables had been transferred to a hospital in another city. 54

Pulmonary ventilation was another possibility, discernible from specific fluctuations of the base-line of

the ECG. Such approach was, however, quite more complex (and slow).

76

3.3.3.2. Model Validity: Tools for an Evaluation

A. Mutual Information

i. Concept

Mutual Information is a statistical operation able to evaluate the degree of inter-

dependence of two variables. It doesn’t give preference to any specific tendency of relation.

For two discrete random variables X and Y composed of the same number of elements,

Mutual Information equation assumes the form

FG�H; J� � K K��L, M� log � ��L, M��L�. ��M��NOPQOR �11�,

in which P(x, y) is the joint probability distribution function of X and Y, while P(x) and P(y) refer

to the probability distribution functions of X and Y respectively. The closer the result gets to

zero, the less dependent Y is on X.

ii. Implementation and data analysis

One developed a function to compute the mutual information given a pair of vectors.

The probability P(x=xi) was calculated as the ratio between the number of times the

value xi appeared in vector X and the total number of elements included in the later (same

applied to P(y=yi)).

Moreover, one built the joint histogram for the elements of both X and Y (that is, a 2x2

matrix) so that the joint probabilities P(x=xi, y=yi) could be calculated as the ratio between the

entry (xi, yi) and the size of X (or of Y)55

.

The Mutual Information was calculated between SBP/DBP and the time the determined

PTTs, PATs and PEPs.

B. Correlation Coefficient

i. Concept

The correlation coefficient of two variables evaluates the intensity of the linear

relationship between them. Its absolute value varies between 0 and 1, indicating non-existent

55

For more reasonable results, the elements of the two vectors were previously rounded to the unit.

77

or plenary linearity respectively. Moreover, a negative correlation suggests a negative/indirect

relationship, while a positive one denounces a positive/direct relationship.


One resorted to Matlab®’s corrcoef function.

Given the concept of correlation, the independent variable (BP) must enable a linear

relationship with the dependent variable (a time interval). Given the general form of the

Möens-Korteweg derived functions,

BP = A f(time interval) + B �12�,

one can define the adequate parameters to the provide the function with. Being so,

there is a linear relationship between BP and log(time interval) in the case of the logarithmic

model (equation (4) of Chapter 2). Analogously, the quadratic model (equation (5) of the same

chapter) establishes linearity between BP and (time interval)-2.

This way, one calculated the correlation coefficient between SBP/DBP and both the

logarithm and inverse of all the determined time intervals.

C. Mean Squared Prediction Error

i. Concept

Mean squared prediction error (MSPE) of an estimator is statistical tool capable of

evaluating the deviation relatively to the true value of the quantity being estimated. For a

variable Y composed of n samples, one has

FS��J� � 1" K[ T MUVW MXT& ]YXZ[

�13�,

where MX represent the estimated values of Y, and M\X, the true/expected values.


The developed routine selected 90% of the samples of input vectors at random, which

were used to calculate the constants A and B of equations (6) or (7) of Chapter 2. In other

words, these 90% served to establish the predictive model, which was applied to the initially

excluded BP samples (10%) in order to calculate the estimated BP values. Afterwards one

78

computed the prediction error as the difference between each pair of estimated and expected

BP values. The described procedure was executed for ten times in total, being the final MSPE

the average of the values achieved in each iteration.

Similarly to correlation, MSPE assumes a linear relationship (Table 4). One calculated the

MSPE between SBP/DBP and both the logarithm and inverse of all the determined time

intervals.

Table 4. Systematization of the adequate parameters to use in each statistical approach.

CONCLUSION

One established a system of functions that received synchronized data files and

returned the value of PEPs, PATs and PTTs calculated in different ways as well as a statistical

analysis on the validation of BP assessed values.

For that purpose, in first place one needed to hold an appreciable number of pairs of

measured BP and each of the determined time intervals. One had access to two databases –

own-acquired and Philips-provided.

BP = A f(TIME INTERVAL) + B

f = TIME INTERVAL f = log(TIME INTERVAL) f = 1/(TIME INTERVAL)2

Mutual Information ��

Correlation Coefficient � ��

MSPE � ��

79

50

100

150

HR

(bp

m)

Subject 03

-100

0

100

PE

Ps

(ms)

PEP.HS

PEP.PPG

0

100

200

300

400

PA

Ts

(ms)

PATmax

PAT75

PATmin

0 2 4 6 8 10

0

100

200

300

400

PT

Ts

(ms)

samples

PTT.HSmax

PTT.PPGmax

PTT.HSmin

PTT.PPGmin

PTT.HS75

PTT.PPG75

PTT.DN

FOURTH CH APTER

RESULTS AND DISCUSSION

4.1 | IN-HOUSE ACQUIRED DATA

4.1.1 | Systolic and Vascular Time Intervals Determination

Figs. 1 and 2 expose the several time intervals determined for two of the tested

subjects. At this point one shall emphasize that each sample corresponds to the value obtained

per acquisition, which implies that results are at least separated by a period of 20 seconds56

from each other.

Fig. 1. Time intervals of a healthy 41 years old male who regularly performed sports.

Each sample refers to a 20 seconds data recording.

56

One remembers that after each sequence of four 20-seconds acquisitions there was a new assault of

physical activity, which lasted not less than 10 minutes.

80

20

40

60

80

HR

(bp

m)

Subject 04

0

50

100P

EP

s (m

s)

PEP.HS

PEP.PPG

0

200

400

PA

Ts

(ms)

PATmax

PAT75

PATmin

0 2 4 6 8 10

-100

0

100

200

300

400

PT

Ts

(ms)

samples

PTT.HSmax

PTT.PPGmax

PTT.HSmin

PTT.PPGmin

PTT.HS75

PTT.PPG75

PTT.DN

-50

0

50

100

PE

P (

ms)

PEP.HS

PEP.PPG

100

200

300

400

PA

Ts

(ms)

PATmin

PAT75

PATmax

1 2 3 4 5 6 7

0

100

200

300

400

500

subjects

PT

Ts

(ms)

PTT.HSmax

PTT.HS75

PTT.HSmin

PTT.PPGmax

PTT.PPG75

PTT.PPGmin

PTT.DN'Location

Fig. 2. Time intervals of a healthy 29 years old male.

Fig. 3. Mean values of PEPs, PATs and PTTs calculated for each subject.

81

While not always evident, there are hints on the negative influence of HR on the

determined time intervals, as expected. On the other side, in general, one identifies some

extent of a relationship – linearity, one means – between the obtained time intervals,

especially PATs and PEPs. Following conjectures are organized by type of time interval.

i. PEP analysis

In spite of distinctly determined, the two PEPs suggest variations in the same direction

(correlations up to 0.79 per subject). However, in general, PEP.HS is evidently more stable

(presenting less variance) than PEP.PPG.

