Effects of material properties and geometry on electrocardiographic forward simulations

Training machine learning models with synthetic data improves the prediction of ventricular origin in outflow tract ventricular arrhythmias

In order to determine the site of origin (SOO) in outflow tract ventricular arrhythmias (OTVAs) before an ablation procedure, several algorithms based on manual identification of electrocardiogram (ECG) features, have been developed. However, the reported accuracy decreases when tested with different datasets. Machine learning algorithms can automatize the process and improve generalization, but their performance is hampered by the lack of large enough OTVA databases. We propose the use of detailed electrophysiological simulations of OTVAs to train a machine learning classification model to predict the ventricular origin of the SOO of ectopic beats. We generated a synthetic database of 12-lead ECGs (2,496 signals) by running multiple simulations from the most typical OTVA SOO in 16 patient-specific geometries. Two types of input data were considered in the classification, raw and feature ECG signals. From the simulated raw 12-lead ECG, we analyzed the contribution of each lead in the predictions, keeping the best ones for the training process. For feature-based analysis, we used entropy-based methods to rank the obtained features. A cross-validation process was included to evaluate the machine learning model. Following, two clinical OTVA databases from different hospitals, including ECGs from 365 patients, were used as test-sets to assess the generalization of the proposed approach. The results show that V2 was the best lead for classification. Prediction of the SOO in OTVA, using both raw signals or features for classification, presented high accuracy values (>0.96). Generalization of the network trained on simulated data was good for both patient datasets (accuracy of 0.86 and 0.84, respectively) and presented better values than using exclusively real ECGs for classification (accuracy of 0.84 and 0.76 for each dataset). The use of simulated ECG data for training machine learning-based classification algorithms is critical to obtain good SOO predictions in OTVA compared to real data alone. The fast implementation and generalization of the proposed methodology may contribute towards its application to a clinical routine.

The Impact of Torso Signal Processing on Noninvasive Electrocardiographic Imaging Reconstructions

Goal:

To evaluate state-of-the-art signal processing methods for epicardial potential-based noninvasive electrocardiographic imaging reconstructions of single-site pacing data.

Methods:

Experimental data were obtained from two torso-tank setups in which Langendorff-perfused hearts (n = 4) were suspended and potentials recorded simultaneously from torso and epicardial surfaces. 49 different signal processing methods were applied to torso potentials, grouped as i) high-frequency noise removal (HFR) methods ii) baseline drift removal (BDR) methods and iii) combined HFR+BDR. The inverse problem was solved and reconstructed electrograms and activation maps compared to those directly recorded.

Results:

HFR showed no difference compared to not filtering in terms of absolute differences in reconstructed electrogram amplitudes nor median correlation in QRS waveforms (p > 0.05). However, correlation and mean absolute error of activation times and pacing site localization were improved with all methods except a notch filter. HFR applied post-reconstruction produced no differences compared to pre-reconstruction. BDR and BDR+HFR significantly improved absolute and relative difference, and correlation in electrograms (p < 0.05). While BDR+HFR combined improved activation time and pacing site detection, BDR alone produced significantly lower correlation and higher localization errors (p < 0.05).

Conclusion:

BDR improves reconstructed electrogram morphologies and amplitudes due to a reduction in lambda value selected for the inverse problem. The simplest method (resetting the isoelectric point) is sufficient to see these improvements. HFR does not impact electrogram accuracy, but does impact post-processing to extract features such as activation times. Removal of line noise is insufficient to see these changes. HFR should be applied post-reconstruction to ensure over-filtering does not occur.

How Accurate Is Inverse Electrocardiographic Mapping? A Systematic In Vivo Evaluation

BACKGROUND

Inverse electrocardiographic mapping reconstructs cardiac electrical activity from recorded body surface potentials. This noninvasive technique has been used to identify potential ablation targets. Despite this, there has been little systematic evaluation of its reliability.

METHODS

Torso and ventricular epicardial potentials were recorded simultaneously in anesthetized, closed-chest pigs (n=5), during sinus rhythm, epicardial, and endocardial ventricular pacing (70 records in total). Body surface and cardiac electrode positions were determined and registered using magnetic resonance imaging. Epicardial potentials were reconstructed during ventricular activation using experiment-specific magnetic resonance imaging-based thorax models, with homogeneous or inhomogeneous (lungs, skeletal muscle, fat) electrical properties. Coupled finite/boundary element methods and a meshless approach based on the method of fundamental solutions were compared. Inverse mapping underestimated epicardial potentials >2-fold (P<0.0001).

