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# Détection des changements de profil respiratoire des patients sous oxygénothérapie de longue durée

Juliana Alves Pegoraro

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Juliana Alves Pegoraro. Détection des changements de profil respiratoire des patients sous oxygénothérapie de longue durée. Sciences du Vivant [q-bio]. Université de Paris / Université Paris Descartes (Paris 5), 2021. Français. NNT: tel-04015145

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Université de Paris

École doctorale de Sciences Mathématiques de Paris Centre (ED 386)

Laboratoire : Mathématiques Appliquées à Paris 5, MAP5-UMR 8145 CNRS

# Détection des changements de profil respiratoire des patients sous oxygénothérapie de longue durée

par JULIANA ALVES PEGORARO

Thèse de doctorat de Mathématiques appliquées

Dirigée par

ETIENNE BIRMELÉ ET JÉSUS GONZALEZ-BERMEJO

Présentée et soutenue publiquement le ... 22 octobre 2021

Devant le jury composé de :

<table><tr><td>CHRISTOPHE AMBROISE</td><td>PU, Université d'Evry Val d'Essonne</td><td>Examineur</td></tr><tr><td>ETIENNE BIRMELE</td><td>PU, Université de Paris</td><td>Directeur</td></tr><tr><td>MAGALI CHAMPION</td><td>MCU, Université de Paris</td><td>Examinatrice</td></tr><tr><td>JÉSUS GONZALEZ-BERMEJO</td><td>PU-PH, Sorbonne Université</td><td>Co-directeur</td></tr><tr><td>MYRIAM MAUMY-BERTRAND</td><td>MCU-HDR, Université de Technologie de Troyes</td><td>Rapporteure</td></tr><tr><td>JEAN-LOUIS PEPIN</td><td>PU-PH, Université Grenoble-Alpes</td><td>Rapporteur</td></tr><tr><td>PHILIPPE SALAMITOU</td><td>PhD, entreprise Srett</td><td>Invité</td></tr><tr><td>THOMAS SIMILOWSKI</td><td>PU-PH, Sorbonne Université</td><td>Examineur</td></tr></table>
# Détection des changements de profil respiratoire des patients sous oxygénothérapie de longue durée

## Résumé.

La bronchopneumopathie chronique obstructive (BPCO) est l'une des principales causes de mortalité et de morbidité dans le monde. Sa prise en charge représente un véritable fardeau économique et de santé publique, accentué par des périodes de détérioration aiguë de la maladie, appelées exacerbations.

Afin d'améliorer la prise en charge précoce des exacerbations de la BPCO, ce manuscrit de thèse porte sur le développement d'un outil et d'une méthode de détection automatique des anomalies de la mécanique respiratoire chez les patients sous oxygénothérapie de longue durée (OLD), en particulier ceux atteints de la BPCO.

En combinant des intérêts médicaux et industriels, cette thèse est composée de deux phases principales : i. choix des indicateurs à surveiller et développement de la technologie ; ii. surveillance en continu des indicateurs et détection des exacerbations.

Dans la première étape, des études sont menées sur les changements du profil respiratoire pendant les ajustements à court terme de l'équilibre charge-capacité, comme le sommeil et l'exercice, chez des sujets sains et des patients atteints de BPCO. Les enregistrements des signaux bruts de pression nasale permettent de valider les mesures de la fréquence respiratoire et d'évaluer le pouvoir prédictif d'autres descripteurs du signal. L'étude montre que la fréquence respiratoire seule est un indicateur assez pauvre en termes de prédiction des changements respiratoires et que l'ajout de l'un des autres indicateurs proposés améliore le pouvoir de classification. Ainsi, en accord avec les résultats et pour des raisons technologiques, le dispositif de surveillance est mis à jour pour mesurer à la fois la fréquence et l'amplitude respiratoires.

Dans un deuxième temps, le dispositif de surveillance évolué est utilisé pour surveiller des patients atteints de BPCO pendant leur séjour dans un service de réhabilitation après une exacerbation aiguë. Des méthodes supervisées, non supervisées et de détection de la nouveauté sont appliquées aux séries temporelles de la fréquence respiratoire, de l'amplitude et du débit d'oxygène. La classification non supervisée des profils respiratoires montre une variété de motifs, pour la plupart constants pour le même individu.

La comparaison des profils quotidiens d'un même individu indique que le suivi de la fréquence et de l'amplitude respiratoires fournit des informations suffisantes pour l'identification des périodes de changement. Des résultats préliminaires sur la relation de ces changements avec les événements d'exacerbation sont obtenus, justifiant une future collecte de données à plus grande échelle.

**Mots-clés** : Apprentissage automatique ; Séries temporelles ; Détection de la nouveauté ; Médecine personnalisée ; Bronchopneumopathie Chronique Obstructive ; Oxygénothérapie de longue durée.
# Detection of respiratory profile changes in patients under long-term oxygen therapy

## Abstract.

Chronic obstructive pulmonary disease (COPD) is a leading cause of mortality and morbidity worldwide. Its management represents real economic and public health burdens, accentuated by periods of acute disease deterioration, called exacerbations.

In order to improve the early management of COPD exacerbations, this thesis manu-
script focuses on the development of a monitoring device and methods for the automatic
detection of abnormalities of respiratory mechanics in patients under long-term oxygen
therapy (LTOT), in particular those with COPD.

By combining medical and industrial interests, this thesis is composed by two main
phases: i. choice of monitoring features and technology development; ii. continuous fea-
tures monitoring and exacerbation detection.

In the first step, studies are conducted on changes of the respiratory profile during short-
term load-capacity balance adjustments, such as sleep and exercise, in healthy subjects
and COPD patients. Recordings of raw nasal pressure signals allow for the validation
of the respiratory rate measurements and the evaluation of the predictive power of other
descriptors of the signal. The study shows that breathing rate alone is a quite poor feature
in terms of prediction of breathing change and the addition of any of the other proposed
features improves the classification power. Thus, based on the results and for technological
reasons, the monitoring device is updated to measure both breathing rate and amplitude.

In the second step, the evolved monitoring device is used to monitor COPD patients
during their stay in a rehabilitation unit after an acute exacerbation. Supervised, unsuper-
vised and novelty detection methods are applied in the recorded time series of breathing
rate, amplitude and oxygen flow. The unsupervised classification of respiratory profiles
shows a variety of patterns, mainly constant for the same individual.

The comparison of daily profiles from the same individual indicates that the monitoring
of breathing rate and amplitude provides sufficient information for the identification of
periods of change. Preliminary results on the relationship of this changes with exacerbation
events are obtained, justifying a future larger scale data collection.

**Keywords:** Machine learning; Time series; Novelty detection; Personalized medicine; Chronic Obstructive Pulmonary Disease; Long-term oxygen therapy.
# Contents

I Introduction 2

1 COPD 3

1.1 Signs, diagnosis, prognosis 3

1.2 Epidemiology 4

1.2.1 Descriptive epidemiology 4

1.2.2 Analytical epidemiology 4

1.3 COPD severity (GOLD) 5

1.4 Treatments 6

1.5 Exacerbations and economic burden 7

1.6 Problem and hypothesis 8

2 Respiratory mechanics 9

2.1 Lung volumes 10

2.2 Minute ventilation 10

2.3 Pressures and flow 12

2.4 Lung hyperinflation 13

2.5 Respiratory variability and complexity 14

2.6 Respiratory functional explorations 14

2.6.1 Spirometry 15

2.6.2 Polysomnography 16

2.6.3 Exercise testing 16

2.7 Problem and hypothesis 16

3 Telemedecine 18

3.1 Solutions for telemonitoring 18

3.2 Remote monitoring of acute events 19

3.3 Remote monitoring and intelligent exacerbation prediction 20

3.3.1 Exacerbation events 20

3.3.2 Periods type definition 21

3.3.3 Parameters choice 22

3.3.4 Statistical methods 28

3.4 Problem and hypothesis 28

4 Artificial intelligence 29

4.1 Feature extraction from time series 29

4.1.1 Fourier transform 30

4.1.2 ARIMA 31

4.2 Classification in times series 32

4.2.1 Hidden Markov Model 32

4.2.2 Series likelihood under HMM 34
<table><tr><td>4.3</td><td>Supervised classification</td><td>34</td></tr><tr><td>4.3.1</td><td>SuperLearner</td><td>35</td></tr><tr><td>4.3.2</td><td>Mixed effect models</td><td>35</td></tr><tr><td>4.4</td><td>Novelty detection</td><td>36</td></tr><tr><td>4.4.1</td><td>Mahalanobis distance</td><td>36</td></tr><tr><td>4.4.2</td><td>Wasserstein distance</td><td>36</td></tr><tr><td>4.4.3</td><td>Cross-entropy and Kullback-Leibler divergence</td><td>37</td></tr><tr><td>4.4.4</td><td>Methods for time series</td><td>38</td></tr><tr><td>4.5</td><td>Final hypothesis of the investigation</td><td>39</td></tr></table>

## II Technology development 40

### 1 TeleOx® monitoring device 41

1.1 Commercial TeleOx® 42

1.2 TeleOx® adaptation for research 42

### 2 Validation of breathing rate measurements 44

2.1 Study protocol 44

2.2 Signals comparison 44

2.3 Filtering 45

2.4 Flow and volume estimation 46

2.5 Breath-by-breath identification 47

2.5.1 Pressure minima or maxima 48

2.5.2 Signal crossing zero 49

2.5.3 Volume minima and maxima 49

2.5.4 Laplacian of Gaussian filter 49

2.6 Breathing rate estimation 50

2.6.1 Validation of breathing rate measurements 51

### 3 Estimation of indicators of respiratory mechanics profiles 53

3.1 Study protocols 53

3.1.1 Healthy subjects 53

3.1.2 COPD patients 55

3.2 Visual analysis of the events 56

3.2.1 Nasal and oral respiration 56

3.2.2 Deglutition and coughing 57

3.2.3 Speech 58

3.2.4 Rest and exercise 59

3.3 Indicators of respiratory profiles 59

3.3.1 Inspiration-to-expiration times ratio 59

3.3.2 Flow-volume loop 60

3.3.3 Amplitude 60

3.3.4 Cycle-to-cycle variability 60

3.3.5 ARIMA coefficients 61

3.3.6 Fourier transform coefficients 61

3.4 Choice of the parameters 61

3.4.1 Inspiration-to-expiration times ratio 61

3.4.2 Flow-volume loop 62

3.4.3 Amplitude 64
<table><tr><td>3.4.4 Cycle-to-cycle variability</td><td>67</td></tr><tr><td>3.4.5 ARIMA coefficients</td><td>68</td></tr><tr><td>3.4.6 Fourier transform coefficients</td><td>68</td></tr><tr><td>3.5 Conclusion</td><td>68</td></tr></table>

4 Validation of indicators of respiratory mechanics profiles 71

<table><tr><td>4.1 Classification</td><td>71</td></tr><tr><td>4.1.1 Classification data</td><td>71</td></tr><tr><td>4.1.2 Supervised classification under the homogeneity assumption</td><td>71</td></tr><tr><td>4.1.3 Supervised classification with random effects</td><td>72</td></tr><tr><td>4.1.4 One-class classification</td><td>72</td></tr><tr><td>4.2 Results</td><td>73</td></tr><tr><td>4.2.1 Data and feature extraction</td><td>73</td></tr><tr><td>4.2.2 Supervised classification under the homogeneity within the population</td><td>73</td></tr><tr><td>4.2.3 Supervised classification with random effects</td><td>73</td></tr><tr><td>4.2.4 One-class classification</td><td>77</td></tr><tr><td>4.3 Discussion</td><td>78</td></tr><tr><td>4.4 Conclusions</td><td>79</td></tr></table>

5 Remote monitoring 80

<table><tr><td>5.1 TeleOx® algorithm upgrade</td><td>80</td></tr><tr><td>5.2 Real time data acquisition</td><td>80</td></tr><tr><td>5.3 First conclusions</td><td>81</td></tr></table>

III Analysis and results for exacerbation detection 82

1 Medium-term monitoring of chosen features 83

<table><tr><td>1.1 Data acquisition</td><td>83</td></tr><tr><td>1.2 Data treatment</td><td>84</td></tr><tr><td>1.3 Results</td><td>84</td></tr><tr><td>1.4 Discussion</td><td>87</td></tr><tr><td>1.5 Conclusion and perspectives in data treatment</td><td>87</td></tr></table>

2 Automatic detection of respiratory profiles 89

<table><tr><td>2.1 Methods</td><td>89</td></tr><tr><td>2.1.1 Dataset</td><td>89</td></tr><tr><td>2.1.2 Barycenters</td><td>90</td></tr><tr><td>2.1.3 Clustering</td><td>90</td></tr><tr><td>2.2 Results</td><td>91</td></tr><tr><td>2.2.1 Week mean distribution</td><td>91</td></tr><tr><td>2.2.2 Considering all weeks</td><td>91</td></tr><tr><td>2.2.3 Baseline and prodrome weeks</td><td>92</td></tr><tr><td>2.3 Discussion</td><td>94</td></tr><tr><td>2.4 Conclusion</td><td>94</td></tr></table>

3 Automatic detection of respiratory changes 96

<table><tr><td>3.1 Detection of sleep and wakefulness</td><td>96</td></tr><tr><td>3.1.1 Method</td><td>96</td></tr><tr><td>3.1.2 Results</td><td>97</td></tr></table>
<table>
  <tbody>
    <tr>
      <td>3.1.3</td>
      <td>Discussion</td>
      <td>100</td>
    </tr>
    <tr>
      <td>3.2</td>
      <td>Detection of post-exacerbation and stable weeks</td>
      <td>100</td>
    </tr>
    <tr>
      <td>3.2.1</td>
      <td>Methods</td>
      <td>101</td>
    </tr>
    <tr>
      <td>3.2.2</td>
      <td>Results</td>
      <td>102</td>
    </tr>
    <tr>
      <td>3.2.3</td>
      <td>Discussion</td>
      <td>106</td>
    </tr>
    <tr>
      <td>3.3</td>
      <td>Conclusion</td>
      <td>107</td>
    </tr>
    <tr>
      <td>4</td>
      <td>Taking temporality into account using a Hidden Markov Model</td>
      <td>108</td>
    </tr>
    <tr>
      <td>4.1</td>
      <td>Estimation of model parameters</td>
      <td>108</td>
    </tr>
    <tr>
      <td>4.1.1</td>
      <td>Modeling example</td>
      <td>109</td>
    </tr>
    <tr>
      <td>4.2</td>
      <td>Comparing with real physiological states</td>
      <td>110</td>
    </tr>
    <tr>
      <td>4.3</td>
      <td>Initial and final profiles</td>
      <td>112</td>
    </tr>
    <tr>
      <td>4.3.1</td>
      <td>Log-likelihood under the HMM</td>
      <td>112</td>
    </tr>
    <tr>
      <td>4.3.2</td>
      <td>Cross-entropy and Kullback-Leibler divergence</td>
      <td>113</td>
    </tr>
    <tr>
      <td>4.4</td>
      <td>Conclusion</td>
      <td>115</td>
    </tr>
    <tr>
      <td>5</td>
      <td>Exacerbation and novelty detection</td>
      <td>116</td>
    </tr>
    <tr>
      <td>5.1</td>
      <td>One-class metrics</td>
      <td>116</td>
    </tr>
    <tr>
      <td>5.1.1</td>
      <td>Threshold estimation from model sampling</td>
      <td>116</td>
    </tr>
    <tr>
      <td>5.1.2</td>
      <td>Threshold estimation from training anomaly scores</td>
      <td>117</td>
    </tr>
    <tr>
      <td>5.2</td>
      <td>Novelty detection of initial profiles</td>
      <td>118</td>
    </tr>
    <tr>
      <td>5.3</td>
      <td>Novelty detection of prodromal profiles</td>
      <td>119</td>
    </tr>
    <tr>
      <td>5.4</td>
      <td>Detection of less stable days</td>
      <td>121</td>
    </tr>
    <tr>
      <td>5.4.1</td>
      <td>Results for recordings with exacerbation</td>
      <td>123</td>
    </tr>
    <tr>
      <td>5.4.2</td>
      <td>Results for recordings without exacerbation</td>
      <td>125</td>
    </tr>
    <tr>
      <td>5.5</td>
      <td>Conclusion</td>
      <td>129</td>
    </tr>
    <tr>
      <td>6</td>
      <td>Conclusion and perspectives</td>
      <td>131</td>
    </tr>
    <tr>
      <td colspan="2">Bibliography</td>
      <td>133</td>
    </tr>
  </tbody>
</table>
<figure><img src="image_3.png" /></figure>
# Acronyms

**6MWT** 6 minutes walking test.

**ARIMA** Autoregressive Integrated Moving Average.

**COPD** Chronic Obstructive Pulmonary Disease.

**DALY** Disability-Adjusted Life Years.

**FEV1** First second expiratory volume.

**GOLD** Global Initiative for Chronic Obstructive Lung Disease.

**HMM** Hidden Markov Model.

**LTOT** Long-term oxygen therapy.

**NIV** Non-invasive ventilation.

**OVD** Obstructive ventilatory defect.

**SpO2** Oxygen saturation.

**YLL** Years lost to disability.
# Part I

## Introduction
# Chapter 1

## COPD

Chronic Obstructive Pulmonary Disease (COPD) is a chronic disease mostly associated to tobacco smoking and characterized by a chronic dyspnea and repetitive crisis. Although it is treatable and preventable at first stages, COPD is one of the main causes of morbidity and mortality worldwide, being a leading problem of public health [35]. In this chapter, we present the disease, going through different medical aspects. Its complexity, importance and cost for our society are in the core of this work motivation.

### 1.1 Signs, diagnosis, prognosis

COPD is a chronic respiratory disease physiologically characterised by an Obstructive ventilatory defect (OVD) not fully reversible. This means that the patient presents a persistent obstruction in the airways which cannot be reverted with treatment. The first symptom perceived by the patient is dyspnea, present mainly at effort. With the disease evolution, the symptoms become more frequent and multiple, interfering in the patient's life quality.

The diagnosis is done by an examination called spirometry, the most objective and reproducible method for testing lung function [75] (more information in Section 2.6.1). The level of obstruction is quantified by assessing the values of maximum First second expiratory volume (FEV1). The examination is executed before and after bronchodilator administration and, in case of obstruction with little to no reversibility, a COPD is diagnosed.

The characteristics of COPD are near to those presented by patients with asthma. What differentiates both diseases is the complete reversibility after bronchodilator therapy, observed only in asthmatic patients.

Pathologically, COPD is caused by an abnormal lung inflammation due to chronic irritants. It may be associated with chronic bronchitis and/or emphysema, although neither of those conditions are required for COPD diagnosis.

One of the chronic problems, the chronic bronchitis, is associated to mucus hypersecretion, resulting in chronic productive (“wet”) cough. Mucus accumulation may result in airway narrowing and air trapping, in which case it corresponds to COPD. The other problem is the destruction of the parenchymal tissue, resulting in emphysema. The structural issue reduces the lungs capacity to recoil and interfere on gas exchanges.

As the condition evolves, symptoms also develop and become more present. Shortness of breath (dyspnea) is the main symptom. Initially, it only occurs with exertion, but as the disease progresses it may become more severe and be present during simple daily activities. Dyspnea is a subjective sensation, often underestimated by patients, who rarely consult
before an advanced stage of functional deterioration. The evolution of breathing difficulty often leads to a reduction in daily activities and a deterioration in the quality of life. Other symptoms include cough, expectoration and wheeze. The loss of skeletal muscles strength may be a consequence of a dramatic evolution of the disease.

In addition to chronic symptoms, patients may present periods of acute worsening of symptoms, called exacerbations. Exacerbations are characterized by a worsening of a patient's condition beyond daily variations, lasting more than 48 hours or leading to a change in usual treatment [22]. The main trigger are bacterial and/or viral infections. Spikes in pollution and other environmental changes can also trigger exacerbations. However, in about a third of cases no specific triggering factor can be identified [22]. These episodes increase mortality risks and require additional medical care.

## 1.2 Epidemiology

### 1.2.1 Descriptive epidemiology

In France, COPD prevalence was at 7.5% among population over 40. It was estimated to be more important among men and to increase with age, achieving 11.2% for population above 70 years-old [78].

Globally, the prevalence was estimated at 11.7% in 2010, an increase of 69% in two decades [1]. In the same year, COPD ranked third in the list of the leading causes of mortality globally, being responsible for around 3 million deaths [53, 69].

Besides, the COPD prevalence is said to probably be under-estimated. Patients may not contact healthcare until moderate-to-severe stages of the disease and the access to proper examination for diagnostic may be difficult in some contexts, leading to under-diagnosis [33, 42].

COPD is also responsible for an important loss in quality of life. Disability-Adjusted Life Years (DALY) is an indicator that combines Years lost to disability (YLL) and years lost to disability (YLD) to express the number of years of life lost due to premature mortality and to disability. In this way, diseases and injuries that cause low mortality with high disability may be compared with diseases causing high mortality and low disability. Globally, DALY concerning COPD has been increasing. In 2013, COPD was the 5th leading cause of DALY in the world [63]. In the USA, it was in second place in 2010, only behind ischemic heart disease [64].

Moreover, as world's population presents an increase in longevity, the exposure to risk factors and its consequences will be important. It is projected that COPD will remain among the seven leading causes of DALY and the fourth main cause of mortality worldwide [55]. According to the WHO's projections of mortality and causes of death, COPD should represent more that 7 million deaths per year by 2060 [69].

