Detection of Atrial Fibrillation Episodes based on 3D Algebraic Relationships between Cardiac Intervals.

In this study, the notion of perfect matrices of Lagrange differences is employed to detect atrial fibrillation episodes based on three ECG parameters (JT interval, QRS interval, RR interval). The case study comprised 8 healthy individuals and 7 unhealthy individuals, and the mean and standard deviation of age was 65.84 ± 1.4 years, height was 1.75 ± 0.12 m, and weight was 79.4 ± 0.9 kg. Initially, it was demonstrated that the sensitivity of algebraic relationships between cardiac intervals increases when the dimension of the perfect matrices of Lagrange differences is extended from two to three. The baseline dataset was established using statistical algorithms for classification by means of the developed decision support system. The classification helps to determine whether the new incoming candidate has indications of atrial fibrillation or not. The application of probability distribution graphs and semi-gauge indicator techniques aided in visualizing the categorization of the new candidates. Though the study's data are limited, this work provides a strong foundation for (1) validating the sensitivity of the perfect matrices of Lagrange differences, (2) establishing a robust baseline dataset for supervised classification, and (3) classifying new incoming candidates within the classification framework. From a clinical standpoint, the developed approach assists in the early detection of atrial fibrillation in an individual.

The Complexity of the Arterial Blood Pressure Regulation during the Stress Test.

In this study, two categories of persons with normal and high ABP are subjected to the bicycle stress test (9 persons with normal ABP and 10 persons with high ABP). All persons are physically active men but not professional sportsmen. The mean and the standard deviation of age is 41.11 ± 10.21 years; height 178.88 ± 0.071 m; weight 80.53 ± 10.01 kg; body mass index 25.10 ± 2.06 kg/m2. Machine learning algorithms are employed to build a set of rules for the classification of the performance during the stress test. The heart rate, the JT interval, and the blood pressure readings are observed during the load and the recovery phases of the exercise. Although it is obvious that the two groups of persons will behave differently throughout the bicycle stress test, with this novel study, we are able to detect subtle variations in the rate at which these changes occur. This paper proves that these differences are measurable and substantial to detect subtle differences in the self-organization of the human cardiovascular system. It is shown that the data collected during the load phase of the stress test plays a more significant role than the data collected during the recovery phase. The data collected from the two groups of persons are approximated by Gaussian distribution. The introduced classification algorithm based on the statistical analysis and the triangle coordinate system helps to determine whether the reaction of the cardiovascular system of a new candidate is more pronounced by an increased heart rate or an increased blood pressure during the stress test. The developed approach produces valuable information about the self-organization of human cardiovascular system during a physical exercise.

Visualization of Complex Processes in Cardiovascular System during Electrical Auricular Vagus Nerve Stimulation.

The analysis of human physiological systems from the point of view of complex systems theory remains a very ambitious task. The complexity of the problem often encourages the use of innovative mathematical methods analyzing the processes that take place in space and time. The main goal of this paper is to visualize the cardiovascular system during auricular vagus nerve stimulation (aVNS) using the matrix differences to evaluate the dynamic signal interfaces by cointegrating the initial signal data into the matrices during each case. Algebraic relationships between RR/JT and JT/QRS cardiac intervals are used not only to track the cardiovascular changes during aVNS but also to characterize individual features of the person during the transit through the therapy. This paper presents the computational techniques that can visualize the complex dynamical processes taking place in the cardiovascular system using the electrical aVNS therapy. Four healthy volunteers participated in two verum and two placebo experiments. We discovered that the body's reaction to the stimulation was very different in each of the cases, but the presented techniques opened new possibilities for a novel interpretation of the dynamics of the cardiovascular system.

The characterization of the transit through the anaerobic threshold based on relationships between RR and QRS cardiac intervals.

This paper aims to develop a novel computational technique for the detection of the transit through the anaerobic threshold. This technique uses only cardiac intervals derived from the electrocardiogram and is based on algebraic relationships between RR and QRS intervals. Electrocardiograms are measured during the load and the recovery processes. Algebraic relationships between cardiac intervals are used not only to identify the anaerobic threshold but also to characterise individual features of the person during the transit through the threshold. The ratio between carbon dioxide and oxygen in the exhaled air is used to validate the results. The algebraic relationship between cardiac intervals serves as a stand-alone indicator for both the determination of the anaerobic threshold and the characterization of the performance of the person during the load and the recovery processes.