Методи и алгоритми за симулационно моделиране на фрактални процеси

The report presents methods and algorithms for simulation modelling of fractal processes. Fractal processes based on fractal Brownian motion, fractal Gaussian noise and, fractal Gaussian noise-wavelet transformation are simulated. Based on the performed comparative analysis of the algorithms for simulation modelling of fractal processes with respect to the accuracy parameter, it follows that the algorithms based on the models of fractal Gaussian noise and fractal Gaussian noise-wavelet transformation have the smallest relative error with respect to the Hurst parameter. The value of the Hurst parameter is one of the most important characteristics determining the degree of self-similarity of fractal processes. The considered algorithms based on these two models can be applied for modelling of physiological data, including cardiological data, because they have fractal properties.Научното изследване е проведено като част от проекта „Изследване на приложението на нови математически методи за анализ на кардиологични данни“ № КП-06-Н22/5 от 07.12.2018 г., финансиран от Фонд „Научни Изследвания“

Приложение на методи от нелинейната динамика за анализ на вариабилността на сърдечната честота

The article presents the results of the study of the nonlinear properties of the dynamics of the intervals between heartbeats obtained from digital ECG signals of healthy subjects, patients with arrhythmia and patients with heart failure. Data analysis was performed by applying the following two methods of nonlinear dynamics: Recurrence plot and Poincaré plot, comparing with the linear histogram method. The visual evaluation of the repeating diagrams constructed by the Recurrence plot allows obtaining quick information about the behaviour of the studied process. The reduction of the complexity of the process (heart rhythm) and the transition to periodicity is indicative of a pathological change in the regulation of heart rhythm. Poincaré plot is a useful tool when rare and sudden disorders occur against the background of a monotonous heart rate. Cardiovascular diseases significantly affect the dynamics of heart rate, reducing variability.Научното изследване е проведено като част от проекта „Изследване на приложението на нови математически методи за анализ на кардиологични данни“ № КП06-Н22/5 от 07.12.2018 г., финансиран от Фонд „Научни Изследвания“

Методи на нелинейната динамика за анализ на вариабилността на сърдечната честота

The heart rate variability (HRV) analysis, based on the methods of nonlinear dynamics, can provide important information for the physiological interpretation of the functioning of the cardiovascular system and assess the risk of its pathology. The article presents methods for nonlinear analysis of HRV, united in the following groups: fractal, multifractal, graphical and informational. The application of the methods of nonlinear dynamics in the study of the information characteristics of HRV in order to distinguish healthy subjects from sick ones is an important topic from the point of view of the application of the information technologies in the field of non-invasive cardiology. After determining the values of the studied parameters with the developed software and for the distinction of the two studied groups of subjects (healthy controls and patients with arrhythmia) statistical analysis was applied. The statistical analysis was performed by t-test and receiver operating characteristic (ROC) analysis. ROC curves are constructed and the area under the curves is calculated, on the basis of which the quality of the studied methods is evaluated. The results reported in this study may be useful in classifying the states of electrocardiographic signals and serve as a landmark for comparing healthy individuals to individuals with cardiovascular disease. The high information content of the used nonlinear methods for HRV analysis opens perspectives for their future use in the diagnosis and prognosis of cardiovascular diseases.Научното изследване е проведено като част от проекта „Изследване на приложението на нови математически методи за анализ на кардиологични данни“ № КП-06-Н22/5 от 07.12.2018 г., финансиран от Фонд „Научни Изследвания“

Implementing a Web-based Application for Analysis and Evaluation of Heart Rate Variability Using Serverless Architecture

This article is devoted to the development of a web-based application for analysis and evaluation of Heart Rate Variability (HRV) using serverless architecture. Advancements in information algorithms and computing technologies have been playing an increasingly important role in cardiology, as continuous monitoring of patients’ health can be vital to their well-being.  One physiological parameter that can be easily measured and that can provide indispensable insight into the state of the human body is the HRV.  HRV analysis can assess not only the physiological state of the body but also provide the capability to monitor its dynamics and predict future diseases. As the research in the sphere of cardiology is constantly growing there is a multitude of new ways to assess the physiological state of patients and provide an early indicator to pathological conditions. Therefore, there is a need to bring these advances to a growing number of end-users (health-care professionals and patients) in the shortest possible time. To address this problem, this study proposes the development of a web-based application for analysis and evaluation of HRV by applying linear and nonlinear mathematical methods. The application is created using a serverless architectural approach, which allows for fast development time, as there is no need to manage server infrastructure, and for automatic scaling to dynamically match the number of requests. The developer can instead focus on implementing the logic for the HRV analysis algorithms and deliver new improvements at a faster rate. The proposed web application can be accessed by any device that is connected to the Internet and is optimized to handle both an intermittent and a consistent volume of requests. The algorithms implemented in the web application have been validated by examining two groups of subjects (young adults and older adults) using linear and non-linear models. The obtained results from the two groups can be compared with a set of reference values (only for the linear methods) and an assessment can be made whether each studied parameter is within the normal range or outside it (its value is too high or too low). To aid the assessment for HRV, the results obtained by the linear and nonlinear analysis are presented using a set of both graphs and tables

