Nonuniform muscle fiber orientation causes spiral wave drift in a finite element model of cardiac action potential propagation

Right ventricular insertion promotes reinitiation of ventricular fibrillation in defibrillation failure

BACKGROUND

Shocks near defibrillation threshold (nDFT) strength commonly extinguish all ventricular fibrillation (VF) wavefronts, but a train of rapid, well-organized postshock activations (PAs) typically appears before sinus rhythm ensues. If one of the PA waves undergoes partial propagation block (wavebreak), reentry may be induced, causing VF to reinitiate and the shock to fail.

OBJECTIVE

The purpose of this study was to determine whether wavebreak leading to VF reinititation following nDFT shocks occurs preferentially at the right ventricular insertion (RVI), which previous studies have identified as a key site for wavebreak.

METHODS

We used panoramic optical mapping to image the ventricular epicardium of 6 isolated swine hearts during nDFT defibrillation episodes. After each experiment, the hearts were fixed and their geometry scanned with magnetic resonance imaging (MRI). The MRI and mapping datasets were spatially coregistered. For failed shocks, we identified the site of the first wavebreak of a PA wave during VF reinitiation.

RESULTS

We recorded 59 nDFT failures. In 31 of these, the first wavebreak event occurred within 1 cm of the RVI centerline, most commonly on the anterior side of the right ventricular insertion (aRVI) (23/31). The aRVI region occupies 16.8% ± 2.5% of the epicardial surface and would be expected to account for only 10 wavebreaks if they were uniformly distributed. By χ2 analysis, aRVI wavebreaks were significantly overrepresented.

CONCLUSION

The anterior RVI is a key site in promoting nDFT failure. Targeting this site to prevent wavebreak could convert defibrillation failure to success and improve defibrillation efficacy.

Drift of Scroll Waves in a Mathematical Model of a Heterogeneous Human Heart Left Ventricle

Rotating spiral waves of electrical excitation underlie many dangerous cardiac arrhythmias. The heterogeneity of myocardium is one of the factors that affects the dynamics of such waves. In this paper, we present results of our simulations for scroll wave dynamics in a heterogeneous model of the human left ventricle with analytical anatomically based representation of the geometry and anisotropy. We used a set of 18 coupled differential equations developed by ten Tusscher and Panfilov (TP06 model) which describes human ventricular cells based on their measured biophysical properties. We found that apicobasal heterogeneity dramatically changes the scroll wave dynamics. In the homogeneous model, the scroll wave annihilates at the base, but the moderate heterogeneity causes the wave to move to the apex and then continuously rotates around it. The rotation speed increased with the degree of the heterogeneity. However, for large heterogeneity, we observed formation of additional wavebreaks and the onset of complex spatio-temporal patterns. Transmural heterogeneity did not change the dynamics and decreased the lifetime of the scroll wave with an increase in heterogeneity. Results of our numerical experiments show that the apex may be a preferable location of the scroll wave, which may be important for development of clinical interventions.

Muscle Thickness and Curvature Influence Atrial Conduction Velocities

Electroanatomical mapping is currently used to provide clinicians with information about the electrophysiological state of the heart and to guide interventions like ablation. These maps can be used to identify ectopic triggers of an arrhythmia such as atrial fibrillation (AF) or changes in the conduction velocity (CV) that have been associated with poor cell to cell coupling or fibrosis. Unfortunately, many factors are known to affect CV, including membrane excitability, pacing rate, wavefront curvature, and bath loading, making interpretation challenging. In this work, we show how endocardial conduction velocities are also affected by the geometrical factors of muscle thickness and wall curvature. Using an idealized three-dimensional strand, we show that transverse conductivities and boundary conditions can slow down or speed up signal propagation, depending on the curvature of the muscle tissue. In fact, a planar wavefront that is parallel to a straight line normal to the mid-surface does not remain normal to the mid-surface in a curved domain. We further demonstrate that the conclusions drawn from the idealized test case can be used to explain spatial changes in conduction velocities in a patient-specific reconstruction of the left atrial posterior wall. The simulations suggest that the widespread assumption of treating atrial muscle as a two-dimensional manifold for electrophysiological simulations will not accurately represent the endocardial conduction velocities in regions of the heart thicker than 0.5 mm with significant wall curvature.

Multiphysics and multiscale modelling, data-model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics

With heart and cardiovascular diseases continually challenging healthcare systems worldwide, translating basic research on cardiac (patho)physiology into clinical care is essential. Exacerbating this already extensive challenge is the complexity of the heart, relying on its hierarchical structure and function to maintain cardiovascular flow. Computational modelling has been proposed and actively pursued as a tool for accelerating research and translation. Allowing exploration of the relationships between physics, multiscale mechanisms and function, computational modelling provides a platform for improving our understanding of the heart. Further integration of experimental and clinical data through data assimilation and parameter estimation techniques is bringing computational models closer to use in routine clinical practice. This article reviews developments in computational cardiac modelling and how their integration with medical imaging data is providing new pathways for translational cardiac modelling.