RESULTS

Mean correlation coefficients for reconstructed epicardial potential distributions ranged from 0.60±0.08 to 0.64±0.07 across all methods. Epicardial electrograms were recovered with reasonable fidelity at ≈50% of sites (median correlation coefficient, 0.69-0.72), but variation was substantial. General activation spread was reproduced (median correlation coefficient, 0.72-0.78 for activation time maps after spatio-temporal smoothing). Epicardial foci were identified with a median location error ≈16 mm (interquartile range, 9-29 mm). Inverse mapping with meshless method of fundamental solutions was better than with finite/boundary element methods, and the latter were not improved by inclusion of inhomogeneous torso electrical properties.

CONCLUSIONS

Inverse potential mapping provides useful information on the origin and spread of epicardial activation. However the spatio-temporal variability of recovered electrograms limit resolution and must constrain the accuracy with which arrhythmia circuits can be identified independently using this approach.

Personalized Cardiac Computational Models: From Clinical Data to Simulation of Infarct-Related Ventricular Tachycardia

In the chronic stage of myocardial infarction, a significant number of patients develop life-threatening ventricular tachycardias (VT) due to the arrhythmogenic nature of the remodeled myocardium. Radiofrequency ablation (RFA) is a common procedure to isolate reentry pathways across the infarct scar that are responsible for VT. Unfortunately, this strategy show relatively low success rates; up to 50% of patients experience recurrent VT after the procedure. In the last decade, intensive research in the field of computational cardiac electrophysiology (EP) has demonstrated the ability of three-dimensional (3D) cardiac computational models to perform in-silico EP studies. However, the personalization and modeling of certain key components remain challenging, particularly in the case of the infarct border zone (BZ). In this study, we used a clinical dataset from a patient with a history of infarct-related VT to build an image-based 3D ventricular model aimed at computational simulation of cardiac EP, including detailed patient-specific cardiac anatomy and infarct scar geometry. We modeled the BZ in eight different ways by combining the presence or absence of electrical remodeling with four different levels of image-based patchy fibrosis (0, 10, 20, and 30%). A 3D torso model was also constructed to compute the ECG. Patient-specific sinus activation patterns were simulated and validated against the patient's ECG. Subsequently, the pacing protocol used to induce reentrant VTs in the EP laboratory was reproduced in-silico. The clinical VT was induced with different versions of the model and from different pacing points, thus identifying the slow conducting channel responsible for such VT. Finally, the real patient's ECG recorded during VT episodes was used to validate our simulation results and to assess different strategies to model the BZ. Our study showed that reduced conduction velocities and heterogeneity in action potential duration in the BZ are the main factors in promoting reentrant activity. Either electrical remodeling or fibrosis in a degree of at least 30% in the BZ were required to initiate VT. Moreover, this proof-of-concept study confirms the feasibility of developing 3D computational models for cardiac EP able to reproduce cardiac activation in sinus rhythm and during VT, using exclusively non-invasive clinical data.

Learning Domain Shift in Simulated and Clinical Data: Localizing the Origin of Ventricular Activation From 12-Lead Electrocardiograms

Building a data-driven model to localize the origin of ventricular activation from 12-lead electrocardiograms (ECG) requires addressing the challenge of large anatomical and physiological variations across individuals. The alternative of a patient-specific model is, however, difficult to implement in clinical practice because the training data must be obtained through invasive procedures. In this paper, we present a novel approach that overcomes this problem of the scarcity of clinical data by transferring the knowledge from a large set of patient-specific simulation data while utilizing domain adaptation to address the discrepancy between the simulation and clinical data. The method that we have developed quantifies non-uniformly distributed simulation errors, which are then incorporated into the process of domain adaptation in the context of both classification and regression. This yields a quantitative model that, with the addition of 12-lead ECG data from each patient, provides progressively improved patient-specific localizations of the origin of ventricular activation. We evaluated the performance of the presented method in localizing 75 pacing sites on three in-vivo premature ventricular contraction (PVC) patients. We found that the presented model showed an improvement in localization accuracy relative to a model trained on clinical ECG data alone or a model trained on combined simulation and clinical data without considering domain shift. Furthermore, we demonstrated the ability of the presented model to improve the real-time prediction of the origin of ventricular activation with each added clinical ECG data, progressively guiding the clinician towards the target site.

