Heart Sounds, ECG & Fractals

Heart Sounds, ECG & Fractals

The Heart The Heart The heart is a 2-step mechanical pump that is coordinated by precisely timed electrical impulses. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results For the pump to perform optimally, sequential depolarizations of the atria and then the ventricles allow atrial contraction to provide complete diastolic filling of the ventricles. Once the ventricles are filled, rapid activation of the ventricular myocardium allows a synchronized contraction to eject blood most effectively to the great vessels. The END Lets Go!

The upper chambers are the right atrium (RA) and left atrium (LA)
The Heart The Heart The heart is a pulsating pump that composes of four chambers and four heart valves. The upper chambers are the right atrium (RA) and left atrium (LA) The lower chambers are the right ventricle (RV) and left ventricle (LV). ECG Wave Heart sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results For the pump to perform optimally, sequential depolarizations of the atria and then the ventricles allow atrial contraction to provide complete diastolic filling of the ventricles. Once the ventricles are filled, rapid activation of the ventricular myocardium allows a synchronized contraction to eject blood most effectively to the great vessels. The END Lets Go!

Electrophysiology of cardiac conduction
The Heart ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results For the pump to perform optimally, sequential depolarizations of the atria and then the ventricles allow atrial contraction to provide complete diastolic filling of the ventricles. Once the ventricles are filled, rapid activation of the ventricular myocardium allows a synchronized contraction to eject blood most effectively to the great vessels. The END Lets Go!

Heart Valves The Heart ECG Wave Heart Sounds Abnormal Sounds
Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results For the pump to perform optimally, sequential depolarizations of the atria and then the ventricles allow atrial contraction to provide complete diastolic filling of the ventricles. Once the ventricles are filled, rapid activation of the ventricular myocardium allows a synchronized contraction to eject blood most effectively to the great vessels. The END Lets Go!

Events occurring during the cardiac cycle
The Heart The cardiac cycle consists of two basic components: A period of ventricular diastole during which the ventricles are filled with blood. A period of ventricular systole during which blood is propelled out of the heart. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results In normal cardiac conduction, electrical excitation of the heart proceeds in a sequential manner from the atria to the ventricles and is demonstrated on the surface ECG. The END Lets Go!

Events occurring during the cardiac cycle
The Heart Clinically, systole is taken as the interval between the first and the second heart sound. Diastole is considered to be the interval between second heart sound and the first heart sound. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Electrical system The Heart ECG Wave Heart Sounds Abnormal Sounds
Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

What is measured on the ECG
The Heart ECG Wave Heart Sounds Rate and rhythm of the heart. Abnormal Sounds Evidence of heart enlargement. Audicor’s Solution Evidence of damage to the heart Fractal Dimension Impaired blood flow to the heart Sound Analysis Heart rhythm problems Electrolyte imbalance Fractal Results The END Lets Go!

What are the limitations of the ECG
Electrophysiology ECG Wave Heart Sounds The ECG is a static picture Abnormal Sounds Many heart attacks cannot be detected by ECG. Audicor’s Solution Fractal Dimension Many abnormal patterns on an ECG may be non-specific. Sound Analysis The ECG may be normal despite the presence of a cardiac condition Fractal Results 1 may not reflect severe underlying heart problems at a time when the patient is not having any symptoms. In such instances, the ECG as recorded during an exercise stress test may reflect an underlying abnormality while the ECG taken at rest may be normal. 2 Angina, a common heart disorder, cannot usually be detected by a routine ECG. Specialized ECG recordings sometimes help to overcome some limitations. These are: Exercise ECG. This helps to assess the severity of narrowing of the coronary arteries. 3 They may even be a normal variant and not reflect any abnormality at all. The END Lets Go!

QRS complex: right and left ventricular depolarization
ECG wave Electrophysiology ECG Wave Heart Sounds ECG tracings show a pattern of electrical impulses that are generated by the heart. Abnormal Sounds P wave: the sequential activation (depolarization) of the right and left atria Audicor’s Solution QRS complex: right and left ventricular depolarization Fractal Dimension Sound Analysis ST segmet: ventricular repolarization. Fractal Results U wave: origin for this wave is not clear - but probably represents "afterdepolarizations" in the ventricles PR interval: time interval from onset of atrial depolarization (P wave) to onset of ventricular depolarization (QRS complex) QRS duration: duration of ventricular muscle depolarization QT interval: duration of ventricular depolarization and repolarization RR interval: duration of ventricular cardiac cycle (an indicator of ventricular rate) PP interval: duration of atrial cycle (an indicator or atrial rate) The T wave corresponds to electrical relaxation and preparation for their next muscle contraction. The END Lets Go!

ECG wave Electrophysiology Heart sounds Abnormal Sounds
Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results U wave: origin for this wave is not clear - but probably represents "afterdepolarizations" in the ventricles PR interval: time interval from onset of atrial depolarization (P wave) to onset of ventricular depolarization (QRS complex) QRS duration: duration of ventricular muscle depolarization QT interval: duration of ventricular depolarization and repolarization RR interval: duration of ventricular cardiac cycle (an indicator of ventricular rate) PP interval: duration of atrial cycle (an indicator or atrial rate) ML Model Lets Go!

Heart Sounds The Heart The auscultation of the heart may reveal different phenomena called heart sounds and murmurs. Heart sounds are a prolonged series of vibrations of both high and low frequency The murmurs are a longer series of vibrations, mostly of either high or low frequency. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

with respect to their temporal relationship, and are systolic sounds.
Heart Sounds The Heart The sounds heard during auscultation are called the first (S1) and second (S2) heart sounds respectively, with respect to their temporal relationship, and are systolic sounds. Phonocardiography often yields third (S3) and fourth (S4) heart sounds especially in children and in cases of heart disease. These are diastolic sounds. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Heart Sounds Genesis The Heart ECG Wave Heart Sounds Abnormal Sounds
Many hypotheses have been suggested to explain the origin of these sounds. Some being controversial at the time. With the advent of echocardiography the movement of intracardiac structures could be monitored with virtually no time delay. Concerning S1, S2, and S4 these controversies have largely been resolved. However there still exists controversy regarding S3. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

