Generation of ECG signals from a reaction-diffusion model spatially discretized

Tensor cardiography: A novel ECG analysis of deviations in collective myocardial action potential transitions based on point processes and cumulative distribution functions

To improve clinical diagnoses, assessments of potential cardiac disease risk, and predictions of lethal arrhythmias, the analysis of electrocardiograms (ECGs) requires a more accurate method of weighting waveforms to efficiently detect abnormalities that appear as minute strains in the waveforms. In addition, the inverse problem of estimating the myocardial action potential from the ECG has been a longstanding challenge. To analyze the variance of the ECG waveforms and to estimate collective myocardial action potentials (APs) from the ECG, we designed a model equation incorporating the probability densities of Gaussian functions of time-series point processes in the cardiac cycle and dipoles of the collective APs in the myocardium. The equation, which involves taking the difference between the cumulative distribution functions (CDFs) that represent positive endocardial and negative epicardial potentials, fits both R and T waves. The mean, standard deviation, weights, and level of each cumulative distribution function (CDF) are metrics for the variance of the transition state of the collective myocardial AP. Clinical ECGs of myocardial ischemia during coronary intervention show abnormalities in the aforementioned specific elements of the tensor associated with repolarization transition variance earlier than in conventional indicators of ischemia. The tensor can be used to evaluate the beat-to-beat dynamic repolarization changes between the ventricular epi and endocardium in terms of the Mahalanobis distance (MD). This tensor-based cardiography that uses the differences between CDFs to show changes in collective myocardial APs has the potential to be a new analysis tool for ECGs.

Modeling the Electrical Activity of the Heart via Transfer Functions and Genetic Algorithms

Although healthcare and medical technology have advanced significantly over the past few decades, heart disease continues to be a major cause of mortality globally. Electrocardiography (ECG) is one of the most widely used tools for the detection of heart diseases. This study presents a mathematical model based on transfer functions that allows for the exploration and optimization of heart dynamics in Laplace space using a genetic algorithm (GA). The transfer function parameters were fine-tuned using the GA, with clinical ECG records serving as reference signals. The proposed model, which is based on polynomials and delays, approximates a real ECG with a root-mean-square error of 4.7% and an R2 value of 0.72. The model achieves the periodic nature of an ECG signal by using a single periodic impulse input. Its simplicity makes it possible to adjust waveform parameters with a predetermined understanding of their effects, which can be used to generate both arrhythmic patterns and healthy signals. This is a notable advantage over other models that are burdened by a large number of differential equations and many parameters.

Quantum conditional generative adversarial network based on patch method for abnormal electrocardiogram generation

To address the scarcity and class imbalance of abnormal electrocardiogram (ECG) databases, which are crucial in AI-driven diagnostic tools for potential cardiovascular disease detection, this study proposes a novel quantum conditional generative adversarial algorithm (QCGAN-ECG) for generating abnormal ECG signals. The QCGAN-ECG constructs a quantum generator based on patch method. In this method, each sub-generator generates distinct features of abnormal heartbeats in different segments. This patch-based generative algorithm conserves quantum resources and makes QCGAN-ECG practical for near-term quantum devices. Additionally, QCGAN-ECG introduces quantum registers as control conditions. It encodes information about the types and probability distributions of abnormal heartbeats into quantum registers, rendering the entire generative process controllable. Simulation experiments on Pennylane demonstrated that the QCGAN-ECG could generate completely abnormal heartbeats with an average accuracy of 88.8%. Moreover, the QCGAN-ECG can accurately fit the probability distribution of various abnormal ECG data. In the anti-noise experiments, the QCGAN-ECG showcased outstanding robustness across various levels of quantum noise interference. These results demonstrate the effectiveness and potential applicability of the QCGAN-ECG for generating abnormal ECG signals, which will further promote the development of AI-driven cardiac disease diagnosis systems. The source code is available at github.com/VanSWK/QCGAN_ECG.

Model-Driven Analysis of ECG Using Reinforcement Learning

Modeling is essential to better understand the generative mechanisms responsible for experimental observations gathered from complex systems. In this work, we are using such an approach to analyze the electrocardiogram (ECG). We present a systematic framework to decompose ECG signals into sums of overlapping lognormal components. We use reinforcement learning to train a deep neural network to estimate the modeling parameters from an ECG recorded in babies from 1 to 24 months of age. We demonstrate this model-driven approach by showing how the extracted parameters vary with age. From the 751,510 PQRST complexes modeled, 82.7% provided a signal-to-noise ratio that was sufficient for further analysis (>5 dB). After correction for multiple tests, 10 of the 24 modeling parameters exhibited statistical significance below the 0.01 threshold, with absolute Kendall rank correlation coefficients in the [0.27, 0.51] range. These results confirm that this model-driven approach can capture sensitive ECG parameters. Due to its physiological interpretability, this approach can provide a window into latent variables which are important for understanding the heart-beating process and its control by the autonomous nervous system.

