Three-dimensional computer model of the entire human heart for simulation of reentry and tachycardia: gap phenomenon and Wolff-Parkinson-White syndrome

Assessment of the equivalent dipole layer source model in the reconstruction of cardiac activation times on the basis of BSPMs produced by an anisotropic model of the heart

Promising results have been reported in noninvasive estimation of cardiac activation times (AT) using the equivalent dipole layer (EDL) source model in combination with the boundary element method (BEM). However, the assumption of equal anisotropy ratios in the heart that underlies the EDL model does not reflect reality. In the present study, we quantify the errors of the nonlinear AT imaging based on the EDL approximation. Nine different excitation patterns (sinus rhythm and eight ectopic beats) were simulated with the monodomain model. Based on the bidomain theory, the body surface potential maps (BSPMs) were calculated for a realistic finite element volume conductor with an anisotropic heart model. For the forward calculations, three cases of bidomain conductivity tensors in the heart were considered: isotropic, equal, and unequal anisotropy ratios in the intra- and extracellular spaces. In all inverse reconstructions, the EDL model with BEM was employed: AT were estimated by solving the nonlinear optimization problem with the initial guess provided by the fastest route algorithm. Expectedly, the case of unequal anisotropy ratios resulted in larger localization errors for almost all considered activation patterns. For the sinus rhythm, all sites of early activation were correctly estimated with an optimal regularization parameter being used. For the ectopic beats, all but one foci were correctly classified to have either endo- or epicardial origin with an average localization error of 20.4 mm for unequal anisotropy ratio. The obtained results confirm validation studies and suggest that cardiac anisotropy might be neglected in clinical applications of the considered EDL-based inverse procedure.

Assessment of the equivalent dipole layer source model in the reconstruction of cardiac activation times on the basis of BSPMs produced by an anisotropic model of the heart

Promising results have been reported in noninvasive estimation of cardiac activation times (AT) using the equivalent dipole layer (EDL) source model in combination with the boundary element method (BEM). However, the assumption of equal anisotropy ratios in the heart that underlies the EDL model does not reflect reality. In the present study, we quantify the errors of the nonlinear AT imaging based on the EDL approximation. Nine different excitation patterns (sinus rhythm and eight ectopic beats) were simulated with the monodomain model. Based on the bidomain theory, the body surface potential maps (BSPMs) were calculated for a realistic finite element volume conductor with an anisotropic heart model. For the forward calculations, three cases of bidomain conductivity tensors in the heart were considered: isotropic, equal, and unequal anisotropy ratios in the intra- and extracellular spaces. In all inverse reconstructions, the EDL model with BEM was employed: AT were estimated by solving the nonlinear optimization problem with the initial guess provided by the fastest route algorithm. Expectedly, the case of unequal anisotropy ratios resulted in larger localization errors for almost all considered activation patterns. For the sinus rhythm, all sites of early activation were correctly estimated with an optimal regularization parameter being used. For the ectopic beats, all but one foci were correctly classified to have either endo- or epicardial origin with an average localization error of 20.4 mm for unequal anisotropy ratio. The obtained results confirm validation studies and suggest that cardiac anisotropy might be neglected in clinical applications of the considered EDL-based inverse procedure.

Computational generation of the Purkinje network driven by clinical measurements: the case of pathological propagations

To properly describe the electrical activity of the left ventricle, it is necessary to model the Purkinje fibers, responsible for the fast and coordinate ventricular activation, and their interaction with the muscular propagation. The aim of this work is to propose a methodology for the generation of a patient-specific Purkinje network driven by clinical measurements of the activation times related to pathological propagations. In this case, one needs to consider a strongly coupled problem between the network and the muscle, where the feedback from the latter to the former cannot be neglected as in a normal propagation. We apply the proposed strategy to data acquired on three subjects, one of them suffering from muscular conduction problems owing to a scar and the other two with a muscular pre-excitation syndrome (Wolff-Parkinson-White). To assess the accuracy of the proposed method, we compare the results obtained by using the patient-specific Purkinje network generated by our strategy with the ones obtained by using a non-patient-specific network. The results show that the mean absolute errors in the activation time is reduced for all the cases, highlighting the importance of including a patient-specific Purkinje network in computational models.