Sensitivity analysis of ventricular activation and electrocardiogram in tailored models of heart-failure patients

Cardiac resynchronization therapy is not effective in a variable proportion of heart failure patients. An accurate knowledge of each patient's electroanatomical features could be helpful to determine the most appropriate treatment. The goal of this study was to analyze and quantify the sensitivity of left ventricular (LV) activation and the electrocardiogram (ECG) to changes in 39 parameters used to tune realistic anatomical-electrophysiological models of the heart. Electrical activity in the ventricles was simulated using a reaction-diffusion equation. To simulate cellular electrophysiology, the Ten Tusscher-Panfilov 2006 model was used. Intracardiac electrograms and 12-lead ECGs were computed by solving the bidomain equation. Parameters showing the highest sensitivity values were similar in the six patients studied. QRS complex and LV activation times were modulated by the sodium current, the cell surface-to-volume ratio in the LV, and tissue conductivities. The T-wave was modulated by the calcium and rectifier-potassium currents, and the cell surface-to-volume ratio in both ventricles. We conclude that homogeneous changes in ionic currents entail similar effects in all ECG leads, whereas the effects of changes in tissue properties show larger inter-lead variability. The effects of parameter variations are highly consistent between patients and most of the model tuning could be performed with only ~10 parameters.

Equivalent dipole sources to estimate the influence of extracellular myocardial anisotropy in thin-walled cardiac forward models

The extracellular domain of the heart is anisotropic, which affects volume conduction and therefore body surface potentials. This paper tests the hypothesis that when wall thickness is sufficiently small (such as in the atria), the effect of extracellular anisotropy can be estimated by modifying local dipole current sources. A formula based on the Gabor-Nelson equivalent dipole and on the reciprocity theorem is derived to compute a linear transformation of the dipole sources that approximates in an isotropic volume conductor the far-field of the actual sources in an anisotropic volume conductor. It involves solving three Poisson equation (once for all). The results obtained in an atrial model embedded in a boundary-element torso model suggest that when wall thickness is < 3  mm, simulated P waves are weakly altered by extracellular anisotropy during sinus rhythm: an anisotropy ratio of 4:1 typically reduced the longitudinal component of the dipole sources by < 3%, increased the transverse component by < 5%, and increased the transmural component by ≈ 25% (which may be relevant in case of epicardial-endocardial dissociation). Due to uncertainty on experimental conductivity values, it is proposed that atrial extracellular anisotropy may be neglected when computing P waves.

Influence of Modeling Errors on the Initial Estimate for Nonlinear Myocardial Activation Times Imaging Calculated With Fastest Route Algorithm

Noninvasive reconstruction of cardiac electrical activity has a great potential to support clinical decision making, planning, and treatment. Recently, significant progress has been made in the estimation of the cardiac activation from body surface potential maps (BSPMs) using boundary element method (BEM) with the equivalent double layer (EDL) as a source model. In this formulation, noninvasive assessment of activation times results in a nonlinear optimization problem with an initial estimate calculated with the fastest route algorithm (FRA). Each FRA-simulated activation sequence is converted into the ECG. The best initialization is determined by the sequence providing the highest correlation between predicted and measured potentials. We quantitatively assess the effects of the forward modeling errors on the FRA-based initialization. We present three simulation setups to investigate the effects of volume conductor model simplifications, neglecting the cardiac anisotropy and geometrical errors on the localization of ectopic beats starting on the ventricular surface. For the analysis, 12-lead ECG and 99 electrodes BSPM system were used. The areas in the heart exposing the largest localization errors were volume conductor model and electrode configuration specific with an average error <10 mm. The results show the robustness of the FRA-based initialization with respect to the considered modeling errors.

Transmural, interventricular, apicobasal and anteroposterior action potential duration gradients are all essential to the genesis of the concordant and realistic T wave: A whole-heart model study

BACKGROUND

It has been reported that ventricular repolarization dispersion resulting from transmural, apicobasal and interventricular action potential duration (APD) gradients makes the T wave concordant with the QRS complex.

METHOD AND RESULTS

A whole-heart model integrating transmural, apicobasal, interventricular and anteroposterior APD gradients was used, and the corresponding electrocardiograms were simulated to study the influence of these APD gradients on the T-wave amplitudes. The simulation results showed that changing a single APD gradient (e.g., interventricular APD gradient alone) only made substantial changes to the T-wave amplitudes in a limited number of leads and was not able to generate T waves with amplitudes comparable with clinical findings in all leads. A combination of transmural, apicobasal and interventricular APD gradients could simulate T waves with amplitudes similar to clinical values in the limb leads only. Adding the anteroposterior APD gradient into the model greatly improved the consistency between the simulated T-wave amplitudes and the clinical values.

CONCLUSION

The simulation results support that the transmural, apicobasal, interventricular and the anteroposterior APD gradient are all essential to the genesis of the clinical T wave.

