Simulation of QRST Integral Maps With a Membrane-Based Computer Heart Model Employing Parallel Processing

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.

SILICOFCM platform, multiscale modeling of left ventricle from echocardiographic images and drug influence for cardiomyopathy disease

BACKGROUND AND OBJECTIVE

In silico clinical trials are the future of medicine and virtual testing and simulation are the future of medical engineering. The use of a computational platform can reduce costs and time required for developing new models of medical devices and drugs. The computational platform, which is one of the main results of the SILICOFCM project, was developed using state-of-the-art finite element modeling for macro simulation of fluid-structure interaction with micro modeling at the molecular level for drug interaction with the cardiac cells. SILICOFCM platform is using for risk prediction and optimal drug therapy of familial cardiomyopathy in a specific patient.

METHODS

In order to obtain 3D image reconstruction, the U-net architecture was used to determine geometric parameters for the left ventricle which were extracted from the echocardiographic apical and M-mode views. A micro-mechanics cellular model which includes three kinetic processes of sarcomeric proteins interactions was developed. It allows simulation of the drugs which are divided into three major groups defined by the principal action of each drug. Fluid-solid coupling for the left ventricle was presented. A nonlinear material model of the heart wall that was developed by using constitutive curves which include the stress-strain relationship was used.

RESULTS

The results obtained with the parametric model of the left ventricle where pressure-volume (PV) diagrams depend on the change of Ca2+ were presented. It directly affects the ejection fraction. The presented approach with the variation of the left ventricle (LV) geometry and simulations which include the influence of different parameters on the PV diagrams are directly interlinked with drug effects on the heart function. It includes different drugs such as Entresto and Digoxin that directly affect the cardiac PV diagrams and ejection fraction.

CONCLUSIONS

Computational platforms such as the SILICOFCM platform are novel tools for risk prediction of cardiac disease in a specific patient that will certainly open a new avenue for in silico clinical trials in the future.

An ECG generative model of myocardial infarction

Background and Objective Computer-aided diagnosis (CAD) of Myocardial Infarction (MI) using machine learning depends on a large amount of clinical Electrocardiogram (ECG) data. Existing infarct ECG databases face the problem of class imbalance. Data augmentation using generative simulation models is a new approach to effectively address this problem. Methods A multiscale ECG generative model was established for ECG data augmentation. In the cellular layer, an ischemic Action Potential (AP) model was established to generate APs in cardiomyocytes with different transmural regions of infraction or different ischemic durations. In the tissue layer, a probability-driven cellular automata excitation propagation model was established to simulate the propagation speed and direction of excitation. An infarct tissue model and a coronary artery model were established to describe the spatiotemporal diversity of MI. A ventricle model, a human torso model, and a computational model of surface ECG based on field source theory were established in the heart-torso layer. Results The model generated pathological 12-lead ECGs of MI with different topography and different extent. When simulating different ventricular wall infarction, the lesions appear in the same leads as the clinical 12-lead ECG. The ST-segment decreases and the T-wave amplitude decreases, similar to the clinical ECG features when simulating subendocardial ischemia. The average fidelity of the 12-lead ECG the model generated is 95.6%, according to the designed DTW-GRA distance algorithm. Conclusions The generative model considers the electrophysiological properties of the natural heart, the pathology of myocardial infarction, and the diversity of clinical ECGs. The model can provide many reliable samples for machine learning of MI.

The openCARP simulation environment for cardiac electrophysiology

BACKGROUND AND OBJECTIVE

Cardiac electrophysiology is a medical specialty with a long and rich tradition of computational modeling. Nevertheless, no community standard for cardiac electrophysiology simulation software has evolved yet. Here, we present the openCARP simulation environment as one solution that could foster the needs of large parts of this community.

METHODS AND RESULTS

openCARP and the Python-based carputils framework allow developing and sharing simulation pipelines which automate in silico experiments including all modeling and simulation steps to increase reproducibility and productivity. The continuously expanding openCARP user community is supported by tailored infrastructure. Documentation and training material facilitate access to this complementary research tool for new users. After a brief historic review, this paper summarizes requirements for a high-usability electrophysiology simulator and describes how openCARP fulfills them. We introduce the openCARP modeling workflow in a multi-scale example of atrial fibrillation simulations on single cell, tissue, organ and body level and finally outline future development potential.