Parametric modelling of cardiac system multiple measurement signals: an open-source computer framework for performance evaluation of ECG, PCG and ABP event detectors

The major focus of this study is to present a performance accuracy assessment framework based on mathematical modelling of cardiac system multiple measurement signals. Three mathematical algebraic subroutines with simple structural functions for synthetic generation of the synchronously triggered electrocardiogram (ECG), phonocardiogram (PCG) and arterial blood pressure (ABP) signals are described. In the case of ECG signals, normal and abnormal PQRST cycles in complicated conditions such as fascicular ventricular tachycardia, rate dependent conduction block and acute Q-wave infarctions of inferior and anterolateral walls can be simulated. Also, continuous ABP waveform with corresponding individual events such as systolic, diastolic and dicrotic pressures with normal or abnormal morphologies can be generated by another part of the model. In addition, the mathematical synthetic PCG framework is able to generate the S4-S1-S2-S3 cycles in normal and in cardiac disorder conditions such as stenosis, insufficiency, regurgitation and gallop. In the PCG model, the amplitude and frequency content (5-700 Hz) of each sound and variation patterns can be specified. The three proposed models were implemented to generate artificial signals with varies abnormality types and signal-to-noise ratios (SNR), for quantitative detection-delineation performance assessment of several ECG, PCG and ABP individual event detectors designed based on the Hilbert transform, discrete wavelet transform, geometric features such as area curve length (ACLM), the multiple higher order moments (MHOM) metric, and the principal components analysed geometric index (PCAGI). For each method the detection-delineation operating characteristics were obtained automatically in terms of sensitivity, positive predictivity and delineation (segmentation) error rms and checked by the cardiologist. The Matlab m-file script of the synthetic ECG, ABP and PCG signal generators are available in the Appendix.

Combination of computer simulations and experimental measurements as the training dataset for statistical estimation of epicardial activation maps from venous catheter recordings

One of the epicardial mapping techniques requires the insertion of multiple multi-electrode catheters into the coronary vessels. The recordings from the intracoronary catheters reflect the electrical activity on the nearby epicardial sites; however, most of epicardial surface is still inaccessible. In order to overcome this limited access problem, a method called the linear least squares estimation was proposed for the reconstruction of high-resolution maps using sparse measurements. In this technique, the relationship between catheter measurements and the remaining sites on the epicardium is created from previously obtained high-resolution maps (training dataset). Even though open-chest surgery is still a relatively frequent occurrence, an additional burden on the patient to obtain epicardial maps might impose an important risk on the patient. In this study, we hypothesize that epicardial maps created from computer simulations might be used in combination with the experimental data. In order to test this hypothesis, we used high-resolution epicardial activation maps acquired from 13 experiments performed on canine hearts that were stimulated via unipolar pacing from sites distributed all over the epicardium. We investigated the feasibility of the Aliev-Panfilov model that generated focal epicardial arrhythmias on Auckland heart. We started the simulations from the sites that corresponded to the pacing sites on the experimental geometry after a registration procedure between the experimental and simulation geometries. We then compared the simulation results with the corresponding experimental activation maps. Finally, we included simulated activation maps alone (100%) and in combination (simulated maps constituted 90%, 75%, 50%, 25%, 10%, and 0% of the training dataset) with experimental maps in the training set, performed the statistical estimation, and obtained the error statistics. The mean correlation coefficient (CC) between the simulated epicardial activation maps with the experimental maps was 0.88. The results of the estimation indicated that only 2.6 mm localization error and 0.05 CC value degradation occurred on average for the replacement of 75% of the experimental maps with the simulated counterparts. This indicated that including an important percentage from simulations may lead to decreased need for open-chest procedures and less burden on the patients.

Cardiac anisotropy: is it negligible regarding noninvasive activation time imaging?

The aim of this study was to quantify the effect of cardiac anisotropy in the activation-based inverse problem of electrocardiography. Differences of the patterns of simulated body surface potential maps for isotropic and anisotropic conditions were investigated with regard to activation time (AT) imaging of ventricular depolarization. AT maps were estimated by solving the nonlinear inverse ill-posed problem employing spatio-temporal regularization. Four different reference AT maps (sinus rhythm, right-ventricular and septal pacing, accessory pathway) were calculated with a bidomain theory based anisotropic finite-element heart model in combination with a cellular automaton. In this heart model a realistic fiber architecture and conduction system was implemented. Although the anisotropy has some effects on forward solutions, effects on inverse solutions are small indicating that cardiac anisotropy might be negligible for some clinical applications (e.g., imaging of focal events) of our AT imaging approach. The main characteristic events of the AT maps were estimated despite neglected electrical anisotropy in the inverse formulation. The worst correlation coefficient of the estimated AT maps was 0.810 in case of sinus rhythm. However, all characteristic events of the activation pattern were found. The results of this study confirm our clinical validation studies of noninvasive AT imaging in which cardiac anisotropy was neglected.