Detailed Anatomical and Electrophysiological Models of Human Atria and Torso for the Simulation of Atrial Activation

Atrial arrhythmias, and specifically atrial fibrillation (AF), induce rapid and irregular activation patterns that appear on the torso surface as abnormal P-waves in electrocardiograms and body surface potential maps (BSPM). In recent years both P-waves and the BSPM have been used to identify the mechanisms underlying AF, such as localizing ectopic foci or high-frequency rotors. However, the relationship between the activation of the different areas of the atria and the characteristics of the BSPM and P-wave signals are still far from being completely understood. In this work we developed a multi-scale framework, which combines a highly-detailed 3D atrial model and a torso model to study the relationship between atrial activation and surface signals in sinus rhythm. Using this multi scale model, it was revealed that the best places for recording P-waves are the frontal upper right and the frontal and rear left quadrants of the torso. Our results also suggest that only nine regions (of the twenty-one structures in which the atrial surface was divided) make a significant contribution to the BSPM and determine the main P-wave characteristics.

A new algorithm to diagnose atrial ectopic origin from multi lead ECG systems--insights from 3D virtual human atria and torso

Rapid atrial arrhythmias such as atrial fibrillation (AF) predispose to ventricular arrhythmias, sudden cardiac death and stroke. Identifying the origin of atrial ectopic activity from the electrocardiogram (ECG) can help to diagnose the early onset of AF in a cost-effective manner. The complex and rapid atrial electrical activity during AF makes it difficult to obtain detailed information on atrial activation using the standard 12-lead ECG alone. Compared to conventional 12-lead ECG, more detailed ECG lead configurations may provide further information about spatio-temporal dynamics of the body surface potential (BSP) during atrial excitation. We apply a recently developed 3D human atrial model to simulate electrical activity during normal sinus rhythm and ectopic pacing. The atrial model is placed into a newly developed torso model which considers the presence of the lungs, liver and spinal cord. A boundary element method is used to compute the BSP resulting from atrial excitation. Elements of the torso mesh corresponding to the locations of the placement of the electrodes in the standard 12-lead and a more detailed 64-lead ECG configuration were selected. The ectopic focal activity was simulated at various origins across all the different regions of the atria. Simulated BSP maps during normal atrial excitation (i.e. sinoatrial node excitation) were compared to those observed experimentally (obtained from the 64-lead ECG system), showing a strong agreement between the evolution in time of the simulated and experimental data in the P-wave morphology of the ECG and dipole evolution. An algorithm to obtain the location of the stimulus from a 64-lead ECG system was developed. The algorithm presented had a success rate of 93%, meaning that it correctly identified the origin of atrial focus in 75/80 simulations, and involved a general approach relevant to any multi-lead ECG system. This represents a significant improvement over previously developed algorithms.

Reconstruction of normal and abnormal gastric electrical sources using a potential based inverse method

The use of cutaneous recordings to non-invasively characterize gastric slow waves has had limited clinical acceptance, primarily due to the uncertainty in relating the recorded signal to the underlying gastric slow waves. In this study we aim to distinguish and quantitatively reconstruct different slow wave patterns using an inverse algorithm. Slow wave patterns corresponding to normal, retrograde and uncoupled activity at different frequencies were imposed on a stomach surface model. Gaussian noise (10% peak-to-peak) was added to cutaneous potentials and the Greensite-Tikhonov inverse method was used to reconstruct the potentials on the stomach. The effectiveness of the number or location of electrodes on the accuracy of the inverse solutions was investigated using four different electrode configurations. Results showed the reconstructed solutions were able to reliably distinguish the different slow wave patterns and waves with lower frequency were better correlated to the known solution than those with higher. The use of up to 228 electrodes improved the accuracy of the inverse solutions. However, the use of 120 electrodes concentrated around the stomach was able to achieve similar results. The most efficient electrode configuration for our model involved 120 electrodes with an inter-electrode distance of 32 mm.