CONCLUSION

As an open simulator, openCARP can advance the computational cardiac electrophysiology field by making state-of-the-art simulations accessible. In combination with the carputils framework, it offers a tailored software solution for the scientific community and contributes towards increasing use, transparency, standardization and reproducibility of in silico experiments.

Physiological Artifacts and the Implications for Brain-Machine-Interface Design

The accurate measurement of brain activity by Brain-Machine-Interfaces (BMI) and closed-loop Deep Brain Stimulators (DBS) is one of the most important steps in communicating between the brain and subsequent processing blocks. In conventional chest-mounted systems, frequently used in DBS, a significant amount of artifact can be induced in the sensing interface, often as a common-mode signal applied between the case and the sensing electrodes. Attenuating this common-mode signal can be a serious challenge in these systems due to finite common-mode-rejection-ratio (CMRR) capability in the interface. Emerging BMI and DBS devices are being developed which can mount on the skull. Mounting the system on the cranial region can potentially suppress these induced physiological signals by limiting the artifact amplitude. In this study, we model the effect of artifacts by focusing on cardiac activity, using a current- source dipole model in a torso-shaped volume conductor. Performing finite element simulation with the different DBS architectures, we estimate the ECG common mode artifacts for several device architectures. Using this model helps define the overall requirements for the total system CMRR to maintain resolution of brain activity. The results of the simulations estimate that the cardiac artifacts for skull-mounted systems will have a significantly lower effect than non-cranial systems that include the pectoral region. It is expected that with a pectoral mounted device, a minimum of 60-80 dB CMRR is required to suppress the ECG artifact, depending on device placement relative to the cardiac dipole, while in cranially mounted devices, a 0 dB CMRR is sufficient, in the worst-case scenario. In addition, the model suggests existing commercial devices could optimize performance with a right-hand side placement. The methods used for estimating cardiac artifacts can be extended to other sources such as motion/muscle sources. The susceptibility of the device to artifacts has significant implications for the practical translation of closed-loop DBS and BMI, including the choice of biomarkers, the system design requirements, and the surgical placement of the device relative to artifact sources.

Electrocardiographic imaging for cardiac arrhythmias and resynchronization therapy

Use of the 12-lead electrocardiogram (ECG) is fundamental for the assessment of heart disease, including arrhythmias, but cannot always reveal the underlying mechanism or the location of the arrhythmia origin. Electrocardiographic imaging (ECGi) is a non-invasive multi-lead ECG-type imaging tool that enhances conventional 12-lead ECG. Although it is an established technology, its continuous development has been shown to assist in arrhythmic activation mapping and provide insights into the mechanism of cardiac resynchronization therapy (CRT). This review addresses the validity, reliability, and overall feasibility of ECGi for use in a diverse range of arrhythmias. A systematic search limited to full-text human studies published in peer-reviewed journals was performed through Medline via PubMed, using various combinations of three key concepts: ECGi, arrhythmia, and CRT. A total of 456 studies were screened through titles and abstracts. Ultimately, 42 studies were included for literature review. Evidence to date suggests that ECGi can be used to provide diagnostic insights regarding the mechanistic basis of arrhythmias and the location of arrhythmia origin. Furthermore, ECGi can yield valuable information to guide therapeutic decision-making, including during CRT. Several studies have used ECGi as a diagnostic tool for atrial and ventricular arrhythmias. More recently, studies have tested the value of this technique in predicting outcomes of CRT. As a non-invasive method for assessing cardiovascular disease, particularly arrhythmias, ECGi represents a significant advancement over standard procedures in contemporary cardiology. Its full potential has yet to be fully explored.

Three-Dimensional Heart Model-Based Screening of Proarrhythmic Potential by in silico Simulation of Action Potential and Electrocardiograms