A computer model of normal conduction in the human atria

Although considerable progress has been made in understanding the process of wavefront propagation and arrhythmogenesis in human atria, technical concerns and issues of patient safety have limited experimental investigations. The present work describes a finite volume-based computer model of human atrial activation and current flow to complement these studies. Unlike previous representations, the model is three-dimensional, incorporating both the left and right atria and the major muscle bundles of the atria, including the crista terminalis, pectinate muscles, limbus of the fossa ovalis, and Bachmann's bundle. The bundles are represented as anisotropic structures with fiber directions aligned with the bundle axes. Conductivities are assigned to the model to give realistic local conduction velocities within the bundles and bulk tissue. Results from simulations demonstrate the role of the bundles in a normal sinus rhythm and also reveal the patterns of activation in the septum, where experimental mapping has been extremely challenging. To validate the model, the simulated normal activation sequence and conduction velocities at various locations are compared with experimental observations and data. The model is also used to investigate paced activation, and a mechanism of the relative lengthening of left versus right stimulation is presented. Owing to both the realistic geometry and the bundle structures, the model can be used for further analysis of the normal activation sequence and to examine abnormal conduction, including flutter. The full text of this article is available at http://www.circresaha.org.

Validation of three-dimensional conduction models using experimental mapping: are we getting closer?

The anisotropic material properties, irregular geometry, and specialized conduction system of the heart all affect the three-dimensional (3D) spread of electrical activation. A limited number of research groups have tried accounting for these features in 3D conduction models to investigate more thoroughly their observations of cardiac electrical activity in 3D experimental preparations. The full potential of these large scale conduction models, however, has not been realized because of a lack of quantitative validation with experiment. Such validation is critical in order to use the models to predict the electrical response of the myocardium to drugs or electrical stimulation. In this paper, a quantitative, experimental validation of paced activation in a 3D conduction model of a 3 cm x 3 cm x 1 cm section of the ventricular wall is presented. Epicardial and intramural pacing stimuli were applied in the center of a 528 channel electrode plaque sutured to the left ventricle in dogs. Unipolar electrograms were recorded at 2 kHz during and after pacing. Fiber directions within the tissue below the electrodes were estimated histologically and from pace-mapping. Simulated epicardial electrograms were computed for surface paced beats using our 3D bidomain model of the mapped tissue volume incorporating the measured fiber directions. Extracellular potentials and isochronal maps resulting from paced activations in both model and experiment were directly compared. Preliminary results demonstrate that our 3D model reproduces qualitatively such key features of the experimental data as electrogram morphologies and epicardial conduction velocities. Though quantitative agreement between model and experiment was only moderate, the validation approach described herein is an essential first step in assessing the predictive capability of present day conduction models.

Magnetic source imaging in the human heart: estimating cardiac electrical sources from simulated and measured magnetocardiogram data

The estimation of pseudo primary current dipoles on a 2D-manifold in the atrial and ventricular myocardium and septum, and of the transmembrane potential on the endocardium and epicardium, from the magnetic heart field is investigated. The human thorax surrounding the heart is modelled by an inhomogeneous boundary element volume conductor model, including the outer thorax surface and the surfaces of the lungs. The influence of the blood mass is neglected. In the inverse problem Tikhonov's regularisation is applied. The regularisation parameter is determined by the L-curve method. An algorithm for iterative improvement is applied to estimate the pseudo primary current dipoles. Synthetic magnetic field and electric potential data are generated using a cellular automaton model of the entire human heart. Real world magnetic field data for a normal subject are analysed to demonstrate the practicability and effectiveness of the presented method.

Activation and repolarization patterns are governed by different structural characteristics of ventricular myocardium: experimental study with voltage-sensitive dyes and numerical simulations

INTRODUCTION

Substantial progress has been made in our understanding of transmural activation across ventricular muscle through studies of excitation patterns and potential distributions. In contrast, repolarization sequences are poorly understood because of experimental difficulties in mapping action potential durations (APDs) using extracellular electrodes.

METHODS AND RESULTS

Langendorff-perfused guinea pig hearts and isolated coronary-perfused left ventricular sheet preparations were stained with the voltage-sensitive dye RH-421 and optical APs were recorded with a photodiode array. Epicardial maps were constructed using a triangulation method applied to matrices of activation and repolarization times determined from (dF/dt)max and (d2F/dt2)max' respectively. Numerical simulations were carried out based on: (1) a modified Luo-Rudy model; (2) the three-dimensional architecture of ventricular fibers; and (3) the intrinsic spatial distribution of APDs. In ventricular sheets, epicardial stimulation elicited elliptical activation patterns with the major axis aligned with the longitudinal axis of epicardial fibers. When the pacing electrode was progressively inserted from epicardium to endocardium, the major axes rotated gradually, clockwise by 45 degrees, and the eccentricity decreased from 2 to 1.14. Repolarization showed a relatively uniform pattern, independent of pacing site, beginning at the apex and spreading to the base.

