Looking at the second heart sound: A multi-facet study

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Looking at the second heart sound: A multi-facet study Fabio de Lima Hedayioglu Programa Doutoral em Informática Departamento de Ciência de Computadores 2014 Orientador Miguel Tavares Coimbra, Prof. Auxiliar, Faculdade de Ciências da Universidade do Porto Coorientador Sandra da Silva Mattos, UCMF - RHP Contents Acknowledgements 10 Resumo 12 Abstract 14 1 Introduction 16 1.1 Auscultation Through History . . . . . . . . . . . . . . . . . . 16 1.2 Motivation for processing heart sounds . . . . . . . . . . . . . 17 1.3 The importance of the second heart sound . . . . . . . . . . . 18 1.4 Objectives............................. 19 1.5 Contributions ........................... 19 1.6 Publications............................ 19 1.7 Thesisstructure.......................... 20 2 Heart sounds 22 2.1 PhysicsofSound ......................... 22 2.2 Physiology of the heart . . . . . . . . . . . . . . . . . . . . . . 23 2.3 HeartSounds ........................... 25 2.3.1 The first heart sound . . . . . . . . . . . . . . . . . . . 26 2.3.2 The second heart sound . . . . . . . . . . . . . . . . . 27 2.3.3 Clinical assessment of the second heart sound . . . . . 30 2.4 Processing heart sounds . . . . . . . . . . . . . . . . . . . . . 34 2.4.1 Heart sound segmentation . . . . . . . . . . . . . . . . 34 2.5 Heart sound classification . . . . . . . . . . . . . . . . . . . . 36 2 2.6 Challenges of processing the second heart sound . . . . . . . . 38 3 Independent Component Analysis of S2 41 3.1 Introduction to source separation . . . . . . . . . . . . . . . . 41 3.2 Blind source separation and independent component analysis . 41 3.2.1 Historical background . . . . . . . . . . . . . . . . . . 43 3.2.2 Classical ICA . . . . . . . . . . . . . . . . . . . . . . . 44 3.2.3 Sequential Signal Acquisition . . . . . . . . . . . . . . 46 3.3 Experiments............................ 51 3.3.1 Experiment 1: synthetic signals . . . . . . . . . . . . . 52 3.3.2 Experiment 2: foetal and maternal electrocardiogram separation......................... 55 3.3.3 Experiment 3: heart sounds and lung sounds separation 58 3.3.4 Experiment 4: segmentation of the second heart sound 63 3.4 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . 69 3.5 Publications............................ 71 4 Representation of S2 Using Matching Pursuit 72 4.1 Introduction ........................... 72 4.2 PreviousWork .......................... 73 4.3 Methods ............................. 75 4.3.1 Matching pursuit . . . . . . . . . . . . . . . . . . . . . 75 4.3.2 The Model/Dictionary . . . . . . . . . . . . . . . . . . 77 4.4 Experiments............................ 79 4.4.1 Dataset .......................... 79 4.4.2 Experiment 1: denoising/sparse representation of S2 . . 79 4.4.3 Experiment 2: atoms and physiological features . . . . 82 4.5 Conclusions ............................ 84 4.6 Publications............................ 85 5 Energy Based Segmentation of S2 86 5.1 Introduction ........................... 86 5.2 Characterisation of S2 . . . . . . . . . . . . . . . . . . . . . . 87 5.2.1 EnergyofS2 ....................... 90 3 5.2.2 Algorithm......................... 91 5.3 Experiments............................ 94 5.3.1 Normal Auscultations . . . . . . . . . . . . . . . . . . 94 5.3.2 Hyperphonetic Auscultations . . . . . . . . . . . . . . 97 5.3.3 S2 components by auscultation group . . . . . . . . . . 100 5.4 Conclusions ............................102 5.5 Publications............................105 6 Synthetic auscultation generator 106 6.1 Introduction............................106 6.2 Stateoftheart ..........................107 6.3 Synthesis of auscultation . . . . . . . . . . . . . . . . . . . . . 107 6.3.1 First heart sound generation . . . . . . . . . . . . . . . 107 6.3.2 Second heart sound generation . . . . . . . . . . . . . 109 6.3.3 Systole and diastole calculation . . . . . . . . . . . . . 109 6.3.4 Generating an auscultation . . . . . . . . . . . . . . . . 113 6.4 Experiments............................114 6.4.1 Auscultations generation . . . . . . . . . . . . . . . . . 115 6.5 Conclusions ............................121 7 Conclusions and future work 123 Appendix A: Dataset 126 Bibliography 127 4 List of Figures 2.1 The heart in the mediastinum . . . . . . . . . . . . . . . . . . 24 2.2 Anormalheart .......................... 25 2.3 Thecardiaccycle......................... 26 2.4 The M1 and T1 components of the first heart sound . . . . . . 27 2.5 The heart in the mediastinum . . . . . . . . . . . . . . . . . . 28 2.6 The pressure curves in normal subject . . . . . . . . . . . . . 29 2.7 Auscultatory areas . . . . . . . . . . . . . . . . . . . . . . . . 32 2.8 Heart with atrial septal defect . . . . . . . . . . . . . . . . . . 33 3.1 The classical problem of source separation . . . . . . . . . . . 42 3.2 Conventional multichannel acquisition of a set of mixtures . . 47 3.3 Mixed signals recorded sequentially . . . . . . . . . . . . . . . 48 3.4 An overview of the proposed method . . . . . . . . . . . . . . 48 3.5 Source signals and mixtures . . . . . . . . . . . . . . . . . . . 53 3.6 Single sensor signal acquired at three di↵erent locations . . . . 53 3.7 sequential and aligned mixtures . . . . . . . . . . . . . . . . . 54 3.8 FastICA output to unaligned and aligned mixtures . . . . . . 55 3.9 Separated sources by FastICA on simultaneously recorded mixtures................................ 56 3.10 Maternal ECG mixed with foetal ECG . . . . . . . . . . . . . 57 3.11 Output of ECG signals using classical ICA and the proposed method .............................. 58 3.12 Sequential recordings of S2 and lung sounds . . . . . . . . . . 59 3.13 Estimated sources from Sequential recordings of S2 and lung sounds............................... 60 5 3.14Mixturesexplained ........................ 61 3.15 Simultaneous recordings of S2 and lung sounds . . . . . . . . . 62 3.16 Mixtures explained by correlation . . . . . . . . . . . . . . . . 63 3.17 A2, P2 and their mixtures . . . . . . . . . . . . . . . . . . . . 65 3.18 A2 and P2 sources and estimated sources . . . . . . . . . . . . 66 3.19 Recordings with P2 changing its delay . . . . . . . . . . . . . 67 3.20 A2 and P2 sources and estimated sources . . . . . . . . . . . . 68 3.21 The second heart sound acquired using four stethoscopes . . . 68 3.22 The calculated sources . . . . . . . . . . . . . . . . . . . . . . 69 4.1 Graph of Am(t) function with duration set to 60 milliseconds. 78 4.2 The frequency decay of an atom . . . . . . . . . . . . . . . . . 79 4.3 Recorded S2, reconstructed S2 by MP and its residual . . . . . 81 4.4 Histogram of the Pearson correlation between recorded S2 and their calculated atoms . . . . . . . . . . . . . . . . . . . . . . 82 4.5 Scatter plot with two Gaussian clusters separating normal and hyperphonetic auscultations . . . . . . . . . . . . . . . . . . . 84 5.1 Phonocardiogram with A2 and P2 depicted in the middle trace. 87 5.2 Phonocardiogram and recording depicting the X wave . . . . . 88 5.3 The second heart sound from an auscultation from in data set showing the X wave right in the beginning of S2 (circled), followedbyA2andP2. ..................... 89 5.4 Physiological splitting of S2 . . . . . . . . . . . . . . . . . . . 89 5.5 Recorded S2, its calculated energy and the detected A2 and P2. 91 5.6 The non-linear threshold for A2 and P2 detection . . . . . . . 92 5.7 detected A2 and P2 in a normal auscultation and its energy . 94 5.8 Variation in amplitude of A2 and P2 in a normal auscultation 95 5.9 The amplitudes of each A2 and P2 relative to the mean (100%) 96 5.10 P2-A2 split time recorded on every S2 of a normal auscultation 96 5.11 The detected A2 and P2 in a hyperphonetic auscultation and itsenergy ............................. 98 5.12 Variation in amplitude of A2 and P2 in a hyperphonetic auscultation.............................. 98 6 5.13 P2-A2 split time recorded on every S2 of a hyperphonetic auscultation.............................. 99 5.14 Detected A2 and P2 in normal and hyperphonetic auscultation 101 5.15 Separation between normal and hyperphonetic S2 . . . . . . . 102 5.16 Miss-identification of P2 due to very low energy intensity. . . 103 5.17 Incorrectly detected A2 . . . . . . . . . . . . . . . . . . . . . . 104 6.1 Fitfunctions............................112 6.2 The GUI of the simulator with the input fields. . . . . . . . . 116 6.3 Examples of generated auscultations: Hyperphonetic and normal117 6.4 Hyperphonetic and normal auscultations S2 . . . . . . . . . . 118 6.5 Hyperphonetic auscultation generated from normal . . . . . . 120 6.6 Scatter plot with the two synthetic auscultations . . . . . . . . 120 6.7 Comparison between original auscultation and the generated one.................................121 7 List of Tables 2.1 Assesment of the second heart sound . . . . . . . . . . . . . . 40 3.1 The Pearson coefficient between real and estimated sources . . 55 3.2 The Pearson correlation between the mixtures . . . . . . . . . 59 3.3 The Pearson correlation between the sources . . . . . . . . . . 62 3.4 The Pearson correlation between the sources and estimated sources............................... 66 3.5 The Pearson correlation between the mixtures . . . . . . . . . 67 3.6 The Pearson correlation between the mixtures . . . . . . . . . 69 4.1 Confusion matrix: columns has the ground truth and rows has thecluster ............................ 83 5.1 Values of the split time (P2-A2) between inspiration and expiration .............................. 97 5.2 Values of the split time (P2-A2) between inspiration and expiration in a hyperphonetic auscultation . . . . . . . . . . . . 100 5.3 Mann-whitney U test . . . . . . . . . . . . . . . . . . . . . . . 102 6.1 Sv parameters...........................108 6.2 The mean squared errors between the linear and exponential functions..............................111 6.3 Variation of heart rate on di↵erent auscultations . . . . . . . . 114 8 List of Algorithms 3.1 Separation via sequential signal synchronization . . . . . . . . 51 4.1 TheMPalgorithm ........................ 76 5.1 Pseudo-code for detecting A2 and P2 . . . . . . . . . . . . . . 93 5.2 Peak Detection algorithm . . . . . . . . . . . . . . . . . . . . 93 9 Chapter 1 Introduction 1.1 Auscultation Through History Since the early times, mankind knows that the body produces its own sounds and the importance of their interpretation have been recognised early by man. Between 460 B.C. and 370 B.C., Hippocrates mentions cardiac sounds [1], but it was only on the 17th Century that the clinician Ren´e Th´eophile Hyacinthe Laennec created a device that, later, would become the most remarkable symbols of the practitioner: the stethoscope. At this time, in order to hear cardiac sounds, the clinician had to make use of a technique known as ”direct auscultation”, which consists in placing the ear directly on the patient’s chest. This method is as uncomfortable for the clinician as it is for the patient, and a great inconvenience on women’s examination. In hospitals, this method is impractical due to the great corporal contact, causing the risk of infection to increase significantly. In 1816, Laennec (1781-1826) was requested to perform the examination of a woman with a high degree of obesity with general symptoms of cardiopathy. Direct auscultation was considered inappropriate by the woman’s husband. Laennec, taking some sheets of paper, wrapping them up and putting one end of it on the patient’s chest, and the other end on his ear, could hear the heart sounds clearer than using direct auscultation [2]. In 1819, Laennec published the result of his studies on the book: ”Trait´e 16 de L’Auscultation M´ediate, et des maladies des poumons et du coeur” (Treatise on Mediate Auscultation and Diseases of the Chest and Heart) [3]. In this work, he introduced new terms to describe more accurately the heart sounds and murmurs as well as the triple rhythm. Inadequate physiologic knowledge at that time led to a faulty interpretation of heart sounds. This was corrected, however, by the middle of the 19th century. The first recording of heart sounds was made by Hurthle (1895), who connected a microphone to an inductorium, the secondary coil of which stimulated a frog nerve-muscle preparation. At about the same time, Willem Einthoven [4] recorded phonocardiograms (the graphic representation of the sounds which originate in the heart and great vessels), first by means of a capillary electrometer and then with a string galvanometer. The first monograph on phonocardiography was published by O. Weiss in 1909 [5]. Nowadays, stethoscopes are still widely used as the first cardiologic evaluation of patients. It is a non-invasive tool that detects a wide range of functional, hemodynamic and structural anomalies. This is an indicator of the e↵ectiveness of the diagnostic capabilities of the stethoscope as a screening tool: the examination is fast, and can screen a broad range of cardiopathies. 