The negative impact of COPD on the aging population, enhanced by exacerbation prevalence, makes COPD a major public health problem in high-income countries, like France.

### 1.2.2 Analytical epidemiology

Cigarette smoking is known to be the main causal factor for developing COPD. Indeed, in industrialized countries, the majority of deaths caused by COPD are attributed to smoking. For men, they represent 84% between 30 and 69 years-old and 77% above 70 years-old. For women, 62% and 61% respectively [28].
Multiple studies have shown that smoking has a prejudicial effect on lung function. It may affect lung development during childhood and adolescence reducing peak FEV1 and enhancing or anticipating FEV1 decline through adulthood [48, 3, 46, 98, 94, 36, 20].

However, in developing countries, smaller fractions of COPD mortality are attributed to smoking: 49% among men between 30 and 69 years-old and only 20% in the case of women in the same age range. For people with 70 years-old or more, this fraction is even lower: 45 and 12% for men and women respectively [28].

Epidemiological studies have shown that smoking is not the only risk factor for COPD and that never-smokers can develop COPD [50]. In fact, indoor and outdoor air pollution is also associated with increased chances of developing COPD [84, 26, 35]. Generated by the use of biomass fuel and coal for cooking or to pollutants from industries and traffic, these factors are especially important in under development countries.

Moreover, poor socioeconomic status and low level of education have also been shown to be contribute to the risk of developing COPD [40, 73].

Hence, COPD also represents a health problem in low- and middle-income countries. Although the burden levels may vary between countries and populations, COPD is a global issue with worldwide consequences.

## 1.3 COPD severity (GOLD)

The degree of bronchial obstruction can be objectively quantified by spirometry. The intensity of symptoms, especially dyspnea, is more subjective and can be quantified using questionnaires. The frequency of exacerbations and the presence of comorbidities are also important factors in determining the prognosis [35].

Global Initiative for Chronic Obstructive Lung Disease (GOLD) proposes a classification of the severity of COPD according to the severity of their bronchial obstruction (Table 1.1). Spirometry should be performed after administration of an adequate dose of at least one short-acting bronchodilator. For simplicity, predefined thresholds are used by expressing FEV1 as a percentage of the theoretical value for an individual of the same age, sex, weight and height.

<table><caption>Table 1.1 – Classification of airflow limitation severity in COPD</caption><thead><tr><td>Grade</td><td>Severity</td><td>Definition</td></tr></thead><tbody><tr><td>GOLD 1</td><td>mild</td><td>FEV1 ≥ 80%</td></tr><tr><td>GOLD 2</td><td>moderate</td><td>50% ≤ FEV1 &lt; 80%</td></tr><tr><td>GOLD 3</td><td>severe</td><td>30% ≤ FEV1 &lt; 50%</td></tr><tr><td>GOLD 4</td><td>very severe</td><td>FEV1 &lt; 30%</td></tr></tbody></table>

However, this scale does not necessarily correspond to the severity of the symptoms experienced. Different questionnaires have been proposed to quantify it.

The Modified British Medical Research Council (mMRC) questionnaire is a simple measure of breathlessness considered adequate in the past. According to the mMRC, degrees of dyspnea range from 0, for shortness of breath only after heavy exertion, to 4, for shortness of breath while only getting dressed.

Today, other methods are more widely used, as the impact of COPD on the lives of patients goes far beyond dyspnea. The two main ones are the COPD Assessment Test (CAT) and the COPD Control Questionnaire (CCQ). These methods consider different scenarios such as the quality of sleep and the presence of cough and mucus.
Now, a more complete understanding of the impact of COPD on a patient's quality of life must combine symptom assessment with spirometry classification and the risk of exacerbations. Thus, the GOLD scale had to be revised to highlight the importance of preventing exacerbations and to include symptoms described by patients. From 2017, a new classification scheme is used (Table 1.2). It identifies four groups according to two factors of clinical severity: the exacerbation history and the presence of symptoms.

<table><caption>Table 1.2 – Classification of COPD clinical severity</caption><thead><tr><th rowspan="2"></th><th rowspan="2"></th><th colspan="2">Groups</th></tr><tr><th>C</th><th>D</th></tr></thead><tbody><tr><td rowspan="2">Exacerbation history</td><td>≥2 or ≥1 leading to hospitalization</td><td>A</td><td>B</td></tr><tr><td>0 or 1 without hospitalization</td><td colspan="2">mMRC &lt; 2 mMRC≥2<br/>CAT &lt; 10 CAT≥10</td></tr><tr><td colspan="3">Symptoms</td></tr></tbody></table>

The strategy is to combine the classification of the severity of bronchial obstruction (GOLD 1 to 4) with the classification of clinical severity (GOLD A to D). The former allows treatment strategies to be tailored to a specific patient and the latter allows attention to individual therapies and exacerbation prevention.

Thus, the prevention of exacerbation in this very frequent disease is becoming the center of governments' interests, targeting a reduction of hospital readmissions and the costs associated with it [65].

## 1.4 Treatments

Whatever the stage of the disease, patients should receive help in stopping smoking and appropriate pharmacological treatment. Moreover, patients should be given access to respiratory rehabilitation, including exercise training, respiratory physiotherapy and nutritional and therapeutic education. COPD treatment focuses in the improvement of quality of life, with reduction of the symptoms and of future risks of exacerbations.

The reduction of lung function decline is only possible with smoking cessation. It is the single strategy capable of reducing FEV1 decline. It is especially effective when quitting happens earlier in the disease development [48, 94, 20, 90]. Smoking cessation may also reduce the symptoms, risks associated with comorbidities and exacerbations.

Pharmacological treatment is used to reduce current symptoms, improving exercise capacity and quality of life. Although COPD is characterised by an airway obstruction not fully reversible, bronchodilators have shown to have an impact in the reduction of dyspnea. It might be explained by a partial reversibility in the bronchi, a reversibility in the small bronchi not detected by FEV1 measure or still a change not identified in the forced maneuver. Two types of bronchodilators can be used: anticholinergics and β2-agonists, alone or in association. They can be short-acting or long-acting according to the need of treatment for occasional or permanent symptoms, respectively. In some cases long-acting bronchodilators may also be associated with corticosteroids to reduce the symptoms and prevent exacerbation events.

In some specific cases, lung volume reduction surgery and lung transplantation may be considered.

Non-invasive ventilation (NIV) can be prescribed to assist inspiration through a periodic positive pressure. It is often combined with a lower continuous pressure in expiration.
This assistance is delivered through a nasal or face mask. The positive pressure opens the airway to facilitate air passage and gas exchange, reducing the concentration of carbon dioxide in the bloodstream. Thus, it is indicated for patients with chronic or acute hypercapnic respiratory failure. NIV assistance may significantly reduce work of breathing and dyspnea. For some patients, NIV may improve survival after discharge, reduce length of hospitalisation [35] and the risk of hospital readmission [62].

Patients with severe hypoxemia at rest are often prescribed with Long-term oxygen therapy (LTOT) administrated through nasal cannula. Air can be delivered in continuous or pulsed flow according to the oxygen source model. Pulsed oxygen concentrators only deliver oxygen during inspiration while continuous oxygen sources provide steady flow at specified rate. Unlike NIV, oxygen therapy does not generate ventilatory assistance, but increases the oxygen concentration of inspired air.

To avoid carbon dioxide retention, periodic re-evaluation is required, targeting an oxygen saturation between 88 and 92% [35]. LTOT through at least 15 hours per day has shown to improve survival rate in patients with severe hypoxemia [24].

In France, according to the last report of the *Association Nationale pour les Traitements A Domicile, les Innovations et la Recherche* (Antadir), about three quarters of COPD patients were under oxygen-therapy alone or combined with NIV or another treatment, being the most prescribed non-pharmacological treatment [8].

## 1.5 Exacerbations and economic burden

Exacerbations are usually associated with an increase in airway inflammation, mucus production and air trapping, which intensifies dyspnea, expectoration, cough and lung hyperinflation. These enhanced symptoms impact negatively the patient's quality of life [10]. The severity is variable, possibly requiring treatment in the city, in the event of a mild exacerbation, or hospitalization for moderate or severe exacerbations [35]. About half the cases even passes unreported [86, 108].

After an exacerbation, it may take several weeks for the patient to regain his previous physiological condition [75]. After 5 weeks, only 75% of the patients recover to the lung function baseline. After 3 months, 7% still have not [86].

The exacerbations lead to a severe worsening of the disease. With each new exacerbation, the chances of making a new exacerbation and the risk of mortality increase [97], at the same time as the pulmonary functions are weakened [45]. A combination of pulmonary rehabilitation, education and self-management interventions is important to prevent hospitalisations and improve health status and the management of future exacerbations [35].

Early management of exacerbations is essential to reduce mortality and limit the loss of ventilatory capacity. Not seeking treatment in the early stages of exacerbations is associated with poorer quality of life and greater risks of emergency hospital admissions. In the other hand, starting treatment as early as possible has a significant influence on rapid recovery [108].

Besides, exacerbations also represent a significant economic burden. In France, the average cost of COPD is € 5,516 per year per patient. Each exacerbation treated in town has an average additional cost of € 1,467 and those with hospitalization produce an additional cost of around € 8,300 each [51].

A review published in 2020, analysed the costs related to COPD worldwide [42]. They noted that the costs vary across and within countries. The lowest and highest reports of cost related to COPD per patient per year were found in Italy, with € 1,047 for patients
with mild COPD and € 38,820 for patients with very severe COPD. In Italy the mean cost for a hospitalisation due to an exacerbation is on average US$ 3,164 per year, while in the United States a hospitalised exacerbation has the highest cost: US$ 18,120 per year.

Despite the different expenses among countries, the most important cost is related to severe exacerbations requiring hospitalisations. In an attempt to reduce expenses and improve the quality of care, some countries (USA, UK, Australia) have implemented a program to establish penalties for frequent hospital readmissions. In the United States, COPD-related readmissions were not impacted by the COPD-related penalties from the Hospital Readmission Reduction Program [65]. Thereupon, other ways of decreasing the cost of COPD must be explored.

In France, telemonitoring of COPD patients have been contemplated by government funding since 2018, through a project named ETAPES [92]. With the objective of improving health care pathways, focus is given to the monitoring of NIV parameters. However, as previously stated, patients treated with NIV only correspond to a small portion of the population. Therefore, more extensive monitoring tools should be considered to cover a larger number of patients.

## 1.6 Problem and hypothesis

COPD is a complex disease of high prevalence worldwide. It represents one of the main causes of morbidity and mortality, contributing to important economic and public health burdens. The exacerbations are periods of acute deterioration of the disease, able to emphasize its already adverse outcomes.

A good management of the exacerbations is important to reduce the economic and social consequences, but there seems to be a problem in the reporting behavior (many late reported or not reported exacerbation cases).

Our hypothesis is that for reducing COPD consequences in society, it is necessary to stimulate and improve early management of COPD exacerbations by applying new tools and artificial intelligence for the detection of changes in the condition of the patient in respect to his own respiratory mechanics.
# Chapter 2

## Respiratory mechanics

Patients with COPD undergo a series of physiological changes. To understand how this changes influence exacerbations, this chapter explains some important concepts of respiratory mechanics in healthy and COPD patients.

Respiration is a rather complex process, controlled by both voluntary and involuntary components and guided by a set of receptors and neurotransmitters, willing to maintain homeostasis. Breathing needs to adapt to a series of situations. The changes can be environmental like the composition of the air, the presence of irritants (e.g. the pollution) and variation of the temperature and humidity. Daily behaviours and activities also affect breathing, as crying, laughing, speaking, singing, sleeping, exercising and many others, including changes in body position and emotions.

Most time, we are not conscious about those changes. That is because ventilation happens in an involuntary manner, which is essential for life sustenance. The purpose of breathing is to exchange gas between interior and exterior, bringing in oxygen and expelling carbon dioxide.

It is important to differentiate between two types of breathing: the tidal or quiet breathing (also called eupnea) and the forced (or maximal) breathing. The former is associated with resting and involuntary respiration and the latter is related to exercising and conscious breathing.

The two phases of breathing are inspiration and expiration. Succinctly, inspiration happens when a central command is sent through nerves to respiratory muscles that contract. With the contraction, the ribs and the sternum move outwards, increasing the thoracic cavity volume and decreasing its pressure. These modifications will cause air to flow inside the lungs. In quiet breathing the inspiratory muscles are the diaphragm and the external intercostals. In forced inspiration, accessory muscles are also required so thoracic volume increases even more. Some of the respiratory accessory muscles are the sternumcleidomastoid, scalenes and pectoralis minor.

Inspired air, rich in oxygen, is brought to the alveoli, where gas exchange with the bloodstream takes place. The bloodstream loads in oxygen and discharges the carbon dioxide.

In quiet breathing, expiration is completely passive. At the end of inspiration, chemical feedback will inhibit the inspiratory centers in the medulla. The inspiratory muscles relax, the lungs recoil, the thoracic cavity volume decreases while the pressure increases, allowing air to flow out. In case of increased respiratory need, like physical effort or a respiratory trouble, forced expiration requires muscles, as the abdominal wall muscles and the internal intercostals.
## 2.1 Lung volumes

The lung volumes are the amount of air engaged at different phases of the respiratory cycle (Figure 2.1) [34, 74].

The total lung capacity (TLC) is measured when the lungs are at their fullest, after maximal forced inspiration. At TLC the force of the muscles at maximal inspiratory effort and the elastic forces of the respiratory system balance.

<figure><img src="image_4.png" /><figcaption>Figure 2.1 – Representation of the lung volumes</figcaption></figure>

The vital capacity (VC) is the amount of air that can be exchanged with maximal breathing, i.e. the volume that can be exhaled after maximal inspiration. It is composed by :

* Tidal volume ($V_T$): the volume engaged in quiet breathing.

* Expiratory reserve volume (ERV): maximal volume that can be expired from the end of tidal expiration.

* Inspiratory reserve volume (IRV): maximal volume that can be inspired from the end of tidal inspiration.

The inspiratory capacity (IC) is the maximal volume that can be inspired after a tidal expiration ($IC = IRV + V_T$).

The volume of air from the TLC that does not participate in the VC is called residual volume (RV). It is the volume remaining in the lungs even after forced expiration, when the pressure in the respiratory system is balanced out by the effort of the expiratory muscles.

Finally, the functional residual capacity (FRC), also called end-expiratory lung volume (EELV), is the volume remaining in the lungs at the end of tidal expiration.

## 2.2 Minute ventilation

Minute ventilation ($\dot{V}_E$) is the respiratory volume moved in 1 minute. Thus, this indicator of the ventilation is not a volume, but a flow. It is therefore defined by the relation $\dot{V}_E = f_R \times V_T$, where $f_R$ is the respiratory rate and $V_T$ is the tidal volume, which can be visualized as the depth of breathing [102].
Different approaches can be used to increase or decrease the $\dot{V}_E$. The contributions given by the $f_R$ and/or the $V_T$ vary according to the individuals and the types of stimuli. Figure 2.2 presents a schema of those changes in case of increased respiratory demand. As represented in the figure, for increasing the $V_T$ part of ERV and/or IRV is engaged in breathing.

<figure><img src="image_5.png" /><figcaption>Figure 2.2 – Representation of the lung volumes adaptation in case of increased respiratory demand</figcaption></figure>

Even in a healthy individual, the path chosen for increasing the $\dot{V}_E$ has a significant impact on his alveolar ventilation $\dot{V}_A$, the amount of air actually available for gas exchange.

With each breath, part of the inspired volume does not participate in gas exchange. This volume, called physiological dead space ($V_{Dphys}$) is of two types. The first is the anatomical dead space, formed by the airways which do not carry out gas exchange, such as the nose, pharynx and trachea. The second type, called alveolar dead space, includes alveoli that are poorly ventilated or poorly perfused and can be increased in the case of certain respiratory diseases. $V_{Dphys}$ varies from person to person and is constant at each breath. Thus, a larger fraction of the inspired air will not be available for gas exchange during shallower breathing.

The wasted ventilation is represented by $\dot{V}_D = V_{Dphys} \times f_R$. And $\dot{V}_A = \dot{V}_E - \dot{V}_D$.

To respond to changes in ventilation demand, the $\dot{V}_E$ can be adapted by modifying at least one of the following four parameters: i. inspiratory flow and ii. duration of inspiration, which determine the volume at the end of inspiration, and iii. expiratory flow and iv. duration of expiration, which determine the volume at the end of expiration. The combination of these variables will change the tidal volume (by the inspired and exhaled volumes) and/or the respiratory rate (by the duration of inspiration and expiration).

Adapting $f_R$ is the cheapest in terms of the average force exerted by the respiratory muscles. Since different $f_R$ and $V_T$ can be used to obtain the same $\dot{V}_A$, in one extreme we would have a very low $f_R$ which requires a very large $V_T$, requiring muscular strength important to compensate for the elasticity of the lungs and rib cage. And in the other extreme, low $V_T$ associated with too high $f_R$ also represents a significant muscular demand, because of need to compensate for the ventilation wasted by the dead spaces and to undergo
resistance due to higher airflow. The optimal $f_R$ is found between these two extremes [57]. However, in COPD patients, adaptations of $V_T$ may be restricted because of lungs hyperinflation, loss of elasticity or even the reduction of muscles capacities. Similarly, $f_R$, and specially the duration of expiration, is constrained by airway obstruction. In COPD, dyspnea at rest and exercising can be associated with predominant increase of $f_R$ or of $V_T$ [66], being both parameters responsible for the regulation of the $\dot{V}_E$.

## 2.3 Pressures and flow

At each breath, changes in the lungs volumes arise thanks to cyclic pressure variations, following fluid dynamics rules.

Muscles and chest wall movements, in inspiration and in expiration, change the pressure inside the lungs. The pressure gradient is responsible for driving air in or out of the lungs. Fluid flows from a point with higher pressure to a point with lower pressure.

The relationship between the pressure drop and the flow is described by Rohrer's equation (Equation 2.3.1), where $\Delta P$ is the pressure drop, $Q$ is the flow and $k_1$ and $k_2$ are, respectively, the laminar and the turbulent flow coefficients [107, 93].

$$ \Delta P = k_1 Q + k_2 Q^2 \qquad (2.3.1) $$

This equation allows to combine both laminar and turbulent flows, which may occur at different proportions in different locations of the airway system. Laminar flow occurs when fluid flows in parallel layers and takes place essentially in the smaller airways. Turbulent flow, on the other hand, is characterized by chaotic changes in velocity and pressure, happening mostly in larger airways [37].

When the pressure in the thoracic cavity drops below the atmospheric pressure, air is drawn to move inside the lungs. At the end of inspiration, the intrapulmonary pressure is balanced with the atmospheric pressure. Then, respiratory muscles relax, increasing the pressure inside the thoracic cavity and pushing air outside the lungs.

The air passage is more or less difficult according to the airway resistance (Equation 2.3.2).

$$ R = \frac{\Delta P}{Q} \qquad (2.3.2) $$

Where $R$ is the airways resistance, $\Delta P$ is the pressure gradient and $Q$ is the airflow. The airway resistance depends on the diameter of the airway and the type of flow (laminar or turbulent).

The resistance to flow can be estimated according to the Poiseuille's Law in the cases of laminar (Equation 2.3.3) and turbulent (Equation 2.3.4) flows.

$$ R = \frac{8\eta l}{\pi r^4} \qquad (2.3.3) $$

$$ R = \frac{Qfl\eta}{\pi^2 r^5} \qquad (2.3.4) $$

Where $r$ is the airway radius, $l$ is the airway length, $\eta$ is gas viscosity and $f$ is a frictional factor. From these equations, we see that the resistance is inversely proportional to the radius of the airways, but also that a small change in the airway's diameter will have a great impact in its resistance (for example, a half of the radius corresponds to multiplying the resistance by a factor of 16, in the case of laminar flow) [37].
Another factor that influences the ventilation is the compliance of the lungs. The lungs tissue has elastic properties that enables them to distend and to recoil, following inspiration and expiration respectively. The compliance is the capacity of the lungs to stretch and is inversely proportional to the elastance (Equation 2.3.5).

$$E \approx 1/C \qquad (2.3.5)$$

The compliance of the whole respiratory system ($C_{rs}$) combines the compliance of the lungs ($C_L$) and the compliance of the chest wall ($C_{cw}$) [34].

$$\frac{1}{C_{rs}} = \frac{1}{C_L} + \frac{1}{C_{cw}} \qquad (2.3.6)$$

The compliance is inversely proportional to the elastance (Equation 2.3.5) and is computed with rate of the change in volume ($\Delta V$) over the change in pressure due to the respiratory system recoil ($\Delta P$) (Equation 2.3.7) [34].

$$C = \frac{\Delta V}{\Delta P} \qquad (2.3.7)$$

In healthy individuals, inspiration and expiration may be limited by muscles strength and/or lungs compliance, but they are not restricted by the airways resistance. However, in the case of COPD, resistance and lungs compliance play a major role in limiting the airflow. For patients with chronic bronchitis, airways narrowing is responsible for an increase in the resistance to airflow in the airways. Patients diagnosed with emphysema are confronted with an increase in compliance, as lungs elastic fibers are destroyed, which can lead to lungs hyperinflation [37].