S1 & S2 Electrophysiology ECG Measurements Heart Sounds
S1 occurs when the mitral and tricuspid valves close at the beginning of systole. S2 results from closure of the aortic and pulmonic valves at the end of systole. ECG Measurements Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

low frequency sound: 0 - 70 Hz occurring in early ventricular diastole
The Heart ECG Wave Heart Sounds low frequency sound: Hz 50% in the 0-15 Hz band Abnormal sounds occurring in early ventricular diastole Audicor’s Solution Fractal Dimension due to over-distention of the ventricle during the rapid early filling phase Sound Analysis occurs 0.12 – 0.20 secs after S2 Fractal Results 1 may not reflect severe underlying heart problems at a time when the patient is not having any symptoms. In such instances, the ECG as recorded during an exercise stress test may reflect an underlying abnormality while the ECG taken at rest may be normal. 2 Angina, a common heart disorder, cannot usually be detected by a routine ECG. Specialized ECG recordings sometimes help to overcome some limitations. These are: Exercise ECG. This helps to assess the severity of narrowing of the coronary arteries. 3 They may even be a normal variant and not reflect any abnormality at all. The END Lets Go!

The physiological cause and effect of S3
Electrophysiology The third heart sound (S3) occurs 0.12 to 0.20 seconds after S2 in early Diastole. Of the many proposed theories, the most likely explanation is that excessive rapid filling of the ventricle is suddenly halted, causing vibrations that are audible as S3. Pathologic states where an S3 is encountered include anemia, thyrotoxicosis, mitral regurgitation, hypertrophic cardiomyopathy, aortic and tricuspid regurgitation and left ventricular dysfunction. ECG Measurements Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

S4 The Heart ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution
low frequency sound: Hz Abnormal Sounds occuring at the late diastolic filling phase at when the atria contract Audicor’s Solution Fractal Dimension Ventricles have decreased compliance, or receive increased diastolic volume Sound Analysis occurs just before S ms after onset of ECG P wave Fractal Results 1 may not reflect severe underlying heart problems at a time when the patient is not having any symptoms. In such instances, the ECG as recorded during an exercise stress test may reflect an underlying abnormality while the ECG taken at rest may be normal. 2 Angina, a common heart disorder, cannot usually be detected by a routine ECG. Specialized ECG recordings sometimes help to overcome some limitations. These are: Exercise ECG. This helps to assess the severity of narrowing of the coronary arteries. 3 They may even be a normal variant and not reflect any abnormality at all. The END Lets Go!

The physiological cause and effect of S4
Electrophysiology The S4 occurs just before the first heart sound in the cardiac cycle. It is produced in late diastole as a result of atrial contraction causing vibrations of the LV muscle, mitral valve apparatus, and LV blood mass. Disease processes that produce an S4 include hypertension, aortic stenosis and regurgitation, severe mitral regurgitation, cardiomyopathy, and ischemic heart disease. ECG Measurements Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The physiological cause and effect of S3 & S4
Electrophysiology In 1856, Potain first described "gallop rhythm" as an audible phenomenon in which a tripling or quadrupling of heart sounds resembles the canter of a horse. That term is still used to describe a third or fourth heart sound. ECG Measurements Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Electrophysiology Gallops are diastolic events and seem to be related to 2 periods of filling of the ventricles: The rapid filling phase (ventricular diastolic gallop or S3) The presystolic filling phase related to atrial systole (atrial gallop or S4) ECG Measurements Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Electrophysiology Experimental evidence in both humans and animal models suggests that abnormal compliance of the left ventricle is often associated with an S4 and/or a pathological S3. In the early diastolic phase of the cardiac cycle, the left ventricle relaxes and the intraventricular blood pressure falls below that of the left atrium. Therefore, blood flows from the atrium into the ventricle. ECG Measurements Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Electrophysiology This continues until the intraventricular pressure equals the pressure in the atrium and the flow of blood into the ventricle therefore stops. This deceleration of the blood early in diastole produces vibrations inside the ventricle, which can result in an S3 if the vibrations have sufficient energy. The steep left ventricular pressure increase in early diastole causes a reversal of the transmitral pressure gradient and hence a more rapid deceleration of inflow. ECG Measurements Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Electrophysiology Since the vibrations of S3 occur during deceleration of inflow, a conversion of kinetic into vibratory energy is likely. These vibrations are audible if transmitted with enough intensity. The higher the inflow rate (valve regurgitation) and the steeper the rapid filling wave (high filling rates), the greater the deceleration and more likely an S3 will occur. ECG Measurements Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Electrophysiology S3 is produced when the rapidly distending ventricle reaches a point when its distention is checked by the resistance of its wall and the ensuing vibrations are audible as the third heart sound. ECG Measurements Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Electrophysiology The remainder of the filling of the ventricle occurs late in diastole because of active contraction of the atrium. The deceleration of the blood later in diastole also produces vibrations inside the ventricle. If the atrial contraction that produced the late diastolic filling was sufficiently strong and the ventricle is relatively stiff, these vibrations may have enough energy to produce an S4. ECG Measurements Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Heart Sounds Characteristics
The Heart ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The normal range of human hearing lies within the range of 20 Hz – Hz, with maximum sensitivity lying in the speech range; about 1000 Hz to 3000 Hz. The END Lets Go!

Heart Sounds The Heart ECG Wave Heart Sounds Abnormal Sounds
ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results For the pump to perform optimally, sequential depolarizations of the atria and then the ventricles allow atrial contraction to provide complete diastolic filling of the ventricles. Once the ventricles are filled, rapid activation of the ventricular myocardium allows a synchronized contraction to eject blood most effectively to the great vessels. The END Lets Go!

PCG against ECG The Heart ECG Wave Heart Sounds Abnormal Sounds
Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results For the pump to perform optimally, sequential depolarizations of the atria and then the ventricles allow atrial contraction to provide complete diastolic filling of the ventricles. Once the ventricles are filled, rapid activation of the ventricular myocardium allows a synchronized contraction to eject blood most effectively to the great vessels. The END Lets Go!

The relationship between heart sounds and cardiac events
The Heart ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The relationship of cardiac events and the occurrence of heart sounds. From above downward are represented the pressure changes in the right side of the heart, pressure changes in the left side of the heart and the electrocardiogram. The END Lets Go!