Using evolution rule in complex time series comparison

Complex time series appear in numerous applications and are related to some essential physiological and natural systems. Their comparison faces big challenges: 1) with different complexity; 2) with significant phase shift in one series or shift∖on the time axis. Existing methods work well for periodic time-series data, but fail to produce satisfactory results in complex time-series. In this paper, we introduce a novel distance function based on the evolution rule for complex time series comparison. Here, the evolution rule, as the innate generative mechanism of time series, is creatively used to characterize complicated dynamics from complex time series. The comparison includes different level comparisons: the coarse level is to compare the difference in complexity, and the fine level is to compare the difference in actual evolution behavior. The proposed method is inspired by the observation that similar sequences come from the same source, e.g. a person’s heart, in the case of ECG, thus two similar series will have the same innate generative mechanism. The performance has been verified by the conducting experiments, and the experiment results show that the proposed method is superior to the previously existing methods in clustering and classification on some real data sets.

Dynamical behavior analysis of the heart system by the bifurcation structures

The functioning of the heart rhythm can exhibit a wide variety of dynamic behaviours under certain conditions. In the case of rhythm disorders or cardiac arrhythmias, the natural rhythm of the heart is usually involved in the sinoatrial node, the atrioventricular node, the atria of the carotid sinus, etc. The study of heart related disorders requires an important analysis of its rhythm because the regularity of cardiac activity is conditioned by a large number of factors. The cardiac system is made up of a combination of nodes ranging from the sinus node, the atrioventricular node to its Purkinje bundles, which interact with each other via communicative aspects. Due to the nature of their respective dynamics, the above are treated as self-oscillating elements and modelled by nonlinear oscillators. By modelling the cardiac conduction system as a model of three nonlinear oscillators coupled by delayed connections and subjected to external stimuli depicting the behavior of a pacemaker, its dynamic behavior is studied in this paper by nonlinear analysis tools. From an electrocardiogram (ECG) assessment, the heart rhythm reveals normal and pathological rhythms. Three forms of ventricular fibrillation, ventricular flutter, ventricular tachycardia and atrial fibrillation are observed. The results are confirmed by the respective maximum Lyapunov exponents. Considering the cardiac nodes as microchips, using microcontroller simulation technology, the cardiac conduction system was modelled as a network of four ATmega 328P microcontrollers. A similarity with the results obtained numerically can be observed.

Classical harmonic three-body system: an experimental electronic realization

The classical three-body harmonic system in [Formula: see text] ([Formula: see text]) with finite rest lengths and zero total angular momentum [Formula: see text] is considered. This model describes the dynamics of the [Formula: see text] near-equilibrium configurations of three point masses [Formula: see text] with arbitrary pairwise potential [Formula: see text] that solely depends on the relative distances between bodies. It exhibits an interesting mixed regular and chaotic dynamics as a function of the energy and the system parameters. The corresponding harmonic quantum system plays a fundamental role in atomic and molecular physics. In this work we report on a novel electronic experimental realization of the model as a complementary tool to analyze the rich dynamics of the classical system. Our setup allows us to experimentally explore different regions of behavior due to the fact that the intrinsic parameters and initial states of the system are independently set by voltage inputs. Chaotic and periodic motions are characterized employing time series, phase planes, and the largest Lyapunov exponents as a function of the energy and system parameters. The results show an excellent qualitative as well as quantitative agreement between theory and experiment.

ECG Patient Simulator Based on Mathematical Models

In this work, we propose a versatile, low-cost, and tunable electronic device to generate realistic electrocardiogram (ECG) waveforms, capable of simulating ECG of patients within a wide range of possibilities. A visual analysis of the clinical ECG register provides the cardiologist with vital physiological information to determine the patient's heart condition. Because of its clinical significance, there is a strong interest in algorithms and medical ECG measuring devices that acquire, preserve, and process ECG recordings with high fidelity. Bearing this in mind, the proposed electronic device is based on four different mathematical models describing macroscopic heartbeat dynamics with ordinary differential equations. Firstly, we produce full 12-lead ECG profiles by implementing a model comprising a network of heterogeneous oscillators. Then, we implement a discretized reaction-diffusion model in our electronic device to reproduce ECG waveforms from various rhythm disorders. Finally, in order to show the versatility and capabilities of our system, we include two additional models, a ring of three coupled oscillators and a model based on a quasiperiodic motion, which can reproduce a wide range of pathological conditions. With this, the proposed device can reproduce around thirty-two cardiac rhythms with the possibility of exploring different parameter values to simulate new arrhythmias with the same hardware. Our system, which is a hybrid analog-digital circuit, generates realistic ECG signals through digital-to-analog converters whose amplitudes and waveforms are controlled through an interactive and friendly graphic interface. Our ECG patient simulator arises as a promising platform for assessing the performance of electrocardiograph equipment and ECG signal processing software in clinical trials. Additionally the produced 12-lead profiles can be tested in patient monitoring systems.