Toward the virtual stomach: progress in multiscale modeling of gastric electrophysiology and motility

Experimental progress in investigating normal and disordered gastric motility is increasingly being complimented by sophisticated multiscale modeling studies. Mathematical modeling has become a valuable tool in this effort, as there is an ever-increasing need to gain an integrative and quantitative understanding of how physiological mechanisms achieve coordinated functions across multiple biophysical scales. These interdisciplinary efforts have been particularly notable in the area of gastric electrophysiology, where they are beginning to yield a comprehensive and integrated in silico organ modeling framework, or 'virtual stomach'. At the cellular level, a number of biophysically based mathematical cell models have been developed, and these are now being applied in areas including investigations of gastric electrical pacemaker mechanisms, smooth muscle electrophysiology, and electromechanical coupling. At the tissue level, micro-structural models are being creatively developed and employed to investigate clinically significant questions, such as the functional effects of ICC degradation on gastrointestinal (GI) electrical activation. At the organ level, high-resolution electrical mapping and modeling studies are combined to provide improved insights into normal and dysrhythmic gastric electrical activation. These efforts are also enabling detailed forward and inverse modeling studies at the 'whole body' level, with implications for diagnostic techniques for gastric dysrhythmias. These recent advances, together with several others highlighted in this review, collectively demonstrate a powerful trend toward applying mathematical models to effectively investigate structure-function relationships and overcome multiscale challenges in basic and clinical GI research.

Arrhythmic risk biomarkers for the assessment of drug cardiotoxicity: from experiments to computer simulations

In this paper, we illustrate how advanced computational modelling and simulation can be used to investigate drug-induced effects on cardiac electrophysiology and on specific biomarkers of pro-arrhythmic risk. To do so, we first perform a thorough literature review of proposed arrhythmic risk biomarkers from the ionic to the electrocardiogram levels. The review highlights the variety of proposed biomarkers, the complexity of the mechanisms of drug-induced pro-arrhythmia and the existence of significant animal species differences in drug-induced effects on cardiac electrophysiology. Predicting drug-induced pro-arrhythmic risk solely using experiments is challenging both preclinically and clinically, as attested by the rise in the cost of releasing new compounds to the market. Computational modelling and simulation has significantly contributed to the understanding of cardiac electrophysiology and arrhythmias over the last 40 years. In the second part of this paper, we illustrate how state-of-the-art open source computational modelling and simulation tools can be used to simulate multi-scale effects of drug-induced ion channel block in ventricular electrophysiology at the cellular, tissue and whole ventricular levels for different animal species. We believe that the use of computational modelling and simulation in combination with experimental techniques could be a powerful tool for the assessment of drug safety pharmacology.

The application of subspace preconditioned LSQR algorithm for solving the electrocardiography inverse problem

Regularization is an effective method for the solution of ill-posed ECG inverse problems, such as computing epicardial potentials from body surface potentials. The aim of this work was to explore more robust regularization-based solutions through the application of subspace preconditioned LSQR (SP-LSQR) to the study of model-based ECG inverse problems. Here, we presented three different subspace splitting methods, i.e., SVD, wavelet transform and cosine transform schemes, to the design of the preconditioners for ill-posed problems, and to evaluate the performance of algorithms using a realistic heart-torso model simulation protocol. The results demonstrated that when compared with the LSQR, LSQR-Tik and Tik-LSQR method, the SP-LSQR produced higher efficiency and reconstructed more accurate epcicardial potential distributions. Amongst the three applied subspace splitting schemes, the SVD-based preconditioner yielded the best convergence rate and outperformed the other two in seeking the inverse solutions. Moreover, when optimized by the genetic algorithms (GA), the performances of SP-LSQR method were enhanced. The results from this investigation suggested that the SP-LSQR was a useful regularization technique for cardiac inverse problems.

Computational cardiac atlases: from patient to population and back

Integrative models of cardiac physiology are important for understanding disease and planning intervention. Multimodal cardiovascular imaging plays an important role in defining the computational domain, the boundary/initial conditions, and tissue function and properties. Computational models can then be personalized through information derived from in vivo and, when possible, non-invasive images. Efforts are now established to provide Web-accessible structural and functional atlases of the normal and pathological heart for clinical, research and educational purposes. Efficient and robust statistical representations of cardiac morphology and morphodynamics can thereby be obtained, enabling quantitative analysis of images based on such representations. Statistical models of shape and appearance can be built automatically from large populations of image datasets by minimizing manual intervention and data collection. These methods facilitate statistical analysis of regional heart shape and wall motion characteristics across population groups, via the application of parametric mathematical modelling tools. These parametric modelling tools and associated ontological schema also facilitate data fusion between different imaging protocols and modalities as well as other data sources. Statistical priors can also be used to support cardiac image analysis with applications to advanced quantification and subject-specific simulations of computational physiology.