The proarrhythmic risk is a major concern in drug development. The Comprehensive in vitro Proarrhythmia Assay (CiPA) initiative has proposed the JTpeak interval on electrocardiograms (ECGs) and qNet, an in silico metric, as new biomarkers that may overcome the limitations of the hERG assay and QT interval. In this study, we simulated body-surface ECGs from patch-clamp data using realistic models of the ventricles and torso to explore their suitability as new in silico biomarkers for cardiac safety. We tested seven drugs in this study: dofetilide (high proarrhythmic risk), ranolazine, verapamil (QT increasing, but safe), bepridil, cisapride, mexiletine, and diltiazem. Human ventricular geometry was reconstructed from computed tomography (CT) images, and a Purkinje fiber network was mapped onto the endocardial surface. The electrical wave propagation in the ventricles was obtained by solving a reaction-diffusion equation using finite-element methods. The body-surface ECG data were calculated using a torso model that included the ventricles. The effects of the drugs were incorporated in the model by partly blocking the appropriate ion channels. The effects of the drugs on single-cell action potential (AP) were examined first, and three-dimensional (3D) body-surface ECG simulations were performed at free Cmax values of 1×, 5×, and 10×. In the single-cell and ECG simulations at 5× Cmax, dofetilide, but not verapamil or ranolazine, caused arrhythmia. However, the non-increasing JTpeak caused by verapamil and ranolazine that has been observed in humans was not reproduced in our simulation. Our results demonstrate the potential of 3D body-surface ECG simulation as a biomarker for evaluation of the proarrhythmic risk of candidate drugs.

Scalable and Accurate ECG Simulation for Reaction-Diffusion Models of the Human Heart

Realistic electrocardiogram (ECG) simulation with numerical models is important for research linking cellular and molecular physiology to clinically observable signals, and crucial for patient tailoring of numerical heart models. However, ECG simulation with a realistic torso model is computationally much harder than simulation of cardiac activity itself, so that many studies with sophisticated heart models have resorted to crude approximations of the ECG. This paper shows how the classical concept of electrocardiographic lead fields can be used for an ECG simulation method that matches the realism of modern heart models. The accuracy and resource requirements were compared to those of a full-torso solution for the potential and scaling was tested up to 14,336 cores with a heart model consisting of 11 million nodes. Reference ECGs were computed on a 3.3 billion-node heart-torso mesh at 0.2 mm resolution. The results show that the lead-field method is more efficient than a full-torso solution when the number of simulated samples is larger than the number of computed ECG leads. While the initial computation of the lead fields remains a hard and poorly scalable problem, the ECG computation itself scales almost perfectly and, even for several hundreds of ECG leads, takes much less time than the underlying simulation of cardiac activity.

Numerical simulation of electrocardiograms for full cardiac cycles in healthy and pathological conditions

This work is dedicated to the simulation of full cycles of the electrical activity of the heart and the corresponding body surface potential. The model is based on a realistic torso and heart anatomy, including ventricles and atria. One of the specificities of our approach is to model the atria as a surface, which is the kind of data typically provided by medical imaging for thin volumes. The bidomain equations are considered in their usual formulation in the ventricles, and in a surface formulation on the atria. Two ionic models are used: the Courtemanche-Ramirez-Nattel model on the atria and the 'minimal model for human ventricular action potentials' by Bueno-Orovio, Cherry, and Fenton in the ventricles. The heart is weakly coupled to the torso by a Robin boundary condition based on a resistor-capacitor transmission condition. Various electrocardiograms (ECGs) are simulated in healthy and pathological conditions (left and right bundle branch blocks, Bachmann's bundle block, and Wolff-Parkinson-White syndrome). To assess the numerical ECGs, we use several qualitative and quantitative criteria found in the medical literature. Our simulator can also be used to generate the signals measured by a vest of electrodes. This capability is illustrated at the end of the article. Copyright © 2015 John Wiley & Sons, Ltd.

Modeling left and right atrial contributions to the ECG: A dipole-current source approach

This paper presents the mathematical formulation, the numerical validation and several illustrations of a forward-modeling approach based on dipole-current sources to compute the contribution of a part of the heart to the electrocardiogram (ECG). Clinically relevant applications include identifying in the ECG the contributions from the right and the left atrium. In a Courtemanche-based monodomain computer model of the atria and torso, 1000 dipoles distributed throughout the atrial mid-myocardium are found to be sufficient to reproduce body surface potential maps with a relative error <1% during both sinus rhythm and atrial fibrillation. When the boundary element method is applied to solve the forward problem, this approach enables fast offline computation of the ECG contribution of any anatomical part of the atria by applying the principle of superposition to the dipole sources. In the presence of a right-left activation delay (sinus rhythm), pulmonary vein isolation (sinus rhythm) or left-right differences in refractory period (atrial fibrillation), the decomposition of the ECG is shown to help interpret ECG morphology in relation to the atrial substrate. These tools provide a theoretical basis for a deeper understanding of the genesis of the P wave or fibrillatory waves in normal and pathological cases.