1.2 Motivation for processing heart sounds In this thesis, we focus on the processing of heart sounds acquired by auscultation, which has the advantage of being one of the simplest, quickest and most cost e↵ective techniques to identify and diagnose a large number of heart conditions [6]. Cardiac auscultation is a difficult skill to master, which requires extensive training and years of experience [7]. This is because heart sounds are difficult to identify and analyse by the human listener as they are faint, significant events are closely spaced in time (less than 0.03 seconds), and their frequency content is at the lower end of the audible frequency range [8]. Auscultation is a skill that is also subjective to the hearing of the individual [9]. In fact, primary care physicians often never master auscultation [10] and studies have shown that they fail to correctly identify normal beats or benign murmurs 17 in as much as 80% of patients that they refer to cardiologists [10]. These unnecessary referrals represent a high financial cost for the medical system, including the visit to the cardiologist and any further tests that have to be performed [8]. Furthermore, a physician with poor auscultatory skills is also likely to fail to detect pathologies. Although there is no way to quantify how many problems go undiagnosed, it is obvious that this can have disastrous consequences for the individuals whose diseases remain undetected [11]. The difficulty in acquiring and maintaining auscultatory competence is compounded by the general decline in auscultation training in recent years, partly due to the introduction of new diagnostic technologies, and partly because of the scarcity of skilled instructors [6, 10]. Nonetheless, the need for a quick and inexpensive diagnosis method for cardiac disease remains, and this problem has attracted the attention of researchers who have been considering automating all or part of the auscultation procedure. This is an approach that is seen of particular importance for developing countries, where lack of resources may result in limited access to cardiologists, or in nurses taking on the role of primary carers in rural areas [12]. In this work, we are interested in the automatic analysis of the acoustic signal acquired during cardiac auscultation, more specifically, the second heart sound. We aim at identifying certain important features of the heart sound, regardless of whether these correspond to a healthy heart function or indicate the existence of a pathology. 1.3 The importance of the second heart sound The second heart sound is closely related to the systemic circulation, pulmonary circulation and is greatly influenced by the respiratory cycle. Therefore, it is very important in the diagnosis of cardiac diseases. The study of the main features of the second heart sound (amplitude of A2, amplitude of P2 and behaviour of the split), allows the clinician to detect a variety of cardiac conditions related to the pulmonary artery, aortic valve, systemic pressure, pulmonary artery pressure, right and left ventricle, and even some congenital heart defects, such as the Fallot Tetralogy [13, 14, 15, 18 16, 17, 18]. 1.4 Objectives In this thesis we want to look at the second heart sound from three di↵erent physiologically justifiable perspectives: from a purely signal processing perspectives, we assume very little about the signal components, and look at it as source separation problem; then we assume a mathematical structure to the underlying physiological components of the signal, creating a sparse representation; and then, buy trying to mimic the clinician, we extract some features of the physiological components of the signal. 1.5 Contributions Throughout this thesis, some contributions were made. The main ones are listed below: 1. A novel technique using a moving sensor to collect data and simulate signal acquisition from an array of sensors was developed. 2. We developed a physiologically inspired mathematical model for the underlying components of the second heart sound. 3. A new algorithm that mimics the analysis and identification of A2 and P2 performed by the clinician when using a phonocardiogram was created. 4. A novel heart sound simulator that generates synthetic auscultations based on real ones, and with customisable clinically meaningful parameters was developed. 1.6 Publications 1. F. L. Hedayioglu; M. G. Jafari; S. S. Mattos; M. D. Plumbley; M. T. Coimbra, ”Separating sources from sequentially acquired mixtures 19 of heart signals,” Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on , vol., no., pp.653,656, 22-27 May 2011 doi: 10.1109/ICASSP.2011.5946488 2. M. G. Jafari; F. L. Hedayioglu; M. T. Coimbra; M. D. Plumbley, ”Blind source separation of periodic sources from sequentially recorded instantaneous mixtures,” Image and Signal Processing and Analysis (ISPA), 2011 7th International Symposium on , vol., no., pp.540-545, 4-6 Sept. 2011 3. F. L. Hedayioglu; M. G. Jafari; S. S. Mattos; M. D. Plumbley; M. T. Coimbra, “Denoising and segmentation of the second heart sound using matching pursuit,” Engineering in Medicine and Biology Society (EMBC), 2012 Annual International Conference of the IEEE (pp. 34403443). IEEE; (2012, August) 4. F. L. Hedayioglu; M.G. Jafari; S. S. Mattos; M. D. Plumbley; M. T. Coimbra, ”An Exploratory Study On The Segmentation Of The Second Heart Sound”, to be submitted 1.7 Thesis structure Chapter 2 Introduces a brief summary on the physiology of the heart. Chapter 3 Presents a study on the problem of performing source separation on heart signals. Chapter 4 We describe an approach where we developed a physiologically inspired mathematical model for the underlying components of the second heart sound. Chapter 5 In this chapter we postulate that the second heart sound components are peak-like, and the measures provided by these peaks also relates to the underlying components of S2. 20 Chapter 6 we presents a heart sound simulator program that generates synthetic auscultations based on real ones, and with customisable clinically meaningful parameters. Chapter 7 Presents the main conclusions from this work, discuss some issues and presents possible future works on this field. 21 Chapter 2 Heart sounds 2.1 Physics of Sound Sound may be described as the motion of waves of alternating pressure generated by a vibrating object [19]. This vibrating source sets particles in motion and in case of a sound with only one tone, the individual particles move around their resting point, with the same frequency of that tone. In each movement, vibrating particles push others nearby, putting them in motion, therefore creating a chain e↵ect, generating areas of high and low pressure. This alternation between low and high pressure moves away from the sound source and so does the sound wave. Usually those waves can be detected by their mechanical e↵ect on a membrane (it could be a microphone’s membrane or a stethoscope’s diaphragm). A common way of describing a sound is by its intensity, frequency and duration [20]. Di↵erent materials conduct sound, and the nature of this conducting material defines the rate of propagation, varying directly with the elasticity of the conducting material (medium) and inversely with its density. On the human body, the transmission of sound waves is a very complex matter involving three di↵erent modes [21, 22, 23]: •compression wave: the same speed of sound in water (with a speed about 1.5 Km/s) •transverse shear wave: slower than the compression wave, propagates 22 most of the vibratory energy of the body (at about 20 m/s) •surface wave: a mixture between transverse and compression waves, on the surface of the body (at about 20 m/s) When the waves travel from one medium to the other, considerable distortion may be produced: waves may be reflected, refracted, among others, resulting in a loss of energy. Probably for these reasons, when the myocardial tissue is in a close position to the chest wall, heart sounds are well conducted to the body’s surface, since they form a relatively homogeneous medium. However, when the air-filled lung is between the heart and the chest wall, waves must travel more mediums, therefore these waves are weakened considerably and the sound reaching the external surface becomes attenuated. 2.2 Physiology of the heart The heart is an organ mostly constituted by striated cardiac muscle with two main functions: to collect oxygen-rich blood from the lungs and deliver it to all tissues of the body, and to collect blood rich with carbon dioxide from the tissues of the body and pump it to the lungs [24]. Its located inside the thorax, in the middle mediastinum, inside the pericardium membrane (the pericardial cavity), which involves the heart (Figure 2.1). This membrane has inner and outer layers, with a lubricating fluid in between (the pericardial fluid). The fluid allows the inner visceral pericardium to ”glide” against the outer parietal pericardium [25]. The normal heart is composed by four chambers: the two upper chambers have the main function of collecting blood, injecting it into the ventricles, which are much stronger and work as a blood pump. The function of the right atrium and ventricle (right heart) is to collect blood rich in carbon dioxide from the body and pump it to the lungs. There is a one-way flow of blood through the heart, maintained by a set of four valves: the atrioventricular valves (tricuspid and bicuspid) allow blood to flow only from the atria to the ventricle; the semilunar valves (pulmonary and semilunar) allow blood to flow only from the ventricles out of the heart and through the great arteries, 23 Figure 2.1: The position of the heart and the great vessels in the middle mediastinum 1 as depicted in the Figure 2.2. In general, the anatomy of the right side of the heart (also known as right heart) is considerably di↵erent from that of the left heart, especially due to the e↵ort the left heart has to make to pump blood to all tissues in the body; nonetheless the pumping principles of each are basically the same. The cardiac valves passively open and close in response to the direction of the pressure gradient across them. The muscular cells (myocytes) of the ventricles are organised in a circumferential orientation; therefore, when they contract, the tension within the ventricular walls increases the pressure within the chamber. As the ventricular pressure exceeds the pressure in the pulmonary artery (on the right heart) and/or aorta artery (on the left heart), blood is forced out of the ventricular chamber. This contractive phase of the 1picture adapted from the book [25] page 37. 