Moreover, the values of PEP.HS, in spite of higher than the reported in other studies

[37], belong to a concordant range of values. The same cannot be stated concerning PEP.PPG,

whose values do not have a physiological meaning to them, since they are predominantly too

low – or even negative.

In order to get some directions on the origin of such unacceptable results, one also

applied the algorithms to a database containing PEP values directly extracted from the analysis

of echocardiographic exams (referred to as PEP.ECHO from now on), as [65]described. For one

of the subjects, PEP.PPG was surprisingly close to PEP.ECHO and to PEP.HS (consult Annex II,

Table I), while for the remaining three the discrepancy persisted (the mean difference between

PEP.ECHO and PEP.PPG was 41.32 ± 18.75 milliseconds).

Being so, the hypothesis of the influence of the quality and nature of the signals and

respective recording circumstances was discharged (the signals of this third database were

recorded at the resting condition and for the supine position).

One started to believe that the origin of such unexpected PEP.PPG values would lie in

the overestimation of the respective LVET values. In fact, one observed, for subjects of the

own acquired database, that LVET values were consistently larger than those obtained by HS

analysis57

: 305.34 ± 4.64 milliseconds against 245.62 ± 30.68 milliseconds (respectively), for

two of the tested subjects.

Furthermore, while keeping in mind that LVET decreases 1.2 milliseconds58

with the

unitary HR increase [72], one calculated LVET values corrected to the average HR relative to

the own database (80 bpm) and performed the same operation with the LVET values obtained

from HS. For two subjects, the major drift between obtained and corrected values (which was

57

As explained in 2.4.4.3., such LVET values were also obtainable from the addressed HS toolbox; it’s the

LVET (HS) of Table 3 of Chapter 2. It was calculated as from PEP.HS (to determine AOV opening time)

and high frequency signature of S2 (AOV closing time) [65]. 58

For males the decreasing consists, however, in 1.1 milliseconds.

82

not very pronounced, though) was verified, in fact, with the one’s LVET (overestimated in

30.29 ± 7.5 milliseconds, while the LVET calculated from HS was overall underestimated).

Thus, one was led to believe that the reason behind such unviable results for PEP.PPG

related to eventual algorithmic mismatches and/or to the phenomenon of propagation of

errors.

In what concerns to the later, one has that the expected value of a transformation of a

random variable consists in the linear combination of the partial expected values, according to

(σ represents the standard deviation)

�]^�L�_ � ^]��L�_ # K`a^�LX�aLX b&YXZ[

. cX& �14�.

The variance associated with f(x) appears, thus, influenced by the number n of xi

elements – the higher the later, the higher the value of the former.

In one’s specific case, the discrepancy of PEP.PPG values can be interpreted as the

summation of the uncertainties towards the determination of the: a) closure of AOV (whose

onset is determined 10.88 milliseconds earlier than by echocardiography [65]; b) LVET (20

milliseconds); c) R-peak.

Plausible ways of overcoming such problem would include the

optimization/improvement of the algorithms, either by minimizing the error associated to the

determination of LVET or by introducing eventual compensations to cancel the summation of

errors. One didn’t have the chance to act accordingly due to deadline issues.

ii. PAT analysis

The set of determined PATs exhibit clear linearity relatively to each other (correlations

up to 0.98), which was expectable given the stability of the recorded photoplethysmographic

signal.

Furthermore, the values of PATmin accord better with those reported in the Literature

[37] comparatively to PATmax and PAT75, which overestimate them, the same verified for the

PTTs computed as from these later intervals. Such observations guide towards considering the

immediacies of the foot of the PPG as the arrival site of the PW to the periphery for a more

accurate approach.

Such hypothesis has, in fact, a physiological foundation to it, since the slope of the

dominant peak of the PW is defined by factors that also exert influence on PEP itself, namely

83

the left ventricular contractility (as addressed in 2.4.4.1); the higher the later, the higher this

systolic time interval. Being so, using the immediacies of the peak of the PPG curve might

introduce some redundancy in the computing of a PATs and PTTs of differential nature.

iii. PTT analysis

Differential PTTs show variations according to those verified for PAT. In what concerns

to PTT.DN, for some of the subjects it presents a degree of variability similar to the differential

PTTs (Fig. 1) while for others it was clearly more stable (Fig. 2).

PTTs determined from PATmax and PAT75 appear as very highly estimated, condition

aggravated for PTTs computed from PEP.PPG (given the occasional negative values of the

later). Moreover, some of the PTTmin values are too low (as in the examples shown in this

discussion), but in general they fall in the range 70-200 milliseconds, agreeing with some

studies [37].

At this point, one is led towards to rely more on PTT.HSmin and eventually PTT.DN.

Regarding a validation core for PTT, the problem is that absolute references do not exist,

as pointed out in Chapter 2. In an attempt of settling a comparability pool, one applied, once

again, the algorithms to the database containing echocardiographic data and calculated three

differential PTTs by subtracting PEP.ECHO from the respective PPG’s foot, peak, and 75% of the

peak. PTT.DN, in spite of independent from PEP values, was also calculated. Some of the

results are displayed in Table 2 of Annex II, which, however, were not conclusive given the

discrepancy relatively to the expected values and dramatic variability. Extended, more careful

analysis would be required and certainly very useful regarding the establishment of reference

values for PTT.

4.1.2 | Time Intervals and Blood Pressure Surrogates

Figs. 4-8 and 9-13 allude to the relationship between the BP estimated from the

determined time intervals and the expected/measured values, for the systolic and diastolic

cases respectively (the reader might want to consult Tables 1-6 of Annex III).

84

2,73 2,85 2,95 3,07 2,89 3,01 3,05 2,94 2,93 3,03 3,03 3,02

0,00

0,50

1,00

1,50

2,00

2,50

3,00

3,50

4,00

-0,34 -0,41 -0,02 -0,21 -0,24 -0,20 -0,17 -0,01 -0,07 -0,03

0,130,06

-1,00

-0,80

-0,60

-0,40

-0,20

0,00

0,20

0,40

Fig. 5. Bars diagram for Correlation Coefficient (SBP, log (Time Intervals)).

i. Systolic Blood Pressure

Fig. 4. Bars diagram expressing the Mutual Information values for SBP and Time Intervals, for the seven tested

subjects (presented in the body of the bars). In blue, the error bars feature the respective standard deviations.