Spatial-temporal filter effect in a computer model study of ventricular fibrillation

Prediction of countershock success from ventricular fibrillation (VF) ECG is a major challenge in critical care medicine. Recent findings indicate that stable, high frequency mother rotors are one possible mechanism maintaining VF. A computer model study was performed to investigate how epicardiac sources are reflected in the ECG. In the cardiac tissues of two computer models - a model with cubic geometry and a simplified torso model with a left ventricle - a mother rotor was induced by increasing the potassium rectifier current. On the epicardium, the dominant frequency (DF) map revealed a constant DF of 23 Hz (cubic model) and 24.4 Hz (torso model) in the region of the mother rotor, respectively. A sharp drop of frequency (3-18 Hz in the cubic model and 12.4-18 Hz in the torso model) occurred in the surrounding epicardial tissue of chaotic fibrillatory conduction. While no organized pattern was observable on the body surface of the cubic model, the mother rotor frequency can be identified in the anterior surface of the torso model because of the chosen position of the mother rotor in the ventricle (shortest distance to the body surface). Nevertheless, the DFs were damped on the body surfaces of both models (4.6-8.5 Hz in the cubic model and 14.4-16.4 Hz in the torso model). Thus, it was shown in this computer model study that wave propagation transforms the spatial low pass filtering of the thorax into a temporal low pass. In contrast to the resistive-capacitive low pass filter formed by the tissue, this spatial-temporal low pass filter becomes effective at low frequencies (tens of Hertz). This effect damps the high frequency components arising from the heart and it hampers a direct observation of rapid, organized sources of VF in the ECGs, when in an emergency case an artifact-free recording is not possible.

Two hybrid regularization frameworks for solving the electrocardiography inverse problem

In this paper, two hybrid regularization frameworks, LSQR-Tik and Tik-LSQR, which integrate the properties of the direct regularization method (Tikhonov) and the iterative regularization method (LSQR), have been proposed and investigated for solving ECG inverse problems. The LSQR-Tik method is based on the Lanczos process, which yields a sequence of small bidiagonal systems to approximate the original ill-posed problem and then the Tikhonov regularization method is applied to stabilize the projected problem. The Tik-LSQR method is formulated as an iterative LSQR inverse, augmented with a Tikhonov-like prior information term. The performances of these two hybrid methods are evaluated using a realistic heart-torso model simulation protocol, in which the heart surface source method is employed to calculate the simulated epicardial potentials (EPs) from the action potentials (APs), and then the acquired EPs are used to calculate simulated body surface potentials (BSPs). The results show that the regularized solutions obtained by the LSQR-Tik method are approximate to those of the Tikhonov method, the computational cost of the LSQR-Tik method, however, is much less than that of the Tikhonov method. Moreover, the Tik-LSQR scheme can reconstruct the epcicardial potential distribution more accurately, specifically for the BSPs with large noisy cases. This investigation suggests that hybrid regularization methods may be more effective than separate regularization approaches for ECG inverse problems.

Patient-specific volume conductor modeling for non-invasive imaging of cardiac electrophysiology

We propose a general workflow to numerically estimate the spread of electrical excitation in the patients' hearts. To this end, a semi-automatic segmentation pipeline for extracting the volume conductor model of structurally normal hearts is presented. The cardiac electrical source imaging technique aims to provide information about the spread of electrical excitation in order to assist the cardiologist in developing strategies for the treatment of cardiac arrhythmias. The volume conductor models of eight patients were extracted from cine-gated short-axis magnetic resonance imaging (MRI) data. The non-invasive estimation of electrical excitation was compared with the CARTO maps. The development of a volume conductor modeling pipeline for constructing a patient-specific volume conductor model in a fast and accurate way is one essential step to make the technique clinically applicable.

Anatomically realistic torso model for studying the relative decay of gastric electrical and magnetic fields

Non-invasive assessment of the gastro-intestinal system has not obtained widespread clinical acceptance despite the fact that the first electrogastrograms were recorded almost a century ago. One technique that is gaining acceptance for non-invasively assessing the gastrointestinal system is the recording of cutaneous electrogastrograms. It has been proposed that measurement of the gastric magnetic field (magnetogastrogram) may produce more reliable signals in the form of a vector field and also allows the signals to be obtained with non-contact sensors. In this study, an anatomically realistic torso model of the gastrointestinal system is used to investigate the relative decay of electrical and magnetic fields resulting from gastric electrical activity. Typically the electrical fields are measured on the skin surface while the magnetic fields are recorded at locations close to, but not in contact with the skin surface. This is the first study which has used a temporal and multiple dipole source model to simulate resultant electrical and magnetic fields.