The S3 may be a normal finding in patients less than 30 years old.
How do S3 & S4 Help? The Heart Experimental evidence suggests that abnormal compliance of the left ventricle is often associated with an S4 and/or a pathological S3. The S3 may be a normal finding in patients less than 30 years old. However, in older patients, the S3 is usually evidence of impaired ability of the ventricle to contract during systole. The prevalence of the S4 increases with age and usually indicates an abnormal increase in ventricular stiffness ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Clinical significance of S3
The Heart The presence of S3 may be the earliest clue to left ventricular failure. The presence of heart disease and may offer valuable information about diagnosis, prognosis, and treatment. The most useful clinical importance of S3 is in detecting left-sided heart failure, especially in the early stages when other signs may be normal. More recently, S3 was the best predictor of response to digoxin in CHF patients. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Usefulness of S3, S4 & ECG in assisting early detection
The Heart Several types of cardiac disease have characteristic electrical and hemodynamic manifestations. For example, acute myocardial ischemia is typically associated both with displacement of the ST segments of the ECG and with alterations of the mechanical properties of the left ventricle. The latter changes may produce pathological heart sounds – S3 and/or S4. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

S3 In Children The Heart ECG Wave Heart Sounds Abnormal Sounds
The genesis of S3 has been clearly associated with the rapid filling phase of diastole. Present work has shown that S3 occurs earlier in the cardiac cycle with increase in age of child subjects. This supports the hypothesis that S3 is due to L.V. reaching it’s elastic limit during diastole. This notion is supported further by the finding of the spectral energy of S3 is distributed more towards the high frequency of the end of the spectrum with age. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

S3 In Children The Heart ECG Wave Heart Sounds Abnormal Sounds
This is consistent with an increase in stiffness of the L.V. with age. The resonant frequencies of L.V. increase with stiffness. higher frequencies are more attenuated by passage through body tissue than lower frequencies. As the frequency distribution of S3 is shifted to higher frequencies as the child becomes older, it would be expected that the energy in S3 would decrease with age. Thus S3 usually disappears around adulthood, but may reoccur with cardiac pathology. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Combining ECG & Heart Sounds
The Heart Audicor uses an advanced new technology called correlated audioelectric cardiography (COR). This technology builds on the traditional findings of the standard, 12-lead resting ECG, augmenting it by simultaneously acquiring acoustical signals from both the V3 and V4 lead positions. (Two acoustic sensors replace the V3 and V4 ECG electrodes of a standard 12-Lead ECG ) Heart Sounds ECG Wave Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart Audicor CE combines the detection of heart sounds with ECG data in order to provide physicians with additional information that is valuable in assessing: S3 and S4 heart sounds that may be indicative of acute coronary syndrome or heart failure Acute and prior (age-undetermined) myocardial infarction (MI) Ischemia Left ventricular hypertrophy (LVH) Heart Sounds ECG Wave Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart The S3 heart sound is often very difficult to detect by auscultation due to its low frequency and intensity. Noisy clinical environments further complicate this difficulty. To improve the detection of the S3, Inovise Medical, Inc. has developed AUDICOR®, a device that records and algorithmically interprets simultaneous 12-lead ECG and electronic cardiac sound recording ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Audicor Heart Sound Algorithm
The Heart The AUDICOR heart sounds algorithm receives three synchronous inputs: 1. A standard ECG signal 2. Two single-channel sound signals. ECG Wave Heart Sounds Heart Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Processing The Sound Data
The Heart The sound data for each channel is then processed by removing offsets, prescaling, and filtering it into narrow frequency bands to optimize the detection of each S1 through S4 heart sound. Using the ECG as a reference, the S1 and S2 detection time windows are identified for each beat. Utilizing a threshold adaptively computed from a moving window root mean square for each frequency band, the location of each S1 and S2 is determined within the computed detection window. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Detecting S3 The Heart ECG Wave Heart Sounds Abnormal Sounds
The S3 detection time windows are located using information within the ECG and the computed position of the S2 offset. The energy content is determined within the S3 detection time window. Using a set of rules based on frequency and amplitude measurements, possible S3s are detected within the S3 windows. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Detecting S4 The Heart ECG Wave Heart Sounds Abnormal Sounds
The S4 detection time windows are located based on PQ intervals and Q-wave onset positions. Further processing on S4s is similar to that described before for S3s. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

ECG Diagnostic Algorithm
The Heart Superior diagnostic performance up to 84% more sensitive than current systems in acute MI detection, particularly in women was achieved in the following ways : • Developed the computerized ECG diagnostic algorithms using very large clinically correlated databases of over 100,000 ECGs. • Divided the data into demographically balanced learning and test sets to help ensure that it was not overtraining the algorithms using limited sets of data. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results Avoided circularity in developing and testing the algorithms by selecting all cases and non-cases of various diseases using criteria independent of the ECG as follows: - Prior Mls were defined using both coronary angiographic and - ventriculographic data obtained during cardiac catheterization. The cases of prior MI had > 75 percent transluminal narrowing of at least one coronary artery and either akinesia or dyskinesia of the left ventricle in the distribution of the narrow edartery. The non- cases of prior MI had no coronary lesions more severe than minor plaques and no impairment of LV motion. - Acute Mls were identified in patients with clinical symptoms suggesting acute myocardial ischemia and who had elevated biomarkers (CK-MB or Troponin I). Non-cases of acute MI had no abnormal values of cardiac biomarkers. - LVH was detected using measurements of left ventricular mass based on investigational-quality echocardiograms. The left ventricular mass was calculated using the Reichek-Devereaux formula along with empirically determined sex-specific threshold values for LVH. The cases of LVH equaled or exceeded these threshold values, and non- cases had values below the same thresholds. Subsequently, the LVH criteria were validated using measurements of left ventricular mass as an alternative diagnostic method. The END Lets Go!