24 Figure 2.2: A Normal Heart 2 cardiac cycle is known as systole. The pressures are higher in the ventricles than the atria during this systolic phase; hence, the atrioventricular (tricuspid and mitral) valves closes. When the ventricular muscles relax, the pressure inside them falls below those in the atria, the atrioventricular valves open and the ventricles are refilled; this is the diastolic phase. The aortic and pulmonary valves are closed during diastole because the arterial pressures (in the aorta and pulmonary artery) are greater than the intraventricular pressures [26]. This is depicted briefly on Figure 2.3 2.3 Heart Sounds Heart sounds are caused by the dynamic events associated with the heartbeat and the blood flow. They are relatively brief and have di↵erent intensity 2picture adapted from the website: http://healthinessbox.com/2012/01/27/ coronary-heart-disease-chd/ accessed on 23/04/2013 25 Figure 2.7: Auscultatory areas7: A) aortic, B) pulmonary, C) tricuspid and D) mitral ant criteria for diagnosing reversed splitting by auscultation. Another way of identifying the paradoxical splitting of S2 is by identification of A2 and P2 by intensity and transmission: while A2 is audible in most areas of auscultation, P2 tend to be more clearly audible only at the pulmonary and aortic sites. This method, however, may fail in cases of pulmonary artery hypertension second to left ventricular failure, where P2 becomes as loud as A2. Paradoxical splitting indicates significant cardiovascular disease: it is usually caused by either prolongation of left ventricular activation or prolonged left ventricular emptying. With the increase of age, the pulmonary vascular impedance increases and P2 may occur earlier, making normal patients over age 50 possibly exhibiting a single S2 or a narrow split on inspiration. However, normally a single S2 is due to a relatively soft pulmonary component that makes it difficult (or even unable) to auscultate. In healthy infants, children, and young adults the P2 component is not soft and P2 is rarely soft. In older persons under good auscultatory conditions, although soft, it can still usually be auscultated [27, 19, 13]. The inability of hearing P2 may suggest tetralogy of Fallot or pulmonary 7picture adapted from [30] 32 Figure 2.8: Heart with atrial septal defect.8 atresia. Other situations where P2 may be inaudible are either chronic right ventricular failure, or in cases where the aortic component may be masked by the systolic murmur, as it occurs in patients with aortic stenosis [27]. The amplitude (loudness) of each component of S2 is proportional to the respective pressures in the aorta and pulmonary artery at the moment of diastole. Another cause for an increase in the amplitude of A2 or P2 is the dilatation of the aorta or pulmonary artery, respectively. A2 usually presents greater amplitude than P2. The aortic component, therefore, radiates over the chest, whereas P2 is heard mainly in the second left intercostal space with some radiation down the left sternal border [27]. The higher pressure of the aorta is probably the reason why the aortic component has the greater radiation than P2. Since the pulmonary valve and the pulmonary arteries are closer to the chest wall, given the same level of pressure, the pulmonary component will be louder than the aortic component, therefore A2 must have a greater pressure level than P2 [27]. Reasons for a decreased intensity of A2 or P2 may be a sti↵semilunar 8Picture acessed from the website: http://en.wikipedia.org/wiki/File:Atrial_ septal_defect-en.png on 18/09/2013 33 valve, or low pressure beyond the semilunar valve, or deformity of the chest wall or lung. A low intensity of P2 is mostly common in patients with valvular pulmonic stenosis or chronic obstructive lung disease. Valvular aortic stenosis is another reason for a low intensity of the aortic component [27]. An overview of the changes in the volume and split of A2 and P2 can be seen in Table 2.1 2.4 Processing heart sounds As we had seen in this chapter, the main constituents of a cardiac cycle are the first heart sound, the systolic period, the second heart sound (S2) and the diastolic period. Whenever a clinician is performing an auscultation, he tries to identify these individual components, and is trained to analyse related features such as rhythm, timing instants, intensity of heart sound components, and splitting of S2, among others [32, 7]. This analysis allows him to search for murmurs and sound abnormalities that might correspond to specific cardiac pathologies. From a signal processing perspective, processing of heart sounds is not only interesting by itself, but is also an essential first step for the subsequent task of automatic pathology classification. For sake of clarity, we will distinguish two sub-tasks of processing of heart sounds: heart sound segmentation and heart sound classification. 2.4.1 Heart sound segmentation In heart sound segmentation we expect to identify and segment the four main constituents of a cardiac cycle. This is typically accomplished by identifying the position and duration of S1 and S2, using some sort of peak-picking methodology on a pre-processed signal. Liang [33] has used discrete wavelet decomposition and reconstructed the signal using only the most relevant frequency bands. Peak-picking was performed by thresholding the normalised average Shannon energy, and discarding extra peaks via analysis of the mean and variance of peak intervals. Finally, they distinguish between S1 and S2 peaks (assuming that the dia34 stolic period is longer than the systolic one, and that the later has lower variation in duration), and estimate their durations. A classification accuracy of 93% was obtained on 515 periods of PCG signal recordings from 37 digital phonocardiographic recordings. The same authors further improved the statistical significance of their results by obtaining the same accuracy using 1165 cardiac periods from 77 recordings [32], and later attempted murmur classification based on these features and neural network classifiers, obtaining 74% accuracy [34]. Omran [35] has also studied this problem using normalised Shannon entropy after wavelet decomposition of the audio signal, but their experimental methodology is not so convincing. Kumar [36] proposes a method for detection of the third heart sound (S3) that uses novel wavelet transform-simplicity filter, which separates S1, S2 and S3 from background noise and murmurs, then they used a technique developed earlier [37, 38], where S2 is assumed to have a high frequency signature, and S1 is detected by looking at the cardiac cycle. The third heart sound is detected by using temporal thresholds on the low frequency output of the simplicity filter. A sensitivity and specificity of 90.35% and 92.35% respectively was obtained. The same authors, later on also produced a paper on segmentation of cardiac murmur [39], where the simplicity filter is used in conjunction to adaptive thresholding in order to segment heart sounds in presence of murmurs. Moukadem et al.[40] developed a robust heart sound segmentation algorithm by extracting the smoothed envelope of the Shannon energy of the local spectrum calculated by the S-transform [41] for each sample of the signal, for detection of presence of heart sound (S1 or S2), then a windowed version of the envelope is calculated, where the size of the window is changed in order to optimise the energy concentration and consequently, the boundaries of the heart sound. For S1 and S2 identification they use the techniques developed by Kumar et. al in [38, 37]. They also demonstrated that their approach is robust against additive Gaussian noise. Besides the four main components of the cardiac cycle, there is a clinical interest in the analysis of some of its associated sub-components [42, 43]. It has been recognised that S1 may be composed of up to four components 35 produced during ventricular contraction [43], although the complexity of this task has been a very difficult hurdle for the signal processing community. The S2 sound is more well known, being composed of an aortic component (A2), which is produced first during the closure and vibration of the aortic valve, the blood rebound and surrounding tissues, followed by the pulmonary component (P2) produced by a similar process associated with the pulmonary valve [42]. Xu [42] demonstrated a model where each component of S2 can be considered a narrow-band nonlinear chirp signal. Later [44] he adapted and validated this approach for the analysis and synthesis of overlapping A2 and P2 components of S2. To do so, the time-frequency representation of the signal is generated and then estimated and reconstructed using the highest instantaneous phase and amplitude of each component (A2 and P2). In this paper the accuracy evaluation was made by simulated A2 and P2 components having di↵erent overlapping factors. The reported error was between 1% and 6%, proportional to the duration of the overlapping interval. Nigam [45] also presented a method for extracting A2 and P2 components by assuming them as statistically independent. To do so, four simultaneous auscultations are analysed using blind source separation. The main advantage of this method is the lower dependence on the A2-P2 time interval, although it needs a non-conventional 4-sensor stethoscope. 2.5 Heart sound classification The vast majority of papers we have found regarding audio processing algorithms, concern the detection of specific heart pathologies. This highlights the interest of the scientific community on this topic but, there are still some major flaws in most of them such as the absence of a clinical validation step and unconvincing experimental methodologies. Most papers use the well-established pattern recognition approach of feature extraction followed by a classifier. Bentley [46] uses Choi-Williams Distribution (CWD) as features, working with 45 normal/abnormal valve subjects. Some features were determined via visual inspection, others auto36 matically from the CWD by simple rule-based classification. Later [47], the authors show that CWD is a better method to represent the frequencies in PCG and to get heart sound descriptors, than other timefrequency (T-F) representations. According to them, a simple description of the T-F distribution allows an analysis of the heart valve’s condition. However, they highlight the need of a more comprehensive evaluation using a larger population of test patients. Wang [48] proposes a representation of heart sounds that is robust to noise levels of 20dB, using mel-scaled wavelet features. However, details regarding the used dataset are not clear enough for robust conclusions. Liang [49] developed an interesting feature vector extraction algorithm where the systolic signal is decomposed by wavelets into subbands. Then, the best basis set is selected, and the average feature vector of each heart sound recording is calculated. Neural Networks (NN) are used for classifying 20 samples after being trained with 65, obtaining an accuracy of 85%. Turkoglu [50], Ozgur [51] and El-Hanjouri [52] also used wavelets as feature vectors for classification, although they provide too few details regarding the used data sets. Trimmed mean spectrograms are used by Leung [53] to extract features of phonocardiograms. Together with the acoustic intensities in systole and diastole, the authors quantified the distinctive characteristics of di↵erent types of murmurs using NNs. One of the few papers that is conscious about the important clinical validation step is from Kail [54]. The authors propose a novel sound representation (2D and 3D) and feature extraction algorithm using Morlet wavelet scalograms. After manual classification of the resulting graphs performed by two cardiologists on 773 subjects, they clinically validated the features as useful for sound and murmur extraction. Sharif [55] also proposes other features for classification systems based on central finite di↵erences and zero crossing frequency estimation. 