Noninvasive identification of two lesions with local repolarization changes using two dipoles in inverse solution simulation study

BACKGROUND

The method for inverse localization and identification of two distinct simultaneous lesions with changed repolarization in the ventricular myocardium (two-vessel disease) is proposed and its robustness to errors in input data is tested in this simulation study.

METHOD

The inverse solution was obtained from the difference between STT integral body surface potential map computed with repolarization changes and the STT integral map from normal activation. In a numerical model of ventricles 48 cases of two simultaneous lesions and 48 cases of a single lesion were modeled. The effect of the lesions was taken to be represented by two dipoles. The input data were disturbed by three types of added noise. Twenty three characteristics of every obtained inverse solution were defined and four of them were used as the features in discriminant analysis task distinguishing the correct inverse solutions identifying two lesions.

RESULTS

The mean localization error for identified two lesions was 1.1±0.7cm. The sensitivity and specificity of quadratic discriminant analysis with cross-validation and feature selection was higher than 90%.

CONCLUSIONS

The combination of the inverse solution with two dipoles and discriminant analysis allows the identification of two simultaneous lesions without a priori information about the number of lesions.

A simplified 3D model of whole heart electrical activity and 12-lead ECG generation

We present a computationally efficient three-dimensional bidomain model of torso-embedded whole heart electrical activity, with spontaneous initiation of activation in the sinoatrial node, incorporating a specialized conduction system with heterogeneous action potential morphologies throughout the heart. The simplified geometry incorporates the whole heart as a volume source, with heart cavities, lungs, and torso as passive volume conductors. We placed four surface electrodes at the limbs of the torso: V_R, V_L, V_F and V_GND and six electrodes on the chest to simulate the Einthoven, Goldberger-augmented and precordial leads of a standard 12-lead system. By placing additional seven electrodes at the appropriate torso positions, we were also able to calculate the vectorcardiogram of the Frank lead system. Themodel was able to simulate realistic electrocardiogram (ECG) morphologies for the 12 standard leads, orthogonal X, Y, and Z leads, as well as the vectorcardiogram under normal and pathological heart states. Thus, simplified and easy replicable 3D cardiac bidomain model offers a compromise between computational load and model complexity and can be used as an investigative tool to adjust cell, tissue, and whole heart properties, such as setting ischemic lesions or regions of myocardial infarction, to readily investigate their effects on whole ECG morphology.

Patient-specific identification of optimal ubiquitous electrocardiogram (U-ECG) placement using a three-dimensional model of cardiac electrophysiology

A bipolar mini-ECG for ubiquitous healthcare (U-ECG) has been introduced, and various studies using the U-ECG device are in progress. Because it uses two electrodes within a small torso surface area, the design of the U-ECG must be suitable for detecting ECG signals. Using a 3-D model of cardiac electrophysiology, we have developed a simulation method for identifying the optimal placement of U-ECG electrodes on the torso surface. We simulated the heart-torso model to obtain a body surface potential map and ECG waveforms, which were compared with the empirical data. Using this model, we determined the optimal placement of the two U-ECG electrodes, spaced 5 cm apart, for detecting the P, R, and T waves. The ECG data, obtained using the optimal U-ECG placement for a specific wave, showed a clear shape for the target wave, but equivocal shapes for the other waves. The present study provides an efficient simulation method to identify the optimal attachment position and direction of the U-ECG electrodes on the surface of the torso.

Predicting the optimal position and direction of a ubiquitous ECG using a multi-scale model of cardiac electrophysiology

In this study, we determined the optimal position and direction of a one-channel bipolar electrocardiogram (ECG), used ubiquitously in healthcare. To do this, we developed a three-dimensional (3D) electrophysiological model of the heart coupled with a torso model that can generate a virtual body surface potential map (BSPM). Finite element models of the atria and ventricles incorporated the electrophysiological dynamics of atrial and ventricular myocytes, respectively. The torso model, in which the electric wave pattern on the cardiac tissue is reflected onto the body surface, was implemented using a boundary element method. Using the model, we derived the optimal positions of two electrodes, 5 cm apart, of the bipolar ubiquitous ECG (U-ECG) for detecting the P, R, and T waves. This model can be used as a simulation tool to design U-ECG device for use for various arrhythmia and normal patients.