## 2.4 Lung hyperinflation

The increased resistance and compliance presented by patients with COPD have a specially important impact in the expiration. To understand the impact of this parameters in the ventilation of those patients, we can look at the time constant ($\tau$) that is defined by Equation 2.4.1 and corresponds to the time needed for expelling 63% of the air in the lungs [95].

$$\tau = C \times R = \frac{\Delta V}{\Delta P} \times \frac{\Delta P}{\Delta V/\Delta t} \qquad (2.4.1)$$

In healthy subjects at rest, expiring during $4\tau$ achieves 98% of exhalation. At this moment, the respiratory muscles are relaxed and the pressure inside the thoracic cavity balances out with the atmospheric pressure, the remaining volume in the lungs is called relaxation volume ($V_r$). Thus, in the case of healthy subjects at rest, the $V_r$ equals the FRC.

However, when $R$ and/or $C$ are increased, the time constant becomes greater. When the expiratory time is below $4\tau$, the complete exhalation is not reached. In that case, inspiration starts before achieving the $V_r$. Therefore, $FRC > V_r$ and the end-expiratory pressure in the lungs stay above atmospheric pressure (intrinsic positive end-expiratory pressure - PEEPi) [95, 34].

The accumulated effects of air trapping over several consecutive breaths lead to pulmonary hyperinflation, which can be static or dynamic. Dynamic and static hyperinflation can occur together or independently [30].
Static hyperinflation appears when the decreased lung capacity to recoil leads tidal res-
piration to occur at larger lung volumes. Dynamic hyperinflation is related to a temporary
increase in FRC. It happens when the demand in $\dot{V}_E$ is increased, as during exercise. A
raise in $f_R$ leads to shortened expiratory time, while a raise in $V_T$ may be limited by the
reduced IC [95, 34, 30].

Dynamic hyperinflation reversibility is achieved by reducing the breathing rate (thus increasing the expiratory time) and by increasing the airflow (with pharmacological treatments, for instance) [34].

Breathing at higher lung volumes has the benefit of "pushing" the airways and increas-
ing its diameter, which reduces the expiratory flow limitation. However, breathing close to
the TLC means reducing the inspiratory muscles capacities. The diaphragm, for instance,
becomes shorter at its resting position, reducing its capacity to generate pressure. The
work of breathing is significantly increased. The central control may increase the ventilat-
ory demand, but the restriction in the IC and $V_T$ limits the adequate response. This leads
to a neuro-ventilatory dissociation and a rise in dyspnea [96, 95, 67].

Lung hyperinflation has significant consequences in the life of these patients, going from increased dyspnea to increased risk of mortality [67]. Its characteristics need to be taken in consideration when studying COPD respiratory adaptations because of the limitations in the respiratory patterns that it represents.

## 2.5 Respiratory variability and complexity

It is common to think about the respiratory parameters ($f_R$, $V_T$, inspiratory time, expiratory time, etc) as the mean values expressed through a certain time period. However, the measures of central tendency hide an important breathing parameter: the breath-by-breath variability. Indeed, healthy individual's breaths do not overlay perfectly over each other [85].

Central ventilatory drive is produced by a combination of many components and feedback loops. The generated signals are complex and anharmonic, which reflects in the characteristics of the breathing cycles. Thus, at some level, respiratory variability is considered healthy and its lack or excess can be pathological [85, 109].

Airflow complexity and breath-by-breath variability are connected to the neuromech-
anical coupling. It has been shown, for instance, that the administration of bronchodilators
or the use of ventilatory support reduce the mechanical load on respiratory muscles, thus
reducing hyperinflation, improving neuro-mechanical coupling and increasing $V_T$ breath-
by-breath variability [101].

Hence, the presence of respiratory variability is an indicator of good quality of breathing.
It demands however an investigation of respiratory changes in a small scale of time.

The physiological changes experienced by COPD patients directly impact their res-
piratory parameters. This phenomenon can be observed by either an evolution of the
parameters through time or even abnormal values.

## 2.6 Respiratory functional explorations

To evaluate the respiratory function, different functional tests have been designed. They
allow to assess patients specific capacities under controlled conditions, for diagnostic pur-
poses or for quantifying the disease evolution. Traditionally, they are done occasionally,
upon medical prescription. For this reason, they only provide sparse information about
the disease evolution, not allowing for a continuous and frequent follow-up.
### 2.6.1 Spirometry

The spirometric examination is used for measuring the ventilatory function, by quantifying the respiratory volumes and flows at specific conditions. It is the most important examination for diagnosing the COPD because it allows assessing the airway obstructions.

For the test, the patient breaths through the mouth in a device called spirometer. A nose clip is used to avoid air passing through the nose. The test starts by quiet breathing, followed by forced breathing. The patient is invited to exhale as strongly as possible, during at least 6 seconds, before taking a rapid inspiration. The absolute measures can be compared with “predicted values”, estimated for individuals of same sex, age, height and weight.

For COPD diagnosis, the test is executed before and after bronchodilators administration. The most important measurements are maximum first second expiratory volume (FEV1) and the FVC.

The FEV1 indicates the maximal amount of air exhaled during the first second of expiration. Comparison of FEV1 values before and after administration of bronchodilators indicates persistence or reversibility of TVO. With the increase in the airway resistance, FVC can also be reduced. Thus, the ratio FEV1/FVC is different according to different pathologies. In the case of COPD, the reduction in the FEV1 tends to be more important. An FEV1/FVC ratio <70%, persisting after bronchodilator administration and together with symptoms, confirms the diagnosis of COPD. Moreover, a decline in FEV1 has been shown to be related to an increase in the frequency of exacerbations [25].

Spirometry results also include spirograms, which are graphical representations of the results. One current graphic is the flow-volume loop. A schematic representation is given in Figure 2.3.

<figure><img src="image_6.png" /><figcaption>Figure 2.3 – Flow-volume loop representation. Dashed blue loops represent quiet breathing and continuous brown loops represent forced breathing. Light gray loop corresponds to forced healthy breathing for reference. Arrows in the healthy plot indicate the breathing direction.</figcaption></figure>

The flow-volume loop is a visual representation of the relation between flow and volume. As discussed above, it is expected that the airflow is lower at low lung volumes because of the reduced elastic recoil of the lungs. In his graphics, inspiration is represented downwards and expiration upwards. For healthy subjects, there is an important difference between quiet and forced breathing.
This difference is limited in the flow-volume loop of COPD patients. The flow limitation that characterizes the disease can also be observed by a reduction of the peak expiratory flow. If the patient has an hyperinflation, it will be perceived by a drift in the volume axis, the loop remaining at higher lung volumes (note the inversion of the axis as it is customarily presented).

The results of spirometry give an overview of the state of the respiratory system, in particular about its mechanics. The evolution of FEV1 is specially important to the monitoring of COPD progression, since it can be related to increased symptoms and exacerbations. Still, although the exam is safe and painless, the required respiratory effort can be challenging for some patients and the adherence to frequent measuring can be precarious [23, 59].

## 2.6.2 Polysomnography

The polysomnography is the gold standard examination for assess respiration problems during sleep. Patient's physiological indicators are recorded during one night, including breathing rate, heart rate, oxygen saturation, brain activity, eye movements, chest and abdomen movements.

It is a complete examination, presenting high accuracy. However, it relies on specialized medical centers, where the patients sleeps for one night with many wire attachments to the body. Hence, it is not comfortable for the patient and expensive.

## 2.6.3 Exercise testing

The ventilatory limitation that characterises the COPD has extra-pulmonary consequences that cannot be assessed with the spirometry. As previously described, the changes in the respiratory function limit the patients ability to adapt to conditions requiring an increase in ventilation. Thus, patients tend to exercise less. Assessing the patients capacity to walk is an inexpensive way to measure the functional capacity of the patient that reflects in the everyday life quality.

In this context, the 6 minutes walking test (6MWT) is among the most used exercise test for monitoring COPD patients. It consists of measuring the distance walked during a 6 minutes period. The patient is allowed to stop and rest and to choose the walk rhythm. He/she is encouraged to walk the longest distance possible. Heart rate and SpO2 are monitored before and after the test (and sometimes during).

The distance covered is then compared to a theoretical distance, computed from a formula that takes into account the sex, age, height and weigh of the patient [27].

This simple test provides convenient information regarding the patient prognosis. It assesses exercise tolerance as well as the effectiveness of the respiratory rehabilitation. Poor 6MWT results are not only connected to poor quality of life, but are also associated with increased frequency of exacerbation and mortality [25].

## 2.7 Problem and hypothesis

Breathing is a complex process that adapts in different ways to different stressors.

In healthy subjects, breathing takes place with a good balance between respiratory load and compensation capacity. At rest, a small proportion of the capacity of the respiratory muscles is sufficient to compensate for the respiratory loads which are also low. During an increase in the respiratory load (pneumonia, asthma attack, physical exertion, etc.),
the activity of the respiratory muscles can be adapted without exceeding their maximum capacity.

In the other hand, a patient with COPD, even at his baseline, has a precarious load-capacity balance. Its basal level of load is already high because of the resistance in the airways (inflammation of the bronchi, overproduction of mucus and chest distension). To compensate for this excess load, the respiratory muscles of these patients are wore out. In addition, COPD often comes with muscle weakness, which reduces the ability of the respiratory muscles to compensate for this load.

Because of these limitations, COPD patients are more vulnerable to load-capacity imbalances. During an episode of acute respiratory infection, even a moderate increase in the respiratory load may be greater than the compensatory capacity of the respiratory muscles, which are already constrained at baseline. This decompensation generates an increase in symptoms such as dyspnea and coughing and a reduction in oxygen saturation.

Thus, the balance changes related to exacerbations should be perceivable by assessing physiological variables, which are influenced by the respiratory mechanics of the patient. Current evaluations of physiological variables rely in sporadic examinations generally performed in a clinical context.

Our hypothesis is that the continuous monitoring needed could be achieved with monitoring technologies that enable patient monitoring at home.
# Chapter 3

## Telemedecine

Telehealth and telemedicine are two terms used to encompass different types of interventions that use information and communication technologies to provide or support health-care. Their goals include the reduction of the number or duration of hospitalisations, improvement of quality of life through health education, confirmation of treatment adherence, extended accessibility to patients living in isolated areas, quick identification of health decline and cost reduction [5, 12].

Since 2020, the coronavirus disease 19 (COVID-19) pandemic has made the access to face-to-face consultation more limited, and the use of telemedicine more necessary and common. COPD patients tend to be older and with multiple comorbidities, which makes them more vulnerable to COVID-19 complications.

Teleconsultation is one of the modalities of telehealth. It refers to a consultation between patient and healthcare provider, via telephone or internet, in real time or not. There are not many studies assessing the effectiveness, safety and economic outcomes of COPD teleconsultation [12], but in the pandemic context, teleconsultations have become a reality even for COPD patients [35].

Another category of telemedicine more documented in the literature is the telerehabilitation. Remote exercise supervision and counseling through video-conference are part of respiratory telerehabilitation programs, which have become more common since COVID-19 outbreak [103]. For example, before COVID-19, only 2% of pulmonary rehabilitation programs in the United States had access to video conferencing. During the pandemic, it increased to 50%.

Although no improvement compared to traditional rehabilitation has been identified, the vulnerability of COPD patients has justified the value of using remote monitoring during the pandemic. Moreover, study outcomes are rather positive. Telerehabilitation seems to be safe and beneficial for COPD patients and there are evidences of symptoms reduction, exercise tolerance improvement and gain in quality of life [12].

Yet another type of telehealth intervention that has been receiving increasing attention is telemonitoring. It has the potential to complement conventional and remote healthcare and to assist decision making. Although remote monitoring is not yet a regular practice, an important effort is being held for developing the technologies. Further details of studies and tools related to telemonitoring are presented hereafter.

### 3.1 Solutions for telemonitoring

Thanks to the evolution of technology (miniaturization, sensors and data transmission technologies), a rise in portable devices technologies now allows a more continuous assessment
of the patient's physiological variables.

Sporadic spirometry examination, for instance, can now be replaced by more frequent measures thanks to modern spirometer models. With these devices, patients can take daily or weekly measures from home, possibly allowing for a richer comprehension of the patient's disease evolution. Nonetheless, the method requires patient's collaboration and ability to execute the requested maneuver without the technician help, which can lead to usability limitation and less reliable results [7].

Without the need of any specific maneuver, the forced oscillation technique is another technique that can be used to assess respiratory function at home. The device is also placed in the mouth of the patient, that maintains quiet breathing, while the devices quantifies lung mechanical properties (impedance, resistance and reactance of the respiratory system) [7]. The required maneuver is simple, but patient adherence is still essential for maintaining frequent monitoring.

The oxygen level in the blood, indicated by the oxygen saturation (SpO2), is another important physiological parameter for COPD patients. Finger pulse oxymeters are often used by patient for self-monitoring, but modern models are also compatible with remote monitoring. Some models allow for continuous measures, while other rely on intermittent usage. The latter can be uncomfortable for long-term use and thus also depend on regularity of assessment. Moreover, SpO2 is not informative of the health status when the patient is under oxygen therapy, mixing information about physiological oxygenation capacity and treatment adequacy.

Other devices aim for a more continuous monitoring. Many rely on movement detection of some specific body parts, mainly chest and abdomen, often measuring $f_R$, $V_T$ and/or $\dot{V}_E$. Devices often come in form of bands, shirts or sensors taped directly on the skin [29, 54, 7, 66]. Wearable devices can cause discomfort and require a behavioral adaptation for adherence to the method.

These disadvantages could be eliminated by the use of contactless technologies, like radar or cameras, to identify chest displacement [52, 11, 99]. This type of technology has a major drawback that is its fixed position, limiting the monitored space. Thus, focus is being given to the monitoring of sleeping periods only.

Yet another way of approaching the remote monitoring question is to lean on non-pharmacological treatment devices. With this approach, the adherence to monitoring only depends on the adherence to the treatment, which can be a major advantage for the consistency of the data.

Some NIV machines, for instance, are furnished with a monitoring system that records information about adherence, breathing rate and number of respiratory cycles triggered by the patient [4]. In the case of oxygen therapy, the oxygen sources are usually not embedded with a monitoring system, but they can benefit from monitoring devices plugged in the oxygen circuit [91]. Although this approach is limited to the patients under these treatments, it has the convenience of not adding any new constraint or self-discipline, while also furnishing information about treatment suitability.

## 3.2 Remote monitoring of acute events

With the possibility of monitoring patients remotely, some studies have looked into the question of improving the management of COPD patients at home. The methods and monitored parameters are quite variable and the results are not unanimous.

For instance, the PROMETE study used daily measures of spirometry and oximetry to telemonitor COPD patients. Clinical alerts were sent to the clinical monitoring center when
measures were outside chosen thresholds. If considered appropriate, the pneumologist was
then contacted to treat the event, by prescribing a medical treatment by phone, visiting
the patient at home or advising the patient to go to the hospital, according to the gravity
of each case. This study has shown that it is possible to monitor patients at home and
that it allowed for identification of exacerbations and early intervention [87].

However, giving continuity to PROMETE, the study PROMETE II found no difference between telemonitored and not telemonitored groups, while following similar protocol on larger sample and with longer duration. This was interpreted by the authors as a sign that telemonitoring of physiological data alone is not sufficient for identifying exacerbations. According to them, the physiological changes perceived through the monitored measures would only reflect more severe exacerbations, and usually not in its early stages [6].

Similarly, in the CHROMED study, the telemonitoring by forced oscillation technique of 312 patients led to no change in the time to first hospitalisation or in quality of life [106].

Other studies have tested protocols combining telemonitoring with telecommunication between the patient and the healthcare professionals leading to more positive results. The COMET and NetKOL studies used physiologic measures with frequent phone or video calls. They have observed a reduced length of hospitalization after exacerbation, a reduction in mortality [47] and an increased quality of life [104].

In different circumstances, the TeleCRAFT trial observed an increase in the healthcare activity in the telemonitored group, compared with the control group. In this study, telemonitored symptoms and physiological measures could lead to teleconsultation, home visit or hospital visit, according to clinical judgment. Authors hypothesized that this arrangement could create a dependence between the patient and the healthcare providers. Thus, patients on telemonitoring present less developed self-care abilities and they end up relying more on healthcare team decisions [21].

Another problem raised by the authors concerns the treatment of the data. Indeed, some of the studies presented in this section rely on manual data treatment. The remaining studies, use clinical alerts that are based on simple thresholds manually defined by the healthcare professionals, either for each individual or for all patients combined. In both cases, an important effort from healthcare providers is requested to treat data, thresholds or alerts.

Therefore, currently, the detection of events may be suboptimal. For this reason, other studies have been focusing in the use of machine learning based methods that try to detect and predict exacerbation events.

## 3.3 Remote monitoring and intelligent exacerbation prediction

Given the economical and medical interest of predicting exacerbations, several researchers have studied the question. The approaches are quite variable, concerning the exacerbation definition, the parameters monitored and the statistical methods used. Therefore, in this section, some of these differences are detailed.

### 3.3.1 Exacerbation events

Firstly, there is no consensus in the definition of exacerbation. Indeed, as described in Section 1.5, an exacerbation stands for “a worsening beyond daily variation”, which is a subjective criteria. Thus, different studies may use different definitions.
The Anthonisen Criteria is commonly used. It is also called symptom-based criteria, as it defines exacerbation as an increase in three or more symptoms, including at least one major symptom (dyspnea, sputum amount and sputum purulence), during two consecutive days [9]. Variations of this definitions may be used. For example, [23] used a "modified Anthonisen Criteria" where an exacerbation is defined by an increase in two or more symptoms, including at least one major symptom during two consecutive days. Another example is given by [60], that uses variations of the number of major symptoms as one of the conditions for labeling days as low or high risk of exacerbation.

The studies using a symptom-based criteria usually conduct a telemonitoring of the symptoms perceived by the patients. This may be through questionnaires [16], phone calls [112] or smartphone/tablet apps [79, 41, 88, 59]. This allows for labeling data according to patient's perception.

Drug-based criteria uses the start of medication with corticosteroids and/or antibiotics as a sign of the onset of exacerbation. This allows for a less subjective criteria, although the decision to change medication still relies on medical judgement. Besides, there may be a delay between symptoms arise and patient seeking treatment. Thus, it is of note, that some studies will combine symptom- and drug-based criteria, as a confirmation of the relevance of these changes.

Event-based criteria are another type of definition given for those acute events. They are interpreted as non-scheduled healthcare contact, that can go from primary care doctor consultation to the emergency room visits or hospitalizations, depending on each study. Again, this criteria may be biased by a delay in seeking medical contact and/or by the severity of the event.

Some studies have tested multiple definitions of exacerbation, finding different performances according to the criteria [32, 31, 41]. Additionally, from the 367 events in the dataset used in [41], only 50 are confirmed by symptom-, drug- and event-based criteria.

With a more qualitative analysis, [18] compared symptoms and medication data from 19 patients and identified three types of exacerbations. The first group of exacerbations are those for which there is a notable change in the symptoms in precise periods, often accompanied by medication change. The second group contains exacerbations for which the changes in symptoms are less evident. These patients seem to never really achieve baseline and are often under antibiotic treatment. The third group includes patients that often present levels of symptoms that would characterize an exacerbation, but they rarely took antibiotics.

These studies show the relevance of exacerbation definition in the obtained results. In fact, there is no unique definition that can really cover all exacerbation events. Moreover, onset date is easily biased by patient's perception and the delay to seek treatment. Thus, medical judgement may be a more flexible criteria given all exacerbations particularities and if considering that healthcare providers have sufficient information for a less biased exacerbation recognition.

### 3.3.2 Periods type definition

Once the exacerbation event defined, the different periods can be labeled according to health status of the patients. Different studies will also use different methods for labeling data periods. One can, for example, focus on the date of onset of the exacerbation, while others will be interested in the period preceding an exacerbation.

Exacerbation duration is yet another question, as it may be quite variable. [79] defined the end of the exacerbation as the first two consecutive days without worsening of the
symptoms. However, most other authors use fixed duration.

To make opposition to the exacerbation phases, studies also define control or baseline
periods. These are the periods when no acute event was recorded and with sufficient
distance from previous and next exacerbations.

This sufficient distance before and after exacerbations may vary in different studies. These latent periods may also be labeled in some cases. The prodromal phase corresponds to the period preceding an exacerbation, when we can no longer consider that the patient is at his/her baseline but the exacerbation has not yet started. The recovery phase is the one that follows an exacerbation, when the patient has left his or her acute state and before stability is achieved.

The duration of these periods is often given by a fixed value. [49], for example, used one month for the prodromal phase and two weeks for the recovery.

To avoid this fixed approach, [88] has used a finite-state machine (FSM) to define “normal”, “exacerbation” and “transitional” periods. With this mathematical model, the machine models a patient, that can only be in one of the given states at a time: “normal”, “exacerbation” or “transitional”. The transitions are defined according to changes in symptoms and/or medication. For example, it is defined that when a patient in the “normal” state get worsen symptoms, he/she transitions to the “transitional” state if there was no change in medication and to the “exacerbation” state if there was a medication change. Details in the transition rules are given in [88].

This approach showed that patients going from “normal” state to “transitional” and then back to “normal” almost never (97%) need to change medication to do so. This indicates that patients may present a normal variation in the symptoms that do not necessarily imply an acute event.