Material stiffness parameters as potential predictors of presence of left ventricle myocardial infarction: 3D echo-based computational modeling study

Background

Ventricle material properties are difficult to obtain under in vivo conditions and are not readily available in the current literature. It is also desirable to have an initial determination if a patient had an infarction based on echo data before more expensive examinations are recommended. A noninvasive echo-based modeling approach and a predictive method were introduced to determine left ventricle material parameters and differentiate patients with recent myocardial infarction (MI) from those without.

Methods

Echo data were obtained from 10 patients, 5 with MI (Infarct Group) and 5 without (Non-Infarcted Group). Echo-based patient-specific computational left ventricle (LV) models were constructed to quantify LV material properties. All patients were treated equally in the modeling process without using MI information. Systolic and diastolic material parameter values in the Mooney-Rivlin models were adjusted to match echo volume data. The equivalent Young’s modulus (YM) values were obtained for each material stress–strain curve by linear fitting for easy comparison. Predictive logistic regression analysis was used to identify the best parameters for infract prediction.

Results

The LV end-systole material stiffness (ES-YM_f) was the best single predictor among the 12 individual parameters with an area under the receiver operating characteristic (ROC) curve of 0.9841. LV wall thickness (WT), material stiffness in fiber direction at end-systole (ES-YM_f) and material stiffness variation (∆YM_f) had positive correlations with LV ejection fraction with correlation coefficients r = 0.8125, 0.9495 and 0.9619, respectively. The best combination of parameters WT + ∆YM_f was the best over-all predictor with an area under the ROC curve of 0.9951.

Conclusion

Computational modeling and material stiffness parameters may be used as a potential tool to suggest if a patient had infarction based on echo data. Large-scale clinical studies are needed to validate these preliminary findings.

Modeling Active Contraction and Relaxation of Left Ventricle Using Different Zero-load Diastole and Systole Geometries for Better Material Parameter Estimation and Stress/Strain Calculations

Modeling ventricle active contraction based on in vivo data is extremely challenging because of complex ventricle geometry, dynamic heart motion and active contraction where the reference geometry (zero-stress geometry) changes constantly. A new modeling approach using different diastole and systole zero-load geometries was introduced to handle the changing zero-load geometries for more accurate stress/strain calculations. Echo image data were acquired from 5 patients with infarction (Infarct Group) and 10 without (Non-Infarcted Group). Echo-based computational two-layer left ventricle models using one zero-load geometry (1G) and two zero-load geometries (2G) were constructed. Material parameter values in Mooney-Rivlin models were adjusted to match echo volume data. Effective Young's moduli (YM) were calculated for easy comparison. For diastole phase, begin-filling (BF) mean YM value in the fiber direction (YM_f) was 738% higher than its end-diastole (ED) value (645.39 kPa vs. 76.97 kPa, p=3.38E-06). For systole phase, end-systole (ES) YM_f was 903% higher than its begin-ejection (BE) value (1025.10 kPa vs. 102.11 kPa, p=6.10E-05). Comparing systolic and diastolic material properties, ES YM_f was 59% higher than its BF value (1025.10 kPa vs. 645.39 kPa. p=0.0002). BE mean stress value was 514% higher than its ED value (299.69 kPa vs. 48.81 kPa, p=3.39E-06), while BE mean strain value was 31.5% higher than its ED value (0.9417 vs. 0.7162, p=0.004). Similarly, ES mean stress value was 562% higher than its BF value (19.74 kPa vs. 2.98 kPa, p=6.22E-05), and ES mean strain value was 264% higher than its BF value (0.1985 vs. 0.0546, p=3.42E-06). 2G models improved over 1G model limitations and may provide better material parameter estimation and stress/strain calculations.

Asymptotic wave propagation in excitable media

Wave shape and velocity are important issues in reaction-diffusion systems, and are often the result of competition in media with heterogeneous conduction properties. Asymptotic wave front propagation at maximal conduction velocity has been previously reported in the context of anisotropic cardiac tissue, but it is unknown whether this is a universal property of excitable tissues where conduction velocity can be locally modulated by mechanisms other than anisotropy. Here, we investigate the impact of conduction heterogeneities and boundary effects on wave propagation in excitable media. Following a theoretical analysis, we find that wave-front cusps occur where local velocity is reduced and that asymptotic wave fronts propagate at the maximal translational conduction velocity. Simulations performed in different reaction-diffusion systems, including cardiac tissue, confirm our theoretical findings. We conclude that this property can be found in a wide range of reaction-diffusion systems with excitable dynamics and that asymptotic wave-front shapes can be predicted.