37 2.6 Challenges of processing the second heart sound The S1 and S2 sounds can be robustly segmented and is a fundamental first step for most of the work on heart sound processing. There is promising work regarding the extraction of secondary sounds such as A2 and P2, although this is still an open challenge, since there is still great limitations in several aspects of the research developed: there is still a great gap between the medical knowledge and the signal processing results in this area; and the use of some non-standard technological devices, such as a stethoscope with four sensors [45]. The automatic pathology classification scenario is not so evolved. Reviewing some of the papers and simply observing the disparity in the number of publications when compared with the other challenges, we conclude that there is a strong interesting in this topic. The murmur detection and classification seems to be another area where robust results are being obtained, although there is still work to be done in creating techniques in order to produce a morphology-based classification of murmurs. In our opinion, there is still a long way to go before we can have robust automatic classification systems that can be introduced in the clinical routine of hospitals. In this thesis we worked mainly on the segmentation of the second heart sound into its two main components: A2 and P2. The second heart sound is quite important in the detection of several cardiac conditions, as seen in session 2.3.2. The A2 is directly related to the aorta valve, the left heart and the systemic circulation, whilst P2, on the other hand is related to the pulmonary valve, the right heart and the pulmonary circulation. The behaviour of the split between A2 and P2 and how respiration change it during an auscultation is another important indicator of several cardiac conditions, linked to the hemodynamic of the heart, its ventricles and atria. In this way, looking at S2, A2 and P2 can provide a great overview of the heart and its hemody38 namic structure. The auscultation and interpretation of these components even by a clinician, however is of great difficulty, since they are quite short and close to each other in time. Looking into the physiological background given in this chapter, we can see that A2 is produced by the blood rebound caused by the closure of the aortic valve, and that P2 is similarly produced by the closure of the pulmonary valve and its blood rebound. Therefore these components, are produced by independent mechanisms. We explore the possibility of separating these sound components by looking at S2 segmentation using a independent component analysis approach. We also attacked the problem of extracting the subcomponents of S2 by postulating how these subcomponents could be estimated: Still keeping in mind the production of A2 and P2, we can also imagine that the initial nature of the vibratory motion set by their production would generate a high initial amplitude and frequency wave that fades with time (as suggested by Xu et al. [42]). This family of wave forms could be used as a model where A2 and P2 would be instances of: just like once one knows the letters of an alphabet, creating a word is just a matter of selecting the right words in the correct order and ’adding’ them together; the problem of decomposing S2 into instances of waveforms becomes a problem of selecting the waveforms (letters) that best explains the word (S2). Another challenge we tried to solve in this thesis is to lower the gap between the clinical knowledge of S2 and the knowledge produced by signal processing community: clinicians understand A2 and P2 as peaks in the phonocardiogram and most medical literature regarding phonocardiograms and A2 and P2 is based on the measurement of these peaks. This manual measurement, however has a precision problem and the quantification of amplitude of these peaks is still an open problem. 39 Table 2.1: Assesment of the second heart sound, adapted from [31] Character Clinical condition Fixed A2-P2 interval •Atrial septal defect (important clue) Wide splitting, inspiratory increase in A2-P2 •Right-ventricular conduction delay •Idiopathic dilatation of pulmonary artery •Small atrial septal defect (unusual) •Pulmonic stenosis Soft A2 •Aortic sclerosis or stenosis •Hypotension Soft P2 •Pulmonic stenosis •Systemic hypertension Loud A2 •Dilated Aorta •Systemic hypertension Loud P2 •Pulmonary hypertension (important clue) •Dilated pulmonary artery 40 Chapter 3 Independent Component Analysis of S2 3.1 Introduction to source separation In this chapter, we overview the independent component analysis technique for separation of simultaneously acquired signals, we propose a novel technique to perform source separation of a set of independent components assuming that we have access to one moving sensor and that the underlying source signals that we wish to separate are quasi-periodic, as it is the case with cardiac signals. 3.2 Blind source separation and independent component analysis A classic problem in Blind Source Separation (BSS) is the cocktail party problem. The objective is to, given a mixture of sounds, with a given number of microphones (observations), separate each sound into a separate channel: the sources (Figure 3.1). When two or more di↵erent signals are recorded by a single microphone its output is a signal mixture which is a simple weighted sum of the two signals. The relative proportion of each signal in the mixture (signal captured by 41 Figure 3.3: Mixed signals recorded sequentially Figure 3.4: An overview of the proposed method of the signal means that we can simulate an array of nspatially separated sensors which acquire mmixtures by time-shifting to align the mixtures. Thus, x1(k) will be recorded during the time interval k1<k<k 2,x2(k) during k2<k<k 3, etc., with each mixture being zero outside the time interval. To overcome this problem, and apply BSS methods, researchers have proposed introducing novel ways of recording the mixtures using an array of sensors. Nigam and Priemer, for example, propose to use an array of stethoscopes to acquire simultaneous recordings of the heart sounds [45]. This has the drawback of needing to change an established procedure. This would be likely to encounter resistance from its potential users, particularly 48 in the medical profession, where some healthcare innovations have had to be withdrawn due to physicians’ resistance [77]. In addition, using an array of sensors implies an individual adjustment for each patient depending on their age and biotype, making the process burdensome. We propose to leave the measurement process unchanged and address this problem for a particular type of source signal, namely periodic or quasiperiodic sources. We exploit the periodicity property to align the di↵erent waveforms within the recorded mixture. Thus, the signal from the moving sensor is segmented to extract the separate mixture signals. These are then artificially synchronised and treated as if they were acquired simultaneously from an array of sensors. As a result, any pre-existing source separation algorithm can be used to extract the underlying sources. We make two main assumptions: 1. A single sensor is placed at several pre-defined locations and records the mixture at that location for a specified length of time, approximately equal for all locations 2. The source signals are periodic or quasi-periodic. In our algorithm, the sensor is a stethoscope that is placed at particular locations in the thoracic region, during the routine listening of the heart sounds. As result, the signal from the moving sensor can be segmented to extract the mixture signals, which are then artificially synchronised and treated as if they were acquired simultaneously from an array of sensors. Then, any ICA algorithm can be used to extract the underlying sources. In this chapter we aim to describe this technique for acquiring signals using a moving sensor. We do this in a way that is inconspicuous to the clinician (in the case of auscultation), who remains free to perform a routine examination, including listening to the heart sounds sequentially at four standard sites, as shown in Figure 2.7. In the scheme that we present, only one sensor is available, and it is firstly used to acquire a mixture of the sources from location A on the chest 49 (see Figure 3.4. The same sensor is then placed at the B location and so on, until all observations are obtained. The sensor signal, x(k), contains the heart signal from the four locations, with periods of silence when the sensor is being relocated. Note that the timing between the source signals is not a↵ected by the way the signals are acquired. In order to generate a mixture signal vector as in equation 3.9, we proposed to segment ¯x(k)into four signals, so that the i-th heart signal is given by ˜x(k)=8 < : ¯xi(k)ifki<k<k i+1 0 otherwise (3.9) where kirepresents the time at which recording at the next thoracic location begins (e.g. the sensor is placed at A at time k1, at B at time k2, and so on). We align the signals, so that they can be presented to the ICA algorithm as if they were acquired simultaneously. In doing this, we exploit the quasi-periodicity of the heart cycle. We seek to align the peaks of the mixtures in ˜xi(k), according to ˆxi(k)=8 < : ˜xi(kki)ifi=1 ˜xi(k(ki+i)) otherwise (i>1) (3.10) where iis the relative time shift to get the peaks to align. Since we are simulating several sensors capturing the heart sounds at the same time, we use the cross-correlation function (equation 3.11) in order to select the delay that maximises the similarity between the mixtures, therefore aligning the signals in a way that simulates an array of sensors capturing the heart sounds simultaneously. i,j = max( PNm1 n=0 ˜xi(m)⇤˜xj(n+m)) for i6=j(3.11) The final step in our proposed method is to perform blind source separation to recover the original source signals. To do this, we first form the mixture vector ˆx(k)=[ˆx1(k), ..., ˆxn(k)]Tcontaining the aligned measurements ˆxi(k) from equation 3.11, at the desired sensor locations. This is now 50 the conventional observed vector as shown in equation 3.4. If we assume that there are as many sensors as sources, and that the mixing process is instantaneous, we can apply any BSS algorithm to estimate the source. Here, we select the FastICA algorithm [78], because it is well-established, has been extensively studied, and is routinely used in a variety of applications. The algorithm is summarised below: Algorithm 3.1 Separation via sequential signal synchronization 1. Segment the observed signal to extract the recordings a the di↵erent locations using: ˜xi(k)=⇢¯xi(k)ifki<k<k i+1 0 otherwise where kirepresents the time at which the next recording begins. 2. Align the mixture signals using ˆxi(k)=⇢˜xi(kki)ifi=1 ˜xi(k(ki+i)) otherwise (i>1) 3. Form the mixture vector ˆx (k)=[ˆx1(k),...,ˆxn(k)]T 4. Perform ICA. 3.3 Experiments In this section we will test the development technique and compare it with classical ICA on di↵erent signals. The first experiment is performed with synthetic and noiseless periodic signals, as an initial proof of concept, where the sequential auscultation is also simulated. The remaining experiments explore the periodicity of di↵erent heart signals. In the second experiment we tackle the biomedical engineering problem of separating the foetal electrocardiogram (FECG) from the maternal one. The electrical signal is collected through skin electrodes attached to the mother’s body, therefore mixing the foetal electrocardiogram to the maternal electro51 cardiogram [79, 80]. The third experiment deals with the problem of separating heart sounds from the lungs sounds [81]. This is a common problem through auscultation, since, as it happens with the previous problem, due to the sensor’s proximity to both heart and lungs, the heart sounds are mixed to the lung sounds, making the auscultatory procedure more difficult. In the last experiment we try to separate the two subcomponents of the second heart sound. In order to do so, we first try to separate A2 and P2 using the synthetic model we developed in chapter 4, then we proceed to extract A2 and P2 in real signals. 