3.3.3 Parameters choice

The prediction of exacerbations is studied through different combinations of parameters.
Table 3.1 summarizes the parameters of choice in different studies of exacerbation detection.

Telemonitored patients are often equipped with one or more devices used to record physiological measures. Data can be collected manually a posteriori or be sent for a secured data center through Internet.

Some measuring devices include spirometry (FEV1, inspiratory and expiratory times), oximetry (SpO2, pulse rate, breathing rate) and forced-oscillation technique (reactance and resistance). Other physiological indicators also studied in the context of exacerbation prediction are: blood pressure, weight, body temperature and breathing rate.

Prediction models based on physiological data lead to promising results although often
combined poor sensitivity and/or specificity. For example, models based on heart rate,
SpO2 and breathing rate achieved a sensitivity ranging from 60%-80% with specificity
between 68%-36% in [88]. This corresponds to correctly identifying 6 out of 10 prodromal
periods, while missclassifying 3 stable periods out of 10. Or, in case of targeting 8 predicted
exacerbations out of 10, obtaining 6 false alarms out of 10.

For [43], the best results were achieved when using the standard variation of the SpO2 computed over 30-day periods. Sensitivity of 70% with a specificity of 95% were obtained, but dataset comprised only 9 patients. In [68], the best model used 135 variables, comprising physiological data from oximetry and spirometry among with symptoms and medication. With a sensitivity of 80%, model's specificity was close to 60%.

Moreover, these measuring devices have the particularity of requiring intervention to
measure acquisition. Thus, although patients were requested to acquire new measures daily
or weekly, some studies reported inconsistent measurement frequency [68, 88, 43]. Also, measuring devices can sometimes be used by other people, such as a patient's relative, creating outliers in the dataset [43].

Less dependent on manual measures, some monitoring devices coupled with non-pharmacological treatments record relevant data from the patient's respiration. NIV machines, for example, can measure the breathing rate, percentage of triggered cycles, adherence to treatment, unintentional leaks and expired tidal volume [16, 15, 44]. Patients under oxygen therapy were monitored about breathing rate and adherence to the treatment [110]. However, although data is measured continuously during the treatment, studies usually retain only one measure of each indicator by day.

In [16], the risk of exacerbation was increased when breathing rate (sensitivity 46.2% and specificity 89.7%) or the number of NIV cycles triggered by the patient (sensitivity 53.8% and specificity 76.2%) was considered abnormally high for at least 2 days out of five consecutive days. For [15], on the other hand, it was the variation of the breathing rate that achieved the best results. A model based on standard deviation of breathing rate over 10-day period resulted in sensitivity of 61.9% and specificity of 75.6%. Similarly, the variation of the daily adherence to NIV treatment was also a predictor of exacerbation with sensitivity of 81.0% and specificity of 63.4%.

In the most recent study with NIV data, [44] was capable of predicting exacerbations based only on breathing rate with 93.5% sensitivity and 64.8% specificity. The model performance was increased when combining breathing rate with the number of days with abnormal values of daily use, leaks and tidal volume.

To our knowledge, [110] is the only study that tries to predict exacerbations with LTOT data. In this study an increase in breathing rate was able to predict exacerbations with a sensitivity of 66% and specificity of 93%, 24 hours before exacerbation.

Non physiological data were also used in exacerbation prediction investigations. [68] tried to complement physiological data with weather data, but no improvement was observed in their models. [49] were interested in the information contained in the population incidence and found that prediction of exacerbations was improved when using the frequency of exacerbation in all other patients monitored as one of the indicators.

Among those numerous options, the choice of the monitored parameters is not trivial. In fact, the importance of the different indicators varies among studies, that use different datasets and methods. The balance between sensitivity and specificity is extremely important in clinical decision support. While low sensitivity may leave many important events undetected, low specificity leads to high amount of false alarms, which represents an increased workload for healthcare providers and can lead to mistrust in the system.

Moreover, methods requiring patient or caregiver intervention often report infrequent measurements, which may limit the system long-term usability. That is the case of methods based on daily questionnaires, spirometry, forced-oscillation technique and oximetry. In this sense, physiological measures based on a non-pharmacological treatments have the advantage of not adding a new constraint for the patient.

The ease of use, the inclusion of most patients and the reliability of the monitoring device and its measures are essential to build a functional and trustworthy exacerbation detection method. Hence, indicators from oxygen therapy are good candidates for monitoring respiratory mechanics, still barely studied.
<table><caption>Table 3.1 – Summary of publications on exacerbation detection.</caption><thead><tr><th>Features</th><th>Performance</th><th>Advantages</th><th>Drawbacks</th><th>Reference</th></tr></thead><tbody><tr><td>Breathing rate</td><td>Sensitivity: 63%<br>Specificity: 85%</td><td>Online learning of “normality” limits. Data from non-contact biomotion sensor, no additional intervention needed. Any patient, independently of his/her treatment.</td><td>Limited sample (11 patients). Because of common sleep disorders in COPD patients, measurements may mix waking and sleeping periods and/or be biased by apnea events. Although multiple measures of breathing rate, each night is represented by its median or mode only.</td><td>[11]</td></tr><tr><td>Breathing rate, NIV adherence</td><td>For f<sub>B</sub>:<br>AUC: 0.675<br>Sensitivity: 57.1%<br>Specificity: 87.8%</td><td>Online learning of “normality” limits. Data from NIV, no additional sensor or intervention</td><td>Limited sensitivity or specificity. Day is represented by a single value of each feature.</td><td>[15]</td></tr><tr><td>Breathing rate, NIV adherence, % cycles triggered by the patient</td><td>For f<sub>B</sub>:<br>Sensitivity: 46.2%<br>Specificity: 89.7%<br>For %Trigg:<br>Sensitivity: 53.8%<br>Specificity: 76.2%</td><td>For daily adherence:<br>AUC: 0.703<br>Sensitivity: 81.0%<br>Specificity: 63.9%</td><td>Online learning of “normality” limits. Data from NIV, no additional sensor or intervention.</td><td>[16]</td></tr></tbody></table>
<table><caption>Table 3.1 – Summary of publications on exacerbation detection.</caption><thead><tr><th>Features</th><th>Performance</th><th>Advantages</th><th>Drawbacks</th><th>Reference</th></tr></thead><tbody><tr><td>Wavelets from respiratory sounds</td><td>Sensitivity: 78.1%<br>Specificity: 95.9%</td><td>Good performance, exacerbations were detected on average 4.4 days prior to onset.</td><td>Recordings need intervention from patient. Limited sample (15 patients, 41 exacerbations).</td><td>[31]</td></tr><tr><td>SpO2</td><td>AUC: 0.78<br>Sensitivity: 70%<br>Specificity: 95%</td><td>Low false positive alerts.</td><td>Missing data and outliers. Limited data (10 exacerbation periods and 19 control periods)</td><td>[43]</td></tr><tr><td>Breathing rate, daily usage, leaks and tidal</td><td>For f<sub>R</sub>:<br>AUC: 0.833<br>Sensitivity: 93.5%<br>Specificity: 64.8%<br>Performance is increased when combining breathing rate with other parameters, although exact performance values are not presented.</td><td>Data from NIV, no additional sensor or intervention.</td><td>Low specificity with breathing rate alone, high false positive alerts. Day is represented by a single value of each feature.</td><td>[44]</td></tr><tr><td>SpO2, weight and exacerbation incidence in population</td><td>AUC: 0.746</td><td>Three optimal predictors chosen among 29 candidate predictors.</td><td>Irregular frequency of measurements. The study considered exacerbation and control periods of 30 days with at least 3 measurements (rare measurements increase impact of outliers).</td><td>[49]</td></tr></tbody></table>
<table><caption>Table 3.1 – Summary of publications on exacerbation detection.</caption><thead><tr><th>Features</th><th>Performance</th><th>Advantages</th><th>Drawbacks</th><th>Reference</th></tr></thead><tbody><tr><td>FEV1, SpO2 and weight</td><td>Sensitivity: 61.1%<br>Specificity: 80.4%</td><td>Chosen method (CART) capable of handling missing data.</td><td>Classification between “low-risk” and “high risk” days, intermediate days were excluded from analysis. Limited sample (21 patients). Authors reported important amount of missing data.</td><td>[60]</td></tr><tr><td>Heart rate, SpO2, spirometry, symptoms, medication and weather</td><td>AUC: 0.740<br>Sensitivity: 80%<br>Specificity: 60%</td><td>Different machine learning methods were tested over the dataset, obtaining similar results.</td><td>The best model comprises 135 variables, leading to difficult interpretation. Authors reported important amount of missing data.</td><td>[68]</td></tr><tr><td>Heart rate, SpO2, breathing rate</td><td>AUC: 0.682<br>Sensitivity: 60%<br>Specificity: 68%</td><td>Exacerbation periods are defined by Finite State Machine according to self-reported symptoms and medication.</td><td>Daily recording with oximeter resulted in irregular number of recordings.</td><td>[88]</td></tr><tr><td>Breathing rate</td><td>24h before exacerbation:<br>Sensitivity: 66%<br>Specificity: 93%</td><td>Comparison with patient's own baseline. Data from oxygen therapy, no additional intervention.</td><td>Although recordings contain breathing rate at different times of the day, only the daily mean is used.</td><td>[110]</td></tr><tr><td></td><td>48h before exacerbation:<br>Sensitivity: 72%<br>Specificity: 77%</td><td></td><td></td><td></td></tr></tbody></table>
<table><caption>Table 3.1 – Summary of publications on exacerbation detection.</caption><thead><tr><th>Features</th><th>Performance</th><th>Advantages</th><th>Drawbacks</th><th>Reference</th></tr></thead><tbody><tr><td>Variability of inspiratory reactance from forced oscillation technique</td><td>AUC: 0.72<br>Sensibility: 69%<br>Specificity: 70%</td><td>Comparison with patient's own baseline. Consistent time of measuring.</td><td>Limited sample (15 patients, 37 exacerbations). Although missing data was not reported as a problem in this study, measurements require daily intervention by patients.</td><td>[112]</td></tr></tbody></table>
### 3.3.4 Statistical methods

A variety of statistical methods were applied to the exacerbation prediction problem. Most of them are supervised methods, including logistic regression [49, 88, 44], linear mixed-effects models [112], Classification And Regression Tree (CART) [60], random forest [31], among others.

All these methods have in common that they need to be trained with examples of both classes (baseline and exacerbation). In practice, for a model to be generalizable, it needs to learn the classification rules from a sufficient amount of baseline and exacerbation cases.

That is the major pitfall of supervised approaches, specially common in medical problems. Not only there is an important variability between patients and events, but also events tend to be rarer than normal cases. In the case of exacerbation prediction, for instance, it is unrealistic to aim for a dataset that contemplates all kinds of acute events.

Other studies have approached the problem by using novelty detection methods [15, 11, 16]. The idea behind these methods relies in defining the “normality” class that corresponds to the patient’s baseline. New days are then compared to this normality class and labelled as “normal” or “abnormal”. In these studies, frequent abnormal days were related to exacerbation onset.

Although supervised algorithm are useful at highlighting suitable parameters, they are hardly applicable in real life exacerbation detection, because of the high variability as previously stated. For this reason, novelty detection methods are more convenient for those situations.

## 3.4 Problem and hypothesis

The evolution of telecommunication technology has enabled the development of telemedicine and the diversification of its modalities. Different devices are now able to monitor physiological measures generating an important amount of data.

Numerous approaches have been tested in these data, already revealing the possibility of premature detection of acute exacerbations. However, these studies rely mainly in devices requiring intervention for data acquisition or in a reduced amount of daily data.

Our hypothesis is that a more continuous, autonomous and detailed monitoring of the patients’ respiration could lead to a richer insight in their healthy state, if associated with the appropriate artificial intelligence methods.
# Chapter 4

## Artificial intelligence

Remote monitoring devices allow for more detailed monitoring of COPD patients. However, these physiological measurements can quickly amass into large amounts of data, because of both the frequency of measurements and the number of patients concerned. Manual treatment of these data can rapidly become impossible.

Artificial intelligence has the potential to learn from previously recorded data to assist future clinical practice. It is not only capable of treating large amounts of data, in a continuous and automatic manner, but it can also learn previously unknown insights from the data.

In the case of COPD, the detection or prediction of worsening phases, like the exacerbations, is in the center of interests. In this chapter, we present the methods used in the different stages of this work.

### 4.1 Feature extraction from time series

A time series is a sequence of observations of the same phenomena at different points in time. Time series have the particularity of being indexed by time, which means that their points are not exchangeable and their order matters.

Time series can be presented at different scales of time according to the characteristic time of the observed phenomena. In fact, knowing how fast the changes of interest occur is essential to focus on the right scale of monitoring.

For example, the respiration process can be monitored with a sampling rate of multiple measures per second. The resulting time series may enable to observe each individual breath and to study the variations within and between breaths. However, when interest is given to the evolution of breathing within a day, week or month, a high sampling rate may become irrelevant or even disadvantageous.

Thus, feature extraction may be required to change time scale, also reduce dimensionality, reduce noise, treat missing data or change of space [100, 58].

Aggregation methods, for a start, can be employed to compress time series. The simplest aggregation method correspond to averaging the series over a subsequence.

The parameters that model the series can also be used to represent it. If the series can be modeled by a straight line, for instance, the slope and intercept may be sufficient. Still, more complex models for time series can also be used, like ARIMA.

Signal processing may be used to study data series in a different space. Fourier transforms, for instance, transform data from the time spectrum to the frequency spectrum, which can be useful for highlighting certain characteristics of the signal or focusing in a frequency range of interest.
### 4.1.1 Fourier transform

According to the theory of Fourier series, any periodic signal can be decomposed in sines and cosines at different frequencies and magnitudes (Equation 4.1.1).

$$g(t) = \frac{1}{2}a_0 + \sum_{n=1}^{\infty} (a_n \sin(2\pi nt) + b_n \cos(2\pi nt)) \quad (4.1.1)$$

The coefficients $a_n$ and $b_n$ correspond to the relative weights of each of the sinusoids that compose the function $g(t)$.

The Fourier transformation generalizes this reasoning for non-periodic functions and defines the relation between a signal $g(t)$ in the time domain and its representation $\hat{g}(f)$ in the frequency domain. The Equation 4.1.2 defines $\hat{g}(f)$ as a function of $g(t)$ and complex exponential. Complex exponentials are a convenient way of combining sine and cosine terms with the same frequency, as is stated by the Euler's formula $e^{jx} = \cos x + j \sin x$. The use of complex exponential makes computation easier and mathematically more elegant.

$$\hat{g}(f) = \int_{-\infty}^{\infty} g(t)e^{-j2\pi ft} \quad (4.1.2)$$

Since it is a transformation, no information is lost. In other words, $\hat{g}(f)$ contains the information for reconstructing $g(t)$ by combining sinusoids with different frequencies (Equation 4.1.3).

$$g(t) = \int_{-\infty}^{\infty} \hat{g}(f)e^{j2\pi ft} \quad (4.1.3)$$

In real world applications, sampling is not continuous and time frame is finite. Thus, the frequency spectrum $\{X_k\} : X_0, X_1, \dots, X_{N-1}$ of a sequence $\{x_n\} : x_0, x_1, \dots, x_{N-1}$ with $N$ samples can be estimated with a discrete Fourier transformation (Equation 4.1.4).

$$X_k = \sum_{n=0}^{N} x_n e^{-j \frac{2\pi k n}{N}} \quad (4.1.4)$$

$X_k$ are the Fourier coefficients that describe $x_n$ in the frequency domain. $X_k$ are complex numbers comprising a real part, noted $Re(X_k)$, and an imaginary part, noted $Im(X_k)$, that together encode the magnitude and phase of the complex sinusoidal component at frequency $k/N$. The magnitude $Mag$ is the absolute value of the complex number (Equation 4.1.5) and the phase $\theta$ is its angle (Equation 4.1.6).

$$Mag_k = |X_k| = \sqrt{Re(X_k)^2 + Im(X_k)^2} \quad (4.1.5)$$

$$\theta_k = \arctan \frac{Im(X_k)}{Re(X_k)} \quad (4.1.6)$$

In the discrete case, the frequency spectrum is limited by the sampling rate. According to the Nyquist-Shannon sampling theorem, the highest frequency in a signal is $Fs/2$, where $Fs$ is the signal's sample frequency. Moreover, the resolution in the frequency domain is given by $Fs/N$. Thus, for improved frequency resolution, sampling should be more frequent and/or more abundant.
## 4.1.2 ARIMA

Autoregressive Integrated Moving Average (ARIMA) is a modelisation approach for time series data relying on the assumption that the signal is autoregressive, that is the value at each time point can be written as resulting from a linear model according to the preceding points and their errors [17].

An ARIMA model is a combination of three components: i. the autoregression (AR) stands for a model where variable regresses according to its own preceding values; ii. the integrated (I) component refers to the differentiation of the original series so it becomes stationary; iii. the moving average (MA) introduces a linear regression of residual errors in the lagged observations. ARIMA is traditionally noted ARIMA(p,d,q), where p,d,q are non negative integers and represent, respectively, the number of autoregressive terms, the degree of differencing and the order of the moving average model. ARIMA is a generalization of the ARMA model, where a differencing phase is not performed. Thus, ARIMA(p,0,q) is the same as ARMA(p,q).

The differencing step is included in the ARIMA models to ensure the stationarity condition, necessary for the autogressive part of the model. Non-stationary series have properties that depend on time. For example, mean and variance may not be constant through time. One way of achieving stationarity is by differentiating the series.

Therefore, for an original univariate time series $y_1...y_t...$, the differenced series (Equation 4.1.7) replaces it in the autoregression and moving average models.

$$y'_{t} = y_{t} - y_{t-1} \qquad (4.1.7)$$

The series may remain non-stationary after the first differentiation, in which case, a second-order differencing may help achieving stationarity (Equation 4.1.8). The number of differencing steps is indicated by $d$ and the integrated model is represented by $I(d)$.

$$y''_{t} = y'_{t} - y'_{t-1} = y_{t} - 2y_{t-1} + y_{t-2} \qquad (4.1.8)$$

Autoregressive models consist of fitting a linear function in the $p$ preceding values to predict $y_t$ (Equation 4.1.9) and are referred to as AR($p$).

$$y_t = \mu + \sum_{i=1}^{p} \phi_i \cdot y_{t-i} + \epsilon_t \qquad (4.1.9)$$

$\mu$ is the signal constant, $\phi_i$ are the autoregression coefficients and $\epsilon_t$ is the random error related to the observation $y_t$.

A moving average model holds that the values in the series vary around the mean value of the series. In other words, a value in the series can be estimated by the $q$ preceding deviations from the mean (Equation 4.1.10). This model is represented by MA($q$).

$$y_t = \mu + \sum_{i=1}^{q} \theta_i \cdot \epsilon_{t-i} + \epsilon_t \qquad (4.1.10)$$

$\mu$ is the signal constant, $\theta_i$ are the moving average coefficients and $\epsilon_t$ is the random error related to the observation $y_t$.

The autoregression, the differenciation and the moving average models can be combined in a single mixed model. For example, the ARIMA(1,1,1) model follows the prediction Equation 4.1.11, where $\mu$, $\phi$ and $\theta$ are learned from the data.

$$y_t = \mu + y_{t-1} + \phi \cdot (y_{t-1} - y_{t-2}) - \theta \cdot \epsilon_{t-1} + \epsilon_t \qquad (4.1.11)$$
## 4.2 Classification in times series

With the extraction of the right features, the monitoring of longer characteristic time can evidence physiological changes in different scales of time, like days, weeks and months. For instance, a hidden Markov model can be used to identify different hidden states with a non supervised classification method.

### 4.2.1 Hidden Markov Model

A Markov model is a stochastic model that describes a Markov process. Markov process is a chain of events where the probability of the event at time $t + 1$ depends only on the event at time $t$, and not on previous events (on $t-1, t-2, ...$). This assumption is defined in Equation 4.2.1 for a sequence of states $s_0, s_1, ..., s_T$.

$$P(s_t = i|s_0, \dots, s_{t-1}) = P(s_t = i|s_{t-1}) \qquad (4.2.1)$$

A representation of a Markov chain with two states $i$ and $j$ is given in Figure 4.1. The series $S = s_0, s_1, ..., s_T$ is a series of states that can get values $i$ or $j$. The Markov chain is described by the parameters $\Pi_i = P(s_0 = i)$, the initial state probability, and $A = \{a_{ij}\} = P(s_t = j|s_{t-1} = i)$, the transition probability matrix, which is independent of time.

<figure><img src="image_7.png" /><figcaption>Figure 4.1 – Markov chain diagrams for two observable states</figcaption></figure>

In the Hidden Markov Model (HMM) the series of states $S = s_0, s_1, ..., s_T$ is not directly observed. Instead, the observations $O = o_0, o_1, ..., o_T$ are variables that depend on the hidden state. Thus, a new parameter $B = \{b_j(o_t)\} = P(o_t|s_t = j)$ defines the emission probabilities.

<figure><img src="image_8.png" /><figcaption>Figure 4.2 – Hidden Markov model diagrams for two hidden states</figcaption></figure>
## Estimate the model parameters

A hidden Markov model is described by the parameter $\Theta = (A, B, \Pi)$. $\Theta$ can be estimated from the observed data using the Baum-Welch algorithm, which is a special case of the expectation-maximization (EM) algorithm [2].