Structural contributions to fibrillatory rotors in a patient-derived computational model of the atria

AIMS

The aim of this study was to investigate structural contributions to the maintenance of rotors in human atrial fibrillation (AF) and possible mechanisms of termination.

METHODS AND RESULTS

A three-dimensional human biatrial finite element model based on patient-derived computed tomography and arrhythmia observed at electrophysiology study was used to study AF. With normal physiological electrical conductivity and effective refractory periods (ERPs), wave break failed to sustain reentrant activity or electrical rotors. With depressed excitability, decreased conduction anisotropy, and shorter ERP characteristic of AF, reentrant rotors were readily maintained. Rotors were transiently or permanently trapped by fibre discontinuities on the lateral wall of the right atrium near the tricuspid valve orifice and adjacent to the crista terminalis, both known sites of right atrial arrhythmias. Modelling inexcitable regions near the rotor tip to simulate fibrosis anchored the rotors, converting the arrhythmia to macro-reentry. Accordingly, increasing the spatial core of inexcitable tissue decreased the frequency of rotation, widened the excitable gap, and enabled an external wave to impinge on the rotor core and displace the source.

CONCLUSION

These model findings highlight the importance of structural features in rotor dynamics and suggest that regions of fibrosis may anchor fibrillatory rotors. Increasing extent of fibrosis and scar may eventually convert fibrillation to excitable gap reentry. Such macro-reentry can then be eliminated by extending the obstacle or by external stimuli that penetrate the excitable gap.

Infarcted Left Ventricles Have Stiffer Material Properties and Lower Stiffness Variation: Three-Dimensional Echo-Based Modeling to Quantify In Vivo Ventricle Material Properties

Methods to quantify ventricle material properties noninvasively using in vivo data are of great important in clinical applications. An ultrasound echo-based computational modeling approach was proposed to quantify left ventricle (LV) material properties, curvature, and stress/strain conditions and find differences between normal LV and LV with infarct. Echo image data were acquired from five patients with myocardial infarction (I-Group) and five healthy volunteers as control (H-Group). Finite element models were constructed to obtain ventricle stress and strain conditions. Material stiffening and softening were used to model ventricle active contraction and relaxation. Systolic and diastolic material parameter values were obtained by adjusting the models to match echo volume data. Young's modulus (YM) value was obtained for each material stress-strain curve for easy comparison. LV wall thickness, circumferential and longitudinal curvatures (C- and L-curvature), material parameter values, and stress/strain values were recorded for analysis. Using the mean value of H-Group as the base value, at end-diastole, I-Group mean YM value for the fiber direction stress-strain curve was 54% stiffer than that of H-Group (136.24 kPa versus 88.68 kPa). At end-systole, the mean YM values from the two groups were similar (175.84 kPa versus 200.2 kPa). More interestingly, H-Group end-systole mean YM was 126% higher that its end-diastole value, while I-Group end-systole mean YM was only 29% higher that its end-diastole value. This indicated that H-Group had much greater systole-diastole material stiffness variations. At beginning-of-ejection (BE), LV ejection fraction (LVEF) showed positive correlation with C-curvature, stress, and strain, and negative correlation with LV volume, respectively. At beginning-of-filling (BF), LVEF showed positive correlation with C-curvature and strain, but negative correlation with stress and LV volume, respectively. Using averaged values of two groups at BE, I-Group stress, strain, and wall thickness were 32%, 29%, and 18% lower (thinner), respectively, compared to those of H-Group. L-curvature from I-Group was 61% higher than that from H-Group. Difference in C-curvature between the two groups was not statistically significant. Our results indicated that our modeling approach has the potential to determine in vivo ventricle material properties, which in turn could lead to methods to infer presence of infarct from LV contractibility and material stiffness variations. Quantitative differences in LV volume, curvatures, stress, strain, and wall thickness between the two groups were provided.

Drift laws for spiral waves on curved anisotropic surfaces

Rotating spiral waves organize spatial patterns in chemical, physical, and biological excitable systems. Factors affecting their dynamics, such as spatiotemporal drift, are of great interest for particular applications. Here, we propose a quantitative description for spiral wave dynamics on curved surfaces which shows that for a wide class of systems, including the Belousov-Zhabotinsky reaction and anisotropic cardiac tissue, the Ricci curvature scalar of the surface is the main determinant of spiral wave drift. The theory provides explicit equations for spiral wave drift direction, drift velocity, and the period of rotation. Depending on the parameters, the drift can be directed to the regions of either maximal or minimal Ricci scalar curvature, which was verified by direct numerical simulations.