Mathematical modeling and simulation of ventricular activation sequences: implications for cardiac resynchronization therapy

Next to clinical and experimental research, mathematical modeling plays a crucial role in medicine. Biomedical research takes place on many different levels, from molecules to the whole organism. Due to the complexity of biological systems, the interactions between components are often difficult or impossible to understand without the help of mathematical models. Mathematical models of cardiac electrophysiology have made a tremendous progress since the first numerical ECG simulations in the 1960s. This paper briefly reviews the development of this field and discusses some example cases where models have helped us forward, emphasizing applications that are relevant for the study of heart failure and cardiac resynchronization therapy.

Influence of individual torso geometry on inverse solution to 2 dipoles

BACKGROUND

The purpose of this study was to observe the influence of variety in individual torso geometries on the results of inverse solution to 2 dipoles.

METHODS

The inverse solution to 2 dipoles was computed from the measured data on 8 patients using either standard torso with various shapes and sizes of the heart and lungs in it or using various outer torso geometries with the same inhomogeneities. The vertical position of the heart relative to the fourth intercostal level was kept constant in all models. The results were compared with the reference solution computed in standard torso.

RESULTS

The inverse solution was influenced in 4 of 8 cases by changes of torso geometry and only in 1 of 8 cases by changes of internal inhomogeneities.

CONCLUSIONS

The use of individual torso geometry with the knowledge of the true heart position is very important for correct inverse results.

Parallelized computation for computer simulation of electrocardiograms using personal computers with multi-core CPU and general-purpose GPU

Biological computations like electrocardiological modelling and simulation usually require high-performance computing environments. This paper introduces an implementation of parallel computation for computer simulation of electrocardiograms (ECGs) in a personal computer environment with an Intel CPU of Core (TM) 2 Quad Q6600 and a GPU of Geforce 8800GT, with software support by OpenMP and CUDA. It was tested in three parallelization device setups: (a) a four-core CPU without a general-purpose GPU, (b) a general-purpose GPU plus 1 core of CPU, and (c) a four-core CPU plus a general-purpose GPU. To effectively take advantage of a multi-core CPU and a general-purpose GPU, an algorithm based on load-prediction dynamic scheduling was developed and applied to setting (c). In the simulation with 1600 time steps, the speedup of the parallel computation as compared to the serial computation was 3.9 in setting (a), 16.8 in setting (b), and 20.0 in setting (c). This study demonstrates that a current PC with a multi-core CPU and a general-purpose GPU provides a good environment for parallel computations in biological modelling and simulation studies.

Mathematical modeling of electrocardiograms: a numerical study

This paper deals with the numerical simulation of electrocardiograms (ECG). Our aim is to devise a mathematical model, based on partial differential equations, which is able to provide realistic 12-lead ECGs. The main ingredients of this model are classical: the bidomain equations coupled to a phenomenological ionic model in the heart, and a generalized Laplace equation in the torso. The obtention of realistic ECGs relies on other important features--including heart-torso transmission conditions, anisotropy, cell heterogeneity and His bundle modeling--that are discussed in detail. The numerical implementation is based on state-of-the-art numerical methods: domain decomposition techniques and second order semi-implicit time marching schemes, offering a good compromise between accuracy, stability and efficiency. The numerical ECGs obtained with this approach show correct amplitudes, shapes and polarities, in all the 12 standard leads. The relevance of every modeling choice is carefully discussed and the numerical ECG sensitivity to the model parameters investigated.

Validation of a simple model for the morphology of the T wave in unipolar electrograms

Local unipolar electrograms (UEGs) permit assessment of local activation and repolarization times at multiple sites simultaneously. However, UEG-based indexes of local repolarization are still debated, in particular for positive T waves. Previous experimental and computer modeling studies have not been able to terminate the debate. In this study we validate a simple theoretical model of the UEG and use it to explain how repolarization statistics in the UEG relate to those in the action potential. The model reconstructs the UEG by taking the difference between an inverted local action potential and a position-independent remote signal. In normal tissue, this extremely simple model predicts T-wave morphology with surprising accuracy while explaining in a readily understandable way why the instant of repolarization is always related to the steepest upstroke of the UEG, both in positive and negative T waves, and why positive T waves are related to early repolarizing sites, whereas negative T waves are related to late repolarizing sites.