85

0,36

0,11

0,00

0,16 0,18 0,15 0,18

-0,030,04

0,02

-0,10 -0,08

-0,60

-0,40

-0,20

0,00

0,20

0,40

0,60

0,80Correlation Coefficient (SBP, (TI)-2)

121,09 98,51 121,83

225,12 185,60 211,84179,33

128,44

133,84 213,55

92,08

108,94

-200,00

-100,00

0,00

100,00

200,00

300,00

400,00

500,00

600,00

0,36

0,11

0,00

0,16 0,18 0,15 0,18

-0,030,04

0,02

-0,10 -0,08

-0,60

-0,40

-0,20

0,00

0,20

0,40

0,60

0,80Correlation Coefficient (SBP, (TI)-2)

124,83 128,27 2432,65

129261,47

990003,54

134266,16

796,01 224,56 299,10 130,17 132,10 575,17

0,00

500000,00

1000000,00

1500000,00

2000000,00

2500000,00

3000000,00

3500000,00

4000000,00

0,36

0,11

0,00

0,16 0,18 0,15 0,18

-0,030,04

0,02

-0,10 -0,08

-0,60

-0,40

-0,20

0,00

0,20

0,40

0,60

0,80

Fig. 6. Bars diagram for Correlation Coefficient (SBP, (Time Intervals)-2

).

Fig. 7. Bars diagram for MSPE (SBP, log (Time Intervals)) (in milliseconds).

Fig. 8. Bars diagram for MSPE (SBP, ((Time Intervals)-2

) (in milliseconds).

86

2,73 2,81 2,90 3,07 2,91 2,99 3,01 2,96 2,89 3,01 2,98 2,96

0,00

0,50

1,00

1,50

2,00

2,50

3,00

3,50

4,00

0,12

-0,01

0,140,06 0,07 0,07 0,05 0,07

0,120,10

0,14

0,04

-0,50

-0,40

-0,30

-0,20

-0,10

0,00

0,10

0,20

0,30

0,40

-0,110,04

-0,12 -0,02 -0,03 -0,07 -0,010,05

-0,11 -0,10 -0,10 -0,08

-0,60

-0,50

-0,40

-0,30

-0,20

-0,10

0,00

0,10

0,20

0,30

0,40

0,50

i. Diastolic Blood Pressure

Fig. 9. Bars diagram for Mutual Information (DBP, Time Intervals).

Fig. 10. Bars diagram for Correlation Coefficient (DBP, log (Time Intervals)).

Fig. 11. Bars diagram for Correlation Coefficient (DBP, (Time Intervals)-2

).

87

51,99 46,17 2773,44

181158,17

1017828,46

115,23 105,20 63,83 109,60 42,56 49,20 61,45

-2000000,00

-1000000,00

0,00

1000000,00

2000000,00

3000000,00

4000000,00

42,19 29,92 49,0851,64

100,69

72,27 73,67

45,47

68,9756,59

44,48 36,44

-100,00

-50,00

0,00

50,00

100,00

150,00

200,00

250,00

300,00

Fig. 12. Bars diagram for MSPE (DBP, log (Time Intervals)) (in milliseconds).

Fig. 13. Bars diagram for MSPE (DBP, (Time Intervals)-2


Firstly, it’s important to recall that one had to compare estimated systemic (i.e., relative

to the path comprehended from aorta to finger arteries) with expected local BP values,

measured on the brachial artery. Even so, the reliability of the approach is still accredited,

since the losses in BP across the systemic vascular tree are essentially due to the resistance

offered to the blood flow by the aortic artery (implied in the terms R1 and R2 of the Windkessel

conception [Chapter 2]), and one believes both values – estimated and expected – to be

linearly related. This way, as left clear in Chapter 3, one wasn’t trying to relate absolute

quantities, but rather variations of such.

The analysis based in the mutual information provided similar results for all the time

intervals, both for systolic and diastolic cases.

88

Moreover, in general one obtained low correlations – in some cases negative, contrarily

to what one would expect given the direct linear relationship between BP and either the

logarithm or the squared inverse of PTT). The biggest correlations (in absolute and algebraic

value) were achieved for PTT.HSmin and PEP.HS, but also for PEP.PPG and PTT.PPGmin.

Relatively to the later set, it’s still not appropriate to even point towards any direction, since

such values do not make sense of the physiological point of view.

In what concerns to the MSPE analysis, too elevated errors were generally returned

(superior to the full magnitude of the respective time intervals). Nevertheless, it was observed

a tendency of time intervals of maximum nature to exhibit the biggest errors (PATmax in

particular). On the other side, there was a tendency for smallest errors to be verified for

PEP.PPG and PTT.PPGmin, which again, won’t allow one to proceed on any further

considerations.

Finishing this discussion, the conducted statistical evaluation proved inconclusive seeing

that no BP values estimated by the models revealed a consistent or significantly higher

relationship with the expected values for a specific time interval. One were suggested,

however, that time intervals calculated by the PPG-HS-ECG approach and with reference to the

foot of the peripheral PW can indeed be promising.

Ways of getting possible more elucidative results would be to: a) try different

algorithmic approaches (developing and applying other concepts besides the data filtering

based in HR stability); b) test with other statistical (eventually more sophisticated) approaches;

c) get and test higher volumes of more accurate data. At this point, one shall mention the

limitations derived from the process of acquisition prone to abate the reliability/accuracy

while increasing the uncertainty/dispersion of results. This way, one points out the: a)

available few data and number of tested subjects; b) fortuitous incidents (for example, ECG

electrodes taking off from the skin); c) inexperience of the operators (and consequent less

effective pick up of a good HS quality); d) various artefacts inevitably introduced by the

subjects, such as movements of finger and limbs; e) sources of ambient noise (air fans, people

talking and moving around, etc.). Being so, one believes that the interference of noise and

introduction of possible artefacts, which, in conjunction with the scarcity of the available data,

inevitably guided towards some pronounced bias in the results.

Finally, one points out that the simplicity of the protocol and the limitations on the

equipment itself – mere discrete measurements using an arm cuff – contributed to the poor

expression, credence and value of the results.

89

50

100

150

HR

(bp

m)

Ergometric exercise

0

100

200

PEPs

(ms)

PEP.ICG

0

200

400

600

PAT

s (m

s)

PATmax

PAT75

PATmin

10 20 30 40 50 60 70 80 90 100

-100

0

100

200

300

400

500

600

PTTs

(ms)

samples

PTT.ICGmax

PTT.ICG75

PTT.ICGmin

4.2 | PHILIPS DATA

4.2.1 | Systolic and Vascular Time Intervals Determination

Figs. 14, 15 and 16 show the results obtained for a compilation of data samples from

various subjects. It is relevant to remember that, for the same subject, samples are separated

from each other by a lapse of 3 to 4 minutes of duration.

Fig. 14. Time intervals determined for various subjects corresponding to a protocol based on ergometric exercising.