Графични методи за автоматичен анализ на нелинейните характеристики на ЕКГ сигнали

Automatic analysis of ECG signals makes it possible to assess the health status of patients, reducing the likelihood of human error and ensuring optimal and accurate results. The presentation of heart rate in the form of a dynamic series of RR intervals (intervals between successive heartbeats) and the application of graphical methods (Poincaré plot, Detrended Fluctuation Analysis and Multifractal Detrended Fuctuation Analysis) for analysis are an objective and non-invasive way to obtain information about the functional state of the organism. The present study presents the results of graphical analysis of RR interval series based on ECG signals of healthy and unhealthy subjects. The analysis is performed with the help of developed software for determining the nonlinear characteristics of the studied signals and the formation of graphical assessment of the health status of patients.Научното изследване е проведено като част от проекта „Изследване на приложението на нови математически методи за анализ на кардиологични данни“ № КП-06-Н22/5 от 07.12.2018 г., финансиран от Фонд „Научни Изследвания“

Анализ на вариабилността на сърдечната честота с използване на фотоплетизмографски и електрокардиографски сигнали

Heart rate variability (HRV) is a non-invasive marker for monitoring the physiological condition of patients and assisting in the diagnosis of cardiovascular disease. The aim of this study was to investigate the consistency between HRV parameters based on photoplethysmographic (PPG) and electrocardiographic (ECG) signals. Parameters from the linear analysis in the time domain were studied. The time domain indices are standardized and widely used to calculate HRV. These indices are statistical and geometric measurements. The statistical calculations of the successive heart rate intervals (RR interval series) are strictly interrelated (SDNN, SDANN, RMSSD, pNN50), while geometric measurements are based on TINN and HRVTi parameters. The ECG and PPG signals of a healthy individual were examined. The obtained results show a very good agreement between the HRV parameters obtained from the two types of signals. In view of this finding, it can be concluded that the PPG offers an alternative ECG option for HRV analysis without compromising accuracy. The correspondence between the studied parameters applied to the two types of signals provides potential support for the idea of using PPG instead of ECG in the extraction and analysis of HRV in outpatient cardiac monitoring of healthy individuals and patients with cardiovascular disease. A study of two groups of individuals: healthy and with cardiovascular disease based on PPG signals by applying the method: analysis in the time domain. The obtained results show that with the used method the two studied groups of subjects can be distinguished.Научното изследване е проведено като част от проекта „Изследване на приложението на нови математически методи за анализ на кардиологични данни“ по договор № КП-06-Н22/5 от 07.12.2018 г., финансиран от Фонд „Научни Изследвания“

Фактори, влияещи върху вариабилността на сърдечната честота

The heart rate is individual for each person and it is influenced by various factors that lead to its increase or decrease. Good cardiac function is a prerequisite for a healthy life, and heart rate variability (HRV) analysis is a powerful tool for assessing the autonomic nervous system (ANS), in which the sympathetic and parasympathetic systems interact to regulate cardiac function of the vascular system. A high HRV is associated with a good state of health, while a low HRV is associated not only with pathological conditions in the activity of the cardiovascular system, but also with a number of other factors, such as: overweight, type 2 diabetes, stress and others. Tracking HRV over time and matching segments of data related to specific activities or life events can provide unique information about a person's physical and psychological health. On the basis of the obtained results, it can be concluded that the indices of HRV can be used as non-specific indicators of the impact of factors of a different nature on the human body.Научното изследване е проведено като част от проекта „Изследване на приложението на нови математически методи за анализ на кардиологични данни“ № КП-06-Н22/5 от 07.12.2018 г., финансиран от Фонд „Научни Изследвания“

Parameter optimization for local polynomial approximation based intersection confidence interval filter using genetic algorithm: an application for brain MRI image de-noising