CONCLUSION

In experiments and simulations, the helical rotation of epicardial excitation isochrones caused by pacing at increasing depth in the myocardium correlated with the helical three-dimensional architecture of ventricular fibers. In contrast, repolarization was independent of the activation sequence and was mainly guided by spatial differences in APDs between apex and base.

The antiarrhythmic effect of verapamil on atrioventricular re-entry in the Wolff-Parkinson-White syndrome: a computer model study

Verapamil is supposed to suppress the initiation of circus movement supraventricular tachycardia by affecting the atrioventricular node. In electrophysiological tests, programmed stimulation is usually performed by using the same location for pacing and premature stimulus. Spontaneous ectopic activity starts from a different location than the sinus node and can therefore find altered re-entry conditions. In this study a 3D computer model based on Huygen's principle is used for simulation of the spread of excitation in the human heart in combination with a posterobasal, right or left lateral accessory pathway (AP). The effect of verapamil on properties of the atrioventricular node were modelled by prolonging the effective refractory period and basal conduction time. For each of the three APs, ectopic foci at the atrial base and between sinus node and AP were modelled at various coupling intervals for investigating re-entrant activation. In the control state (without verapamil) only orthodromic echoes were found. The maximum echo zone (EZ) range was found near the AP. If stimuli were selected further away from the AP on the atrial basis, the EZ range decreased until no EZ was found. The EZ range decreased from it's maximum value near the AP, towards the difference of the effective refractory periods between AP and AV-node near the sinus node Verapamil abolished the EZ in case of a posteroseptal AP. For a lateral AP the administration of verapamil resulted in an orthodromic and antidromic EZ depending on the atrial premature activation site. A maximum orthodromic EZ was found for premature stimuli near the AP. As stimulus site moved away from the AP, the EZ range first decreased continuously to zero leading eventually to an antidromic EZ. These findings suggest the important influence of the site of premature stimuli with respect to the accessory pathway and AV-node on the inducibility of atrial re-entry.

Localisation of myocardial ischaemia from the magnetocardiogram using current density reconstruction method: computer simulation study

A computer simulation study is performed to investigate the method of current density reconstruction to localise myocardial ischaemia. A computer model of the entire human heart is used to simulate the excitation and repolarisation process in eight topographically different cases of myocardial ischaemia. The associated magnetocardiogram is calculated at 37 positions of the KRENIKON biomagnetic measurement equipment. The method of current density reconstruction is applied at the S-point (the last discernible deviation from the ST-segment at the end of the QRS-complex) of the MCG to find characteristics of the myocardial ischaemia simulated by the model. The results show that it is possible to determine the location of the ischaemia. The current density distribution may be interpreted physiologically in terms of the so-called 'injury-current'. This indicates that magnetocardiography might be a suitable method for noninvasive ischaemia diagnosis, and further investigations of the current density reconstruction method for the injury current should be performed on patients with ischaemic heart disease.

A computer heart model incorporating anisotropic propagation. I. Model construction and simulation of normal activation

Present-day computer models of the entire heart, capable of simulating the activation isochrones and subsequently the body surface potentials, focus on considerations of myocardial anisotropy. Myocardial anisotropy enters into play at two levels, first by affecting the spatial pattern of activation owing to faster propagation along cardiac fibers and second by altering the equivalent dipole sources used to calculate the surface potentials. The construction of a new and detailed model of the human heart is described, based on 132 transverse sections obtained following a computed tomography scan of a frozen human heart whose chambers were inflated with pressurized air. The entire heart anatomy was reconstructed as a three-dimensional array of approximately 250,000 points spaced 1 mm apart. Conduction in the thin-walled atria was assumed isotropic from the sinus node region to the atrioventricular node, where it was subject to a 50 ms delay. A two-tier representation of the specialized conduction system was used, with the initial segments of the left and right bundles represented by a system of cables that feeds to the second tier, which is a sheet of conduction tissue representing the distal Purkinje system. Approximately 1,120 "Purkinje-myocardium" junctions present at the terminations of the cables and sprinkled uniformly over the sheet, transmit the excitation to the ventricles. A stylized representation of myocardial fiber rotation was incorporated into the ventricles and the local fiber direction at each model point used to compute the velocity of propagation to its nearest neighbors. Accordingly, the activation times of the entire ventricular myocardium could be determined using the 1,120 or so Purkinje-myocardium junctions as start points. While myocardial anisotropy was considered in the ventricular propagation process, it was ignored in the computation of the equivalent dipole sources. Nevertheless, the computed electrocardiogram, vectorcardiogram, and body surface potential maps obtained with the new heart model properly positioned inside an inhomogeneous torso model were all within normal limits.