The Heart • Accounted for differences in gender and age, emphasizing features that discriminate between prior and acute MI. • Avoided circularity in developing and testing the algorithms by selecting all cases and non-cases of various diseases using criteria independent of the ECG ECG Wave Heart sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart • Criteria for IMI is based upon the relationships between portions of the vectorcardiographic (VCG) QRS loop in the frontal plane and the corresponding portions of the ECG QRS complexes recorded in leads II and III. • Commercial ECG algorithms for detection of prior myocardial infarction (MI) predominantly rely on QRS criteria and on established qualitative ST and T changes. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart • Two distinct new approaches for quantifying ST and T changes to assist with the detection of prior MI. 1. The first method uses the mean axes of vectorcardiographic T-loops taken from the inverse Dower transform of the 12- lead ECG to indicate ischemic regions of the left ventricular wall. 2. The second method establishes regional scores for residual ST elevation supportive of ischemia or infarction. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart • These 2 ST-T measures qualify borderline QRS infarct criteria, resulting in composite criteria having higher sensitivities and specificities than QRS criteria alone. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart LVH is defined as values of the ECG left ventricular mass index (LVMI) >116 g/m(2) in men or >104 g/m(2) in women. Univariate linear regression was performed separately on the male and female subjects in the Learning Set to find all the ECG parameters that correlated significantly with LVMI. Multivariate linear regression (MLR) was applied to these parameters to identify the 4 variables for each sex that discriminated best between the subjects with and without LVH. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results LVH - left ventricular hypertrophy The END Lets Go!

The Heart ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution
Diagnostic Performance of a Computerized Algorithm for Augmenting the ECG with Acoustical Data The Heart Results: The following data show the ability of the computerized acoustical algorithm to detect an S3 or an S4 in patients in a variety of clinical settings. The performance of the algorithm is compared to a consensus of 2 experienced cardiologists concerning the audibility of the recorded S3 or the S4 in the each of the same patients. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results LVH - left ventricular hypertrophy The eND Lets Go!

Diagnostic Performance of a Computerized Algorithm for Augmenting the ECG with Acoustical Data The Heart ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Audicor Analysis The Heart ECG Wave Heart Sounds Abnormal Sounds
Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results This patient has a nondiagnostic ECG. However, the AUDICOR algorithm detected an S3. In this patient, where this is suspicion for heart failure the presence of an S3 is highly suggestive of ADHF (Acute Decompensated Heart Failure). Prompt treatment may begin prior to the results of other laboratory tests The END Lets Go!

Audicor Analysis The Heart ECG Wave Heart Sounds Abnormal Sounds
Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The ECG reveals evidence of the patient’s old anterior infarct, possible LVH and nonspecific ST-T changes that were unchanged from a previous ECG. However, the AUDICOR also detected an S3. With this objective finding in a patient where the examining physician has a clinical suspicion of ADHF, treatment may now begin. The END Lets Go!

The AUDICOR Decision Pathway – EMS
The Heart ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Acute myocardial ischemia often displaces the ST segments in the ECG.
ECG, Hemodynamic & Acoustical Findings: Experimental Model of Myocardial Ischemia The Heart Acute myocardial ischemia often displaces the ST segments in the ECG. However, since the specificity and sensitivity for ischemia of ST segment displacement are imperfect Echocardiography and radionuclide studies are often used to augment the ECG in evaluating patients for ischemia. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

ECG, Hemodynamic & Acoustical Findings: Experimental Model of Myocardial Ischemia
The Heart Ischemia also has hemodynamic effects that include reduced left ventricular (LV) contractility and compliance. These hemodynamic changes are typically associated with a third and fourth heart sound (S3 and S4), respectively. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

ECG, Hemodynamic & Acoustical Findings: Experimental Model of Myocardial Ischemia The Heart Conclusion: Detecting and recording heart sounds may improve the identification of acute myocardial ischemia as the cause of ST segment abnormalities. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

ECG & Acoustical Data in the detection of Left Ventricular Enlargement
The Heart The presence of 3rd and 4th heart sounds was associated mainly with relative prolongation of the PR interval and with flattening or negativity of T waves in multiple leads. Conversely these sounds were not associated with the abnormalities of QRS voltage traditionally attributed to increased left ventricular mass. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