90

4060

80

100

120H

R (bp

m)

Valsalva manoeuvre

50

100

150

PE

Ps

(ms)

PEP.ICG

0

100

200

300

400

500

PAT

s (m

s)

PATmax

PAT75

PATmin

0 10 20 30 40 50 60 70

0

100

200

300

400

PT

Ts

(ms)

samples

PTT.ICGmax

PTT.ICG75

PTT.ICGmin

50

100

150

HR

(bp

m)

Postural change

0

100

200

PEPs

(ms)

PEP.ICG

100

200

300

400

500

PATs

(ms)

PATmax

PAT75

PATmin

10 20 30 40 50 60 70 80 90

-100

0

100

200

300

400

500

PTTs

(ms)

samples

PTT.ICGmax

PTT.ICG75

PTT.ICGmin

Fig.15. Time intervals determined for various subjects for Valsalva manoeuvre.

Fig.16. Time intervals determined for various subjects for a protocol based in postural change.

91

The negative influence of the HR on the different time intervals is evident.

On the other hand, in general, the range in which PEP.ICG values fall is coincident with

the presented by PEP.HS. Also, PEP.ICG presents high variability (as was expectable from an

inter-subject analysis).

PATmin seems to be the best estimator, the same applying to the PTT computed from it

(that is, PTT.ICGmin). Moreover, the introduction of artefacts possibly distorted some of the

results in the computation of PATs (and consequently, of PTTs), more apparent in protocols

which implied body motion (outliers in Figs. 14 and 16). Such motion artefacts affected the

ECG, therefrom resulting erroneous R-peaks detection, which enacted, in its turn, improper

PPG segmentation and maximum/minimum determination.

4.2.2 | Time Intervals and Blood Pressure Surrogates

Figs. 17-21 and 22-26 illustrate the relationship between estimated and expected

SBP/DBP for the three protocols and various subjects (Tables 7-12 in Annex IV).

i. Systolic Blood Pressure

Fig. 17. Bars diagram for Mutual Information (SBP, Time Intervals).

2,89 2,72 2,933,24 3,12 3,14

3,48

0,00

0,50

1,00

1,50

2,00

2,50

3,00

3,50

4,00

PEP.ICG PATmin PAT75 PATmax PTT.ICGmin PTT.ICG75 PTT.ICGmax

92

-0,40 -0,28 -0,27 -0,25 -0,23 -0,25 -0,24

-0,80

-0,70

-0,60

-0,50

-0,40

-0,30

-0,20

-0,10

0,00


Fig. 18. Bars diagram for Correlation Coefficient (SBP, log (Time Intervals)).

0,40 0,24 0,23 0,22 0,20 0,21 0,27

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80


170,00 213,63 194,85 185,77 197,07 204,23 199,94

-200,00

-100,00

0,00

100,00

200,00

300,00

400,00

500,00

600,00


Fig. 20. Bars diagram for MSPE (SBP, log (Time Intervals)) (in milliseconds).

Fig. 19. Bars diagram for Correlation Coefficient (SBP, (Time Intervals)-2

).

93

154,07 266,68 216,45 193,83 397,21 224,57 195,360,00

100,00

200,00

300,00

400,00

500,00

600,00

700,00

800,00


-0,10 -0,16 -0,16 -0,16 -0,12 -0,15 -0,16

-0,35

-0,30

-0,25

-0,20

-0,15

-0,10

-0,05

0,00

0,05

0,10

0,15

0,20


Fig. 23. Bars diagram for Correlation Coefficient (DBP, log(Time Intervals)).

Fig. 21. Bars diagram for MSPE (SBP, (Time Intervals)-2


ii. Diastolic Blood Pressure

2,582,32

2,632,96 2,79 2,85

3,12

0,00

0,50

1,00

1,50

2,00

2,50

3,00

3,50


Fig. 22. Bars diagram for Mutual Information (DBP, (Time Intervals)).

94

0,10 0,15 0,17 0,17 0,04 0,03 0,11

-0,20

-0,10

0,00

0,10

0,20

0,30

0,40


Fig. 24. Bars diagram for Correlation Coefficient (DBP, (Time Intervals)-2).

90,19 80,80 78,81 69,09 121,86 110,91 90,57

0,00

50,00

100,00

150,00

200,00

250,00


Fig. 26. Bars diagram for MSPE (DBP, (Time Intervals)-2) (in milliseconds).

83,5771,30 74,85 77,49

93,40 90,1382,90

0,00

20,00

40,00

60,00

80,00

100,00

120,00


Fig. 25. Bars diagram for MSPE (DBP, log(Time Intervals)) (in milliseconds).

95

Similarly to what happened before, the analysis based on mutual information wasn’t

elucidative per se. Nevertheless, one can presume, contrarily to the expected, a more

pronounced relationship for BP values estimated from intervals referred to the PPG peaks:

PATmax and, consequently, the PTT value calculated from it (PTT.ICGmax).

Once again, the highest correlations (in spite of still low) were verified for intervals

computed with reference to the peaks of PPG, mainly for PATs. On the other side, the

consistently returned negative values from the correlation analysis on the logarithm of the

time intervals indicates a negative dependence between the later and BP, unlike is established

for the theoretical models.

The MSPE analysis, in spite of not providing much of a consistency, suggested biggest

errors towards time intervals determined with base to the onsets of PPG (PATmins and

respective PTTs) – unlike the previous results (4.1.2).

Summarizing, while not enough elucidative, the conduced statistical evaluation gave

hints of observations contrary to what one expected – more accuracy in defining, per cycle,

PAT and PTT until the peaks of the PPG waveform.

It’s important to recall that the characteristics of the algorithms behind the computation

of PEP.ICG were not known.

Once again, ways of getting possible more reliable results would be to test higher

volumes of data with other statistical approaches.

96

FIFTH CH APTER

CONCLUSION

5.1 | FINAL CONCLUSIONS

The main objectives for this study were to explore the dependency of BP with PTT,

according to the Möens-Korteweg/Hughes theory, the closest possible to the continuous basis.

Additionally, this later vascular time interval was supposed to be determined by different

approaches, with the intention of identifying which one(s) would provide the most reliable,

accurate experimental definition.

For such meeting, one acquired ECG, PPG and HS signals, determining, from these,

cardiovascular time intervals such as PEP, PAT, PTT. One subsequently performed an

evaluation based on three distinct statistical tools: mutual information, correlation and mean

squared prediction error between values proportional to estimated BP (from the determined

time intervals) and expected BP (measured experimentally).

Although the required steps were completed, the algorithmic optimization/validation

phase was conditioned for reasons of the (scarcity of the) available time. On the other hand,

the experimental concretization was limiting and the BP measurements were carried out in a

discrete basis, one per 20 seconds (more than 30 heart cycles, in average). The proposed

objectives were, thus, partially achieved since one was not able to discern any clear

dependence tendencies or to draw any solid conclusions from the statistical evaluation. One’s

results were not reliable, elucidative enough.