GENE EXPRESSION OF STRETCH-ACTIVATED CHANNELS AND MECHANOELECTRIC FEEDBACK IN THE HEART

1. Mechanoelectric feedback (MEF) in the heart is the process by which mechanical forces on the myocardium can change its electrical properties. Mechanoelectric feedback has been demonstrated in many animal models, ranging from isolated cells, through isolated hearts to whole animals. In humans, MEF has been demonstrated directly in both the atria and the ventricles. It seems likely that MEF provides either the trigger or the substrate for some types of clinically important arrhythmias. 2. Mechanoelectric feedback may arise because of the presence of stretch-sensitive (or mechano-sensitive) ion channels in the cell membrane of the cardiac myocytes. Two types have been demonstrated: (i) a non-specific cation channel (stretch-activated channel (SAC); conductance of approximately 25 pS); and (ii) a potassium channel with a conductance of approximately 100 pS. The gene coding for the SAC has not yet been identified. The gene for the potassium channel is likely to be TREK, a member of the tandem pore potassium channel gene family. We have recorded stretch-sensitive potassium channels in rat isolated myocytes that have the properties of TREK channels expressed in heterologous systems. 3. It has been shown that TREK mRNA is expressed heterogeneously in the rat ventricular wall, with 17-fold more expression in endocardial compared with epicardial cells. This difference is reflected in the TREK currents recorded from endocardial and epicardial cells using whole-cell patch-clamp techniques, although the difference in current density was less pronounced (approximately threefold). Consistent with this, we show here that when the ventricle is stretched by inflation of an intraventricular balloon in a Langendorff perfused rat isolated heart, action potential shortening was more pronounced in the endocardium (30% shortening at 40 mmHg) compared with that in the epicardium (10% shortening at the same pressure). 4. Computer models of the mechanics of the (pig) heart show pronounced spatial variations in strain in the myocardium with large transmural differences (in the left ventricle in particular) and also large differences between the base and apex of the ventricle. 5. The importance of MEF and the non-homogeneous gene expression and strain distribution for arrhythmias is discussed.

Computational simulations of the human magneto- and electroenterogram

Many functional pathologies of the small intestine are difficult to diagnose clinically without an invasive surgical intervention. Often such conditions are associated with a disruption of the normal electrical activity occurring within the musculature of the small intestine. The far field electrical signals on the torso surface arising from the electrical activity within the small intestine cannot be reliably measured. However, it has been shown that abnormal electrical activity in the small intestine can be distinguished by recording the magnetic fields of intestinal origin immediately outside the torso surface. We have developed an anatomically-based computational model to simulate slow wave propagation in the small intestine, the resulting cutaneous electrical field and the magnetic field outside the torso. Using both a one-dimensional and a three-dimensional model of the duodenum we investigate the degree of detail that is required to realistically simulate this far field activity. Our results indicate that some of the qualitative behavior in the far field activity can be replicated using a one-dimensional model, although there are clear situations where the greater level modeling detail is required.

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.

Multiscale modelling of human gastric electric activity: can the electrogastrogram detect functional electrical uncoupling?

During recent years there has been a growing interest in the assessment of gastric electrical health through cutaneous abdominal recordings. The analysis of such recordings is largely limited to an inspection of frequency dynamics, and this has raised doubts as to whether functional gastric electrical uncoupling can be detected using this technique. We describe here a computational approach to the problem in which the equations governing the underlying physics of the problem have been solved over an anatomically detailed human torso geometry. Cellular electrical activity was embedded within a stomach tissue model, and this was coupled to the torso using an equivalent current source approach. Simulations were performed in which normal and functionally uncoupled (through the introduction of an ectopic antral pacemaker) gastric slow wave activity was present, and corresponding cutaneous electrogastrograms were produced. These were subsequently analysed using the currently recommended techniques, and it was found that the functionally uncoupled situation was indistinguishable from normal slow wave activity using this approach.

Semiautomatic volume conductor modeling pipeline for imaging the cardiac electrophysiology noninvasively

In this paper we present an approach for extracting patient individual volume conductor models (VCM) using volume data acquired from Magnetic Resonance Imaging (MRI) for computational biology of electrical excitation in the patient's heart. The VCM consists of the compartments chest surface, lung surfaces, the atrial and ventricular myocardium, and the blood masses. For each compartment a segmentation approach with no or little necessity of user interaction was implemented and integrated into a VCM segmentation pipeline to enable the inverse problem of electrocardiography to become clinical applicable. The segmentation pipeline was tested using volume data from ten patients with structurally normal hearts.