ECG & Acoustical Data in the detection of Left Ventricular Enlargement
The Heart Conclusion: ECG and acoustical data can detect abnormalities of ventricular function that the cardiac diseases responsible for LVE produce. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Detecting Hemodynamic Abnormalities Using ECG and Cardiac Acoustical Data The Heart Background: Hemodynamic abnormalities can produce ECG changes. For example, the ECG evidence of left ventricular hypertrophy (LVH) is a consequence of the hemodynamic abnormalities that produced the LVH. However they hypothesized that abnormal hemodynamics are more likely to predict the presence of a third heart sound (S3) than of ECG findings. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart Conclusions: ECG Wave
Detecting Hemodynamic Abnormalities Using ECG and Cardiac Acoustical Data The Heart Conclusions: The electronically recorded S3 is associated with a wider range of hemodynamic abnormalities than is ECG evidence of LVH, ST-T or prior MI and can therefore augment the diagnostic capabilities of the ECG. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Using Simultaneous ECG and Acoustical Data to Evaluate and Monitor Patients with Cardiac Disease The Heart Background: Acute myocardial ischemia is associated with hemodynamic as well as ECG abnormalities. For example, impaired left ventricular (LV) systolic function can produce a third heart sound (S3) that previous research, as reflected in the ACC/AHA Practice Guidelines, has shown to be associated with increased clinical risk. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Using Simultaneous ECG and Acoustical Data to Evaluate and Monitor Patients with Cardiac Disease The Heart Results: In the 89 pre-cath patients, the recorded S3 had a sensitivity /specificity for detecting an LV ejection fraction <50% and LV enddiastolic pressure >15mmHg of 13/21 (sens, 62%); 60/68 (spec, 88%). In the acute MI patient, acoustical changes preceded ECG changes and a new S3 appeared shortly after the onset of the acute MI. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Using Simultaneous ECG and Acoustical Data to Evaluate and Monitor Patients with Cardiac Disease The Heart Conclusions: Electronically recorded S3 identifies patients with impaired LV systolic function and recorded heart sounds can be added to multi-parameter monitoring of patients with suspected acute MI. ECG Wave Heart Sounds Abnormal Sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Automatic Segmentation of Heart Sound Signals Using Hidden Markov Models
The Heart Segmentation of heart sounds into their component segments, using Hidden Markov Models. The heart sounds data is preprocessed into feature vectors, where the feature vectors are comprised of the average Shannon energy of the heart sound signal, the delta Shannon energy, and the delta-delta Shannon energy. ECG Wave Heart Sounds Abnormal Sounds HMM Models Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Pre-processing The Heart ECG Wave Heart Sounds Abnormal Sounds
The system filters the original heart sound signal using a band-pass filter with cutoff frequencies at 30 Hz and 200 Hz. Next, the signal is normalized according to: Then, it calculates the average Shannon energy In continuous 0.04-second segments, with 0.02 seconds of overlap per segment. ECG Wave Heart Sounds Abnormal Sounds HMM Models Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Shannon energy emphasizes the medium intensity signals and attenuates the high intensity signals. This tends to make medium and high intensity signals similar in amplitude. The system calculates the average Shannon energy of each frame, where Xnorm is the normalized heart signal, using: ECG Wave Heart Sounds Abnormal Sounds HMM Models Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Then, the system normalizes the average Shannon energy over all of the frames, where is the average Shannon energy for frame t the mean value the standard deviation ECG Wave Heart Sounds Abnormal Sounds HMM Models Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Mel-spaced filterbanks
The Heart Next, the system extracts the spectral Characteristics from the heart sound signal. Since the average duration of the S1 sound is 0.16 seconds (empirical), the system divides the signal into 0.15-second frames, with 0.02 seconds of overlap for each frame. The frequency spectrum of S1 contains peaks in the 10 to 50 Hz range and the 50 to 140 Hz range, while the frequency spectrum of S2 Contains peaks in the 10 to 80 Hz range, the 80 to 200 Hz range, and the 220 to 400 Hz range. As a result, this study limits the spectral feature extraction between the frequencies of 10 Hz and 430 Hz. ECG Wave Heart Sounds Abnormal Sounds HMM Models Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart Mel-Spaced filter banks provide a simple method for extracting spectral characteristics from an acoustic signal. This method involves creating a set of triangular filter banks across the spectrum. The filterbanks are equally spaced along the mel-scale, as defined in: ECG Wave Heart Sounds Abnormal Sounds HMM Models Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart Equal spacing on the mel-scale provides non- Linear spacing on the normal frequency axis. This non-linear spacing means that there are numerous, small banks at the lower frequencies and sparse, large banks at the Higher frequencies. Since most of the energy of the heart sounds is in the lower frequency ranges, using a mel- scale matches the frequency spectrum of the heart sounds. ECG Wave Heart Sounds Abnormal Sounds HMM Models Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart Each triangular filter is multiplied by the Discrete Fourier transfer of the heart sound frame and summed. This creates a set of frequency bins, where each bin represents a portion of the frequency spectrum. ECG Wave Heart Sounds Abnormal Sounds HMM Models Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Regression coefficients
The Heart The final feature extraction step is to calculate a set of regression coefficients. Regression coefficients are used to represent the changes in each feature over time. The system computes the first order regression (delta coefficients) and the second order Coefficients (delta-delta coefficients) using the following regression formula: ECG Wave Heart Sounds Abnormal Sounds HMM Models Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Regression coefficients
The Heart The system combines the Shannon energy, the Spectral features, and the regression coefficients into a single feature vector per frame. It stores these feature vectors for later use in the training and testing of the heart sound HMM. ECG Wave Heart Sounds Abnormal Sounds HMM Models Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Heart sound Hidden Markov Model
The Heart One can model the phonocardiogram signal as a four state HMM: The first state corresponds to S1. The second state corresponds to the silence during the systolic period. The third state corresponds to S2. The fourth state corresponds to the silence during the diastolic period. ECG Wave Heart Sounds Abnormal Sounds HMM Models Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart ECG Wave Heart Sounds Abnormal Sounds HMM Models Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart This model ignores the possibility of the S3 and S4 heart sounds, because these sounds are difficult to hear and record; therefore, they are most likely not noticeable in the heart sound data. ECG Wave Heart Sounds Abnormal Sounds HMM Models Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart This four state HMM is useful for modeling the sequence of symbols (or labels) of the phonocardiogram; However, it is too simple to accurately model The transitions between sound and silence. One solution is to embed another HMM inside of each of the heart sound symbol states. The embedded HMM models the signal as it traverses a specific labeled region of the signal. ECG Wave Heart Sounds Abnormal Sounds HMM Models Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart Using this combined approach, we can model both the high-level state sequence of our signal (S1-sil-S2-sil) and the continuous transitions of the signal. This type of model is similar to how a speech processing system has a high-level probabilistic grammar to model the transition of words or phonemes, and an embedded HMM for each Phoneme. ECG Wave Heart Sounds Abnormal Sounds HMM Models Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Discussion The Heart ECG Wave Heart Sounds Abnormal Sounds HMM Models
Shannon Energy features with and without the Melspaced filterbank features are nearly identical in performance. Shannon Energy features are better suited for lowering the frame error rate while Mel-spaced filterbanks are better suited for lowering the model error rate. Mel-spaced filterbanks are marginally better as features for noisy PCGs than Clean PCGs. ECG Wave Heart Sounds Abnormal Sounds HMM Models Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

FFT S3 Analysis The Heart ECG Wave Heart Sounds Abnormal Sounds FFT
The PCG and ECG data were sampled at a rate of 2042 Hz (this gave a Nyquist frequency of about 1000 Hz). The signals are then digitized by means of a two channel, 8 bit analogue to digital converter controlled by an Intel 8085 microprocessor based system (sdk85) with 8k memory. Each sampled datum was represented as an unsigned hexadecimal number. These files are then simultaneously plotted by means of a graphics terminal. ECG Wave Heart Sounds Abnormal Sounds FFT Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