As the main suggestions for possible improvements of the described work (besides of

algorithmic nature), one highlights the importance of more controlled data acquisitions (less

interference of artifacts and noise, clinical guidance, etc.), of gathering higher volumes of data

(number of subjects and signals) and of using a more effective method to perform BP

measurements, in a more accurate and continuous basis (for example, with equipments like

PORTAPRES® – not to mention intra-arterial methods).

The reported studies have, thus, a prototypical nature to them. Their concept and

strategies are definitely worth further extending.

97

5.2 | SUGGESTIONS FOR FURTHER STUDIES

In the context of the reported studies, subsequent foci of interest would possibly

include:

i. Improving data acquisitions

Such would imply to test the algorithms in clinical environment and to create a database

of appreciable vastness, containing continuous (or semi-continuous) SBP/DBP measurements,

ECG, PPG, HS signals and echocardiographic data.

ii. Exploring and validating the innovative approach to determine PTT

That can be used, once proved its eventual accuracy, to determine the PEP itself, as

the difference between PAT and PTT.

iii. Studying the dynamics of BP relatively to other hemodynamic parameters

Such as HR, for example.

iv. Studying intra-specific calibration

Determining the subject-specific constants present in the Möens-Korteweg/Hughes

theory, which are associated with the parameter L, that is, the length of the path comprised

from the very beginning of the aorta to peripheral arterial ramifications.

v. Relating central (aortic) with peripheral BP

It means to model the losses verified in SBP and DBP across the systemic arterial tree

(accounting for the resistance offered by vascular walls to the blood flow). For such purpose,

the Windkessel model constitutes a good starting point. The approach would undeniably be

very useful given the typical modus operandi of non-invasive, ergonomic, ambulatory

instrumentation for BP assessment.

98

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104

ANNEX I - IN-HOUSE ACQUIRED DATA – EXPERIMENTAL PROTOCOL

OBJECTIVES

It is intended to guide a non-clinical collection of a set of post physical exercising signals

and parameters, for a small group of subjects.

PARAMETERS AND SIGNALS TO ACQUIRE

� BP;

� PPG;

� HS;

� ECG.

EQUIPMENT

� Patient monitor with ECG, PPG and HR;

� Stethoscope (with integrated ECG);

� ECG equipment (electrodes and cables);

� Oscillometric device to measure BP;

� Pulse oximeter (to use in the finger);

� Acquisition interfaces for each acquisition platform;

� Ergometric bicycle;

� Long rubber tube;

� Weight scale and tape measure.

PROCEDURE

There will be a set of twelve data co-recordings, three cycles of four recording periods

each. One is considering a single operator, for which the following instructions are directed.

1. Start by contextualizing the volunteer about the general protocol.

Annotate personal data such as sex, age, height, body mass, cardiovascular health

status, lifestyle (regular practice of physical exercise).

Use the rubber tube to delineate a reliable arterial path, from the top of the heart until

the extremity of the index finger; annotate the measurement.

105

2. Place the cuff on the brachial artery (upper arm, at heart’s level) and the oximeter on

the index finger of the opposite body side.

Get the ECG electrodes (three for each equipment, monitor and stethoscope). Place a

pair on each wrist and the third one near the inner side of the ankle. Connect them to the

cables and to the respective equipments.

Start up the acquisition of ECG and PPG (from the monitor).

3. Ask the subject to pedal without interruptions for about five minutes until the HR show

some stability around 160 heart beats per minute.

4. The volunteer remains seated (preferentially on a chair placed next to the bicycle)

while the operator places the stethoscope in the left sternum border zone and set it where the

sound quality display (minimal signal noise) and higher amplitude.

The operator must control the measurement of BP. Once the cuff filling is completed

(that is, the end of interfering noise), the operator shall initiate the acquisition of HS, for a

period 20 seconds.

It’s extremely important to assure that the subject remains still and stable during the

acquisitions in order to minimize the introduction of hydrostatic and motion artefacts.

5. Repeat point 4 three times, until the stabilization of HR.

6. Repeat from point 1 to point 5 two times.

106

ANNEX I I - EXPERIMENTAL RESULTS FOR VASCULAR AND SYSTOLIC TIME INTERVALS

PEP.HS PEP.PPG PEP.ECHO

PEP.ECHO -

PEP.HS

PEP.ECHO -

PEP.PPG LVET.HS LVET.PPG LVET.HS corrected LVET.PPG corrected

A

44,67 34,92 48,80 4,13 13,88 286,26 296,00 271,86 281,60

42,00 35,07 70,12 28,12 35,05 286,41 293,33 273,21 280,13

48,67 36,96 55,33 6,66 18,36 278,96 290,67 264,56 276,27

45,33 36,84 62,15 16,82 25,32 284,84 293,33 265,64 274,13

42,67 42,94 69,73 27,06 26,79 288,27 288,00 269,07 268,80

49,00 32,44 76,89 27,89 44,46 282,10 298,67 267,70 284,27

47,67 33,61 62,54 14,88 28,94 284,61 298,67 271,41 285,47

45,00 50,17 62,47 17,47 12,31 290,50 285,33 277,30 272,13

45,33 44,23 54,85 9,52 10,62 289,56 290,67 281,16 282,27

43,00 44,34 78,18 35,18 33,84 289,34 288,00 277,34 276,00

48,00 39,00 78,56 30,56 39,56 284,33 293,33 268,73 277,73

45,33 43,40 62,58 17,24 19,17 288,74 290,67 270,74 272,67

46,67 26,05 62,28 15,61 36,23 286,05 306,67 272,85 293,47

47,00 44,75 77,44 30,44 32,69 288,42 290,67 272,82 275,07

40,67 35,33 63,29 22,62 27,96 290,67 296,00 275,07 280,40

45,33 39,36 78,25 32,92 38,89 290,03 296,00 278,03 284,00

Mean 45,40 38,71 66,47 21,07 27,75 286,82 293,50 272,34 279,02

SD 2,42 6,01 9,45 9,64 10,40 3,28 5,20 4,64 6,18

B

37,33 -5,46 69,85 32,52 75,31 261,21 304,00 244,71 287,50

41,00 9,29 62,07 21,07 52,79 272,29 304,00 256,89 288,60

50,00 17,09 69,01 19,01 51,92 265,75 298,67 250,35 283,27

48,67 16,75 69,69 21,02 52,94 266,75 298,67 250,25 282,17

41,00 6,24 69,71 28,71 63,46 261,24 296,00 246,94 281,70

49,00 22,20 69,75 20,75 47,55 263,87 290,67 248,47 275,27

51,00 23,36 76,47 25,47 53,11 263,03 290,67 249,83 277,47

48,67 18,63 55,75 7,08 37,11 265,97 296,00 252,77 282,80

39,67 14,77 70,02 30,36 55,25 290,67 265,77 278,57 253,67

38,67 -12,60 70,26 31,60 82,86 293,33 242,07 280,13 228,87

49,33 11,65 70,39 21,06 58,74 296,00 258,31 282,80 245,11

47,33 15,68 77,35 30,01 61,67 298,67 267,01 284,37 252,71

47,67 8,85 70,45 22,78 61,60 298,67 259,85 281,07 242,25

Mean 45,33 11,27 69,29 23,96 58,02 276,73 282,44 262,09 267,80

SD 4,94 10,41 5,45 6,95 11,69 15,79 20,81 16,18 20,30

Table 1. Calculation of various time intervals for two subjects A and B.