The objective of the algorithm is to find the local maximum for $\Theta^* = \underset{\Theta}{\operatorname{argmax}} (O|\Theta)$ through iterations of the forward and backward steps.

$\Theta$ is initialized randomly or with prior information. The algorithm starts with the forward procedure that consists of estimating $\alpha_t(j) = P(o_0, o_1, \dots, o_t, s_t = j|\Theta)$, the probability of observing $O_{0:t}$ and being at state $j$ at time $t$. The computation is recursive, with the following equations:

Initialization: $\alpha_0(i) = \pi_i \times b_i(o_0)$

Recursion: $\alpha_{t+1}(i) = b_i(o_{t+1}) \sum_{j}^{N} \alpha_t(j) a_{ji}$, with $1 \le j \le N, 0 \le t \le T$

Next, the backward procedure is used to estimate $\beta_t(j) = P(o_{t+1}, \dots, o_T|s_t = j, \Theta)$, the probability of future observations $O_{t+1:T}$ given that the state is $j$ at time $t$. Recursive computation used following equations:

Initialization: $\beta_T(i) = 1$

Recursion: $\beta_t(i) = \sum_{j}^{N} \beta_{t+1}(j) a_{ij} b_j(o_{t+1})$, with $1 \le j \le N, 0 \le t \le T$

Then, two temporary variables are estimated. The state occupation probability $\gamma_t(i) = P(s_t = i|O, \Theta)$ is the probability of occupying state $i$ at time $t$ given the series of observations $O$ and the parameters $\Theta$. $\xi_t(i, j) = P(s_t = i, s_{t+1} = j|O, \Theta)$ is the probability of occupying state $i$ at time $t$ and state $j$ at time $t+1$ given the observation $O$ and the parameters $\Theta$.

$$\gamma_t(i) = \frac{P(O, s_t = i|\Theta)}{P(O|\Theta)} = \frac{\alpha_t(i)\beta_t(i)}{\sum_j^N \alpha_t(j)\beta_t(j)}$$

$$\xi_t(i, j) = \frac{P(s_t = i, s_{t+1} = j, O|\Theta)}{P(O|\Theta)} = \frac{\alpha_t(i)a_{ij}\beta_t(j)b_j(o_{t+1})}{\sum_t^N \sum_w^N \alpha_t(k)a_{kw}\beta_{t+1}(w)b_w(p_{t+1})}$$

Finally, the parameters are updated using:

$$\pi_i^* = \gamma_0(1)$$

$$a_{ij}^* = \frac{\sum_{t=1}^{T-1} \xi_t(i, j)}{\sum_{t=1}^{T-1} \gamma_t(i)}$$

$$b_i^*(v_k) = \frac{\sum_{t=1}^{T} 1_{o_t=v_k} \gamma_t(i)}{\sum_{t=1}^{T} \gamma_t(i)}, \text{ with } 1_{o_t=v_k} = \begin{cases} 1 & \text{if } o_t = v_k \\ 0 & \text{otherwise} \end{cases}$$

If model estimation is based on $R$ sequences of observation $O_1, \dots, O_R$, the temporary variables $\gamma_{r,t}(i)$ and $\xi_{r,t}(i, j)$ are estimated for each sequence of observations and the parameters $\pi, A$ and $B$ are updated according to the following equations:
$$
\begin{align*}
\pi_i^* &= \frac{\sum_{r=1}^{R} \gamma_0(1)}{R} \\
a_{ij}^* &= \frac{\sum_{r=1}^{R} \sum_{t=1}^{T-1} \xi_{r,t}(i, j)}{\sum_{r=1}^{R} \sum_{t=1}^{T-1} \gamma_{r,t}(i)} \\
b_i^*(v_k) &= \frac{\sum_{r=1}^{R} \sum_{t=1}^{T} 1_{o_{r,t}=v_k} \gamma_{r,t}(i)}{\sum_{r=1}^{R} \sum_{t=1}^{T} \gamma_{r,t}(i)}, \quad \text{with } 1_{o_t=v_k} = \begin{cases} 1 & \text{if } o_t = v_k \\ 0 & \text{otherwise} \end{cases}
\end{align*}
$$

These steps are repeated iteratively until convergence.

4.2.2 Series likelihood under HMM

The likelihood of a sequence of observations given the model parameters can be estimated using the Forward algorithm. Instead of considering all marginal conditions, the Forward algorithm considers the conditional independence rule of the HMM that states that the observation $o_t$ only depends on the state $s_t$ and that the current state $s_t$ only depends on the previous state $s_{t-1}$.

Thus, the probability of the observation $o_t$ being in state $i$ ($\alpha_t(i)$) can be estimated according to the probabilities associated to the previous observations $o_{0:t}$. The recursive computation of the likelihood of the sequence of observations correspond to the forward procedure that was used to estimate the model parameters.

Estimate the optimal sequence of hidden states

The most probable sequence of hidden states $S^*$ given the observed series $O$ and the model parameters $\Theta$ can be estimated with the Viterbi algorithm [2].

The Viterbi algorithm relies on dynamic programming methods. A recursive computa-
tion is run by assuming that the most likely series of hidden states $S^*_{0:t}$ is generated by the
most likely series $S^*_{0:t-1}$. In other words, the probability $\delta_t(i)$ of the best state sequence
for generating the observations $o_{0:t}$ and ending at state $i$ can be recursively estimated with
the following equations:

Initialization: $\delta_0(i) = \pi_i \times b_i(o_0)$

Recursion: $\delta_t(i) = \max_j^{N} \delta_{t-1}(s_j)a_{ij}b_i(o_t)$

The series that maximizes this probability is the optimal sequence of hidden states.

4.3 Supervised classification

Supervised learning methods use labeled data to fit a function that can be used to infer
the labeling of new examples. Linear regression, logistic regression, decision trees, support-
vector machines are just a few examples of the numerous algorithms existing for this task.

Different methods perform differently for a same prediction problem. Thus, the method
choice can affect the performance and conclusions. To overcome this difficulty, the Super-
Learner algorithm proposes a combination of methods aiming for the best possible per-
formance without overfitting.
In some cases, it is necessary to take into account dependency between observations. For example, when repeated measures are originated from each subject. In this case, the random effect related to individuality needs to be combined to the fixed effects of interest by applying mixed effect models.

### 4.3.1 SuperLearner

SuperLearner [105, 72] is a supervised learning algorithm that uses an ensemble learning model to achieve the best performance. By considering a weighted combination of several supervised learning methods through cross validation, the algorithm achieves performances at least as good as the best performing candidate learning method.

SuperLearner algorithm starts by splitting the *n* samples in the data into *v*-folds. Each of this folds is used as a validation fold, while the samples in the remaining folds are used for training.

Each of the *K* candidate learning methods is trained with the training data and used for making predictions for the validation fold. A *n* × *L* matrix *Z* is built containing the predictions for out-of-fold samples for each candidate learning method.

Then, a meta-model is trained over the predicted outcomes *Z*. This model can be a linear regression, a logistic regression or other supervised learning model, fitting the observed classes *Y* onto the predicted outcomes *Z* from the candidate learning methods.

Finally, new predictions can be made by computing the predictions for each of the trained candidate learning models and combining them with the trained meta-model.

### 4.3.2 Mixed effect models

Mixed effect models are models that combine fixed and random effects.

Fixed effects are the variables that affect the response variable. Typically, these are the variables of interest that were deliberately measured from the population. On the opposite, random effects generally cannot be controlled in the study. They are usually variables that define groups within the population, thus making the points not independent from each other.

For example, in case of multiple measures from each individual, the measures are considered fixed effects, while the individuals are random effects.

Thus, linear mixed effect models take the form of Equation 4.3.1, where the first term models the fixed effects over the whole population and the second a term defines the random effects.

$$y = X\beta + Zu + \epsilon \quad (4.3.1)$$

The response variable *y* is a vector *n* × 1, where *n* is the number of samples in the dataset. It is modeled according to the fixed effects design matrix *X*, of dimension *n* × *p*, and the random effects design matrix *Z*, of dimension *n* × *q*, where *p* is the number of fixed effects variables and *q* the number of random effect levels in the model.

The vector *β*, *p* × 1, contains the regression coefficients of the fixed effects. Similarly, *u* is a vector of dimension *q* × 1 that contains the coefficients of the random effects. The model is completed by a *n* × 1 error term *ε*, that follows a multivariate normal distribution.

A generalization of the linear mixed effects model is used when the error distribution models are not normally distributed, because the response variable are counts or binary categories, for instance.

In generalized mixed effects models, the response variable is related to the linear predictor through a link function *g*(*y*) (Equation 4.3.2).
$$E(Y) = X\beta + Zu \qquad (4.3.2)$$

Typically, the choice of the link function depends on the type of the response data. For example, a log link function is proposed when the response variable is a count of occurrences and a logit link function when the response variable is binary.

## 4.4 Novelty detection

As previously stated, exacerbations are rare and variable deviations from patients’ normal state. For this reasons, it would be difficult to know and describe all possible types of events that a patient can come across. Instead, we want to focus on the change that is related to the advent of an exacerbation.

The approach of novelty detection, or one-class classification, methods consists of describing a “normality” class, from which new points can be classified as belonging or not. They are often used in medical problems modelling, in which a lot of the data belongs to “normality” while the “abnormal” events not only are rare, but also variable, meaning that the characteristics of abnormality may not be known a priori [58, 2].

Typically, the novelty detection approach involves estimating a model with the training data that is capable of describing the normal behaviour of the data. Then, test data can be compared to this reference model with a metric of distance or dissimilarity. The anomaly score $S(y)$ of the series $y$ can be compared to a threshold $\lambda$ that defines if the series is “normal” (if $S(y) < \lambda$) or not (otherwise). Moreover, the final solution can be achieved by using a single anomaly score or by multiple anomaly scores, based in different detection techniques, aggregated into one final anomaly score.

Metrics of dissimilarity and distance are commonly used as anomaly scores. Some metrics are only defined for comparing a single point while other enable the comparison between sets of points and/or distributions.

### 4.4.1 Mahalanobis distance

The Mahalanobis distance [56, 2] allows to calculate the distance of a point to a distribution. Moreover, it takes into account the variance-covariance matrix of the variables in the reference distribution, giving different weights depending on the position of the point with respect to the distribution. Given a training data of mean $\mu$ and variance-covariance matrix $\Sigma$, the Mahalanobis distance of a new measure $x$ to the training data is defined by the following equation.

$$d(x) = [(x - \mu)'\Sigma^{-1}(x - \mu)]^{1/2} \qquad (4.4.1)$$

The underlying idea is to consider that reference data are spread according to a multidimensional normal law (which shape is given by the variance-covariance matrix) and that the distance grows as the distribution of that law decreases. Figure 4.3 presents an example of the Mahalanobis distance from a reference distribution in the plane breathing rate-amplitude.

### 4.4.2 Wasserstein distance

The distance between two distributions can be quantified using optimal transport theory. The idea behind it can be explained with the pile of sand analogy. We consider an initial
<figure><img src="image_9.png" /><figcaption>Figure 4.3 – Example of Mahalanobis distances from reference points in the breathing rate-amplitude plan</figcaption></figure>

distribution of mass $\mu$ that describes the pile of sand. We wish to move each grain of sand so the final distribution is $\nu$. The ground cost for transporting one grain of sand from position $x$ to position $y$ is defined by the cost function $c(x, y)$. The optimal distance between the piles is the distance that minimizes the overall cost of transportation [71, 76]. The Wasserstein distance is this optimal value, that quantifies the similarity between two distributions.

For the comparison of sets of points, discrete distributions are defined according to the points weights and locations. Equation 4.4.2 defines the discrete distribution $\mu$, according to the weights $\alpha$ and locations of points $x_1, \dots, x_n$, where $\delta_x$ is the Dirac at position $x$.

$$ \mu = \sum_{i=1}^{n} \alpha_i \delta_{x_i} \qquad (4.4.2) $$

In Kantorovich formulation for discrete distributions, the distance between $\mu$ and $\nu$ can be estimated according to Equation 4.4.3, where $\Pi$ are the admissible transport plans between $\mu$ and $\nu$. The transport plan can be understood as the matrix that defines the amount of sand $\pi_{ij}$ that is to be transported from $x_i$ to $y_j$. Thus, the mass moved from each distribution corresponds to its initial mass ($\sum_{j=1}^{m} \pi_{ij} = \mu$ and $\sum_{i=1}^{n} \pi_{ij} = \nu$) and the mass displaced is always positive ($\pi_{ij} \ge 0$).

$$ W(\mu, \nu) = \min_{\pi \in \Pi} \sum_{i=1}^{n} \sum_{j=1}^{m} \pi_{ij} c(x_i, y_j) \qquad (4.4.3) $$

For comparing distributions $\mu$ and $\nu$, they are required to have the same total mass. Thus, the weights $\alpha$ can be adapted to agree with this condition. If the weights within a set of $n$ points are uniform, $\alpha_i = 1/n$ can be used.

### 4.4.3 Cross-entropy and Kullback-Leibler divergence

The cross-entropy and the Kullback-Leibler divergence are two metrics originated from the field of information theory. Both metrics quantify the difference between two probability
distributions over the same set of events and are commonly used as loss functions in classification learning algorithms.

The cross-entropy $H(P, Q)$ of the estimated probability distribution $Q$ with respect to the reference (true) probability distribution $P$ is given by the Equation 4.4.4, by comparing the probabilities at each of the $N$ discrete or categorical classes.

$$H(P, Q) = -\sum_{i=1}^{N} P_i \log Q_i \qquad (4.4.4)$$

Similar to the cross entropy, the Kullback-Leibler divergence quantifies the divergence between the distributions according to Equation 4.4.5.

$$D_{KL}(P||Q) = \sum_{i=1}^{N} P(i) \log \frac{P_i}{Q_i} \qquad (4.4.5)$$

The Kullback-Leibler divergence quantifies the additional entropy of $Q$ with respect to $P$, while the cross-entropy measures the total entropy. In other words, the cross-entropy is the Kullback-Leibler divergence plus the entropy of the reference distribution $P$ (Equation 4.4.6).

$$H(P, Q) = H(P) + D_{KL}(P||Q) \qquad (4.4.6)$$

Hence, both metrics are minimized when $P = Q$, which means $D_{KL} = 0$ and $H(P, Q) = H(P)$.

In both cross-entropy and Kullback-Leibler divergence, it is important to use $Q$ as the observed probability distribution and $P$ as the reference probability distribution. Indeed, both metrics are not distances, since the inversion of the distributions lead to different results. A symmetric version of the cross-entropy (Equation 4.4.7) may be used, as proposed by [111].

$$H_s(p, q) = \sum_{i=1}^{N} (Q_i - P_i) \log \frac{Q_i}{P_i} \qquad (4.4.7)$$

### 4.4.4 Methods for time series

In time series problems, the order of the data points may be critical for detecting “abnormal” events. Instead of atypical points or distributions, the detection of atypical sequences in a set of sequences or atypical subsequences within a time series require specific novelty detection techniques. Three examples of techniques used for detecting anomalous time series are similarity-based, prediction-based or HMM-based [100].

Similarity-based techniques rely on the pairwise distances between test and training data. They assume that anomalous series are distant from normal series and that this difference can be captured by the chosen metric. Same length series can be compared point-by-point with an Euclidean distance, while the Dynamic Time Warping distance gives more flexibility for time distortion [77]. Similarity can also be measured with respect to the parameters of models fitted with each of the compared sequences [58]. For example, the difference between ARIMA parameters ($\hat{\mu}_{train}, \hat{\phi}_{train}, \hat{\theta}_{train}$) fitted to the training series and ($\hat{\mu}_{test}, \hat{\phi}_{test}, \hat{\theta}_{test}$) fitted to the test series can be the anomaly score for the test data.

Prediction-based techniques are mainly used for the detection of anomalous observations within the time series [100]. With this approach, a model is fitted to the training data
and used to forecast the following point, which is then compared to the observed point.
ARIMA models are also often used with this approach.

In the Hidden Markov Model-based approaches, a HMM is trained with the training
time series. Considering that HMM really captures the “normal” process, the probability of
observing the test time series under the model can be estimated. Moreover, the estimated
hidden states can provide an explanation of why a sequence is considered atypical [2].

The reference models that describe the “normality” can be static or evolve as new data arrive. In case of online learning, training series can be periodically updated with a fixed number of most recent observations. The objective is to maintain the reference model relevant for this time-changing process, while keeping computational costs reasonable.

Different techniques can be considered depending on the field of application. The
distance metric, the model, the size of the time window and the boundaries of normality
are among the choices that have to be made in order to obtain the best results.

**4.5 Final hypothesis of the investigation**

The consequences of COPD in today's society deserve increased attention, especially with
regard to the premature management of exacerbations. This management could be im-
proved by allying the use of remote monitoring devices with adequate artificial intelligence
methods.

First, the monitoring device should be able to assess pertinent features of the respiratory
mechanic state of the patients in his day-to-day life.

Then, the device is to be combined with some of the numerous artificial intelligence
methods available to address dimension reduction and classification of time series data.
Since exacerbations are variable and rare events, our hypothesis is that the best approach
is not to model exacerbations, but to have sufficient data to describe variations within
normality, from which a deviation may indicate the rise of an exacerbation.
# Part II

## Technology development
# Chapter 1

## TeleOx® monitoring device

Worldwide, COPD is a major cause of mortality and loss of quality of life. The disease evolution is traditionally assessed with respect to changes in the respiratory mechanics and in the capacity to execute daily activities. Spirometry and 6MWT are two examinations that allow to quantifying COPD evolution through time. Still, these examinations can only help understanding the long-term evolution of COPD.

Acute exacerbations are rare events that affect the respiratory mechanics and the activity capacity of the patient in shorter periods of time, not being spontaneously detected with sporadic examinations. For this reason, a more continuous monitoring from “real life” parameters could be a powerful tool to complement COPD patients follow-up.

Aiming for a detailed monitoring, while minimizing the need of patient intervention, TeleOx® (Srett, Boulogne-Billancourt, France) is the monitoring device of choice in the different phases of this work.

TeleOx® is a medical device designed to evaluate adherence and treatment efficacy in LTOT patients. The device is placed on the oxygen circuit between the source and the nasal cannula of the patient (Figure 1.1), adding no new constraints for the patient. It allows for a continuous follow-up, with no invasive device nor manipulation needed.

<figure><img src="image_10.png" /><figcaption>Figure 1.1 – Oxygen circuit with TeleOx®</figcaption></figure>

In the following sections, the characteristics of the TeleOx® device are briefly explained, in both its commercial application and its research purpose adaptation.
## 1.1 Commercial TeleOx®

TeleOx® is a medical device class IIa CE marked. It was developed to be a portable and efficient device for remote monitoring patients under LTOT with flow rates between 0.5 and 5 liters per minute. With a total weight of 35g (including the battery), it has a power autonomy of one year. It was patented in 2018 as "Oxygen therapy monitoring device and method" [82, 83].

The device periodically acquires data from two microphones and two barometric pressure sensors. Sensors are actively measuring during 45 seconds every 5 minutes and are inactive (under sleep mode) otherwise. This approach warrants a reduction in energy consumption, crucial to the autonomy and portability of the device. At the same time, the window length and its frequency are considered sufficient to apprehend significant physiological and behavioral changes.

The sensors take new measurements every 0.1 seconds, resulting in a sampling rate of 10 Hz. The two microphones are used to compute the instantaneous frequency, measured in Hz, at which the gas flow oscillates in the oscillation chamber inside the device (called pulse counter). The ambient pressure and the flow tube pressure are measured by each of the barometric pressure sensors. The pressure difference is computed (in Pa) and corresponds to patient's nasal pressure.

During data acquisition, an embedded algorithm computes several parameters of interest. The algorithm is not described in details hereafter because of confidentiality issues. However, for the good understanding of some of the analysis described in the following chapters, some specifications are given.

The pulse counter signal is acquired during 12.8 seconds and used to detect the presence of the oxygen source. If no source is detected, the device goes back to sleep mode and no other parameter is computed. Otherwise, the acquisition continues until the 45 seconds period acquisition is completed. The combination of this signal with the volume of the oscillation chamber inside the device gives an estimation of the oxygen flow rate.

The pulse counter signal and the pressure difference signal are then used to detect the type of oxygen source (continuous or pulse source) and the presence of the patient on the therapy circuit.

Besides, the algorithm verifies the quality of the signals. One example of bad quality signal is given when the lengths of detected respirations are too variable. This can indicate some artifact in the measuring acquisition. To avoid inaccurate measurements, TeleOx® chooses to not to compute physiological parameters for this period.

If the patient is well identified and the signals quality is sufficient, the breathing rate is computed from the pressure difference signal.

The parameters oxygen flow rate, oxygen source type, presence of the patient and breathing rate, completed with current time, are recorded in the device memory for further upload in a server. First, data is retrieved through a smartphone or tablet application that connects with the TeleOx® through BlueTooth. Then, data is sent to the secured server where it can be visualised through a user-friendly interface, the Vestalis platform.

Once the parameters registered, the pulse counter signal and the pressure difference signal are rejected and the device goes back to sleep mode for the next 4.25 minutes.

## 1.2 TeleOx® adaptation for research

For research purposes, the TeleOx® firmware was adapted so the raw signals of pulse counter and pressure difference are kept with the computed parameters. This firmware
version is hereafter called raw data mode.