Conditional generation of medical time series for extrapolation to underrepresented populations

The widespread adoption of electronic health records (EHRs) and subsequent increased availability of longitudinal healthcare data has led to significant advances in our understanding of health and disease with direct and immediate impact on the development of new diagnostics and therapeutic treatment options. However, access to EHRs is often restricted due to their perceived sensitive nature and associated legal concerns, and the cohorts therein typically are those seen at a specific hospital or network of hospitals and therefore not representative of the wider population of patients. Here, we present HealthGen, a new approach for the conditional generation of synthetic EHRs that maintains an accurate representation of real patient characteristics, temporal information and missingness patterns. We demonstrate experimentally that HealthGen generates synthetic cohorts that are significantly more faithful to real patient EHRs than the current state-of-the-art, and that augmenting real data sets with conditionally generated cohorts of underrepresented subpopulations of patients can significantly enhance the generalisability of models derived from these data sets to different patient populations. Synthetic conditionally generated EHRs could help increase the accessibility of longitudinal healthcare data sets and improve the generalisability of inferences made from these data sets to underrepresented populations.

Transmission and Decryption of the Audio Signal Masked with ECG by FDM Method

Today, the use of these methods as hybrids has provided the motivation to be a solution to important problems, since the existing methods are insufficient at some points in ensuring the security of personal data. In data security, the inability to decrypt and decrypt the signal to be encrypted retrospectively has always been the subject of research in terms of privacy. At this point, it was preferred to use the electrocardiography (ECG) signal, which is a signal that shows the vital signs of the human body and is also difficult to copy. In the study, firstly, the emulator circuit was obtained by using the mathematical model of the ECG signal. With this obtained signal, the audio signals are masked. The audio signal masked on the transmitter side and the signals providing synchronization were transmitted to the receiver side over a single channel using the frequency division multiplexing (FDM) method. Then, the sliding mode control (SMC) method was chosen for the synchronization of the ECG emulator circuits on the receiver and transmitter side. Histogram, spectral, mean square error (MSE), peak signal to noise ratio (PSNR), key space and key sensitivity, NSCR (number of sample change rate), UACI (unified average changing intensity) and PESQ (perceptual evaluation of speech quality) analyses were used to check the accuracy of the system. These analyses showed that the ECG encoding method has faster unit change, reduces synchronization time, minimizes losses and improves the security of the masked signal compared to other methods sent from two channels. Finally, use of an arrhythmia ECG signal for the synchronization signal on both the transmitter and receiver sides, the synchronization of this signal with the SMC method and the testing of a live audio recording in addition to the conversation, distinguishes the study from other existing studies and reveals its originality.

Interactive Effects of Heart Rate Variability and P-QRS-T on the Power Density Spectra of ECG Signals

Different from the traditional methods of assessing the cardiac activities through heart rhythm statistics or P-QRS-T complexes separately, this study demonstrates their interactive effects on the power density spectrum (PDS) of ECG signal with applications for the diagnosis of ST-segment elevation myocardial infarction (STEMI) diseases. Firstly, a mathematical model of the PDS of ECG signal with a random pacing pulse train (PPT) mimicking S-A node firings was derived. Secondly, an experimental PDS analysis was performed on clinical ECG signals from 49 STEMI patients and 42 healthy subjects in PTB Diagnostic Database. It was found that besides the interactive effects which are consistent between theoretical and experimental results, the ECG PDSs of STEMI patients exhibited consistently significant power shift towards lower frequency range in ST-elevated leads in comparison with those of reference leads and leads of health subjects with the highest median frequency shift ratios at 51.39 12.94% found in anterior MI. Thirdly, the results of ECG simulation with systematic changes in PPT firing statistics over various lengths of ECG data ranging from 10s to 60 mins revealed that the mean and median frequency parameters were less affected by the heart rhythm statistics and the data length but more depended on the alterations of P-QRS-T complexes, which were further confirmed on 33 more STEMI patients in European ST-T Database, demonstrating that the frequency indexes could be potentially used as alternative indicators for STEMI diagnosis even with ultra-short-term ECG recordings suitable for wearable and mobile health applications in living-free environments.

Multi-Chaotic Analysis of Inter-Beat (R-R) Intervals in Cardiac Signals for Discrimination between Normal and Pathological Classes

Cardiac signals have complex structures representing a combination of simpler structures. In this paper, we develop a new data analytic tool that can extract the complex structures of cardiac signals using the framework of multi-chaotic analysis, which is based on the p-norm for calculating the largest Lyapunov exponent (LLE). Appling the p-norm is useful for deriving the spectrum of the generalized largest Lyapunov exponents (GLLE), which is characterized by the width of the spectrum (which we denote by W). This quantity measures the degree of multi-chaos of the process and can potentially be used to discriminate between different classes of cardiac signals. We propose the joint use of the GLLE and spectrum width to investigate the multi-chaotic behavior of inter-beat (R-R) intervals of cardiac signals recorded from 54 healthy subjects (hs), 44 subjects diagnosed with congestive heart failure (chf), and 25 subjects diagnosed with atrial fibrillation (af). With the proposed approach, we build a regression model for the diagnosis of pathology. Multi-chaotic analysis showed a good performance, allowing the underlying dynamics of the system that generates the heart beat to be examined and expert systems to be built for the diagnosis of cardiac pathologies.