107

ANNEX I I - EXPERIMENTAL RESULTS FOR VASCULAR AND SYSTOLIC TIME INTERVALS

PTT.ECHOmin PTT.ECHO75 PTT.ECHOmax PTT.DN

424,91 371,88 427,88 424,91

394,88 345,92 393,92 394,88

377,91 314,45 362,45 377,91

-61,92 154,08 210,08 160,15

-53,93 162,07 218,07 171,47

-62,12 -14,13 25,87 -23,92

356,09 468,09 524,09 533,33

290,44 418,44 474,44 481,24

440,99 688,99 728,99 682,58

384,36 664,36 704,36 615,26

466,18 658,18 698,18 666,67

973,75 -29,34 10,66 973,75

-183,16 -68,80 -68,80 -183,16

Table 2. PTTs calculated with PEP values determined from echocardiography.

While not determined from PEP.ECHO, PTT.DN was also calculated for the same data.

ANNEX I I I – STATISTICAL EVALUATION FOR IN-HOUSE ACQUIRED DATA

CORRELATION COEFFICIENT (SBP, log(Time Interval))

Time Interval PEP.HS PEP.PPG PATmin PAT75 PATmax PTT.HSmax PTT.HS75 PTT.HSmin PTT.PPGmax PTT.PPG75 PTT.PPGmin PTT.DN

Subject 1 -0,48 N/A -0,51 -0,52 -0,56 -0,55 -0,51 -0,48 -0,54 -0,47 -0,42 -0,37

Subject 2 -0,29 N/A -0,52 -0,41 -0,39 -0,37 -0,39 -0,52 -0,49 -0,51 -0,61 -0,63

Subject 3 0,03 N/A 0,02 0,06 0,07 0,07 0,05 -0,11 -0,04 -0,06 -0,14 0,12

Subject 4 -0,71 -0,94 0,48 -0,61 -0,59 -0,52 -0,52 0,54 -0,29 -0,24 0,86 0,30

Subject 5 -0,49 0,00 0,44 0,67 0,51 0,56 0,70 0,49 0,57 0,67 0,48 0,30

Subject 6 -0,43 -0,20 0,21 -0,34 -0,31 -0,20 -0,21 0,31 0,00 0,04 0,39 0,27

Subject 7 0,00 -0,52 -0,27 -0,35 -0,38 -0,38 -0,36 -0,27 0,32 0,37 0,35 0,42

Mean -0,34 -0,41 -0,02 -0,21 -0,24 -0,20 -0,17 -0,01 -0,07 -0,03 0,13 0,06

SD 0,27 0,41 0,42 0,44 0,39 0,39 0,43 0,45 0,41 0,43 0,53 0,40

CORRELATION COEFFICIENT (SBP, (Time Interval)-2

)


Subject 1 0,50 -0,17 0,43 0,46 0,49 0,43 0,39 0,30 0,49 0,42 0,36 0,26

Subject 2 0,32 0,88 0,54 0,28 0,25 0,22 0,39 0,53 0,37 0,41 0,56 0,47

Subject 3 -0,08 0,40 -0,13 -0,13 -0,13 0,00 0,15 -0,16 -0,08 -0,07 0,02 -0,17

Subject 4 0,71 0,43 -0,39 0,54 0,53 0,46 0,46 -0,38 0,34 0,30 -0,65 -0,31

Subject 5 0,56 -0,19 -0,46 -0,64 -0,53 -0,57 -0,65 -0,46 -0,56 -0,62 -0,43 -0,31

Subject 6 0,43 -0,25 -0,22 0,31 0,28 0,18 0,19 -0,24 0,01 -0,02 -0,33 -0,24

Subject 7 0,04 -0,31 0,24 0,32 0,36 0,36 0,33 0,23 -0,26 -0,29 -0,19 -0,25

Mean 0,36 0,11 0,00 0,16 0,18 0,15 0,18 -0,03 0,04 0,02 -0,10 -0,08

SD 0,28 0,46 0,40 0,41 0,38 0,36 0,38 0,38 0,38 0,39 0,44 0,31

Table 2. The N/A results came from a negative mean value of PEP.PPG for the respective subjects.

109

MEAN SQUARED PREDICTION ERROR (SBP, log(Time Interval))


Subject 1 171,73 203,07 232,59 203,79 192,20 238,41 161,45 267,69 129,27 89,84 185,93 223,07

Subject 2 231,83 335,48 280,04 195,73 197,52 116,95 223,37 106,95 289,62 131,21 120,33 93,64

Subject 3 36,37 36,85 48,98 54,92 541,94 401,92 61,84 52,43 31,65 91,80 86,30 24,89

Subject 4 61,95 14,46 17,15 975,01 125,23 587,56 696,32 350,25 215,82 943,05 101,17 208,10

Subject 5 263,92 28,23 150,69 61,16 203,63 53,44 27,60 63,95 83,44 91,30 49,84 67,10

Subject 6 33,25 45,41 68,69 56,73 18,15 57,74 59,35 28,47 98,01 113,04 40,81 61,23

Subject 7 48,57 26,06 54,70 28,52 20,56 26,87 25,39 29,33 89,05 34,64 60,16 84,57

Mean 121,09 98,51 121,83 225,12 185,60 211,84 179,33 128,44 133,84 213,55 92,08 108,94

SD 99,06 123,13 101,43 338,26 176,26 212,16 239,60 128,33 88,77 323,04 50,26 76,13

MEAN SQUARED PREDICTION ERROR (SBP, (Time Interval)-2

)


Subject 1 244,67 257,01 204,99 205,67 64,01 274,64 155,40 253,39 148,74 135,27 180,30 328,29

Subject 2 264,88 54,48 151,67 252,60 1853,78 939215,03 235,79 208,88 312,83 268,06 179,79 3112,01

Subject 3 57,89 50,74 16165,95 904001,38 6926249,86 38,22 18,75 774,48 689,49 44,20 75,95 82,12

Subject 4 70,54 311,30 297,44 210,44 1609,00 74,50 5016,50 126,11 799,03 253,59 271,84 270,50

Subject 5 135,82 86,44 77,83 79,44 55,63 137,79 67,19 82,82 50,30 81,08 104,15 111,33

Subject 6 53,27 91,52 50,54 37,34 138,27 76,94 24,21 77,78 57,98 80,14 67,66 62,23

Subject 7 46,72 46,41 80,11 43,44 54,20 46,00 54,25 48,47 35,31 48,87 44,99 59,74

Mean 124,83 128,27 2432,65 129261,47 990003,54 134266,16 796,01 224,56 299,10 130,17 132,10 575,17

SD 93,76 109,03 6056,43 341628,20 2617638,70 354949,10 1862,70 253,58 320,09 94,15 81,45 1123,71

Table 3.