CHASTE: incorporating a novel multi-scale spatial and temporal algorithm into a large-scale open source library

Recent work has described the software engineering and computational infrastructure that has been set up as part of the Cancer, Heart and Soft Tissue Environment (CHASTE) project. CHASTE is an open source software package that currently has heart and cancer modelling functionality. This software has been written using a programming paradigm imported from the commercial sector and has resulted in a code that has been subject to a far more rigorous testing procedure than that is usual in this field. In this paper, we explain how new functionality may be incorporated into CHASTE. Whiteley has developed a numerical algorithm for solving the bidomain equations that uses the multi-scale (MS) nature of the physiology modelled to enhance computational efficiency. Using a simple geometry in two dimensions and a purpose-built code, this algorithm was reported to give an increase in computational efficiency of more than two orders of magnitude. In this paper, we begin by reviewing numerical methods currently in use for solving the bidomain equations, explaining how these methods may be developed to use the MS algorithm discussed above. We then demonstrate the use of this algorithm within the CHASTE framework for solving the monodomain and bidomain equations in a three-dimensional realistic heart geometry. Finally, we discuss how CHASTE may be developed to include new physiological functionality--such as modelling a beating heart and fluid flow in the heart--and how new algorithms aimed at increasing the efficiency of the code may be incorporated.

Cardiac anisotropy in boundary-element models for the electrocardiogram

The boundary-element method (BEM) is widely used for electrocardiogram (ECG) simulation. Its major disadvantage is its perceived inability to deal with the anisotropic electric conductivity of the myocardial interstitium, which led researchers to represent only intracellular anisotropy or neglect anisotropy altogether. We computed ECGs with a BEM model based on dipole sources that accounted for a “compound” anisotropy ratio. The ECGs were compared with those computed by a finite-difference model, in which intracellular and interstitial anisotropy could be represented without compromise. For a given set of conductivities, we always found a compound anisotropy value that led to acceptable differences between BEM and finite-difference results. In contrast, a fully isotropic model produced unacceptably large differences. A model that accounted only for intracellular anisotropy showed intermediate performance. We conclude that using a compound anisotropy ratio allows BEM-based ECG models to more accurately represent both anisotropies.

Theoretical analysis of the magnetocardiographic pattern for reentry wave propagation in a three-dimensional human heart model

We present a computational study of reentry wave propagation using electrophysiological models of human cardiac cells and the associated magnetic field map of a human heart. We examined the details of magnetic field variation and related physiological parameters for reentry waves in two-dimensional (2-D) human atrial tissue and a three-dimensional (3-D) human ventricle model. A 3-D mesh system representing the human ventricle was reconstructed from the surface geometry of a human heart. We used existing human cardiac cell models to simulate action potential (AP) propagation in atrial tissue and 3-D ventricular geometry, and a finite element method and the Galerkin approximation to discretize the 3-D domain spatially. The reentry wave was generated using an S1-S2 protocol. The calculations of the magnetic field pattern assumed a horizontally layered conductor for reentry wave propagation in the 3-D ventricle. We also compared the AP and magnetocardiograph (MCG) magnitudes during reentry wave propagation to those during normal wave propagation. The temporal changes in the reentry wave motion and magnetic field map patterns were also analyzed using two well-known MCG parameters: the current dipole direction and strength. The current vector in a reentry wave forms a rotating spiral. We delineated the magnetic field using the changes in the vector angle during a reentry wave, demonstrating that the MCG pattern can be helpful for theoretical analysis of reentry waves.

A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart

A bidomain reaction-diffusion model of the human heart was developed, and potentials resulting from normal depolarization and repolarization were compared with results from a compatible monodomain model. Comparisons were made for an empty isolated heart and for a heart with fluid-filled ventricles. Both sinus rhythm and ectopic activation were simulated. The bidomain model took 2 days on 32 processors to simulate a complete cardiac cycle. Differences between monodomain and bidomain results were extremely small, even for the extracellular potentials, which in case of the monodomain model were computed with a high-resolution forward model. Propagation of activation was 2% faster in the bidomain model than in the monodomain model. Electrograms computed with monodomain and bidomain models were visually indistinguishable. We conclude that, in the absence of applied currents, propagating action potentials on the scale of a human heart can be studied with a monodomain model.