With this configuration, the device performs continuous acquisition (no sleep phases). Parameters computation follows the same algorithm as previously described. Thus, they are estimated over windows of 45 or 12.8 seconds, according to the presence of the oxygen source.

Therefore, the amount of data recorded is much superior to the commercial version, which limits the data acquisition to eight hours of continuous recording. After this period, TeleOx® goes to sleep mode.

Data (pulse counter signal, pressure difference signal and computed parameters) can be retrieved locally through a gateway. All data is erased from device's memory when starting a new data acquisition.

With this tool and its adapted version, it is possible to track breathing under different time scales. In this section, focus is given to changes in respiratory mechanics that occur over the course of a few minutes, with the goal of aggregating the raw signals recorded with the research version into valid and useful features.
# Chapter 2

## Validation of breathing rate measurements

The interest of monitoring the breathing rate has been described in many different health-related situations [66]. For COPD patients in particular, changes in the breathing rate have been linked to the development of exacerbations in several studies. Thus, the first feature of choice for respiration monitoring with TeleOx® is the breathing rate.

In this chapter, the clinical study accomplished for the validation of breathing rate measurements by TeleOx® is presented. It aims to compare the respiratory signals and indicators measured by TeleOx® with those recorded by a polygraph. This chapter is based on the article [91], where focus is given on the validation of the breathing rate estimation.

### 2.1 Study protocol

This monocentric observational study was approved by the institutional board (CEPRO No. 2016-005). COPD patients under nasal oxygen therapy with flow rates between 0.5 and 5.0 litres per minute, without mechanical ventilation and without any other respiratory pathology were eligible to the study if they benefited from a ventilatory polygraph record for other reasons. Thus, the recordings correspond to nocturnal periods.

TeleOx® used were in the raw data mode. The reference polygraph (Nox T3®, Nox Medical Inc. Reykjavik, Iceland) data is collected using the manufacturer's software Noxturnal®.

Fourteen patients were included in this study.

### 2.2 Signals comparison

First, raw signals from TeleOx® and the polygraph are visually compared. Figure 2.1 presents 7 hours of recordings from one of those patients. Signals are manually aligned as the measuring devices may present some variation between recorded time.

The first signal comes from the polygraph and is considered the reference, it is measured in $cmH_2O$ at 200 Hz. The second signal is the raw pressure signal from TeleOx®, measured in $Pa$ at 10 Hz. The signals present similar profiles. The signal measured by TeleOx® is not centered in zero, as it is commonly presented for the nasal pressure.

The recordings from another patient are presented in the Figure 2.2.

In this case, there is a discrepancy between the signals, specially concerning a drift in the pressure.
<figure><img src="image_11.png" /><figcaption>Figure 2.1 – Patient 1 - 7-hour recording from polygraph and TeleOx®</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Figure 2.2 – Patient 2 - 7-hour recording from polygraph and TeleOx®</figcaption></figure>

## 2.3 Filtering

Filtering is done according to TeleOx® algorithm. Since in its commercial mode, raw signals are erased after 45-second recordings, filtering is also based on 45-second windows.

First, TeleOx® filters the raw pressure signal using the pressure signal itself and the pulse counter signal. The first 9.6 seconds of the signal are only used for calibration. This process is property of Srett and is not detailed here.

A baseline signal is computed as the moving average of the past filtered pressure values. The baseline signal is subtracted from the pressure signal generating a new signal, that oscillates around zero. Each of this steps is presented in Figure 2.3

The complete resulting filtered signals are given for previous examples in Figures 2.1 and 2.2 for comparison.

We zoom in the signals from each of those patients presenting a 30-second window comparison between the polygraph nasal pressure signal and the TeleOx® pressure signal after filtration in Figure 2.4.

The profiles of each breath are well aligned, indicating a good correspondence between the measuring devices.
<figure><img src="image_13.png" /></figure>

Figure 2.3 – Representation of the filtering steps for a 45-second window. Signals from polygraph and from TeleOx® are presented in black and blue, respectively. Red dashed line indicates the estimated baseline.

<figure><img src="image_14.png" /></figure>

Figure 2.4 – 30 seconds superposition of pressure signals from the polygraph and TeleOx® for patients 1 and 2

Moreover, we note the difference between the scales in the y-axis. Our hypothesis is that this difference is due to individual characteristics as anatomy of the nose or even positioning of the nasal cannula. Still, this should not affect the computation of breathing rate.

## 2.4 Flow and volume estimation

As previously described, pressure change is related to flow according to the Rohrer's equation (Equation 2.3.1). In the case of the nasal pressure, laminar and turbulent components are present in the airflow.

Solow and Sandham [93] have studied the contributions of those regimens in healthy
subjects breathing. After the estimation of the Rohrer's equation coefficients, the study has pointed to a prevalence of turbulent flow, with $k_2 >> k_1$.

In another study, an alternative method consists of describing the pressure-flow relationship by the power equation $\Delta P = aQ^b$ [107]. With this equation, $b$ gives insights about the prevalent flow regimen while $a$ represents the resistance. In this study, nasal pressure-flow relationship was mainly characterized by turbulent flow, with $b$ coefficients close to 1.75. Two of the subjects included in the study presented an increased resistance, which was explained by an upper respiratory tract infection. Still, the flow regimen was not altered by the increased resistance. Authors hypothesize that the prevalence of turbulent nasal airflow is probably not altered by changes in nasal geometry. Besides, it's interesting to note that inspiratory flow was presented as more turbulent than at expiration. After exercise, $b$ coefficients at inspiration were even closer to 2.

Finally, as much as Rohrer's equation is the proper solution for estimating the flow, it requires periodic calibration to inspiration and expiration. A simpler and reasonable solution would be to apply a quadratic model keeping only the turbulent component of the flow [61].

By definition, the airflow rate is the amount of air passing per unit of time. Thus, the volume variation can be defined by integrating the flow with respect to the time in the interval $[t_i, t_f]$ (Equation 2.4.1).

$$Q = \frac{dV}{dt} \rightarrow \Delta V = \int_{t_i}^{t_f} Q dt \qquad (2.4.1)$$

Thus, we propose that respiration flow and volume variation can be roughly estimated from the filtered TeleOx® pressure signal, using $Q_{TO} = -sign(P_{TO})\sqrt{abs(P_{TO})}$ and $dV_{TO} = \int Q_{TO}dt$. One example of the resulting curves is given in Figure 2.5.

<figure><img src="image_15.png" /><figcaption>Figure 2.5 – Example of flow and volume estimations from TeleOx® pressure signal</figcaption></figure>

Inspiration is represented by negative pressure and positive flow rate, as it is commonly the case in the literature and by different measuring devices.

## 2.5 Breath-by-breath identification

To better analyse respiration periods, we study the detection of inspiratory and expiratory periods. Typically, negative pressures indicate inspiration and positive pressures indicate expiration. However, TeleOx signals were artificially centralized around pressure 0 Pa,
which may lead to some distortion from truth. Thus, different methods were tested to identify inspiration and expiration cycles.

First, the signal is interpolated using a piece-wise cubic interpolation at twice the original sampling rate (resulting in 20 Hz). This is done to ensure more precision for the time detection, specially at high respiratory rates.

Then, the resulting signal is filtered with a moving average over 11 points, the sliding window being centered in the current position. This step is important to avoid detection caused by noise.

Figure 2.6 gives an example of what the detection is expected to look like in a previously filtered signal. Expiration often starts with important pressure changes and finishes with a plateau. Thus, inspiration is considered to begin as soon as the expiratory plateau finishes and pressure falls. Expiration begins somewhere between the minimum and maximum pressures in the cycle.

<figure><img src="image_16.png" /><figcaption>Figure 2.6 – Manual estimation of inspiration (blue) and expiration (red) periods for 10-second window example from TeleOx® pressure signal.</figcaption></figure>

In this example, the transitions from expiration to inspiration are not perfectly aligned with 0 Pa. This divergence is due to some inadequacy in the filtering step, hence the difficulty of identifying the phases with precision.

### 2.5.1 Pressure minima or maxima

The signal minima can be used as an approximation of the breathing separation. In this method, it is considered that a breath starts at the maximal inspiratory flow (pressure minima) and ends in the following maximal inspiratory flow. Another option would be to consider the pressure signal maxima, separating the breaths at the maximal expiratory flows.

<figure><img src="image_17.png" /><figcaption>Figure 2.7 – Minima (red triangles) and maxima (blue triangles) of the pressure signal presented as proxies of breath-by-breath separation</figcaption></figure>

This method has the inconvenience of not identifying precisely inspiratory and expiratory periods. However, the distances between two consecutive minima or two consecutive maxima are good approximations of breaths’ duration.
### 2.5.2 Signal crossing zero

Times corresponding to a zero crossing in the filtered signal are detected and identified as beginning of inspiration or beginning of expiration according to the slope around the given time. The beginning of an inspiration is characterized by a positive slope around the zero crossing. The beginning of expiration is indicated by zero crossing with negative slope.

<figure><img src="image_18.png" /><figcaption>Figure 2.8 – Breath-by-breath identification based on pressure signal zero-crossing detection. Red and blue triangles indicate detected inspiration and expiration beginnings respectively.</figcaption></figure>

The onset of inspiration and expiration are represented by the last moments before the zero crossing, i.e. when the signal changes from negative to positive and vice versa. Despite interpolating the signal at twice the original sampling rate, in some breaths the instant associated with the zero crossing may not be as precise, especially at high respiratory rates.

Once the limits of each respiration are detected, they can be validated as a "real breath" or as noise, according to the estimated volume allocated to the breath.

### 2.5.3 Volume minima and maxima

Inspiration starts at the peak of respiratory system deflation and ends when the respiratory system is most inflated. Thus, in this method, the volume is estimated according to previous section. This estimation is then used for identifying the beginning of inspirations and expirations by the signal minima and maxima respectively.

<figure><img src="image_19.png" /><figcaption>Figure 2.9 – Breath-by-breath identification based on the estimated volume signal. Red and blue triangles indicate detected inspiration and expiration beginnings respectively.</figcaption></figure>

### 2.5.4 Laplacian of Gaussian filter

The detection of the limits of inspiration and expiration can be interpreted as an edge detection problem. Very common in image processing, this operation consists of detecting points of important intensity change. Different methods use the signal's first or second derivative to detect the edges.
The Laplacian is a differential operator that is given by the sum of the second partial derivatives with respect to each independent variable. In the case of our 1-dimensional signal, it corresponds to the second derivative of the signal with respect to time. Since derivatives are very sensible to noise, we start by running a supplemental smoothing of the signal by using a Gaussian smoothing filter.

The Figure 2.10 shows an example of pressure signal with its first and second derivatives. In the first derivative, steep slopes from the original signal are represented by large magnitudes. In the second derivative, an increasing slope in the first derivative is presented as positive magnitudes, while a decreasing slope in the first derivative is viewed as negative magnitude in the second derivative. Thus, the signal edge can be detected when the second derivative crosses zero. Because of the sampling rate limitation, the last instant before the zero crossing defines the signal edge. At high slopes in the derivative, the chosen instant may be distant from zero.

<figure><img src="image_20.png" /><figcaption>Figure 2.10 – Different steps of breath-by-breath identification based on the Laplacian Gaussian filtering. Red and blue triangles indicate detected inspiration and expiration beginnings respectively.</figcaption></figure>

Since the derivative of a convolution product is equal to the derivative of one of the functions convoluted to the other function (as indicated by Equation 2.5.1), we first compute the Laplacian of Gaussian (LoG) operator, which is afterwards convoluted with the signal.

$$ \frac{\partial}{\partial x}(f * g) = \frac{\partial f}{\partial x} * g = \frac{\partial g}{\partial x} * f \qquad (2.5.1) $$

Despite the complexity of this method compared to other methods tested, there is no significant increase in performance with the Laplacian of Gaussian filtering. After treatment with TeleOx® algorithm, pressure signals seem to be sufficiently centered in a way that zero-crossing is a good indicator of inspiration and expiration beginnings.

## 2.6 Breathing rate estimation

As previously described, breathing rate seems to be an important feature to monitor COPD patients. Thus, its implementation in TeleOx® algorithm was a priority.

To ensure robustness in the measures, breathing rate is computed as the inverse of the median breathing length in the 45-second window.

For the same reason, the method used to compute the breathing lengths is based on the pressure minima and maxima. Durations are computed as the distances between two consecutive minima or two consecutive maxima. This allows for measuring twice as many time intervals as the real number of respirations in the period, in the case where all peaks are well detected. Besides, the use of the median measure allows for ignoring missed or wrongly identified peaks, that will lead to too long or short durations compared to other
breathing in the period. Whenever the measured durations are too variable, TeleOx® chooses to identify this period as poor quality, not outputting a breathing measure.

### 2.6.1 Validation of breathing rate measurements

From the polygraphy protocol, the recordings from 14 patients resulted in 1099 valid TeleOx® measurement points. The breathing rate measurements agreement between TeleOx® and Nox-T3 was estimated using the Bland-Altman method and Passing-Bablok regression method.

The Passing-Bablok regression is a nonparametric method based in the linear regression $y = a + bx$ between paired measures $(x, y)$ from each device [70]. For robustness, $b$ is estimated as the median of all slopes between two points (except when $b = 0/0$ or $b = -1$). Then, $a = \text{median}(y_i - bx_i)$. Perfect agreement between the devices should obtain an intercept $a = 0$ and slope $b = 1$. Thus, two methods are considered to agree when 0 is in the confidence interval of $a$ and 1 is in the confidence interval of $b$.

In the Bland-Altman analysis, the difference between the paired measurements is plotted in function of the average measurement for each point [14]. If the mean difference between the measures is different from zero, it indicates the presence of a fixed bias. Moreover, the limits of agreement at 95% give an estimate of the dispersion of the measurements differences.

<figure><img src="image_21.png" /><figcaption>(a) Bland-Altman plot. Dashed blue lines indicate bias. Dashed red lines present the 95% limits of agreement of the differences.</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>(b) Passing-Bablok regression. Solid blue line indicates the Passing-Bablok regression line. Dashed red line indicates identity. Blue area represents the uncertainty envelope.</figcaption></figure>

Figure 2.11 – Comparisons of 1099 breathing rate measurements by TeleOx® and the polygraph.

The bias computed by Bland-Altman method is 0.046 within [-3.865, 3.957] limits of agreement at 95%. Passing-Bablok regression shows a $b$ slope at 0.998 within [0.976, 1.000] interval and an intercept $a$ at -0.036 within [-0.217, 0.325] interval.

In [81], breathing rate telemonitoring devices were compared using Bland-Altman method. Five monitoring systems based in impedance measures, photoplethysmography, camera, accelerometer and chest elastic band were compared. The reference monitoring
device was Oxycon Mobile® (CareFusion®, San Diego, CA, USA), a portable device capable of spirometry and oxygen saturation measures.

Best agreements were achieved with the chest-band and the accelerometer with bias -1.60 and -2.18 and limits of agreement [-9.99, 6.80] and [-8.63, 4.27], respectively. Compared to these devices, the measurement bias of TeleOx® is far smaller and its limits of agreement interval is narrower.

No analysis considering each subject separately was carried because most subjects present a narrow range of breathing rate combined with a small sample size, interfering method comparison.
# Chapter 3

## Estimation of indicators of respiratory mechanics profiles

As we have been able to verify, the treated signal from TeleOx® pressure sensors resembles to the nasal pressure signal measured by the polygraph. Therefore, it contains information about the patient's breathing. At this point, this information is reduced to a single median respiratory rate value per 45-second period, but other parameters could be computed to better describe breathing.

To verify which indicators could be estimated from TeleOx® signals, two study protocols were designed to record respiration from healthy individuals and COPD patients. These indicators should be able to describe respiratory mechanics changes, ideally in the exacerbation context.

Our final goal is to describe respiratory changes related to exacerbations, however, those are rare and complex events requiring long periods of follow-up. Therefore, we choose to start by studying changes in the load-capacity balance corresponding to rest and exercising.

### 3.1 Study protocols

Two study protocols were used to record raw data TeleOx® signals from healthy individuals and COPD patients. Data was collected from a set of twenty healthy subjects and eight patients with COPD from two different protocols.

#### 3.1.1 Healthy subjects

Healthy subjects study protocol was named "Identification of respiratory patterns in healthy individuals from nasal pressure signals". This prospective and monocentric physiological study, corresponds to an interventional research involving human beings with minimal risks and constraints, which conforms to the category 2 of the Jardé law, the French legislation that regulates clinical research in humans.

The main objective of the study was to determine the parameters which would allow the detection of a passage from one given situation to another (i. rest, ii. drink, iii. coughing episodes, iv. talking, v. mouth breathing, vi. physical exertion (jumping) and vii. recovery).

Twenty adult healthy volunteers were included in the study. Non-inclusion criteria included minor, pregnant woman, protected adult, person deprived of liberty, person under judicial protection, existence of respiratory pathology and the absence of social security affiliation.
In this trial, oxygen therapy was simulated by replacing the oxygen source by an air source. A raw data mode TeleOx® was placed in the air circuit, between the air source and the nasal cannula. The air flow rate was constant during each recording. Each subject followed instructions for a total of 30 minutes. They were requested to execute the following activities:

* Two forced breathing (inspiration and expiration) to mark the beginning of the recording.

* 9 minutes of quiet breathing. Subjects were asked to read a text to focus on an activity other than breathing.

* 1 minute for drinking water. Subjects could swallow slowly or not, with or without pausing.

* 1 minute of quite breathing.

* 1 minute for coughing. Subjects were asked to cough at least 2 or 3 times during this period.

* 1 minute of quite breathing.

* 1 minute for reading aloud.

* 1 minute of quite breathing.

* 1 minute of breathing through the mouth.

* 1 minute of quite breathing.

* 3 minutes of exercising. Patients were asked to jump or run in place. Patients were allowed to manage their own effort.

* 10 minutes of quite breathing.

Recordings were retrieved after each test and stored locally for posterior analysis. All the necessary precautions to ensure the confidentiality of the information relating to the tests have been carried out.

The study was approved by an ethics committee (Comité de Protection des Personnes - Île de France II on 5 November 2018) and was registered in the ClinicalTrials.gov registry under number NCT03753386 before inclusion of the first participant. All participants provided written informed consent for study participation.

The Figure 3.1 presents two examples of raw signals recordings from two healthy subjects.

<figure><img src="image_23.png" /><figcaption>Figure 3.1 – Examples of raw signals for two healthy subjects recording. Light gray areas indicate drinking, coughing, speaking and breathing through the mouth periods. Darker gray areas indicate exercise period.</figcaption></figure>
Subject A recording was done under 3 L/min air flow rate and subject B under 1 L/min

3.1.2 COPD patients

The second study protocol was named "Analysis of changes in respiratory parameters preceding exacerbation in COPD patients under oxygen therapy". This was a monocentric, observational and retrospective study. This study does not enter the Jardé law, since data was collected as part of the usual clinical management. The protocol was review and approved (CEPRO 2018-021) by the Institutional Review Board of the French speaking society for respiratory medicine - Société de Pneumologie de Langue Française.

Patients were enrolled while hospitalized at the Respiratory and neuro-respiratory follow-up and rehabilitation care unit of the Service de Pneumologie, Médecine Intensive et Réanimation, Groupe Hospitalier Pitié-Salpêtrière. The inclusion criteria required that patients had COPD, were under oxygen therapy and monitored with a TeleOx®. Patients provided signed consent.

Respiratory and neuro-respiratory follow-up and rehabilitation care unit (*Soins de suite et de réadaptation respiratoires et neuro-respiratoire*, SSR respiratoire for short) receives patients with COPD that were hospitalised after an exacerbation. After this hospitalisation, often in a pulmonology service, and before returning home, the *SSR respiratoire* proposes a multidisciplinary respiratory rehabilitation, including medical support, physiotherapy, social assistance, dietetics and psychological support, etc.

After admission, patients are examined by the medical team and their functional capacities are tested with a 6MWT, among other tests. Stays last approximately six weeks. During this period, the following daily schedule is proposed to each patient:

7:00 - wake up

8:30 - breakfast

9:30 - cycling or treadmill session

11:30 - therapeutic education session

12:30 - lunch

14:00 - gymnastics - group 1

15:00 - gymnastics - group 2

16:00 - therapeutic education session

During the two-hour window allocated to the cycling or treadmill session, patients can arrive at different times and the length of exercising may vary from patient to patient and between days. Patients may start the rehabilitation at a very limited exercise capacity. Through time they can progress by increasing the load of the exercise bike, the speed in the treadmill and/or the total exercising time.

In the afternoon, the gymnastics sessions administered by physiotherapists complement the exercise training. Two sessions of one hour each are proposed and patients usually stay during a complete session, although the groups may vary from day to day.

Daily, two therapeutic education sessions are proposed. The objective is to teach the patients how to better manage the disease. Thus, they will learn about the illness, the treatments and how to identify and deal with acute events. Each session has a theme
and is addressed by one of the multidisciplinary healthcare professionals (doctor, nurse, physiotherapist, dietitian, etc). This session last about an hour, where patients are invited to listen to the professional, watch a video, discuss and ask questions.

Most patients were only monitored with TeleOx® in the commercial mode. Eight patients had the regular TeleOx® replaced by a raw data mode TeleOx® during one day. The devices were switched in the morning (around 10 am) and, eight hours later, the raw data TeleOx® was recovered and the regular TeleOx® was plugged back.