Magnetic resonance imaging (MRI) is extensively exploited for more accuratepathological changes as well as diagnosis. Conversely, MRI suffers from variousshortcomings such as ambient noise from the environment, acquisition noise from theequipment, the presence of background tissue, breathing motion, body fat, etc.Consequently, noise reduction is critical as diverse types of the generated noise limit the efficiency of the medical image diagnosis. Local polynomial approximation basedintersection confidence interval (LPA-ICI) filter is one of the effective de-noising filters.This filter requires an adjustment of the ICI parameters for efficient window size selection.From the wide range of ICI parametric values, finding out the best set of tunes values is itselfan optimization problem. The present study proposed a novel technique for parameteroptimization of LPA-ICI filter using genetic algorithm (GA) for brain MR imagesde-noising. The experimental results proved that the proposed method outperforms theLPA-ICI method for de-noising in terms of various performance metrics for different noisevariance levels. Obtained results reports that the ICI parameter values depend on the noisevariance and the concerned under test image

Chinese-chi and Kundalini yoga Meditations Effects on the Autonomic Nervous System: Comparative Study

Cardiac disease is one of the major causes for death all over the world. Heart rate variability (HRV) is a significant parameter that used in assessing Autonomous Nervous System (ANS) activity. Generally, the 2D Poincare′ plot and 3D Poincaré plot of the HRV signals reflect the effect of different external stimuli on the ANS. Meditation is one of such external stimulus, which has different techniques with different types of effects on the ANS. Chinese Chi-meditation and Kundalini yoga are two different effective meditation techniques. The current work is interested with the analysis of the HRV signals under the effect of these two based on meditation techniques. The 2D and 3D Poincare′ plots are generally plotted by fitting respectively an ellipse/ellipsoid to the dense region of the constructed Poincare′ plot of HRV signals. However, the 2D and 3D Poincaré plots sometimes fail to describe the proper behaviour of the system. Thus in this study, a three-dimensional frequency-delay plot is proposed to properly distinguish these two famous meditation techniques by analyzing their effects on ANS. This proposed 3D frequency-delay plot is applied on HRV signals of eight persons practicing same Chi-meditation and four other persons practising same Kundalini yoga. To substantiate the result for larger sample of data, statistical Student t-test is applied, which shows a satisfactory result in this context. The experimental results established that the Chi-meditation has large impact on the HRV compared to the Kundalini yoga

GRAPHICAL METHODS FOR NON-LINEAR ANALYSIS OF ELECTROCARDIOGRAPHIC DATA

INTRODUCTION: One of the most widely used methods for studying the bioelectric activity of the heart is the electrocardiogram (ECG). An important diagnostic parameter that can be determined by the ECG is heart rate variability (HRV), which takes into account the difference between successive strokes of the heart. Changing HRV can be an indicator of a number of disease states, such as low HRV levels can show poor health that is not only associated with cardiovascular disease but also with other diseases such as internal, nervous, mental, and other disorders.&#x0D; OBJECTIVES:  The subject of this article is the study of 24-hour ECG signals by applying non-linear graphical methods for HRV analysis. The non-linear graphical methods aim at obtaining graphical and quantitative information on the cardiovascular status of the study groups to complement the information obtained from traditional linear methods of analysis.&#x0D; METHODS: For the non-linear analysis of HRV, graphical methods were used: Poincaré plot and Recurrence plot were used, which are suitable for the examination of electrocardiographic signals. Two groups of people were investigated: 20 healthy controls and 20 patients with arrhythmia.&#x0D; RESULTS: Based on the nonlinear analysis of RR time series, the graphs of a healthy subject and a patient with arrhythmia were constructed using the Poincare plot. The graph of the healthy subject has the shape of a comet, while the graph of the patient with arrhythmia has the shape of a fan. The quantitative characteristics of patients with arrhythmia significantly change compared to the healthy subjects. The SD1 (p &lt;0.003) and SD2 (p &lt;0.0001) values decreased in patients with arrhythmia compared to the healthy controls. This reduction leads to reduction of the areas of the ellipse in the patients with arryhthmia. The ratio of SD1/SD2 (p &lt;0.05) is lower for the healthy controls. The graphs obtained by the Recurrence plot of the investigated signals differ in healthy subjects and in patients with arrhythmia. For a healthy subject, the graph has a diagonal line and fewer squares showing a higher HRV. The graph of a patient with arrhythmia contains more squares, indicating periodicity in the investigated signal. The Recurrence Quantification Analysis showed that the values of the investigated parameters DET% (p &lt;0.0001), REC% (p &lt;0.0001) and ENTR (p &lt;0.001) in patients with arrhythmia are increased.&#x0D; CONCLUSIONS:  The importance of the graphical nonlinear methods used for the analysis of HRV consists in forming a parametric and graphical assessment of the patient's health status.</jats:p