FFT S3 Analysis The Heart ECG Wave Heart Sounds Abnormal Sounds FFT
The ECG was used as a time reference for the PCG plot, which aided in obtaining the starting and end points of S3. Each PCG file was multiplied by a file containing a hamming window ( cosθ) co-positioned with the S3, but zero everywhere else. This had the effect of extracting the S3 from the PCG file and multiplying it by a window function. A conventional FFT is then applied to these files to produce the S3 spectra. ECG Wave Heart Sounds Abnormal Sounds FFT Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Why FFT does not work for S3
The Heart When applying it to the short duration S3, the FFT suffers from a fundamental limitation in frequency resolution determined by the window size. The FFT gives poor resolution for S3 spectral analysis. The time duration of S3 is relatively short (50 ms). This short observation time, combined with the spectral blurring effects of the window function accounts for the poor resolution of the FFT method. ECG Wave Heart Sounds Abnormal Sounds FFT Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart The major limitation of the FFT approach to spectral analysis is that of frequency resolution, i.e. the capability of distinguishing between closely spaced spectral peaks. The FFT resolution is about 1/T, where T is the available data time. Hence, when dealing with short data lengths the resolution is restricted. ECG Wave Heart Sounds Abnormal Sounds FFT Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart Another problem inherent to the FFT method is the effect of spectral “leakage”. In FFT analysis a real signal represents a truncated function, which is equivalent to multiplying it by a “window” function. The resultant FFT spectrum contains energy due to both the signal itself and the window function. The result is the spectrum of the convolution of the signal and window functions. This leakage can be reduced by appropriate design of the window function, but this always results in reduced frequency resolution. ECG Wave Heart Sounds Abnormal Sounds FFT Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Maximum Entropy Spectral Analysis
The Heart Classical spectral analysis requires the assumptions, about the signal under analysis, of long samples of data and of stationarity. However in real applications of biomedical spectral analysis both these assumptions are violated. In the case of the spectral analysis of S3, the time duration is short enough to consider it stationary; but the assumption of a long signal history is obviously erroneous. ECG Wave Heart Sounds Abnormal Sounds MESA Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Maximum Entropy Spectral Analysis
The Heart The MESA technique has been demonstrated to produce superior spectral resolution when compared with more traditional methods, especially for short data lengths [Burg 1967, Kay 1981, Ulrych 1975]. Another advantage of MESA is that one can use a simple rectangular window as there is no spectral “leakage”. Studies have shown that FFT is incapable of satisfactorily resolving the frequency peaks of in S3 and introduces unwanted leakage. However the Maximum Entropy Method is capable of satisfactory resolution with no leakage. ECG Wave Heart Sounds Abnormal Sounds MESA Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Conclusions The Heart ECG Wave Heart Sounds Abnormal Sounds
Research has shown that S3 can significantly enhance heart disease analysis. The normal range of human hearing lies within the range of 20 Hz – Hz, with maximum sensitivity lying in the speech range; about 1000 Hz to 3000 Hz. In order to be heard, low frequency sounds such as S3, must attain energy levels thousands of times greater than those needed by vibrations within the speech range. ECG Wave Heart Sounds Abnormal Sounds Future Research Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Conclusions The Heart ECG Wave Heart Sounds Abnormal Sounds
Thus the extraction of S3 & S4 is almost entirely dependant on the development of accurate automated methods. Following a review of the literature it is apparent that a truly successful S3 & S4 detection algorithm has yet to be developed. ECG Wave Heart Sounds Abnormal Sounds Future Research Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Future Research The Heart ECG Wave Heart Sounds Abnormal Sounds
My future research may be focused on developing an accurate S3 & S4 detection algorithm. ECG Wave Heart Sounds Abnormal Sounds Future Research Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Thank You The End The Heart ECG Wave Heart Sounds Abnormal Sounds
Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Stop!

Fractal Definition The Heart ECG Wave Heart Sounds Abnormal sounds
An object which appears self-similar under varying degrees of magnification. In effect, possessing symmetry across scale, with each small part of the object replicating the structure of the whole. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Self-similarity The Heart ECG Wave Heart Sounds Abnormal sounds
Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Fractal Dimension The Heart ECG Wave Heart Sounds Abnormal sounds
All fractals are characterized by their own dimension, which is usually a non-integer dimension, that is greater than their topological dimension and less than their Euclidean dimension. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Fractal Dimension The Heart ECG Wave Heart Sounds Abnormal sounds
This definition of fractal dimension is often used as an alternative definition of fractal objects. However, the fractal dimension may be estimated in numerous ways, such as the box-counting dimension and the variance dimension. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Chaotic dynamics The Heart ECG Wave Heart Sounds Abnormal sounds
A chaotic system refers to a system that never exactly repeats its behavior. Regardless of how long we let the model run for, we would never come across a repetition in the waveform due to its aperiodic feature. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Chaos The Heart ECG Wave Heart Sounds Abnormal sounds
This behavior is known as chaos. By plotting the models variables against each other we receive a visualization of the dynamics of the system. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

In two dimensions these plots are known as phase portraits.
The Heart The phase portrait will have the same form although the model is started with different initial conditions, the system will be attracted to this type of final solution. In two dimensions these plots are known as phase portraits. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Strange Attractors The Heart ECG Wave Heart Sounds Abnormal sounds
This plot is known as the attractor of the system. The attractors for chaotic systems are termed strange attractors. The fractal structures of these strange attractors may be classified by calculating their fractal dimensions. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Cantor Set The Heart ECG Wave Heart Sounds Abnormal sounds
The cantor set consists of an infinite set of disappearing line segments in the unit interval. The set is generated by iteratively removing the middle third of line segments, resulting in a collection of infinitely many disappearing line segments lying on the unit Both the line segments individual and combined length approach zero as the number of line segments approach infinity. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Cantor Set The Heart ECG Wave Heart Sounds Abnormal sounds
Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The initial unit line segment is known as the initiator of the set. The first step, to remove the middle third of the initiator, is known as the generator, as it is the repeated iteration of this step on subsequent line segments that is generating the set. This procedure, by removing the middle third of the line segments, is repeated to infinity. Nevertheless, only after an infinite number of iterations do we obtain the Cantor set. The self-similar properties of the Cantor set are obvious as each sub-set is a Cantor set itself. That is, each Cantor set is made up of an infinite number of copies of itself. The END Lets Go!