3.3.1 Experiment 1: synthetic signals In this section we investigate how well our approach performs in recovering the original sources in a number of settings. Firstly, we consider the separation of three known synthetic signals, to assess the separation performance that can be achieved using the method in Algorithm 3.1. We then evaluate the performance of the algorithm on two problems using heart-related signals acquired using a single sensor. We begin by instantaneously mixing the three periodic signals shown defined by equation 3.13, where square function generates a square wave. The mixture is shown in the three upper plots of Figure 3.5, using the following mixing matrix: A=0 B @ 0.6948 0.0344 0.7655 0.3171 0.4387 0.7952 0.9502 0.3816 0.1869 1 C A(3.12) s1(k)=sin(0.01k⇡) s2(k)=square(0.01k⇡) s3(k)=sin(0.05k⇡)cos(0.0016k⇡) (3.13) The resulting mixed signals are shown in the three lower plots of Figure 3.5. The mixtures were then randomly shifted, in order to simulate the 52 Figure 3.5: Three periodic source signals (upper three plots) and the mixtures obtained when a mixing matrix A is applied (lower three plots) placing of the sensor at a particular location, which will occur randomly during the fundamental period of the mixture. Figure 3.6 shows an example of a single signal acquired in this case by relocating the sensor at three di↵erent positions. The three resulting delayed mixtures can be seen in the upper three plot of Figure 3.7, and it shows that the length of each mixture is now di↵erent. The lower three plots in the figure show the mixtures after alignment. Comparing these to the mixtures in Figure 3.5, we can see that the algorithm has successfully aligned the mixtures. Figure 3.6: Example of single sensor signal acquired at three di↵erent locations. The regions between the mixtures, when the sensor is relocated, are set to zero The separation was performed using FastICA. The upper three plots in Figure 3.8 show the sources recovered when separation was performed from the delayed mixtures. In this case the sources are not separated, because they 53 Figure 3.7: The mixtures in Figure 3.5 were delayed randomly, and the corresponding waveforms are shown in the upper three plots. The three lower plots show the signals aligned with the proposed approach. Looking at the peaks, we can see that the signals have been successfully aligned. are e↵ectively not recorded simultaneously. The three lower plots in the figure show performance following alignment of the mixtures; they show that the algorithm successfully recover the source signals from the aligned mixtures. Finally, Figure 3.9 shows the separation results from the mixtures that were recorded simultaneously (i.e. those in Figure 3.5). Comparing this to the results in Figure 3.8, it is clear that the performance of the proposed method is comparable to that of FastICA based of on the conventional recording set up. In addition to visual inspection, we can see in the following matrix that the Pearson coefficient between the real sources (s1,s 2,s 3) and the estimated sources of the state of the art method (y1,y 2,y 3)andtheproposedmethod (y4,y 5,y 6) are high: 54 s1s2s3 y10.0007 0.0108 1 y210.002 0.0007 y30.0108 1 0.002 y40.0085 0.9759 0.006 y50.9730 0.0165 0.0034 y60.0027 0.0061 0.9915 Table 3.1: The Pearson coefficient between real and estimated sources Figure 3.8: Separated sources when FastICA is applied to the delayed mixtures (upper three plots), and when it is applied to the aligned mixtures (lower three plots). The sources are incorrectly recovered from the delayed mixtures, while following alignment the correct sources are identified 3.3.2 Experiment 2: foetal and maternal electrocardiogram separation Heart signals include the electrocardiogram (ECG) signal, and heart sounds. To further illustrate the proposed methodology, we decided to apply it to ECG signals, and separation of maternal and foetal ECG. The ECG is a 55 Figure 3.9: Sources separated using FastICA on the initial, non-delayed mixtures, which are recorded simultaneously recording of the di↵erence in potential between two electrodes during the cardiac cycle, and provides important information about the performance of the heart. ECG signal analysis typically entails removal of noise and interference. A related problem is the removal of maternal ECG (MECG) components from ECG signals recorded during pregnancy, also known as foetal ECG extraction. When risk factors are present during pregnancy, electrocardiograms, along with other measurement methods, may be of vital importance to both mother and child. This problem has been studied at length [82], and several ICA algorithms have been used to extract the foetal heartbeat. Therefore, we use our algorithm to address this problem, as a step to establish the validity of the proposed method. We perform this experiment by simulating a relocated sensor, then aligning the mixtures, and compared the output of ICA applied on this set of mixtures, with the output of conventional ICA. We used the signals described in [77]. To simulate a relocating sensor, we selected random sections of the recorded signals from each of four sensors. We then aligned the sections as described previously and applied FastICA [83] to perform source separation. Figure 3.10a shows the mixture signals, while Figure 3.10b illustrates the simulated sequential signals, prior to alignment. 56 (a) (b) Figure 3.10: Maternal ECG mixed with foetal ECG. a) is the classical input to ICA, and b) the input for the proposed method. The separated signals are illustrated in Figures 3.11a and 3.11b, where the latter shows the output of the FastICA algorithm using the classical approach (note that in the first signal of both figures has the higher heart rate, from the foetus), while the former shows the output of the FastICA algorithm using the proposed method. The matrix 3.14 shows a high Pearson correlation between the outputs of the classical method (y1,y 2,y 3,y 4) and the outputs of the proposed method (y5,y 6,y 7). Comparing the two figures, we can see that the proposed algorithm successfully extract the foetal ECG (identified by the higher heart frequency), and generally recovers the same sources as conventional ICA. The scaling ambiguity of ICA causes the di↵erence in the second source extracted by the two algorithms. ⇢= 2 6 6 6 6 6 6 4 y1y2y3y4 y50.7843 0.1164 0.2192 0.3768 y60.0948 0.8450 0.4698 0.1163 y70.1292 0.6185 0.7024 0.2608 y80.1827 0.111 0.6185 0.8463 3 7 7 7 7 7 7 5 (3.14) 57 second heart sound. Synthetic A2 and P2 As a model of A2 and P2 we are using a developed model based on non-linear chirp signals (further details on the development of this model on Chapter 4), expressed by equations 3.17 and 3.18: gn(s, u, f1,f 2,t)= 1 psa(t)sin(f1t 10 +2f2rt 10 2f2) (3.17) a(t)=(1e t 8)e t 16 sin(⇡t 60)0t60ms (3.18) Where sis the scale, uis the displacement (or shift), f1is the atom’s highest frequency and f2is the atom’s lowest frequency. The calculation of these parameters was performed using the Matching Pursuit technique, as described on Chapter 4. The simulation mixing matrix (3.19) reproduces an auscultation in a normal subject. We used the clinical information about how well A2 and P2 can be heart throughout the auscultations sites (chapter 2.6): A2 is stronger than P2 in all auscultation sites; A2 is better heard in the aortic site (matrix element A11); P2 is best heart in the pulmonary site (matrix element A22); and in the other sites, P2 is quite faint (matrix elementsA32and A42) and A2 is stronger (matrix elementsA31and A41). A=2 6 6 6 6 4 60 20 50 25 12 5 10 5 3 7 7 7 7 5 (3.19) Experiment 4.A: ICA with fixed split (simultaneous recording) In the noiseless case, we mixed the A2 and P2 atoms, using the previous mixing matrix, producing four noiseless mixtures simulating a simultaneous recording: 64 Figure 3.17: A2 and P2 (left) and their mixtures (right): simultaneous recordings and noiseless As we can see in the correlation matrix Rx, although these mixtures are very similar, it is still possible to perform the separation, since we have more mixtures than sources. Rx=2 6 6 6 6 4 10.8589 0.9985 0.7441 0.8589 1 0.8853 0.9812 0.9985 0.8853 1 0.7790 0.7441 0.9812 0.7790 1 3 7 7 7 7 5 (3.20) The eigenvalues of the correlation matrix, on the other hand, correctly shows that we have some information about the total number of components present in the mixture: S=2 6 6 6 6 4 3359282.95 0 0 0 0 1491118.70 0 001.0878 0 0000.2698 3 7 7 7 7 5 (3.21) We can clearly see two high eigenvalues and two quite low eigenvalues, as we only have two sources in our mixtures. As it is correctly separated (Figure 3.18). We can also see that both calculated sources are highly correlated to the original signals, as we can see in the correlation table below: 65 x1x2y1y2 x110.0091 0.1270 0.9918 x20.0091 1 0.9906 0.1360 y10.1270 0.9906 1 0.0001 y20.9918 0.1360 0.0001 1 Table 3.4: The Pearson correlation between the sources and estimated sources Figure 3.18: Left: A2 and P2 sources and Right: estimated sources Experiment 4.B: ICA with variable split (sequential recording) In this experiment, we mixed the A2 and P2 atoms, using the previous mixing matrix, and, for each mixture the delay P2 was of: 09,14,15,17 milliseconds - this is to simulate a real sequential recording where the cardiac cycle always has some small di↵erences in the position of P2 (chapter 2.6, section 2.3.2). The four noiseless mixtures are sown in Figure 3.19: The normalised correlation matrix Rxof the mixtures shows that although there is a variable shift in one of the components of the mixtures, the mixtures are still highly correlated, as it happens in the case with multiple sensors: Rx=2 6 6 6 6 4 10.9031 0.8404 0.7448 0.9031 1 0.9611 0.8487 0.8404 0.9611 1 0.9540 0.7448 0.8487 0.9540 1 3 7 7 7 7 5 (3.22) The coefficient of linear correlation between the mixtures shows a lower 66 Figure 3.19: The recordings with P2 changing its delay to A2 (09,14,15,17 milliseconds, respectively) mixture1mixture2mixture3mixture4 mixture10.5715 0.8483 0.6293 mixture20.0708 0.7357 mixture30.2020 Table 3.5: The Pearson correlation between the mixtures linear correlation (compared to the fixed split case), indicating some nonlinearity in the mixing process introduced by the variable shift: However, the eigenvalues still indicates the presence of two components: S=2 6 6 6 6 4 3.0963 0 0 0 00.1436 0 0 000.0224 0 0000.0004 3 7 7 7 7 5 (3.23) Two values are reasonably high if compared to each other, although in this case they are much lower than the case with multiple sensors, it is still enough to recover the original sources, as can be seen in Figure 3.20: 67 Figure 3.20: Left: A2 and P2 sources and Right: estimated sources Experiment 4.C: ICA with recorded S2 with four sensors In this experiment we used four stethoscopes on the areas depicted on Figure 3.4, selected the second heart sound as seen in Figure 3.21 and performed ICA on the mixtures. Figure 3.21: The second heart sound acquired using four stethoscopes The eigenvalues of this mixture shows four components: S=2 6 6 6 6 4 42.1716 0 0 0 023.7645 0 0 0018.3842 0 0006.8032 3 7 7 7 7 5 (3.24) In addition, the Pearson correlation between the mixtures shows they have low linearity: 68 mixture1mixture2mixture3mixture4 mixture10.6702 0.7217 0.5835 mixture20.9132 0.6978 mixture30.6197 (3.25) Table 3.6: The Pearson correlation between the mixtures The exception here are mixture2and mixture3,whichcorrespondstothe Aortic and Pulmonary auscultation areas of auscultation. Although these mixtures have high linearity, they di↵er very little, and don’t add much information to the system, since they are the two closest locations: most of the mixtures still have low linearity. This problem leads to a source extraction where although one estimated source (although still mixed) is calculated, and the other one is a mixture buried in noise: Figure 3.22: The calculated sources In addition, the second calculated source of Figure 3.22 is similar to the first three mixtures and the first calculated source doesn’t have a particular dominant signal. 