Simulation of Brugada syndrome using cellular and three-dimensional whole-heart modeling approaches

Brugada syndrome (BS) is a genetic disease identified by an abnormal electrocardiogram (ECG) (mainly abnormal ECGs associated with right bundle branch block and ST-elevation in right precordial leads). BS can lead to increased risk of sudden cardiac death. Experimental studies on human ventricular myocardium with BS have been limited due to difficulties in obtaining data. Thus, the use of computer simulation is an important alternative. Most previous BS simulations were based on animal heart cell models. However, due to species differences, the use of human heart cell models, especially a model with three-dimensional whole-heart anatomical structure, is needed. In this study, we developed a model of the human ventricular action potential (AP) based on refining the ten Tusscher et al (2004 Am. J. Physiol. Heart Circ. Physiol. 286 H1573-89) model to incorporate newly available experimental data of some major ionic currents of human ventricular myocytes. These modified channels include the L-type calcium current (I(CaL)), fast sodium current (I(Na)), transient outward potassium current (I(to)), rapidly and slowly delayed rectifier potassium currents (I(Kr) and I(Ks)) and inward rectifier potassium current (I(Ki)). Transmural heterogeneity of APs for epicardial, endocardial and mid-myocardial (M) cells was simulated by varying the maximum conductance of I(Ks) and I(to). The modified AP models were then used to simulate the effects of BS on cellular AP and body surface potentials using a three-dimensional dynamic heart-torso model. Our main findings are as follows. (1) BS has little effect on the AP of endocardial or mid-myocardial cells, but has a large impact on the AP of epicardial cells. (2) A likely region of BS with abnormal cell AP is near the right ventricular outflow track, and the resulting ST-segment elevation is located in the median precordium area. These simulation results are consistent with experimental findings reported in the literature. The model can reproduce a variety of electrophysiological behaviors and provides a good basis for understanding the genesis of abnormal ECG under the condition of BS disease.

Effect of cardiac motion on body surface electrocardiographic potentials: an MRI-based simulation study

This paper describes an electrical model of cardiac ventricles incorporating real geometry and motion. The heart anatomy and its motion through the cardiac cycle are obtained from segmentations of multiple-slice MRI time sequences; the special conduction system is constructed using an automated mapping procedure from an existing static heart model. The heart model is mounted in an anatomically realistic voxel model of the human body. The cardiac electrical source and surface potentials are determined numerically using both a finite-difference scheme and a boundary-element method with the incorporation of the motion of the heart. The electrocardiograms (ECG) and body surface potential maps are calculated and compared to the static simulation in the resting heart. The simulations demonstrate that introducing motion into the cardiac model modifies the ECG signals, with the most obvious change occurring during the T-wave at peak contraction of the ventricles. Body surface potential maps differ in some local positions during the T-wave, which may be of importance to a number of cardiac models, including those incorporating inverse methods.

Analysis of cardiac ventricular wall motion based on a three-dimensional electromechanical biventricular model

This paper describes a biventricular model, which couples the electrical and mechanical properties of the heart, and computer simulations of ventricular wall motion and deformation by means of a biventricular model. In the constructed electromechanical model, the mechanical analysis was based on composite material theory and the finite-element method; the propagation of electrical excitation was simulated using an electrical heart model, and the resulting active forces were used to calculate ventricular wall motion. Regional deformation and Lagrangian strain tensors were calculated during the systole phase. Displacements, minimum principal strains and torsion angle were used to describe the motion of the two ventricles. The simulations showed that during the period of systole, (1) the right ventricular free wall moves towards the septum, and at the same time, the base and middle of the free wall move towards the apex, which reduces the volume of the right ventricle; the minimum principle strain (E3) is largest at the apex, then at the middle of the free wall and its direction is in the approximate direction of the epicardial muscle fibres; (2) the base and middle of the left ventricular free wall move towards the apex and the apex remains almost static; the torsion angle is largest at the apex; the minimum principle strain E3 is largest at the apex and its direction on the surface of the middle wall of the left ventricle is roughly in the fibre orientation. These results are in good accordance with results obtained from MR tagging images reported in the literature. This study suggests that such an electromechanical biventricular model has the potential to be used to assess the mechanical function of the two ventricles, and also could improve the accuracy of ECG simulation when it is used in heart-torso model-based body surface potential simulation studies.