In this protocol, the oxygen flow rate can be changed during recording, according to the patient's needs and habits, either by the patient himself or by the medical staff.

Thus, two types of datasets come from this study protocol. One, with mid-term (days or weeks) follow-up of patients, containing only the computed parameters. And the other, with short-term (8 hours) follow-up, containing both computed parameters and pulse counter and pressure difference raw signals. An example of the latter is presented in Figure 3.2.

<figure><img src="image_24.png" /><figcaption>Figure 3.2 – Example of raw signals for a COPD patient recording. Darker gray areas indicate assumed exercise sessions.</figcaption></figure>

## 3.2 Visual analysis of the events

In this section, we compare the events recorded in the healthy subjects study protocol according to the pressure signal. Inspiration beginnings are estimated using the zero crossing method.

Figures 3.3 to 3.6 present one period of each situation for four subjects chosen randomly among the 20 recorded subjects.

### 3.2.1 Nasal and oral respiration

For most subjects, even when trying to breath through the mouth, some nasal pressure oscillation is still recorded by the device, although with smaller magnitudes. In other cases (e.g. Subject 02 in Figure 3.4), the nasal signal can become so depressed that breath detection is no longer possible.
<figure><img src="image_25.png" /><figcaption>Figure 3.3 – Nasal pressure during different situations for subject 01. Red triangles indicate detected beginning of inspiration.</figcaption></figure>

<figure><img src="image_26.png" /><figcaption>Figure 3.4 – Nasal pressure during different situations for subject 02. Red triangles indicate detected beginning of inspiration.</figcaption></figure>

### 3.2.2 Deglutition and coughing

The periods concerning drinking and coughing were executed differently by each subject, since there was no precise instructions about the moments and intensities of these actions.

This reflects in the signals recorded. For subjects 01 and 02, all breathing comprised in the coughing period present different shapes than resting breathing. Subjects 03 and 04, on the other hand, included some respiration similar to normal respiration in the coughing period.

In which concerns the drinking, subjects 01, 02 and 03 present irregular breathing all along the periods, while subject 04 seems to have started drinking only at the end of the period.

Coughing is sometimes associated by “pointy” profiles, indicating a rapid change in pressure. Deglutition is accompanied by extra oscillations in pressure inside a respiratory
<figure><img src="image_27.png" /><figcaption>Figure 3.5 – Nasal pressure during different situations for subject 03. Red triangles indicate detected beginning of inspiration.</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>Figure 3.6 – Nasal pressure during different situations for subject 04. Red triangles indicate detected beginning of inspiration.</figcaption></figure>

cycle. Both seem to be related to a variety of signal shapes.

### 3.2.3 Speech

Speech is produced with the passage of air in the vocal tract and mouth. Thus, expiratory signal is often not present in nasal pressure signal while speaking. Besides, it is often characterised by a longer expiration, which can be observed in the plateaus in the speaking periods of subjects 01, 02 and 03. The magnitude of the recorded inspirations are variable and is also observable for subjects 01, 02 and 03. This indicates that at least part of inspirations is nasal.

When air is inspired only through the mouth, there is no oscillation in the nasal pressure signal. It's the case for subject 4 (Figure 3.6), for whom the breath-by-breath detection is no longer possible.
### 3.2.4 Rest and exercise

Quiet breathing from different subjects vary in rate, magnitude and shape. Subject 02 presents longer and more ample respiratory cycles than the other subjects presented here. The normal respiration period presented for subject 04 starts with a deeper respiration, followed by quite constant and shallow breaths.

When the subject is exercising, there is an important increase in the amplitude of the recorded signal. Moreover, the breathing rate is also increased.

In this study protocol, subjects were free to manage the intensity of the effort executed.

In conclusion of this first analysis, we decided to let down automatic detection of oral breathing, deglutition, coughing and speech. Firstly, because the periods concerning these events present important inter-individual variability and our sampling size is limited. Secondly, because these events are also present in the COPD recordings, but with unknown positions. Thus, we opt to consider that oral breathing, deglutition, coughing and speech are part of the normal breathing at rest.

## 3.3 Indicators of respiratory profiles

In this section, we discuss some indicators that are though to be interesting to monitor. Only periods where continuous oxygen source and patient presence are detected are analysed, these are called "valid periods". Pulsed oxygen sources produce important pressure variations that hide the subjects' nasal pressure signal. Thus, periods recorded under pulsed oxygen sources are discarded.

Explored indicators were chosen according to physiological and mathematical reasoning. For example, it comes from medical knowledge that an increase in the breathing rate combined with short expiratory time is related to lungs hyperinflation phenomena [67, 30, 19]. Thus, monitoring inspiration-to-expiration times ratio may be informative of the capacity of patients with COPD emptying their lungs. In the same way, the level of cycle-by-cycle variability is related to pathological or healthy status [86, 109].

The signals are also modeled with two types of time series models. We consider ARIMA models and Fourier transformation.

### 3.3.1 Inspiration-to-expiration times ratio

As previously discussed, inspiratory and expiratory times adapt according to different physiological conditions. The inspiration-to-expiration ratio allows for monitoring the proportion of time spend in each situation at the breathing cycle.

To estimate this indicator, we first use the zero crossing method to detect the beginning of each inspiration and expiration. Then, inspiratory times $t_i$ are computed as the distance between an inspiration beginning and the following expiratory beginning. Similarly, expiratory times $t_e$ are estimated as the distance between the expiratory beginning and the following inspiratory beginning.

The ratio is estimated as the median $t_i$ over the median $t_e$ in the analysed period. Once again, we assume there is low variation between the cycles inside the same period. Thus, in the case of correct breath-by-breath detection, results obtained with the median $t_i$ and the median $t_e$ should be similar to those obtained based on consecutive measures of $t_i$ and $t_e$. In that way, results will be more stable in cases of inspiration and expiration detection errors.
Besides, the inspiration-to-expiration times ratio is only computed in periods where at least three inspirations and three expiration were detected. This threshold corresponds to three respiratory cycles in the 35.4 seconds valid period, or a breathing rate of 5 breaths/minute.

### 3.3.2 Flow-volume loop

Flow-volume loops are typical visual representations of spirometry results. In the case of the examination, patients breath through the mouth while using a nose clip. That way, the complete respiratory signal can be recorded.

In the case of TeleOx® recordings, only the nasal pressure variation can be detected.

Each respiratory cycle is separated by using consecutive inspiration beginnings detected with the zero crossing method. For each cycle, flow and volume signals are estimated according to the equations from the previous chapter.

A period is then described according to the mean form of its loops. Descriptors of the form are area, perimeter, circularity and inspiratory and expiratory flow at 75th percentile of total volume the cycle.

### 3.3.3 Amplitude

More than a change in breathing rate, a visual analysis of healthy records shows a significant change in signal amplitude during different moments of recording.

Two options are tested for computing the amplitude. The first measure correspond to the total amplitude of a breathing cycle, which is the distance from a valley to a peak (Figure 3.7a). The second measure correspond to the inspiratory amplitude, which is simply the prominence of each valley in the already treated signal (Figure 3.7b. For each period, only the median of values computed with each method are kept.

<figure><img src="image_29.png" /><figcaption>Figure 3.7 – Schema for amplitude computation on nasal pressure signal.</figcaption></figure>

### 3.3.4 Cycle-to-cycle variability

Healthy breathing comprises natural cycle-to-cycle variability, which means that each respiratory cycle is not exactly the same as previous or following cycles. One way of measuring this variability is by computing the coefficient of variation.

The coefficient of variation is defined as the ratio between the standard deviation and the mean of the measures, allowing to judge the dispersion of the measurements around the mean.

In a study of breath-by-breath variability in COPD patients before and after bronchodilator, it was observed an increase in the coefficient of variation of instantaneous breathing frequency after the drug administration [101].
Thus, we analyse the changes in variability in our datasets by computing the coefficients of variation of the detected lengths of respiratory cycles, according to the pressure minima and maxima method.

### 3.3.5 ARIMA coefficients

ARIMA was used to model each valid period in healthy and COPD datasets. For future comparison of ARIMA parameters, a single model formula was chosen to fit all periods to allow comparisons of the estimated parameters.

First, stationarity in healthy and COPD periods was analysed with autocorrelation function. Almost all periods in healthy data are already stationary, which is not the case in COPD data. Thus, we choose $d = 1$, so almost all periods in both datasets are stationary.

For $p$ and $q$, the decision is more arbitrary. Indeed the best fit model is quite variable for each period. The ARIMA(1,1,1) model (Equation 4.1.11) is chosen because it has only 3 parameters to estimate while combining the autoregressive and moving average process.

So, for every recording period, parameters ($\hat{\mu}, \hat{\phi}, \hat{\theta}$) are estimated to describe the temporal dynamics of the signal.

### 3.3.6 Fourier transform coefficients

Another way of analysing frequency, amplitude and variability of the signals is by using Fourier transforms.

Discrete Fourier transformation is performed over the 45-second raw signals (without TeleOx® filtration) after subtraction of the DC component (signal average). Thus, for each recording period, the signal is composed by 450 points sampled at 10Hz. This results in a frequency resolution of $10/450 = 0.0222$Hz.

Besides, only frequencies below 2 Hz are kept, so the number of features is limited. A breathing rate of 2 Hz already has no physiological sense, so we can consider that above this frequency we would only be analyzing noise.

Therefore, each recording period is represented by an array of length 91, corresponding to frequencies 0 to 2Hz, with 0.0222Hz resolution.

## 3.4 Choice of the parameters

### 3.4.1 Inspiration-to-expiration times ratio

With the described method, the inspiration-to-expiration times ratio for healthy subject is $0.8548 \pm 0.2727$ and for COPD patients $0.8466 \pm 0.5355$. All points are presented in Figure 3.8 with the corresponding breathing rates.

In normal spontaneous breathing, the inspiration-to-expiration times ratio is usually 0.5. In the presence of expiratory flow obstruction, we would expect COPD patients to present longer expiratory times. However, we observe many periods with high inspiration-to-expiration times ratio. For example, a ratio of 2 indicates that inspiration time was twice the expiratory duration.

In the healthy dataset, 5 out of 20 periods with inspiration-to-expiration times ratio estimation above 1.5 happen in the coughing period. The others take place in rest, speech, exercise or post-exercise periods. An example from each condition is presented in Figure 3.9.
<figure><img src="image_30.png" /><figcaption>Figure 3.8 – Inspiration-to-expiration times ratio estimation over all valid recorded periods in healthy and COPD datasets</figcaption></figure>

In both rest, exercise and post-exercise examples, the zero crossing points do not cor-
respond precisely to the end of expiration. These small variations reduce true expiration
time while increasing inspiration time, biasing the estimated result.

Examples from the COPD dataset of periods with inspiration-to-expiration times ratio
above 2 are presented in Figure 3.10.

In those periods, what spoils the detection of the expiration beginnings are the partially
or completely missing peaks. This is probably related to the presence of oral respiration, at
different proportions along the period. This results in some inspiration times including the
duration of two consecutive breathing cycles (e.g. the first respiration in the left example)
or in expiration beginnings being detected in the middle of actual expiration, when the
nasal pressure becomes more important (e.g. the last respiration in the right example).

Periods where the inspiration-to-expiration times ratio estimation equals zero are peri-
ods where less than three inspiration and three expirations are detected. This corresponds
to 3.33 % of all valid periods. The only example in the healthy dataset corresponds to a
drinking period, while in COPD dataset, it happens to periods with any given breathing
rate.

Inspiration-to-expiration times ratio is a known indicator of the respiratory mechanics,
especially relevant in the study of airway obstruction in COPD patients. Although med-
ically interesting, the automatic estimation of this indicator is not robust enough, notably
in respiration cycles where the expiration is partially or completely missing in the recorded
signal, which are common in COPD recordings.

**3.4.2 Flow-volume loop**

Figure 3.11 presents a period example for each event. All periods belong to the same healthy subject recording.

At the end of a cycle, it would be expected that the signals go back to initial conditions
(flow and volume equal zero). However, it is often not the case. This may be due to i.
variations in the proportion of nasal and oral airflow, ii. differences in the inspiratory and
expiratory resistances, not taken into account in the estimations, iii. lack of precision in
the breath-by-breath detection.

This justifies our choice of starting each breath loop separately at flow and volume equal zero. Plotting the whole period in a single continuous period causes a drift in volume, restraining our discussion about the loops' shape.
<figure><img src="image_31.png" /><figcaption>Figure 3.9 – Examples of periods with computed inspiration-to-expiration times ratio above 1.5 from healthy dataset. Red and blue triangles indicate detected inspiration and expiration beginnings respectively.</figcaption></figure>

Inside each period, loops present similar shapes while keeping some intra-period variability. Although the obtained shapes don't correspond to real spirograms, this indicates that the shapes could be able to describe different respiratory events. Nonetheless, this method is too dependent on the breath-by-breath detection. Figure 3.12 shows the flow-volume loops for the same periods as Figure 3.10, where inspiration-to-expiration times ratio was shown to be spoiled by incorrect inspiration and expiration phases detection.

Individually, the shapes inside periods with poor breath-by-breath detection are not proper loops. Besides, the shapes are quite variable inside these periods. Consequently, the analysis is based on the form of flow-volume loops from the nasal pressure signal is considered unstable.

In fact, spirometry flow-volume loops are established representations of the patient's respiratory mechanics in a well defined examination (limited leaks and controlled respirat-
<figure><img src="image_32.png" /><figcaption>Figure 3.10 – Periods with computed inspiration-to-expiration times ratio above 2 from COPD dataset. Red and blue triangles indicate detected inspiration and expiration beginnings respectively.</figcaption></figure>

In this sense, the approach based on TeleOx® recordings is too sensitive to breath-by-breath detection errors and to the proportion of nasal and oral airflow.

### 3.4.3 Amplitude

Results obtained with the methods represented in Figure 3.7 are compared for all 2856 valid periods from the healthy and COPD datasets (Figure 3.13).

The two outliers come from recordings in the COPD dataset. The concerned periods are presented in Figure 3.14.

All periods, have the particularity of presenting important changes in the magnitude of the pressure signal after the calibration period.

The first presented period has a pressure signal profile similar to recordings under pulsed oxygen sources. In the pulse counter signal, it is verified that during the calibration phase (first 9.6 seconds), the oxygen source was delivering a continuous flow. Unluckily, the change to a pulsed oxygen source occur just a few seconds after the calibration phase, leading to a misclassification of the period source.

In the other period, although the oxygen source used is in continuous mode, oscillations of the delivered flow caused artifacts in the treated pressure signal.

Although both periods represent a difficulty for the amplitude computation, they don't have any problem at estimating the breathing rate, as most peaks and valleys seem to have been well identified.

Moreover, in 0.32 % of the periods, the inspiration-expiration amplitude could not be computed, against 0.14 % for the inspiratory amplitude.

All periods where the inspiration-expiration amplitude is not computed come from COPD recordings. Figure 3.15 presents a few examples. In most periods, no peak is detected. This profiles probably correspond to oral expiration with nasal inspiration and/or speech.

Periods where inspiratory amplitude could not be computed also come from COPD dataset. In these cases, no inspiration is detected. Periods' signals are presented in Figure 3.16.

It is interesting to note that except for the first period in Figure 3.16, all other periods present a change in the pulse counter signal. The second period example present a change in the oxygen flow just after the calibration phase.

In the two last period examples, the decline of the pulse counter signal starts just after the calibration phase. It possibly corresponds to a drop in oxygen flow related to
<figure><img src="image_33.png" /><figcaption>Figure 3.11 – Flow-volume loops at different periods for the same subject. Flow and volume signals were estimated from pressure signal, units are arbitrary.</figcaption></figure>

<figure><img src="image_34.png" /><figcaption>Figure 3.12 – Flow-volume loops for periods presented in Figure 3.10</figcaption></figure>
<figure><img src="image_35.png" /><figcaption>Figure 3.13 – Comparison between inspiration-expiration amplitude and inspiratory amplitude</figcaption></figure>

<figure><img src="image_36.png" /><figcaption>Figure 3.14 – Periods resulting in outlier amplitudes</figcaption></figure>

<figure><img src="image_37.png" /><figcaption>Figure 3.15 – Periods where inspiration-expiration amplitude could not be estimated in COPD dataset.</figcaption></figure>
<figure><img src="image_38.png" /><figcaption>Figure 3.16 – Periods where inspiration-expiration amplitude and inspiratory amplitude could not be estimated in COPD dataset.</figcaption></figure>

a depletion of the oxygen cylinder. Succeeding periods also present a decreasing pulse counter signal until a period where the oxygen source is no longer detected. The algorithm treatment of the pressure signal is better achieved in the periods where the slope of the descending pulse counter signal is already present in the calibration phase.

After the exclusion of periods with outlier values or with amplitude not estimated, inspiration-expiration amplitude and inspiratory amplitude have a correlation of 0.9319 (confidence interval: 0.9269-0.9366). Therefore, given that the inspiratory amplitude requires less computational resources, we choose to keep only the inspiratory amplitude for further analysis.

Hereafter, the amplitude refers to the median amplitude at inspiration, which corresponds to the distance between pressure signal minima and the estimated baseline.

### 3.4.4 Cycle-to-cycle variability

The coefficients of variation of the breathing lengths are 0.2286 ± 0.1355 for the healthy subjects and 0.4897 ± 0.1267 for the COPD patients. All points are presented in Figure 3.17 with the corresponding breathing rates.

Contrary to expected, periods from COPD dataset present higher variability than those from healthy dataset. The higher variability in COPD recordings is probably related to the extended use with less rigid constraint of the oxygen therapy.

During the protocol with healthy subjects, a good positioning of nasal canula was ensured during the 30 minutes of recording, together with the respect of the respiration instructions. In opposite, many of the periods from COPD recordings can contain coughs, speech, bad placement of the nasal canula and more frequent oral breathing.
<figure><img src="image_39.png" /><figcaption>Figure 3.17 – Within periods variability in healthy and COPD datasets</figcaption></figure>

### 3.4.5 ARIMA coefficients

Figure 3.18 gives examples of ARIMA coefficients estimated for a healthy subject and a COPD patient.

As expected, $\hat{\mu}$ values oscillate very close around zero, except for some periods from COPD dataset example.

### 3.4.6 Fourier transform coefficients

Figure 3.19 presents the absolute values of the Fourier transformations for same subjects in Figure 3.18. Lighter colors indicate higher magnitudes in the given frequency at given period.

In the healthy dataset example, the exercise period (between minutes 17 and 20) is easily recognizable with its higher magnitudes at higher frequencies. There is a new change in the frequency spectrum, as soon as the subject stops exercising. However, without immediate return to initial condition.

In the COPD dataset example, an increase in the magnitude and frequency is observed around 10am. Besides, between 10 and 11am, there seems to be harmonic frequencies.

## 3.5 Conclusion

In this chapter different features are extracted from the TeleOx® signals.

As discussed in the previous chapter, TeleOx® raw signals are similar to the nasal pressure signals recorded with a polygraph. However, in opposition to polygraph signals, TeleOx recordings may present a drift in the pressure signal which is addressed by removing an estimated offset. With this method, peaks are well preserved, allowing for satisfactory estimation of breathing rate, but the detection of beginnings of inspiration and expiration by zero-crossing may be biased. Thus, features based on zero crossing detection were abandoned in further analysis.

Moreover, noise is specially present in the COPD dataset, where cough, oral breathing, nasal canula misplacement, among other events, are regularly present. That explains the former choice of basing breathing rate estimation in the median value by the TeleOx® algorithm. Therefore, we consider that recorded signals are not sufficient for precise estimation of cycle-to-cycle variability.
<figure><img src="image_40.png" /><figcaption>(a) Healthy subject</figcaption></figure>

<figure><img src="image_41.png" /><figcaption>(b) COPD patient</figcaption></figure>

Figure 3.18 – Examples of series of estimated ARIMA coefficients from complete raw data recordings.

Consequently, features that are kept as potential indicators of respiratory mechanics profiles are breathing rate, amplitude, ARIMA coefficients and Fourier coefficients. In the next chapter, we test the pertinence of these variables in the detection of changes in the load-capacity balance.
<figure><img src="image_42.png" /><figcaption>Figure 3.19 – Examples of frequency spectrum from complete raw data recordings.</figcaption></figure>
# Chapter 4

# Validation of indicators of respiratory mechanics profiles

In this chapter, previously computed indicators are compared according to their capacities of detecting changes in the rest-effort context.

First, the performances of the indicators, alone or combined, are tested using a large number of supervised learning methods under the assumption of homogeneity within the population. Then, inter-individual variability is considered in models where individuality is included as a random factor. Finally, the indicators' ability to detect abnormality is also verified with a one-class classification method.

## 4.1 Classification

### 4.1.1 Classification data

Healthy and COPD datasets were recovered according to previously described study protocols. For both datasets, non-overlapping sequences of 45 seconds of raw signal are kept for analysis whenever oxygen source and patient presence are detected, together with a good signal quality according to TeleOx® algorithm. Each of those sequences is transformed in vectorial data by extracting the breathing rate, amplitude, ARIMA coefficients and Fourier coefficients, according to methods described in the previous chapter.

For each recording in the healthy dataset, the first 23 periods are considered as rest/reference. Drinking, coughing, speaking and mouth breathing are included in the reference class, since those events are expected to happen as the "normality" for patients with COPD. The following 4 points correspond to exercising. The last 13 points are a transition between effort and rest and thus are not used for classification methods.