3.4 Discussion and conclusions We studied the problem of performing source separation on heart signals. A novel technique using a moving sensor to collect data and simulate signal acquisition from an array of sensors was developed. This technique only requires the sensor to move and the signal to be at least semi-cyclic. The 69 proposed method has the following advantages when compared with the use of an array of sensors: 1. An array of sensors for collecting auscultations would have to be developed. 2. The array of sensors would have to be adjusted for each patient depending on the size and shape of the chest. 3. The clinical routine would have to be adapted in order to use this array. The proposed technique worked on synthetic data as well as in the problem of separating maternal ECG from the foetal ECG. On the problem of separating heart sounds from lung sounds, the results suggest that some mixtures are non-linear and it appeared that the number of observations is less than the number of possible independent sources. This could be due to the changes in the chest volume caused by the respiration, making the mixing matrix change over time. Another possibility is that tissues on the chest make the mixture convolutive or the sensors are receiving di↵erent sources of noise. We believe that other techniques, such as convolutive independent analysis or even other techniques such as dependent component analysis could be more e↵ective in solving this problem. The problem of separating A2 and P2 from the second heart sound, however, proved to be much more harder in a number of ways: Validation: A2 and P2 are very short bursts of sound, there is also a very short time interval between them (in some cases they can overlap completely). Hence, the location in time and validation of these underlying components has been shown very difficult. An extra and parallel measurement with great time resolution would have to be performed to locate in time these components. ICA Ambiguities: ICA can identify the time where each underlying occurs. This information is important in identifying some cardiac diseases. However, due to the amplitude ambiguity, important information regarding the amplitude of each component is lost. This information is 70 particularly important in identifying some diseases such as pulmonary and systemic pressure levels. Mixtures: Experiments have suggested that the mixing process on the human chest is likely to not be an instantaneous mixture: di↵erent tissues on the sound pathway may produce reverberation, leading to a convolutive mixing matrix; or the internal natural movement of the heart and lungs inside the middle mediastinum may lead to several mixing matrices that depends on the relative positions and instant volume of these organs. To conclude, although we demonstrated the potential of the proposed technique on synthetic and real signals, we could not successfully segment components of the heart sounds using ICA. However, we created a technique that allows the use of ICA using only a single moving sensor (as long as the captured signal is a semi-cyclic one). In addition, a by-product of the research presented in this chapter was the creation of mathematical models of A2 and P2. These will be the discussed further in the next chapter along with their theoretical development. 3.5 Publications The work developed in this chapter generated the following publications: 1. F. L. Hedayioglu; M. G. Jafari; S. S. Mattos; M. D. Plumbley; M. T. Coimbra, ”Separating sources from sequentially acquired mixtures of heart signals,” Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on , vol., no., pp.653,656, 22-27 May 2011 doi: 10.1109/ICASSP.2011.5946488 [87] 2. M. G. Jafari; F. L. Hedayioglu; M. T. Coimbra; M. D. Plumbley, ”Blind source separation of periodic sources from sequentially recorded instantaneous mixtures,” Image and Signal Processing and Analysis (ISPA), 2011 7th International Symposium on , vol., no., pp.540-545, 4-6 Sept. 2011 [88] 71 Chapter 4 Representation of S2 Using Matching Pursuit 4.1 Introduction In the last chapter, we adopted an approach where we made very few assumptions regarding the signal components. We aimed to obtain underlying individual components, which when mixed resulted in the collected auscultation signal. This is theoretically possible since we are essentially facing a blind-source separation problem that explores that di↵erent auscultations sites have di↵erent mixtures of each signal. Results using ICA were interesting but somewhat limited, possibly due to the convoluted nature of the gathered mixtures. In this chapter we describe an approach where we assume that the signal components can be modelled by a specific function such as non-linear chirp signals [42, 44]. This is a powerful simplification that transforms the problem into an optimisation one, in which we try to discover the component mixture that better explains the observed signal. From a physiological perspective this is quite reasonable since the mechanical process that produces heart sounds is well-known. It is limited, however, to patients that have ‘standard’ heart sounds and, depending on the chosen algorithm, might be a↵ected by the presence of murmurs. However, since the search space is very large, sub72 optimal algorithms are needed in order to find the best combination of signal components that explain the observation. Matching pursuit is one of these sub-optimal algorithms that has the advantage of solving this problem with few components. In this chapter we show that matching pursuit using a dictionary of non-linear chirp signals can give us quite good results for this approach and has good physiological meaning. 4.2 Previous Work T. Tran et al. in [89] describes a heart sound synthesiser that models the heart sound as produced exclusively by heart valves: mitral and tricuspid for S1, and aortic and pulmonary for S2. The heart sound components are modelled using chirps with linear frequency decay on a normalised envelope (equation 4.3). A(t, T, ↵A)=(1 exp(t 0.2T)) sin( ⇡ 2TT)1 ↵A ⇡ (4.1) D(t, T, ↵D)=(1 exp(t 0.4T)) cos( ⇡ 2Tt)1 ↵D ⇡ (4.2) c(t, T, A, D, fo,f i)= A(t, T, ↵A)D(t, T, ↵D) max(A(t, T, A)D(t, T, ↵D)) sin((fo+fi)⇡t) (4.3) Where tis the time, Tis the duration of the transient, Ais the rate of attack, Dis the rate of decay, fois the initial frequency and fiis the final frequency. According to the authors, the component amplitude variation is calculated proportionally to that of real clinically recorded heart sounds. The authors, however, does not provide a comparison between the synthetic sounds produced by their equations and real recorded ones. Xuan Zhang et. al. in [90] performed matching pursuit on 11 auscultation signals from an educational CD, containing some common pathological and normal auscultations recorded under an ideal and noiseless environment. They added Gaussian noise to the 11 auscultations, producing a dataset of 22 auscultations in total. Then, they applied matching pursuit using a re73 2 6 6 6 6 6 6 6 6 6 6 6 6 4 f0ff 500 499 500 498 . . .. . . 22 21 22 20 21 20 3 7 7 7 7 7 7 7 7 7 7 7 7 5 (4.16) We can easily see that the memory and speed demands for the MP algorithm can be enormous and saving memory and improving speed is a real problem. The size of the dictionary is great (over 115000 atoms). In order to optimise the memory usage of the dictionary, we opted to not build a dictionary with the atoms’ signal, but only with their frequency parameters and generate the atoms on demand as we search the dictionary. We also parallelized the matching pursuit algorithm in order to improve the processing speed. As a result, a noiseless signal that is an approximation of S2 was generated for each annotated S2 in our dataset (Figure 4.3). 80 Figure 4.3: Recorded S2 (top), reconstructed S2 by MP (middle) and its residual (bottom) The high correlation between the approximated S2 and the original one shows that this method can provide a good approximation of the real S2 (Figure 4.4). The example of this reconstructed S2’s energy also captured 91.5% of the total energy of the recorded S2 (10.6), leaving a residual with only 8.5% of the total signal energy. We now have a sparse representation of the second heart sound: this representation needs only 2 atoms and each atom (Equations 4.10 and 4.11) needs four parameters: the scale s;shiftu;lowestfrequencyandfrequency variation (fo,f)torepresenteachcomponentofS2component. Intotal only 8 parameters are required to fully reconstruct S2: (sa,u a,f oa,fa,s p,u p,f op,fp). 81 Figure 4.4: Histogram of the Pearson correlation between all recorded and reconstructed S2 from the dataset (n=1858). 4.4.3 Experiment 2: atoms and physiological features The objective of this session is to show that since these atoms are physiologically inspired, they also have some information that may be useful to draw conclusions regarding the physiological components of the second heart sound. The direct measurement of A2 and P2 from a normal auscultation has been proven quite difficult: these components have a very short duration, there is a significant overlap between them and auscultations may have a high level of noise. However, indirect inference of A2 and P2 is possible: if an auscultated patient has PAH, then the P2 component of S2 has an increased amplitude (and energy) if compared with a normal P2 (as seen in section 2.3.2). Therefore we use the total energy x2of the fully reconstructed S2 as a parameter. A second parameter used is the time di↵erence between the starting time of A2 and P2 atom (uPuA). The latter feature is based on the fact that commonly the PAH (with right heart failure) can impose a delay on P2, making the time di↵erence between these components greater. We used the Expectation Maximisation algorithm to cluster the data into two sets, as we can see in Figure 4.5: The cluster 0 (smaller, lower left of 82 the graph) is very compact and is coincident with the normal auscultations, showing that normality in terms of energy and split is well defined. The cluster 1, on the other hand, is much more disperse and covers most of the hyperphonetic heart sounds. The confusion matrix is shown in Table 4.1. We used the formulas in equations 4.17, 4.18 and 4.19, for calculating the accuracy, precision and balanced precision respectively, where TP is the number of true positives, TN is the number of true negatives, FP is the number of false positives and FN is the number of false negatives. For detecting normal auscultations (cluster 0) we found 70.27% accuracy, 91.30% precision and balanced accuracy of 70.71%. Accuracy =100⇤TP +TN TP +FP +FN +TN (4.17) Precision =100⇤TP TP +FP (4.18) Balanced Accuracy =100⇤(0.5⇤TP TP +FN +0.5⇤TN TN +FP) (4.19) Normal Hp Cluster 0 21 2 Cluster 1 5 9 Table 4.1: Confusion matrix: columns has the ground truth and rows has the cluster (4.20) 83 Figure 4.5: Scatter plot with the two Gaussian cluster’s contour lines separating normal and hyperphonetic heart sounds. The xaxis has the median of all di↵erences between the starting time of A2 and P2 atom (uPuA), the yaxis has the median total energy (x2) of the reconstructed S2. The legend displays the clinician classification of the auscultations. 