110

Table 4.

MUTUAL INFORMATION (DBP, Time Interval)


Subject 1 3,09 3,52 3,66 3,81 3,66 3,66 3,52 3,66 3,47 3,81 3,66 3,81

Subject 2 2,42 2,75 2,19 2,92 2,58 2,92 2,92 2,92 2,75 2,75 2,75 2,92

Subject 3 2,69 3,02 3,19 3,19 3,19 3,19 3,19 3,19 3,02 3,19 3,19 3,02

Subject 4 2,58 2,42 2,25 2,42 2,42 2,42 2,42 2,42 2,25 2,58 2,42 2,36

Subject 5 3,09 2,72 3,24 3,24 3,09 3,24 3,24 2,87 3,24 3,09 3,09 3,09

Subject 6 3,09 2,81 3,09 3,24 2,95 2,95 3,24 2,95 2,81 3,09 3,09 3,09

Subject 7 2,15 2,42 2,68 2,68 2,50 2,55 2,55 2,68 2,68 2,55 2,68 2,42

Mean 2,73 2,81 2,90 3,07 2,91 2,99 3,01 2,96 2,89 3,01 2,98 2,96

SD 0,38 0,38 0,55 0,45 0,45 0,43 0,40 0,39 0,40 0,44 0,41 0,49

Table 5.

MUTUAL INFORMATION (SBP, Time Interval)


Subject 1 2,95 3,38 3,52 3,66 3,52 3,52 3,38 3,52 3,32 3,66 3,52 3,66

Subject 2 2,92 3,42 2,86 3,42 3,08 3,42 3,42 3,42 3,25 3,25 3,42 3,42

Subject 3 2,25 2,58 2,58 2,75 2,58 2,75 2,75 2,75 2,75 2,75 2,75 2,58

Subject 4 3,08 2,92 2,92 2,92 2,92 2,92 2,92 2,75 2,75 3,08 2,92 2,86

Subject 5 2,82 2,45 2,97 2,97 2,82 2,97 2,97 2,60 2,97 2,82 2,82 2,97

Subject 6 3,09 2,81 3,09 3,24 2,95 2,95 3,24 2,95 2,81 3,09 3,09 3,09

Subject 7 2,02 2,42 2,68 2,55 2,37 2,55 2,68 2,55 2,68 2,55 2,68 2,55

Mean 2,73 2,85 2,95 3,07 2,89 3,01 3,05 2,94 2,93 3,03 3,03 3,02

SD 0,43 0,41 0,31 0,39 0,37 0,35 0,30 0,39 0,26 0,37 0,33 0,41

111

Table 6. The N/A results came from a negative mean value of PEP.PPG for the respective subjects.

CORRELATION COEFFICIENT (DBP, log(Time Interval))


Subject 1 0,69 N/A 0,52 0,56 0,61 0,59 0,54 0,46 0,59 0,51 0,43 0,46

Subject 2 -0,07 N/A -0,14 -0,12 -0,15 -0,07 -0,08 -0,14 -0,13 -0,12 -0,16 -0,21

Subject 3 0,55 N/A -0,12 -0,08 -0,07 -0,08 -0,11 -0,28 -0,11 -0,13 -0,17 0,13

Subject 4 -0,15 -0,11 0,38 -0,36 -0,36 -0,35 -0,34 0,19 -0,44 -0,46 0,19 -0,54

Subject 5 -0,02 0,23 0,40 0,40 0,35 0,34 0,36 0,38 0,36 0,35 0,39 0,21

Subject 6 0,11 0,32 0,29 0,31 0,32 0,29 0,29 0,26 0,39 0,41 0,30 0,42

Subject 7 -0,28 -0,51 -0,36 -0,30 -0,23 -0,20 -0,27 -0,35 0,15 0,10 0,03 -0,16

Mean 0,12 -0,01 0,14 0,06 0,07 0,07 0,05 0,07 0,12 0,10 0,14 0,04

SD 0,36 0,38 0,34 0,36 0,36 0,34 0,34 0,33 0,36 0,35 0,25 0,37

CORRELATION COEFFICIENT (DBP, (Time Interval)-2

)


Subject 1 -0,70 0,31 -0,39 -0,46 -0,52 -0,44 -0,36 -0,20 -0,52 -0,43 -0,31 -0,33

Subject 2 0,08 0,37 0,19 0,29 0,32 -0,22 -0,04 0,11 0,21 0,16 0,18 0,22

Subject 3 -0,55 -0,10 0,03 0,02 0,02 0,15 0,29 0,21 0,05 0,07 0,17 -0,52

Subject 4 0,11 -0,10 -0,39 0,31 0,31 0,29 0,28 0,42 0,37 0,39 -0,06 0,52

Subject 5 0,04 -0,18 -0,39 -0,39 -0,35 -0,33 -0,36 -0,36 -0,37 -0,38 -0,43 -0,28

Subject 6 -0,11 -0,16 -0,33 -0,28 -0,28 -0,23 -0,23 -0,31 -0,36 -0,38 -0,29 -0,48

Subject 7 0,35 0,16 0,44 0,36 0,29 0,26 0,34 0,45 -0,16 -0,11 0,03 0,27

Mean -0,11 0,04 -0,12 -0,02 -0,03 -0,07 -0,01 0,05 -0,11 -0,10 -0,10 -0,08

SD 0,38 0,23 0,34 0,35 0,35 0,30 0,32 0,34 0,33 0,32 0,24 0,41

112

Table 7.