The Koch curve The Heart ECG Wave Heart Sounds Abnormal sounds
The iterative procedure used to construct the Koch curve begins, similar to the Cantor set, with the initiator of the set as the unit line segment. The generator is constructed by removing the middle third of the line segment and then replace it with two equal segments formed as two sides of a triangle. The process is repeated an infinite number of times to produce the Koch curve. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Koch curve The Heart ECG Wave Heart Sounds Abnormal sounds
Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The Koch curve is constructed by iteratively removing the middle third of the line segments and replaces it with two segments formed as two sides of a triangle. Once again, as we can see from the figure, each sub-segment is a scaled down copy of the generator, and consequently, the Koch curve possesses self-similarity. Furthermore, the Koch curve has infinite length due to the construction process. At each step of the generation, the length of the curve is increased by 4/3 of the length of the curve in the preceding step, resulting in an infinite length. The END Lets Go!

Regular Fractals The Heart ECG Wave Heart Sounds Abnormal sounds
Regular fractals are fractal objects that possess exact self-similarity, objects with structures comprising of exact copies of themselves at all magnifications. The most commonly known regular fractals are possibly the Cantor set and the Koch curve, both simply constructed using an iterative procedure. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Random Fractals The Heart ECG Wave Heart Sounds Abnormal sounds
Random fractals are statistically self-similar. Each small part of a random fractal has the same statistical properties as the whole. Random fractals may be constructed mathematically by introducing a random feature in the generating process of a regular fractal. For instance, when generating the Cantor set any third of the line segment is removed instead of the middle third. Many properties of natural objects and phenomena may be described using random fractals. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Fractal boundaries The Heart ECG Wave Heart Sounds Abnormal sounds
In order for a fractal curve to be classified as a fractal boundary it must meet two conditions: The curve must be non-crossing, meaning that the fractal curve does not intersect itself 2. As the fractal curve is zoomed in it reveals more structure (details). ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results A coastline is statistically self-similar, as a randomly selected segment of the coastline possesses the same statistical properties over all scales of magnifications. Hence, coastlines are random fractal curves, and furthermore, are random fractal boundaries. Although all natural fractals only possess self-similarity over a finite range of scales, the range is often sufficiently large in order to use fractal geometry in classifying the object. A coastline is statistically self-similar allowing more details to be revealed as it is zoomed in. Furthermore, the coastline do not intersects itself. When a fractal curve meets these conditions it is said to be a fractal boundary. The END Lets Go!

Dimension measurements are suitable in order to characterize and quantify the statistical self-similarity property of random fractal boundaries. As random fractals do not possess exact self-similarity the similarity dimension may not be used. Instead we define estimates of the fractal dimension of random fractals, which do not require the exact self-similar property. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The box counting dimension
The Heart The box counting dimension, enables non-integer dimensions to be found for fractal curves. covers the object in self-similar boxes. In order to determine the box counting dimension of a fractal object, the object is covered with elements or boxes of side length ε. The number of boxes, N, required to cover the object together with the side length ε is then used to determine the dimension. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart The straight line is covered with elements of length ε, for simplicity we assume that the line is of unit length. In order to cover the line N elements are required regardless of the dimension of the elements, here illustrated as cubes. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart To cover the unit line segment any elements with a dimension greater than or equal to the dimension of the line itself may be used, and still only require N of them. This leads to the following expression: ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results where the exponent of ε is equal to one regardless of the dimension of the elements, and actually is the box counting dimension of the line. The END Lets Go!

The Heart If, in stead, the same procedure would be applied to a plane of unit area, the expression received would be: Similar reasoning with a 3-dimensional object would lead to: ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart In general, in order to cover an object of unit hypervolume the number of elements reuired are: In logarithmic form: ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart By disregarding the assumption of unit hypervolume, a general expression of the box counting dimension may be received: where V is the hypervolume of the fractal object. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart By rearranging the expression it is easy to see that it is an equation of the straight line, where the gradient of the line is the box counting dimension of the object, and by plotting log(N) against log(1/ε) for various elements with different side lengths d the box counting dimension may be determined: ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart To obtain a measure of the box counting dimension there are different methods of covering the fractal object. Three of them are illustrated below. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart The first method illustrated is covering the curve by placing boxes against each other in a way that a minimum number of boxes are being used. Another method is to cover the fractal object with a grid of boxes and count the number of boxes that contain a part of the curve. The last method illustrated is covering the curve with circles instead of boxes, placed in a similar way as with the boxes in the first method. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart Regardless of which method being used, the box counting dimension is still obtained from the derivate of the plot of log(N) against log(1/ε): ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The box counting dimension is estimated as the plot of log(N) against log(ε). The estimations are normally performed either by selecting two points and calculate the slope between them or, by adjusting a best fitted and calculate its slope. The END Lets Go!

The Heart Normally, in practical applications, the box counting dimension is estimated by selecting two points at small values of ε in the plot, resulting in an estimation given by: To receive a more accurate estimate of the box counting dimension a best fitted line may be drawn through the points at small values of ε. The slope, and consequently the box counting dimension, is then calculated from this best fitted line. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Regular Brownian motion
The Heart Regular Brownian motion, or Brownian motion, is named after its discoverer Robert Brown. He observed that small particles floating in water underwent rapid irregular motions due to their bombardment by water molecules. If a group of particles is released at a certain location the bombarding molecules will cause the particles to spread out, diffuse, through time. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart The trajectories of particles undergoing Brownian motion in the plane may cross over themselves. Hence, Brownian motion may not be classified as a fractal boundary. Furthermore, as the Brownian trajectory is zoomed into, more structure is revealed, indicating that the statistical self-similarity features of the Brownian trajectory extends over all scales of magnification ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The left-hand plot illustrates a trajectory of a particle undergoing Brownian motion that unlike fractal boundaries may cross over themselves. The self-similar properties of a Brownian motion become apparent when comparing the two images, if the scale was left out it would be impossible to distinguish between the original and zoomed in image. The END Lets Go!

The Heart If the Brownian motion is sampled at intervals of and the positions of the sampled points at time are denoted by , then the observed steps taken in the two coordinate directions and both follows a Gaussian probability distribution. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The steps taken in a Brownian motion follow a Gaussian distribution, here illustrated with zero mean and unit standard deviation. The END Lets Go!