4.5 Conclusions In this chapter we developed an approach where we modelled the structure of A2 and P2 as non-linear chirp signals and applied matching pursuit in order to find the parameters of these components. This method has the advantage of generating a sparse representation for the second heart sound and to create a noiseless representation of the original heart sound. In the first study our results show a high correlation between the recorded and reconstructed S2. It can be seen that just two atoms are enough to capture the main features of the signal and produce noiseless reconstructed version of the original S2. It is also seen that although in general, matching pursuit produces reconstructed signals with high correlation with the original ones (Figure 4.4), the cases where a lower correlation is obtained can be explained by the greedy nature of the MP technique used, where a suboptimal solution is found. This may be further improved by developing other 84 search strategies, for instance: maximising the energy of each first interaction of the MP algorithm may lead in some cases to a sub-optimal solution (having the most energy of the S2 captured by only one component, leaving the second component to capture noise), a more sensible strategy could favour the selection of atoms with a more balanced contribution to S2 (therefore, they would tend to represent more relevant features of the signal). In the second study we demonstrated that since the atoms are physiologically inspired, they also express information that may be related to physiological components of S2. After using the Expectation Maximisation algorithm we have shown that the total energy x2of the fully reconstructed S2 and the time di↵erence between the starting time of A2 and P2 atom (uPuA)canbe used to cluster the normal heart sounds, achieving 70.27% accuracy, 91.13% precision and balanced accuracy of 70.71%. 4.6 Publications The work developed in this chapter generated the following publications: 1. F. L. Hedayioglu; M. G. Jafari; S. S. Mattos; M. D. Plumbley; M. T. Coimbra, “Denoising and segmentation of the second heart sound using matching pursuit,” Engineering in Medicine and Biology Society (EMBC), 2012 Annual International Conference of the IEEE (pp. 34403443). IEEE; (2012, August) [101] 2. F. L. Hedayioglu; M.G. Jafari; S. S. Mattos; M. D. Plumbley; M. T. Coimbra, ”An Exploratory Study On The Segmentation Of The Second Heart Sound”, to be submitted 85 Chapter 5 Energy Based Segmentation of S2 5.1 Introduction In the previous chapter we modelled the second heart sound as the sum of non-linear decaying chirp atoms and showed that features produced by these atoms can be used to extract information about the underlying physiological components of S2. In this chapter we postulate that the second heart sound components are peak-like, and the measurement of their amplitude and delay can also relate to the underlying physiological components of S2. In fact, this is the very same procedure carried out by doctors when reading a phonocardiogram: they consider the positive amplitude of the peaks of each component (Figure 5.1). However, phonocardiograms require an acoustically isolated room [13, 19], and calibration is required on every new patient [13, 19, 102, 103, 104, 105]. In addition, each phonocardiogram manufacturer produces his own set of filters, making standardisation and calibration a complex problem [19, 102, 103, 105]. 86 Figure 5.1: Phonocardiogram with A2 and P2 depicted in the middle trace. Two evident advantages of the proposed approach in this chapter are the direct correlation it yields with the medical procedure and its computational simplicity. In addition to that, a threshold where an auscultation can be considered normal or hyperphonetic was also inferred. A second advantage is its low memory and low processing demands, allowing it to be easily incorporated into portable devices. 5.2 Characterisation of S2 Before going into details about the this method, a small review of some facts about the second heart sound and phonocardiographic measurements is in place in order to better understand the rationale behind the procedure proposed in this chapter. For more details, please refer to chapter 2.6. The second heart sound is the sound generated by the closure of the semilunar valves [106]. The closure of these valves, however is usually not synchronous, causing S2 to split. The A2 component originates in the aorta and is well transmitted to the pulmonary artery, whereas the P2 component 87 Figure 5.2: A phonocardiogram of a human subject depicting the X wave1. originates in the pulmonary artery and is poorly transmitted to the aorta because of its smaller magnitude and the thicker wall of the aorta. Both components are generated by the sharp wave of back blood flow produced by the valves closure. In addition to these components, sometimes there is a third component, namely the X component preceding A2 by an average of 7 milliseconds [13, 107, 16]. This small X component can be found also in the external phonocardiogram and within the left ventricle: It may be explained by a vibration of the left ventricular wall when systolic contraction ceases and the pressure drops rapidly (Figure 5.3 and 5.2). 88 Figure 5.3: The second heart sound from an auscultation from in data set showing the X wave right in the beginning of S2 (circled), followed by A2 and P2. Normal respiration causes A2 and P2 to be closer in expiration and more widely separated in expiration (Figure 5.4). This is produced by the delay on P2 because of the transient prolongation of right ventricle contraction, and the shortened left-ventricular systole, and earlier A2. Figure 5.4: Physiological splitting of S2 (adapted from [13], p. 23). In order to be di↵erentiated and heard as two distinct sounds, the A2-P2 interval should be greater than 0.03 seconds. In normal adult patients, during expiration, A2-P2 is typically less than 0.03 seconds, being considered superimposed in 90% of normal persons [108, 109], therefore it may sound as a single beat to the ear. If the split is greater than 0.04 seconds in expiration, then it is usually abnormal (split in expiration is an important clue to 1picture adapted from [13] 89 Figure 5.9: The amplitudes of each A2 and P2 relative to the mean (100%) Figure 5.10: P2-A2 split time recorded on every S2 of a normal auscultation. The green horizontal line represents the median. Values below this line expected to be part of the expiration cycle whilst values above the line are considered part of the inspiration cycle. 96 As we can see in Table 5.1, the mean inspiratory split of 0.0302 seconds is within the literature range of a mean inspiratory split between 0.03 to 0.04 seconds. The mean expiratory value of 0.0145 seconds, with a minimum value of 0.0125 seconds and maximum value of 0.016 seconds means that on expiration, S2 is heard as a ’single’ one and no split is heard, again, in accordance with the literature. Estimated Inspiration Mean split 0.0302 Median split 0.0323 Min split 0.0170 Max split 0.0412 Number of S2 32 a) Estimated Expiration Mean split 0.0145 Median split 0.0145 Min split 0.0125 Max split 0.016 Number of S2 34 b) Table 5.1: Values of the split time (P2-A2) between inspiration a) and expiration b). All values are in seconds 5.3.2 Hyperphonetic Auscultations The same analysis was made on hyperphonetic auscultations (auscultations where the P2 component is louder than the normal case): we measured the amplitude values and the split (time interval between the detected P2 and A2) to compare against the literature findings. A hyperphonetic auscultation can be seen at Figure 5.11: 97 Figure 5.11: The detected A2 and P2 in a hyperphonetic auscultation (top), and its energy (bottom) On Figure 5.12 we can notice that P2’s amplitude is greater in overall if compared to Figure 5.8. Another point worth noting is the variation of amplitude and split of S2: this shows the influence of respiration on the split and amplitude of both components. Figure 5.12: Variation in amplitude of A2 and P2: notice how the amplitude of P2 (red square) is generally greater than P2 on Figure 5.8, sometimes it reaches a slightly greater amplitude than A2, as it can be seen at 21.5 seconds. 98 Figure 5.13: P2-A2 split time recorded on every S2 of a hyperphonetic auscultation. The green horizontal line represents the median. Figure 5.13 shows the beat by beat values of the split of S2. We can notice the larger split on estimated inspiration (points above the green line). Also, compared with the normal case (Figure 5.10), the inspiratory values are higher, varies more, and the same happens with the expiratory values. Table 5.2 contains the values for the estimated inspiration and estimated expiration. Although these values are overall higher than the normal auscultation (Table 5.1), the estimated inspiration mean values are within the upper literature limit for normality [108, 109, 13], but the estimated expiration mean values are higher than normal: since the split is greater than 0.020 seconds, an experienced cardiologist may hear a discrete split of the second heart sound. 99 Estimated Inspiration Mean split 0.0390 Median split 0.0395 Min split 0.0312 Max split 0.0465 Number of S2 16 a) Estimated Expiration Mean split 0.0245 Median split 0.0252 Min split 0.0187 Max split 0.0295 Number of S2 19 b) Table 5.2: Values of the split time (P2-A2) between inspiration a) and expiration b). All values are in seconds 5.3.3 S2 components by auscultation group As seen in section 2.3.2, and in the section 5.2, besides the split information, another important feature on A2 and P2 components is their amplitude: a number of papers have shown that the amplitude of A2 and P2 are correlated to the pressure in their respective arteries [108, 16, 19, 13, 15, 111]. This information about the amplitude of these components is paramount on the diagnosis of heart conditions. Such as, the pulmonary artery hypertension (PAP). As described on sections 4.4.3 and 5.2, the main indicator of PAP is an hyperphonetic P2. The hyperphonesis of P2 is not only defined by the absolute amplitude of P2. The clinician looks at the overall amplitude of the second heart sound, and apply his experience and common sense to judge if the given P2 component is hyperphonetic or normal. Besides, the amplitude of A2 and P2 also depends on a number of factors, such as: placement of stethoscope, patient’s body mass index, etc. Therefore, the absolute amplitude of A2 and P2 may vary in such a way that measuring P2 alone is not enough to quantify P2 hyperphonesis. (Figure 5.14). 100 Figure 5.14: Detected A2 (diamond) and P2 (square): in a normal auscultation (top left: signal, bottom left: energy), and in a hyperphonetic auscultation (top right: signal, bottom right: energy). In this experiment, we looked into the amplitudes of A2 and P2 of auscultations diagnosed as normal and hyperphonetic in order to build a feature that separates normal and hyperphonetic auscultations. We intend to turn the clinician’s subjective judgement of hyperphonesis into an objective one. We found out that, as expected, the absolute value value of the amplitude of P2 is not a feature capable of separating normal from hyperphonetic auscultations, but the amplitude of P2 divided the amplitude of A2 do provide us with a feature that is good enough to separate these two groups. For each auscultation, in order to have one feature value that is more resilient to outliers, we calculate the median P2/A2, as we can see in Equation 5.3, where x[P21]andx[A2i] is the amplitude of the first P2 and A2 in the ith S2 of an auscultation with nsecond heart sounds. The groups can be seen at Figure 5.15. median(x[P21] x[A21],x[P22] x[A22],···,x[P2n1] x[A2n1],x[P2n] x[A2n]) (5.3) 101 Normal Hyperphonetic n26 11 Mean ranks 14.3 30.2 U266 20 Table 5.3: Mann-whitney U test Figure 5.15: Separation between normal and hyperphonetic S2. The outlier is due to an auscultation were the detection of A2 and P2 failed due to high level of noise. The Mann-Whitney U test [112] reported these two groups statistically di↵erent on the median P2/A2 of each auscultation with P<0.0001 and mean ranks of 14.3and30.2 for the normal and hyperphonetic groups respectively (Table 5.3). It is also observed that with a threshold of P2 A2=0.7, the two groups can be separated with 89.7% accuracy, 75% precision and balanced accuracy of 92.59%. 