Mathematical Modeling of Electrocardiograms: A Numerical Study (original) (raw)

Numerical simulation of electrocardiograms

MS&A, 2012

This chapter presents a concise overview of various mathematical and numerical problems raised by the simulation of electrocardiograms (ECGs). A model for the propagation of the electrical activation in the heart and in the torso is proposed. Some of its mathematical properties are analyzed. This model is not aimed at reproducing the complex phenomena taking place at the microscopic level. It has been devised to produce realistic healthy ECGs, and some pathological ones, with a reasonable level of complexity. It relies on various assumptions that are carefully discussed through their impact on the ECGs. The coupling between the heart and the torso is a critical numerical issue which is addressed. In particular efficient coupling strategies based on explicit algorithms are presented and analyzed. The chapter ends with some preliminary results of a reduced order model based on the Proper Orthogonal Decomposition (POD) method.

Mathematical Modeling and Utility of the Derived 22-LEAD Electrocardiogram

Journal of the American College of Cardiology, 2011

Background: The cardiac electrical field is dipolar and is measured by the electrocardiogram (ECG) which may be described by a 3 lead-vector space. There are 22 leads used in clinical practice including the standard 12-lead ECG, right heart leads V3R-V6R, posterior leads V7-V9, and the vectorcardiographic (VCG) leads X, Y, Z. It would be advantageous to derive these 22 ECG leads from just 3 measured leads using a universal patient coefficient matrix (UPCM) that can be computed using simplex optimization (SOP). The objective is to derive the ECG (dECG) from 3 measured leads using a SOP-computed UPCM and calculate the quantitative and qualitative correlations with the measured ECG (mECG). Methods: A total of 371 mECGs of varying morphology for both men and women age 18 and older were acquired including 371 standard 12-lead ECGs, 353 VCGs, 75 right heart ECGs, and 34 posterior ECGs. The ECG morphologies included normals, acute MIs, LVH, bundle branch blocks, paced beats, PVCs, and non-specific STT types. Each ECG was interpreted by 2 physicians who were blinded reference standards. The SOP technique was used to derive a UPCM from an additional training set of 20 ECGs. Leads I, aVF, and V2 from the mECGs were chosen as the 3 lead-vector basis orthogonal lead set from which the dECGs were synthesized. The derived vs. measured test case ECGs were compared using Pearson and Kappa statistics. Results: The dECGs showed high correlation with mECGs overall by Pearson correlations (0.84-0.88). No clinically significant differences were noted in 98.1% of the dECGs. ECG rate, rhythm, segment, and axis interpretations showed 100% correlation. Acute MI differentiation showed 100% correlation. Kappa analysis of the mECG vs. dECG showed high overall correlations (0.73-1.00). Conclusions: The 22-lead ECG can be derived from just 3 measured leads using the SOP technique. The comparison of the mECGs and dECGs shows high quantitative and qualitative correlations. Using this technology a 22-lead derived ECG can be displayed instantaneously in real-time to enhance patient observation capabilities and will allow for a convenient and cost effective acquisition and analysis of the ECG in telemetry and critical care areas of health care.

Design a simple model of electrocardiograph

Design a Simple Model of Electrocardiograph

The electrocardiograph is an electronic instrument used to produce a written record of the electrical activity of the heart. The electrical waveform produced by the heart is called an electrocardiogram or ECG (sometimes EKG after the German spelling). The various features of the ECG can be related to the pumping activity of the heart and is thus used in the diagnosis of the heart disease. The electrocardiograph system described in this module is a simplified one, but it will perform the same basic functions as a more sophisticated commercial instrument. It has been designed to demonstrate the underlying principles of electrocardiograph operation in terms of the functions of individual stages and their interrelationships in the system. Although the simplified version may not include special features found on more complex commercial instruments, an understanding of the operating principles of this model should help in properly using commercial instruments and in understanding its oper...

Modeling as a Tool for Understanding of Changes in ECG Signals

2015

An updated program for modeling simplified heart geometry and simulation of action potentials propagation is presented. The implemented model allows simulation of geometry changes as well as changes in action potentials amplitude and duration. In propagation simulation real conduction velocities can be considered. Two different pathological situations were simulated using the model. First, only geometrical changes were applied simulating the left ventricular hypertrophy, second, only action potentials properties simulating activation propagation velocity were changed. The resulting ECG signals on the torso were very similar. It is shown that modeling and simulation is useful for explaining of discrepant observations in clinical diagnostics.

Towards the Numerical Simulation of Electrocardiograms

Functional Imaging and Modeling of the Heart

We present preliminary results of the numerical simulation of electrocardiograms (ECG). We consider the bidomain equations to model the electrical activity of the heart and a Laplace equation for the torso. The ionic activity is modeled with a Mitchell-Schaeffer dynamics. We use adaptive semi-implicit BDF schemes for the time discretization and a Neumann-Robin domain decomposition algorithm for the space discretization. The obtained ECGs, although not completely satisfactory, are promising. They allow to discuss various modelling assumptions, for example the relevance of cells heterogeneity, the fiber orientation and the coupling conditions with the torso.

Model assisted biosignal analysis of atrial electrograms

tm - Technisches Messen, 2016

Cardiologists measure electric signals inside the human heart aiming at a better diagnosis and optimized therapy of atrial arrhythmias like atrial flutter and atrial fibrillation. The catheters that are used for this purpose are improving: now they are able to pick up the electric signals at up to 64 positions inside the heart simultaneously. The patterns of electric depolarization are sometimes very simple, comparable to plane waves. But in case of patients with severe atrial arrhythmias they can be quite complex: U-turns around a line of block, ectopic centres, break throughs, reentry circuits, rotors, fractionated signals and chaotic patterns are often observed. Methods of biosignal analysis can support the cardiologists in classifying the signals and extract information of high diagnostic relevance. Computer models of the electrophysiology of the human heart can serve to design better algorithms for data analysis and to test algorithms, because the “ground truth” is known.

Physics of Electrocardiogram (ECG)

Physics of ECG , Physics of Electrocardiogram , Lectures of Clinical and Physics of Imaging , LinkedIn , Physics of Diagnostic Radiology , Electrocardiography . Health Science , Health Physics , 2024

- Electrocardiography (ECG or EKG) is a recording of the electrical activity of the heart taken from a variety of angles, such that a 12‑lead ECG 'looks' at the heart electrically through a full 360 degrees. The recording is traditionally made over several seconds to allow assessment of the cardiac rhythm. - It is a non-invasive procedure undertaken by attaching electrodes to the skin of the patient at predefined points, and recording the output via an electrocardiographic machine. - The ECG machine relates the signal received at any given point, electrode, to that at a predefined neutral electrode, producing a resultant vector that is displayed and recorded.