The Heart Consequently, the step lengths between observed points also follows a Gaussian distribution: ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart The methods generally used to construct a Brownian motion in the plane are derived from these features. Hence, the motion is constructed by using steps in the two coordinate directions, ∆x and ∆y randomly selected from a Gaussian distribution. The step length r randomly selected from a Gaussian distribution T he step angel is randomly selected from a uniform distribution between 0 and . ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart The time trace of Brownian motion, B(t), is equal to the time history of the coordinates of a Brownian trajectory, illustrating how the coordinate values vary in time. The construction of a Brownian motion trace is derived from the property that successively increments the trace following a Guassian distribution: ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart Thus, by sampling the Brownian motion trace at discrete times a discrete approximation may be constructed, by summarizing a series of random incremental steps, Thus , is built up as an accumulated sum, ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results Figures 19a-b illustrate the construction procedure of a Brownian motion trace. The incremental steps, R(tj), illustrated in figure 19a are discretely sampled numbers taken from a Gaussian distribution, which are added together according to the above equation. Figure 19b illustrates the first steps in the construction procedure. However, this is not a true fractal, as it does not possess self-similarity at all scales of magnifications. Nevertheless, zooming out far enough will make it impossible to resolve individual steps, and will in fact make it impossible to distinguish from a continuous Brownian motion trace. Therefore, the finite resolution of the generated Brownian motion trace is dependent on the choice of the time increment ∆t. The incremental steps are discrete random numbers taken from a Gaussian distribution with unit variance sampled at unit incremental time (a). In figure (b) the first steps in the construction process of a Brownian motion trace is illustrated. The all-previous incremental steps are added together in order to generate the current value on the Bm trace. The END Lets Go!

The Heart For a continuous Brownian motion trace, B(t), the self-similar properties are apparent as zooming into it. Both the original trace and zoomed in traces displays the similar irregularity, as they are statistically self-similar. However, in order to retain the self-similar properties of the original trace the axes need to be scaled differently. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results Non uniform scaling: This is illustrated in figure 20a-c where the time coordinate each time was scaled up four times, contrary to the spatial coordinate, , which was only scaled up two times each time in order to retain self-similarity. In order to retain the self-similar properties of the Brownian motion trace the axes need to be scaled differently. Notice that in the figure the time coordinate is scaled up four times while the spatial coordinate only is scaled by a factor two. The END Lets Go!

The Heart By considering pairs of points on a Brownian motion trace separated by a time it is possible to state a relationship between the mean absolute separation in B(t) between these points, and the time separation. The obtained expression is given by where the exponent, here equal to ½, is denoted the Hurst exponent, H: ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The procedure is illustrated in figure 21, a window of length Ts slides over the trace averaging the absolute values of ∆B. By sliding a window of length TS over the trace the mean absolute separation in B(t) may be calculated by averaging the absolute difference, ΔB, for each slide step. The END Lets Go!

The Heart The Hurst exponent is the reason why a Brownian motion trace only remains statistically self-similar under scaling when the axes B(t) and t are scaled differently. Consequently, if the time is scaled by a factor A, B(t) must be scaled by a factor in order to retain the similar relationship between and . ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart This is illustrated in the following example where the time t is scaled by the factor A: This property of non-uniform scaling is known as self-affinity, and is the reason for the two scaling factors needed to retain the statistical self-similar properties ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart All particles undergoing Brownian motion diffuse through time in an average sense, the traces start at t=0 where B(t)=0 and continue to spread out from the origin as time increases. If a large number of particles are spreading out from the origin through time, the spreading process may be characterized using averaged statistical properties. When considering diffusion related problems, it is more natural to use the standard deviation, as a measure of the spreading. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart As the standard deviation and are proportional the scaling relationship is given by : The expression is commonly re-expressed as where K is denoted the diffusion coefficient. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The diffusion coefficient is determined as half the slope of the best-fitted line in the variance against time plot. Normally, in practical applications, the diffusion coefficient is obtained by plotting the variance square , against the time and then calculate the slope of the best-fitted line. The diffusion coefficient may then be calculated as the slope divided by two. The END Lets Go!

The Heart It is possible to generate a Brownian motion trace with a certain diffusion coefficient K, by selecting the incremental steps, from a Gaussian distribution where the standard deviation, is given by: Where is the time interval between each sample. Hence, after number of time steps, the time t equals: ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart Combining the above equations will result in that the standard deviation of diffusing particles may be expressed as: ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Fractional Brownian motion
The Heart The fractional Brownian motions, abbreviated fBms, are a generalisation of the regular Brownian motion. The Hurst exponents for fBms range from 0 < H < 1 where the special case of H=0.5 results in regular Brownian motion. Normally, fBms are denoted where the subscript H equals the Hurst exponent that is classifying the motion. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart Similar to regular Brownian motion traces the fBm traces are self-affine processes. In addition, a scaled up part of an fBm requires different scaling factors for the t and axes in order to retain its statistical self-similar properties. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart The scaling relationship between the mean absolute separation along the fBm trace and the time of the separation is expressed as: and similarly the standard deviation of diffusing particles scales as: ~ Where is the fractional diffusion coefficient. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart The fractional diffusion coefficient is obtained by plotting against time since release. This results in a linear relationship, where the slope of the plot corresponds to twice the fractional diffusion coefficient. However, this requires that is known, which is not always the case in practical applications. Instead a logarithmic plot of against time may be used, where the gradient of the best-fitted line through the experimental data equals and the crossing point on the axis equals ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

The Heart ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Heart Sound Analysis with Time Dependent Fractal Dimensions
The Heart First I will explain the construction and use of fractal dimension trajectories, and how the selection of windows affects the appearance of the trajectory. Thereafter follows a description of the different methods used to calculate the dimension trajectories. The description consists of two parts, a brief introduction to the methods containing the necessary theory, followed by some practical considerations that have to be accounted for when applying them to discrete signals. ECG Wave Heart Sounds Abnormal sounds Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Go!

Thank You The End The Heart ECG Wave Heart Sounds Abnormal Sounds
Audicor’s Solution Fractal Dimension Sound Analysis Fractal Results The END Lets Stop!

Heart Sounds, ECG & Fractals

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Heart Sounds, ECG & Fractals

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