Challenges facing validation of noninvasive electrical imaging of the heart

Noninvasive imaging of regional cardiac electrophysiology remains an elusive target. Such imaging is still in its infancy, particularly in comparison to structural imaging modalities such as magnetic resonance imaging (MRI), x-ray computed tomography (CT), and ultrasound. We present an overview of noninvasive ECG imaging, and the challenges and successes of the various techniques across a range of applications. Unlike MRI and CT, reconstructing cardiac electrophysiology from remote body surface measurements is a highly ill-posed problem. We therefore first review the theoretical considerations and associated algorithms that are used to address this issue. We then focus on the important issue of validation, and review and contrast recent advances in this area. Efforts to validate ECG inverse procedures using a modeling-based approach are addressed first. We then discuss various experimental studies that have been conducted to provide appropriate data for robust validations. We present new data that are simultaneously recorded from dense arrays of electrodes on the epicardium and body surface of anesthetized pigs during sinus rhythm, ventricular pacing, and regional ischemia. These data have been obtained specifically to help validate inverse ECG procedures, and form a useful supplement to recent clinical validation studies. Finally, clinical applications and outstanding issues regarding noninvasive imaging of regional cardiac electrophysiology are addressed.

Finite element modelling and simulations in cardiovascular mechanics and cardiology: A bibliography 1993–2004

The paper gives a bibliographical review of the finite element modelling and simulations in cardiovascular mechanics and cardiology from the theoretical as well as practical points of views. The bibliography lists references to papers, conference proceedings and theses/dissertations that were published between 1993 and 2004. At the end of this paper, more than 890 references are given dealing with subjects as: Cardiovascular soft tissue modelling; material properties; mechanisms of cardiovascular components; blood flow; artificial components; cardiac diseases examination; surgery; and other topics.

Giving form to the function of the heart: embedding cellular models in an anatomical framework

A computational framework is presented for integrating the electrical, mechanical, and biochemical functions of the heart. The construction of efficient finite element representations of canine and porcine ventricular geometry and microstructure is outlined. Computational techniques are applied to solve large deformation soft tissue mechanics by using orthotropic constitutive laws for myocardial tissue and models of active tension generation embedded at the Gauss points in the finite element mesh. The reaction-diffusion equations governing electrical current flow in the heart are solved on a grid of deforming material points that access systems of ordinary differential equations representing the cellular processes underlying the cardiac action potential. Navier-Stokes equations are solved to predict coronary blood flow in a system of branching blood vessels embedded in the deforming myocardium.

An anatomical model of the gastric system for producing bioelectric and biomagnetic fields

Between 60 and 70 million people in the United States are affected by gastrointestinal disorders. Many of these conditions are difficult to assess without surgical intervention and accurate noninvasive techniques to aid in clinical assessment are needed. Through the use of a superconducting quantum interference device (SQUID) gradiometer, the weak magnetic field generated as a result of muscular activity in the digestive system can be measured. However, the interpretation of these magnetic recordings remains a significant challenge. We have created an anatomically realistic biophysically based mathematical model of the human digestive system and using this model normal gastric electrical control activity (ECA) has been simulated. The external magnetic fields associated with this gastric ECA have also been computed and are shown to be in qualitative agreement with recordings taken from normal individuals. The model framework thus provides a rational basis from which to begin interpreting magnetic recordings from normal and diseased individuals.

Altered T Wave Dynamics in a Contracting Cardiac Model

INTRODUCTION

The implications of mechanical deformation on calculated body surface potentials are investigated using a coupled biophysically based model.

METHODS AND RESULTS

A cellular model of cardiac excitation-contraction is embedded in an anatomically accurate two-dimensional transverse cross-section of the cardiac ventricles and human torso. Waves of activation and contraction are induced by the application of physiologically realistic boundary conditions and solving the bidomain and finite deformation equations. Body surface potentials are calculated from these activation profiles by solving Laplace's equation in the passive surrounding tissues. The effect of cardiac deformation on electrical activity, induced by contraction, is demonstrated in both single-cell and tissue models. Action potential duration is reduced by 7 msec when the single cell model is subjected to a 10% contraction ramp applied over 400 msec. In the coupled electromechanical tissue model, the T wave of the ECG is shown to occur 18 msec earlier compared to an uncoupled excitation model. To assess the relative effects of myocardial deformation on the ECG, the activation sequence and tissue deformation are separated. The coupled and uncoupled activation sequences are mapped onto the undeforming and deforming meshes, respectively. ECGs are calculated for both mappings.

CONCLUSION

Adding mechanical contraction to a mathematical model of the heart has been shown to shift the T wave on the ECG to the left. Although deformation of the myocardium resulting from contraction reduces the T wave amplitude, cell stretch producing altered cell membrane kinetics is the major component of this temporal shift.