5.4 Conclusions In this chapter, we assumed that A2 and P2 are energy peaks produced by the positive values of the recorded second heart sound. This method mimics the analysis and identification of A2 and P2 performed by the clinician when using a phonocardiogram. Although at first glance this may seem an 102 oversimplification of the components of the second heart sound, the measures produced by this method have direct clinical usage: they are the automatisation of the measures of the phonocardiogram, therefore, the clinical knowledge derived from phonocardiograms are directly applicable to these measurements. We performed two experiments to indirectly validate the detected A2 and P2. In the first experiment we analysed the time-di↵erence (split) between P2 and A2 in a normal subject and in a subject with hyperphonetic auscultation. The respiratory cycle was estimated by calculating the median of the splits and assuming the expiration to be the splits smaller than this median, since according to the literature, the splits are shorter during the expiratory phase, if compared to the splits on the inspiratory phase. In both subjects, the values found are in accordance to the literature. However, in some auscultations, P2 was too faint and was wrongly detected (Figure 5.16). This may occasionally happens, but should not change the overall analysis, since the auscultations used in our dataset where also the ones a clinician hear and give a diagnosis. Figure 5.16: Miss-identification of P2 due to very low energy intensity. In the second experiment, we used the amplitude information to separate the normal auscultations from the hyperphonetic ones. In comparison with the matching pursuit technique, the energy technique had the best performance in separating these groups. 103 The downside of the energy method lies in the peak selection procedure, specially in cases where both A2 and P2 have similar energy and lasts longer than usual. This results in shift information error (Figure 5.17). This kind of situation is more likely to happen if S2 is buried in noise or murmur. This situation, however, can be improved, by using consistency analysis and/or application of a strong filter. A clinician, however, would not be able to listen to the components of the second heart sound in this situation, rendering the validation of this correction quite difficult. Figure 5.17: Incorrectly detected A2: on the first S2, the wrongly detected A2 component has a slightly greater amplitude than the real one, which comes before - compare with the following S2, where the components where detected correctly. Another problem with the energy method is the occurrence of missidentifications of A2 and P2 particularly when auscultations have too low volume and therefore levels of noise are comparable to the heartbeat itself. There are two possible solutions: creating an auditory threshold where detected peaks below that threshold are ignored, or using consistency checks and filtering, which would diminish the problem, however, this solution is beyond the scope of this work and should be explored in the future. 104 5.5 Publications 1. F. Hedayioglu; M. G. Jafari; S. S. Mattos; M. D. Plumbley,; M. T. Coimbra, ”An Exploratory Study On The Segmentation Of The Second Heart Sound”, to be submitted 105 Figure 6.1: Here we can see the two fit function used in a normal auscultation: lin fit is the function on equation 6.7, where pow fit is the exponential function on equation 6.8. Although the di↵erence between them is relatively small, the exponential function clearly provides a better fit. 112 6.3.4 Generating an auscultation To generate an auscultation, the first step is to use a real auscultation as a ’model’ auscultation. Suppose this model auscultation has nannotated S2. From this model, it will be extracted: 1. Atoms parameters: sa,u a,f oa,fafor the first atom, and sp,u p,f op,fp for each one of the nannotated S2. 2. All instantaneous heart rates ihr (Equation 6.6). 3. The parameters for equation 6.8 The second step is to get the parameters for the heart sounds to be produced. In our model, we do not change the first heart sound, since it is beyond the scope of this thesis. We use the parameters from the works in [116, 117]. The atoms used for the generated auscultations will have the same parameters as the ones obtained by the matching pursuit on the selected model auscultation. The user has the freedom to alter the parameters sa,s pand up to produce a proportional amplitude change and increase or decrease in the splits in comparison to the original recording. If the generated auscultation needs more S2 than the available n,the vector of atom parameters will be read in reversal order (e.g.. 0,1,2,...,n 2,n1,n2, ..., 1,0,1,2...). This is done by: index =|xmod (N1) [xmod 2(N1) xmod (N1)]|(6.14) Where xmod yis the remainder of x/y. The third step is to calculate the size of the systoles and diastoles. During an auscultation, the instantaneous heart frequency changes, as we can see in Figure 6.1. Looking at the heart rate variation of the i-th heart cycle is defined by: hr(i)=hr(i)hr(i1) (6.15) where hr(i)istheobservedheartrateofthei-thheartcycle,wecansee that the instantaneous heart rate variation on a beat by beat basis is small, 113 smooth and independent of the mean heart frequency (Table 6.3). Auscultation mean(hr)mean(hr)std(hr) 131 78.2355 0.1218 5.0851 124 69.2848 0.0129 10.1821 111 83.2123 -0.1053 2.7264 114 66.6770 0.0089 6.0314 137 84.5143 0.0965 5.3136 210 81.7844 0.3061 4.9001 112 71.9386 0.0212 5.3857 142 83.2452 -0.0045 2.5998 129 84.7339 -0.4331 7.6970 140 70.2664 -0.0403 5.0126 Table 6.3: Variation of heart rate on di↵erent auscultations. This small beat by beat variation was implemented in our simulator by calculating all instantaneous heart rates of the model auscultation, and then subtracting the average. This leaves us with just these small fluctuations of the heart rate throughout the auscultation. This vector is then added to the mean heart rate frequency informed by the user. This way we can have some variation on the heart rate during the generated auscultation. If the vector is too small to produce an auscultation of the desired duration, then the vector will be read in reversed order following Equation 6.14. 6.4 Experiments Here we show the interface and output of the simulator. The simulator was made in such a way that, being supplied by an auscultation’s systoles and diastoles times, and annotated first and second heart sounds, it can extract automatically all the other parameters in order to use this auscultation as a model to generate new synthetic auscultations in one auscultation site, 114 together with their respective annotations. 6.4.1 Auscultations generation In Figure 6.2, we can see the GUI of the simulator. The input fields are as follows: aDuration of the generated auscultation in seconds bAuscultation’s approximated average heart rate: varies between 60 bpm to 99 bpm cFirst atom’s amplitude factor: This parameter is multiplied by the A2’s atom’s amplitude sa:acceptvaluesbetween0.1to2.0 dSeconds atom’s amplitude factor: This parameter is multiplied by the P2’s atom’s amplitude sp:acceptvaluesbetween0.1to2.0 eSplit variation factor: specify how bigger or shorter the split would be compared to the original auscultation: values range between 0.1 to 2.0 fAuscultation to be selected as model: it will be used to extract the parameters to generate the baseline atoms for S2, heart rate variation, and derive the function for mapping heart rate into diastole time. Currently with 7 normal auscultation and 4 hyperphonetic ones. gDisplay the annotations on the generated auscultation: S1, S2, A2 and P2. 115 a b c d ef g Figure 6.2: The GUI of the simulator with the input fields. The white area displays the generated auscultation and allows the user to change its zoom, pan, in a way similar to the Audacity visual editor[113]. In Figure 6.3a and Figure 6.3b, we can see the amplitude variation throughout the auscultation in a normal and hyperphonetic auscultation, respectively. Since the amplitude and the split vectors are read in the same order, they are in sync with the respiration cycle. However, the volume of the chest in a given respiratory cycle is rarely the same. This will make the heart sound have small di↵erences in their amplitude, caused by this change in the transmission medium. We accounted for this e↵ect by introducing a small random variation (between 0% and 0.1% of the amplitude) in the amplitude of S1 and S2. 116 (a) Normal auscultation (b) A hyperphonetic auscultation Figure 6.3 We can see the first and second heart sound in Figures 6.4a and 6.4b. Since these atoms parameters are calculated based on the matching pursuit algorithm described on chapter 4, they are closely related to the real second heart sounds present in the original auscultation. The visual annotation of A2 and P2, however is related to where the atoms begin, not where the clinician would annotate them, which would be the same as the energy segmentation 117 method, from chapter 5 would detect. (a) Normal auscultation, with S1, S2 and A2 and P2 atoms annotated. (b) An hyperphonetic auscultation with zoom on the heart sounds and their annotations. Figure 6.4 118 One of the great strengths of this heart sound simulator is the capability of customisation: the second heart sound can be changed to exhibit a determined feature: may it be a frequency range or its position in the second heart sound. This was paramount for us when generating a ’custom’ second heart sound to test algorithms. One interesting experiment we performed was the transformation of a normal auscultation into a hyperphonetic one: this was achieved by increasing the P2 amplitude factor and the split factor, as we can see in Figure 6.5 (compare with S2 in a hyperphonetic auscultation in Figure 6.4b or even with Figure 5.14). This is confirmed by the energy method of chapter 5 reported an A2/P2=0.536 for the normal auscultation, where the auscultation made hyperphonetic reported an A2/P2=1.131, a value within the range of hyperphonetic class. We used the method of chapter 4 to generate a scatter plot with the two synthetic auscultations (Figure 6.6). It can be seen that the auscultation generated by the normal model is correctly localised in the lower left cluster that represents normal auscultations. The upper right cluster represents the hyperphonetic auscultations and has the auscultation generated by the same normal model but with the amplitude and split parameters changed to make it an hyperphonetic auscultation. 119 Figure 6.5: Normal auscultation with P2 and Split factor changed in order to make it hyperphonetic. Figure 6.6: Scatter plot with the two synthetic auscultations: the lower left cluster is the normal cluster; and the hyperphonetic cluster is located upper right 120 In Figure 6.7, we can see the di↵erences between the model auscultation and its annotation and the generated auscultation and its annotation: The original auscultation have an average heart rate of 81 bpm, while the generated one has 87 bpm. This change in the heart rate still maintained the natural features of the synthetic heart sound, and, allied with the atoms produced by the matching pursuit method, the synthetic auscultation reproduces the main features of the second heart sound (as can be seen in the same Figure). Figure 6.7: From top: the original auscultation, its manual annotation, the generated auscultation and the automatically generated auscultation. 6.5 Conclusions In this chapter we developed a heart sound simulator program that generates synthetic auscultations based on real ones, and with customisable clinically meaningful parameters. To do so, we also performed a study on the relationship between ventricular diastolic time and instantaneous heart rate and found that a better fit was achieved by using an exponential function. 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