For the recordings from patients with COPD, the labels are not that clear. The approximate periods of exercise (bike session and supervised gymnastics) belong to the exercise class. All other data points are considered as reference. Like the healthy data, the reference certainly includes drinking, coughing, speaking and oral breathing, as well as other events as eating, moving and walking, which are unknown.

### 4.1.2 Supervised classification under the homogeneity assumption

The comparison of features ability to classify rest and effort breathing is first performed in a supervised context under the assumption of homogeneity within the population. In
other words, differences between rest and effort periods are considered as independent from
individuality.

SuperLearner [105, 72] is used in order to limit the influence of the used method. For the present analysis, supervised classification includes rest and effort periods from all subjects from the same dataset (healthy or COPD) combined. Different combinations of features are tested so the ability of classifying rest and effort breathing can be compared. For each combination, a 10-fold cross-validation is chosen for the following list of methods: Mean, Generalised Linear Models (full and AIC optimized models), Bayesian Generalised Linear Models, Kernel k Nearest Neighbors, Random Forests, Recursive Partitionning, XGBoost and Generalised Additive Models. This very wide choice of learning models ensures that a huge space of learning rules is explored for each proposed feature combination, and thus that what is finally compared is not the adequacy of the models to the features but the loss of information between the raw data and the extracted features.

4.1.3 Supervised classification with random effects

To take into account the inter-individual variability, generalized linear mixed effect mod-
els (GLMM) is also applied in the supervised context for healthy and COPD datasets,
separately. As in the previous section, different combinations of features are tested for
comparing the abilities of classifying rest and effort breathing.

Models are built using *glmer* function of the *lme4* package [13] in R, with random intercepts and random slopes. The link function is logit.

The Fourier coefficients cannot be used directly because of the high number of coef-
ficients. To avoid the curse of dimensionality, we perform for each fold a PCA on the
training data and keep the first 5 principal components.

4.1.4 One-class classification

The supervised classification power is not the only criterion to select a combination of
features. Indeed, in the objective application, the algorithm will have to train based only
on a normal class and be able to detect abnormalities.

We choose to compare the abilities for such a task of the features listed in the previous
chapter by using a method based on Mahalanobis distance [56, 2].

For each subject, the data points are divided into training set and validation set. The training set contains only rest points and is used as the reference. The validation set contains both rest and effort points, for which we compute the Mahalanobis distance from the training set. A 5-fold cross-validation method is used to both data from healthy subjects and from patients with COPD. For each subject, healthy or COPD patients, a 5-fold cross validation is used on the resting data: 4 out of the 5 folds are used to learn the mean and variance-covariance matrix.

For the healthy dataset, the distance is computed for the last fold and the exercising
data, ending up with one prediction for each resting point and five predictions for each
exercising point. For the COPD dataset, larger exercising data is available, the distance
is thus computed for the last fold of resting data and one fold of the exercising data. We
thus end up with one prediction for each data point (rest and exercise). This method is
repeated varying the features used: 1. breathing rate; 2. signal amplitude; 3. breathing
rate and amplitude; 4. ARIMA coefficients; 5. breathing rate, amplitude and ARIMA
coefficients and 6. Fourier coefficients.

The dimensionality of Fourier coefficients also needs to be reduced for the one-class
classification method. For each subject, a PCA using training resting data is used to
define the first 5 principal components. Mahalanobis distance and the method described above is then completed using the projected data.

Sensitivity and specificity is given for the cut-off threshold that minimizes the distance from the upper-left corner of the respective ROC curve, that is $\sqrt{FPR^2 + (1 - TPR)^2}$, where FPR is the false positive rate and TPR is the true positive rate.

## 4.2 Results

### 4.2.1 Data and feature extraction

In total, dataset from twenty healthy subjects contains 439 rest periods and 78 effort periods. In the COPD dataset, 1567 rest periods and 571 effort periods were recorded from eight patients. Figures 4.1 and 4.2 show examples from healthy and COPD recordings, respectively, and the corresponding features computed every 45 seconds. COPD recordings often include periods where features are not computed, which correspond to periods where oxygen is not used, patient is not detected or the quality of the signal is considered insufficient.

### 4.2.2 Supervised classification under the homogeneity within the population

Classification methods are performed with healthy and COPD datasets separately. SuperLearner results are presented in Tables 4.1 and 4.2 for healthy and COPD datasets respectively. Figure 4.3 shows the ROC curves for the different combinations of features in both cases.

<table><caption>Table 4.1 – Performance of SuperLearner in exercise detection for the healthy individuals dataset using different predictor variables and performance indices.</caption><thead><tr><th>Predictive variables</th><th>Accuracy</th><th>Sensitivity</th><th>Specificity</th><th>AUC</th></tr></thead><tbody><tr><td>Breathing rate</td><td>0.878</td><td>0.991</td><td>0.244</td><td>0.693 (0.619-0.766)</td></tr><tr><td>Signal amplitude</td><td>0.952</td><td>0.991</td><td>0.731</td><td>0.942 (0.903-0.980)</td></tr><tr><td>ARIMA coefficients</td><td>0.865</td><td>0.964</td><td>0.308</td><td>0.891 (0.852-0.931)</td></tr><tr><td>Breathing rate and signal amplitude</td><td>0.963</td><td>0.984</td><td>0.846</td><td>0.989 (0.982-0.996)</td></tr><tr><td>Breathing rate, signal amplitude and ARIMA coefficients</td><td>0.969</td><td>0.989</td><td>0.859</td><td>0.993 (0.988-0.998)</td></tr><tr><td>Fourier coefficients (frequencies &le; 2 Hz)</td><td>0.946</td><td>0.984</td><td>0.731</td><td>0.984 (0.975-0.993)</td></tr></tbody></table>

The comparison between methods shows a clear hierarchy in their capacity to discriminate rest and exercise. Breathing rate, amplitude and ARIMA coefficients alone are clearly weaker than their combinations and that Fourier coefficients.

There is also a clear difference between healthy individuals and COPD patients but it is difficult to tell if it is due to COPD or to the lesser confidence of the data labelling.

### 4.2.3 Supervised classification with random effects

Generalized linear mixed models (GLMM) performances are presented in Tables 4.3 and 4.4 for healthy and COPD datasets respectively. Figure 4.4 shows the ROC curves for the different combinations of features in both cases.
<figure><img src="image_43.png" /><figcaption>Figure 4.1 – Extracted features example from a healthy subject recording. a. the original pressure signal. b. breathing rate, inspiratory amplitude and ARIMA coefficients extracted from 45-second windows of the pressure signal. c. Fourier coefficients from 45-second windows of the pressure signal.</figcaption></figure>

In the healthy dataset, the hierarchy between the parameters remained the same in comparison with SuperLearner results. The only significant difference being an improvement in the performance with amplitude alone.

In the COPD dataset, the hierarchy also remained similar, although the performance with Fourier coefficients significantly reduced (possibly related to the dimensionality reduction with the ACP). Besides the Fourier coefficients and the combination of breathing rate, amplitude and ARIMA coefficients, all other tested parameters achieved significantly
<figure><img src="image_44.png" /><figcaption>Figure 4.2 – Extracted features example from a COPD patient recording. **a.** the original pressure signal. **b.** breathing rate, inspiratory amplitude and ARIMA coefficients extracted from 45-second windows of the pressure signal. **c.** Fourier coefficients from 45-second windows of the pressure signal.</figcaption></figure>

higher performances when considering the random effects in the population.

Once again, there is a clear difference between the performances with healthy individuals and COPD patients.
<figure><img src="image_45.png" /><figcaption>Figure 4.3 – ROC curves for the detection of exercise periods with SuperLearning using combinations of the proposed features</figcaption></figure>

<table><caption>Table 4.2 – Performance of SuperLearner in exercise detection for the COPD patients dataset using different predictor variables and performance indices.</caption><thead><tr><th>Predictive variables</th><th>Accuracy</th><th>Sensitivity</th><th>Specificity</th><th>AUC</th></tr></thead><tbody><tr><td>Breathing rate</td><td>0.751</td><td>0.996</td><td>0.073</td><td>0.627 (0.600-0.654)</td></tr><tr><td>Signal amplitude</td><td>0.756</td><td>0.982</td><td>0.133</td><td>0.642 (0.616-0.668)</td></tr><tr><td>ARIMA coefficients</td><td>0.748</td><td>0.970</td><td>0.135</td><td>0.690 (0.665-0.714)</td></tr><tr><td>Breathing rate and signal amplitude</td><td>0.771</td><td>0.968</td><td>0.227</td><td>0.712 (0.688-0.737)</td></tr><tr><td>Breathing rate, signal amplitude and ARIMA coefficients</td><td>0.803</td><td>0.964</td><td>0.357</td><td>0.812 (0.792-0.832)</td></tr><tr><td>Fourier coefficients (frequencies &le; 2 Hz)</td><td>0.824</td><td>0.984</td><td>0.393</td><td>0.849 (0.830-0.867)</td></tr></tbody></table>

<figure><img src="image_46.png" /><figcaption>Figure 4.4 – ROC curves for the detection of exercise periods with GLMM using combinations of the proposed features</figcaption></figure>
<table><caption>Table 4.3 – Performance of GLMM in exercise detection for the healthy individuals dataset using different predictor variables and performance indices.</caption><thead><tr><th>Predictive variables</th><th>Accuracy</th><th>Sensitivity</th><th>Specificity</th><th>AUC</th></tr></thead><tbody><tr><td>Breathing rate</td><td>0.886</td><td>0.993</td><td>0.282</td><td>0.734 (0.673-0.794)</td></tr><tr><td>Signal amplitude</td><td>0.957</td><td>0.986</td><td>0.795</td><td>0.987 (0.978-0.995)</td></tr><tr><td>ARIMA coefficients</td><td>0.859</td><td>0.959</td><td>0.295</td><td>0.820 (0.769-0.872)</td></tr><tr><td>Breathing rate and signal amplitude</td><td>0.965</td><td>0.984</td><td>0.859</td><td>0.995 (0.991-1.000)</td></tr><tr><td>Breathing rate, signal amplitude and ARIMA coefficients</td><td>0.963</td><td>0.979</td><td>0.872</td><td>0.977 (0.945-1.000)</td></tr><tr><td>Fourier coefficients (frequencies ≤ 2 Hz)</td><td>0.954</td><td>0.973</td><td>0.846</td><td>0.975 (0.948-1.000)</td></tr></tbody></table>

<table><caption>Table 4.4 – Performance of GLMM in exercise detection for the COPD patients dataset using different predictor variables and performance indices.</caption><thead><tr><th>Predictive variables</th><th>Accuracy</th><th>Sensitivity</th><th>Specificity</th><th>AUC</th></tr></thead><tbody><tr><td>Breathing rate</td><td>0.748</td><td>0.950</td><td>0.194</td><td>0.741 (0.718-0.764)</td></tr><tr><td>Signal amplitude</td><td>0.787</td><td>0.951</td><td>0.338</td><td>0.773 (0.751-0.796)</td></tr><tr><td>ARIMA coefficients</td><td>0.806</td><td>0.945</td><td>0.424</td><td>0.814 (0.793-0.835)</td></tr><tr><td>Breathing rate and signal amplitude</td><td>0.801</td><td>0.939</td><td>0.422</td><td>0.798 (0.776-0.819)</td></tr><tr><td>Breathing rate, signal amplitude and ARIMA coefficients</td><td>0.825</td><td>0.932</td><td>0.531</td><td>0.848 (0.829-0.867)</td></tr><tr><td>Fourier coefficients (frequencies ≤ 2 Hz)</td><td>0.797</td><td>0.933</td><td>0.422</td><td>0.811 (0.791-0.832)</td></tr></tbody></table>

### 4.2.4 One-class classification

ROC curves of the results of one-class classification models based on the Mahalanobis distance are shown in Figure 4.5. The performances obtained by each method are presented in Tables 4.5 and 4.6 for healthy and COPD datasets, respectively.

<figure><img src="image_47.png" /><figcaption>Figure 4.5 – ROC curves for the detection of exercise periods in the one-class context using combinations of the proposed features</figcaption></figure>

In most tested conditions, the performances are slightly weakened compared to the
<table><caption>Table 4.5 – Performance of one-class classification models in exercise detection for the healthy individuals dataset using different predictor variables and performance indices.</caption><thead><tr><th>Predictive variables</th><th>Accuracy</th><th>Sensitivity</th><th>Specificity</th><th>AUC</th></tr></thead><tbody><tr><td>Breathing rate</td><td>0.655</td><td>0.597</td><td>0.706</td><td>0.684 (0.647-0.721)</td></tr><tr><td>Signal amplitude</td><td>0.905</td><td>0.903</td><td>0.907</td><td>0.958 (0.942-0.971)</td></tr><tr><td>ARIMA coefficients</td><td>0.817</td><td>0.795</td><td>0.836</td><td>0.855 (0.828-0.880)</td></tr><tr><td>Breathing rate and signal amplitude</td><td>0.918</td><td>0.887</td><td>0.945</td><td>0.974 (0.964-0.981)</td></tr><tr><td>Breathing rate, signal amplitude and ARIMA coefficients</td><td>0.919</td><td>0.895</td><td>0.941</td><td>0.976 (0.967-0.983)</td></tr><tr><td>Fourier coefficients (frequencies &le; 2 Hz)</td><td>0.929</td><td>0.951</td><td>0.909</td><td>0.971 (0.957-0.979)</td></tr></tbody></table>

<table><caption>Table 4.6 – Performance of one-class classification models in exercise detection for the COPD patients dataset using different predictor variables and performance indices.</caption><thead><tr><th>Predictive variables</th><th>Accuracy</th><th>Sensitivity</th><th>Specificity</th><th>AUC</th></tr></thead><tbody><tr><td>Breathing rate</td><td>0.594</td><td>0.537</td><td>0.615</td><td>0.592 (0.561-0.619)</td></tr><tr><td>Signal amplitude</td><td>0.678</td><td>0.577</td><td>0.715</td><td>0.685 (0.655-0.709)</td></tr><tr><td>ARIMA coefficients</td><td>0.634</td><td>0.610</td><td>0.642</td><td>0.654 (0.627-0.678)</td></tr><tr><td>Breathing rate and signal amplitude</td><td>0.650</td><td>0.629</td><td>0.658</td><td>0.683 (0.656-0.712)</td></tr><tr><td>Breathing rate, signal amplitude and ARIMA coefficients</td><td>0.644</td><td>0.629</td><td>0.649</td><td>0.686 (0.661-0.711)</td></tr><tr><td>Fourier coefficients (frequencies &le; 2 Hz)</td><td>0.655</td><td>0.639</td><td>0.662</td><td>0.705 (0.681-0.731)</td></tr></tbody></table>

supervised context. This was expected, since this method learns only about normal events, while supervised methods have access to both normal and abnormal events to learn the classification rules. The hierarchy between the proposed methods remains however similar, although the superiority of the combination of breathing rate, amplitude and ARIMA coefficient for the COPD dataset disappears.

## 4.3 Discussion

The use of the SuperLearner package enables to combine multiple methods to find the best possible results for a supervised classification problem. In this way, we can compare the performance of different features, without fearing a loss of performance from a bad method choice. For completeness, GLMM takes into account the random effects related to individual respiratory characteristics. The hierarchy of different parameters performance with both supervised method is quite similar in both healthy and COPD datasets.

In the supervised contexts, the breathing rate alone has the lowest performance for classifying rest and effort periods for healthy individuals. Any other feature alone or combined leads to better performance among the considered models. The models combining breathing rate with amplitude, breathing rate with amplitude and ARIMA coefficients and Fourier coefficients present comparable and better performances.

Performances with data from patients with COPD are lower. Indeed, the periods labels are not as precise as for the healthy individuals dataset. Not only the time schedule is approximate, but also these patients may take exercising easier or execute physical
activities in the rest periods. For some of those patients, any movement can become really challenging and be a physical effort, as walking, standing up, showering, etc.

In both cases, this study demonstrates a significant gain in combining breathing rate with amplitude and potentially ARIMA coefficients, or using Fourier decompositions. This gain can be measured in either Accuracy, Sensitivity/Specificity or AUC, and can be medically interpreted by the fact that changing one's breathing rate is not the only way to adapt to changes in the load-capacity balance.

The supervised approach however has a major pitfall, which is that it needs abnormal data to learn the classification rules. In practice, two options are then available: learn rules about the entire population, or monitor patients for a sufficiently long period so several abnormal events are observed for each patient. The first solution is not relevant from a physiological point of view because it disregards the variability between patients. The latter is not attainable, since exacerbations arrive at different frequencies and may differ from one another, even for the same patient.

A novelty detection method, or one-class classification, may thus be preferred in the case of medical data. Normal data acquisition for each individual then allows to detect any possible change in the features. For instance, the second healthy subject presented in the Figure 3.1 increases mainly its breathing rate during the exercising periods. Nevertheless, as soon as the subject sits down, there is an increase in the signal amplitude, a change not described previously. If the model is trained in a supervised manner with rest and effort periods, those first periods after exercising may be considered as rest.

On healthy subjects, the performances obtained using the Mahalanobis distance based model are similar to those obtained with SuperLearner although a bit weaker for some of the predictors.

For the patients with COPD, the loss in performance is greater. Prediction with breathing rate alone achieves the lowest performances. Besides, in the supervised context, the model created by combining breathing rate, amplitude and ARIMA coefficients presented a superior performance than with any other predictive variable. In the unsupervised learning case, this combination is similar to other tested conditions. A slightly higher performance is obtained when using Fourier coefficients, which combines signal's frequency, magnitude and variability.

It is also notable that, although breathing rate alone classifies better than random guessing for both healthy and COPD subjects, its performance is quite poor in all cases as previously described. Combining the breathing rate with any other feature described here seems to be beneficial for the identification of periods of exercising. This observation is again true for all considered classification criteria, that is Accuracy, Sensitivity/Specificity or AUC.

## 4.4 Conclusions

The conclusion of this study is that breathing rate alone is a quite poor feature in terms of prediction of breathing change, in the sense that the addition of any of the other proposed features clearly improves the classification power, in both supervised and novelty detection framework. From this point of view, the most promising features are the Fourier coefficients and the combinations of breathing rate with other predictive variables, notably the signal amplitude.

Besides, although this study do not consider breathing change patterns specifically related to exacerbation events, these new features may also enlighten other kinds of load-capacity balance changes and thus potentially enhance exacerbation prediction methods.
# Chapter 5

## Remote monitoring

Following the study of the previous chapter, two updates have been proposed to improve the use of TeleOx® devices.

The first update concerns the firmware of the device which gains a new monitored variable. This update is directly related to the conclusions of the presented study.

The second update concerns the acquisition of data from TeleOx®, going from manual acquisition to automatic and continuous acquisition. Despite a long felt need, this improvement was accelerated by the pandemic of COVID-19.

### 5.1 TeleOx® algorithm upgrade

The study of new indicators of respiratory mechanics profiles lead to an update in TeleOx® firmware, to consider new features.

Although ARIMA coefficients and Fourier coefficients might add useful information, they require more processing and memory spaces. TeleOx® was designed to be a small device, minimizing any disturbance that it may cause to patients. Thus, ARIMA and Fourier coefficients implementation would demand hardware and firmware adaptations in TeleOx®.

Amplitude on the other hand can be easily computed, benefiting from the already implemented algorithm that estimates breathing rate. Besides, flash memory has sufficient space for one float variable.

Thus, a new version of TeleOx firmware was implemented with additional amplitude computation and registration. All TeleOx® used in following analysis used this new firmware.

This improvement also lead to a new patent concerning the use of breathing rate and amplitude combined for the estimation of a respiratory quality indication.

### 5.2 Real time data acquisition

In the beginning of this work, TeleOx® data acquisition was continuous, but measures were recorded in the device until transmitted to server upon request. This transmission required a small manipulation by connecting a smartphone or tablet to a TeleOx® through Bluetooth with an Android application.

In the context of COVID-19, we developed a new application called TeleOx Seren that enables automatic transmission of data recorded with TeleOx®. This application runs in an Android tablet and connects with associated TeleOx and/or oxymeter. Data is periodically
sent through Internet to the server and can be assessed by healthcare providers in real time
through an online interface.

This project was developed in collaboration with the *Service de Pneumologie et Réan-
imation médicale* at the Hospital Pitié-Salpêtrière. During more than two months, I fre-
quently visited the unit to discuss the needs of healthcare providers in the context of the
pandemic and test prototypes, guiding the technology development until its now available
final version.

Although this application has been developed thinking about remote monitoring of
COVID-19 patients, it is also adapted to home monitoring of COPD patients. Besides,
it allows for real time data treatment and further implementation of alerts of atypical
respiratory profiles.

**5.3 First conclusions**

TeleOx® is a medical device developed to monitor patients’ adherence to oxygen therapy. A first study has confirmed TeleOx® ability to reliably estimate breathing rate.

The second study indicates that other measures complement breathing rate for a better understanding of changes in the respiratory profile. From the results and for technological reasons, amplitude was implemented in a new version of TeleOx® firmware.

New study is required to confirm the clinical interest of monitoring for real life respiratory profile changes, specially in which concerns the detection of acute exacerbations.
# Part III

## Analysis and results for exacerbation detection