MEAN SQUARED PREDICTION ERROR (DBP, log(Time Interval))


Subject 1 11,97 13,51 11,51 15,13 17,10 16,37 16,67 16,36 10,80 24,13 14,78 26,12

Subject 2 27,42 7,76 35,08 65,87 48,04 64,53 32,67 38,24 34,85 81,83 25,84 44,16

Subject 3 69,12 53,44 60,77 66,30 424,84 92,24 294,13 84,19 98,96 100,15 70,95 57,78

Subject 4 31,79 25,86 40,61 46,67 31,51 152,71 34,00 40,38 154,85 22,83 38,94 22,67

Subject 5 28,91 28,66 48,62 45,98 48,42 55,89 37,67 58,19 75,17 60,51 44,78 37,35

Subject 6 99,59 62,64 117,08 79,59 100,73 70,08 70,39 37,95 79,51 62,60 79,84 42,51

Subject 7 26,50 17,53 29,86 41,91 34,21 54,08 30,20 43,00 28,61 44,06 36,26 24,48

Mean 42,19 29,92 49,08 51,64 100,69 72,27 73,67 45,47 68,97 56,59 44,48 36,44

SD 30,77 20,64 33,69 21,15 145,36 42,15 98,58 21,01 49,33 28,68 23,38 12,86

MEAN SQUARED PREDICTION ERROR (DBP, (Time Interval)-2

)


Subject 1 10,06 17,69 15,31 12,10 7,56 14,62 14,73 20,03 15,66 16,85 15,75 18,28

Subject 2 7,01 67,54 35,24 83,44 180,62 15,13 90,87 38,50 24,35 31,27 27,28 44,57

Subject 3 97,83 60,88 19213,66 1267752,13 7124371,88 96,60 62,08 207,84 69,50 84,79 70,09 210,76

Subject 4 50,46 30,06 32,33 90,91 80,99 377,95 468,21 24,44 406,20 25,28 75,95 23,17

Subject 5 77,02 36,26 44,57 73,07 44,87 31,51 43,96 34,30 45,08 47,67 40,18 27,57

Subject 6 97,56 81,08 34,61 68,97 90,37 215,46 13,88 104,98 164,95 82,47 71,25 62,98

Subject 7 24,01 29,64 38,38 26,57 22,95 55,33 42,65 16,73 41,43 9,63 43,91 42,86

Mean 51,99 46,17 2773,44 181158,17 1017828,46 115,23 105,20 63,83 109,60 42,56 49,20 61,45

SD 39,52 23,57 7249,46 479142,90 2692732,54 135,50 162,29 70,28 139,97 30,48 23,62 67,58

ANNEX IV – STATISTICAL EVALUATION FOR PHILIPS DATA

CORRELATION COEFFICIENT (SBP, log(Time Interval))

Time Interval PEP.ICG PATmin PAT75 PATmax PTT.ICGmin PTT.ICG75 PTT.ICGmax

Ergometric Exercise -0,61 -0,38 -0,37 -0,36 -0,28 -0,32 -0,32

Valsalva -0,52 -0,35 -0,34 -0,31 -0,27 -0,33 -0,31

Postural Change -0,09 -0,11 -0,09 -0,09 -0,13 -0,09 -0,09

Mean -0,40 -0,28 -0,27 -0,25 -0,23 -0,25 -0,24

SD 0,28 0,15 0,16 0,14 0,08 0,14 0,13

CORRELATION COEFFICIENT (SBP, (Time Interval)-2

)


Ergometric Exercise 0,66 0,33 0,34 0,34 0,30 0,29 0,27

Valsalva 0,45 0,33 0,25 0,24 0,14 0,13 0,31

Postural Change 0,09 0,07 0,09 0,09 0,16 0,21 0,24

Mean 0,40 0,24 0,23 0,22 0,20 0,21 0,27

SD 0,29 0,15 0,13 0,12 0,08 0,08 0,04

Table 8.

MEAN SQUARED PREDICTION ERROR (SBP, log(Time Interval))



Valsalva 138,01 128,89 156,01 156,75 123,38 127,57 160,34

Postural Change 150,19 158,18 148,49 149,80 144,58 165,34 125,73

Mean 170,00 213,63 194,85 185,77 197,07 204,23 199,94

SD 45,27 122,28 73,88 56,40 109,78 101,82 100,08

MEAN SQUARED PREDICTION ERROR (SBP, (Time Interval)-2

)



Valsalva 157,64 248,05 228,88 197,00 755,68 168,27 142,40

Postural Change 140,93 118,63 123,13 136,82 102,11 161,56 117,50

Mean 154,07 266,68 216,45 193,83 397,21 224,57 195,36

SD 11,77 158,19 87,76 55,50 331,36 103,38 113,98

Table 9.

MUTUAL INFORMATION (SBP, Time Interval)



Valsalva 2,92 2,75 2,91 3,34 3,14 3,12 3,59

Postural Change 2,60 2,29 2,60 2,90 3,04 3,03 3,29

Mean 2,89 2,72 2,93 3,24 3,12 3,14 3,48

SD 0,28 0,41 0,34 0,30 0,07 0,12 0,17

Table 10.

114

CORRELATION COEFFICIENT (DBP, log(Time Interval))


Ergometric Exercise -0,20 -0,14 -0,14 -0,16 -0,04 -0,10 -0,11

Valsalva -0,25 -0,31 -0,30 -0,29 -0,30 -0,30 -0,30

Postural Change 0,16 -0,02 -0,04 -0,04 -0,03 -0,06 -0,06

Mean -0,10 -0,16 -0,16 -0,16 -0,12 -0,15 -0,16

SD 0,23 0,15 0,13 0,13 0,15 0,13 0,12

CORRELATION COEFFICIENT (DBP, (Time Interval)-2

)


Ergometric Exercise 0,15 0,12 0,18 0,18 -0,07 -0,01 -0,03

Valsalva 0,26 0,31 0,27 0,27 0,28 0,10 0,27

Postural Change -0,10 0,03 0,05 0,05 -0,08 -0,01 0,08

Mean 0,10 0,15 0,17 0,17 0,04 0,03 0,11

SD 0,18 0,14 0,11 0,11 0,21 0,06 0,15

Table 11.

MEAN SQUARED PREDICTION ERROR (DBP, log(Time Interval))



Valsalva 104,61 79,18 94,26 88,51 109,07 112,87 82,57

Postural Change 69,03 70,13 63,14 80,99 79,13 73,04 84,82

Mean 83,57 71,30 74,85 77,49 93,40 90,13 82,90

SD 18,66 7,36 16,93 13,12 15,02 20,51 1,77

MEAN SQUARED PREDICTION ERROR (DBP, (Time Interval)-2

)



Valsalva 105,29 94,00 96,38 63,26 213,75 163,34 131,86

Postural Change 87,30 66,02 67,37 63,37 72,57 95,33 68,99

Mean 90,19 80,80 78,81 69,09 121,86 110,91 90,57

SD 13,89 14,05 15,45 10,00 79,64 46,63 35,77

Table 12.

MUTUAL INFORMATION (DBP, Time Interval)



Valsalva 2,65 2,38 2,68 3,11 2,80 2,78 3,19

Postural Change 2,45 2,18 2,52 2,83 2,94 2,98 3,16

Mean 2,58 2,32 2,63 2,96 2,79 2,85 3,12

SD 0,12 0,12 0,10 0,14 0,15 0,11 0,10

Table 13.

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