Attraction and repulsion of spiral waves by inhomogeneity of conduction anisotropy--a model of spiral wave interaction with electrical remodeling of heart tissue

Various forms of heart disease are associated with remodeling of the heart muscle, which results in a perturbation of cell-to-cell electrical coupling. These perturbations may alter the trajectory of spiral wave drift in the heart muscle. We investigate the effect of spatially extended inhomogeneity of transverse cell coupling on the spiral wave trajectory using a simple active media model. The spiral wave was either attracted or repelled from the center of inhomogeneity as a function of cell excitability and gradient of the cell coupling. High levels of excitability resulted in an attraction of the wave to the center of inhomogeneity, whereas low levels resulted in an escape and termination of the spiral wave. The spiral wave drift velocity was related to the gradient of the coupling and the initial position of the wave. In a diseased heart, a region of altered transverse coupling corresponds with local gap junction remodeling that may be responsible for stabilization-destabilization of spiral waves and hence reflect potentially important targets in the treatment of heart arrhythmias.

Panoramic optical mapping shows wavebreak at a consistent anatomical site at the onset of ventricular fibrillation

AIMS

The first seconds of ventricular fibrillation (VF) are well organized and can consist of just one to two rotating waves (rotors). New rotors are spawned when local propagation block causes wave fragmentation. We hypothesized that this process, which leads to fully developed VF, begins at a consistent anatomic site.

METHODS AND RESULTS

We initiated VF with a stimulus timed to the local T-wave in 10 isolated pig hearts. Hearts were stained with a voltage-sensitive dye and four video cameras recorded electrical propagation panoramically across the epicardium. In each VF episode, we identified the position of the first wavebreak event that produced new rotor(s) that persisted for at least one cycle. The first such wavebreak occurred along the anterior right ventricular insertion (ARVI) in 26 of 32 VF episodes. In these episodes, wavebreak sites were 6 ± 4 mm from the midline of the ARVI. In the remaining 6 episodes, wavebreak sites were 24 ± 5 mm from the midline on either the LV or RV. During rapid pacing, conduction speed was locally depressed at the ARVI when waves crossed parallel to the midline. Action potential duration (APD) was slightly longer (2.2 ± 2.1 ms) at the ARVI compared with other sites (P< 0.01). Temporal APD alternans were small and not unique to the break site, suggesting that dynamic APD properties were not the cause of wavebreak.

CONCLUSION

The ARVI is the dominant site for wavebreak at the onset of VF in normal myocardium. This may be due to the anatomic complexity of the region.

Multi-Physics MRI-Based Two-Layer Fluid-Structure Interaction Anisotropic Models of Human Right and Left Ventricles with Different Patch Materials: Cardiac Function Assessment and Mechanical Stress Analysis

Multi-physics right and left ventricle (RV/LV) fluid-structure interaction (FSI) models were introduced to perform mechanical stress analysis and evaluate the effect of patch materials on RV function. The FSI models included three different patch materials (Dacron scaffold, treated pericardium, and contracting myocardium), two-layer construction, fiber orientation, and active anisotropic material properties. The models were constructed based on cardiac magnetic resonance (CMR) images acquired from a patient with severe RV dilatation and solved by ADINA. Our results indicate that the patch model with contracting myocardium leads to decreased stress level in the patch area, improved RV function and patch area contractility.

Image-Based Patient-Specific Ventricle Models with Fluid-Structure Interaction for Cardiac Function Assessment and Surgical Design Optimization

Recent advances in medical imaging technology and computational modeling techniques are making it possible that patient-specific computational ventricle models be constructed and used to test surgical hypotheses and replace empirical and often risky clinical experimentation to examine the efficiency and suitability of various reconstructive procedures in diseased hearts. In this paper, we provide a brief review on recent development in ventricle modeling and its potential application in surgical planning and management of tetralogy of Fallot (ToF) patients. Aspects of data acquisition, model selection and construction, tissue material properties, ventricle layer structure and tissue fiber orientations, pressure condition, model validation and virtual surgery procedures (changing patient-specific ventricle data and perform computer simulation) were reviewed. Results from a case study using patient-specific cardiac magnetic resonance (CMR) imaging and right/left ventricle and patch (RV/LV/Patch) combination model with fluid-structure interactions (FSI) were reported. The models were used to evaluate and optimize human pulmonary valve replacement/insertion (PVR) surgical procedure and patch design and test a surgical hypothesis that PVR with small patch and aggressive scar tissue trimming in PVR surgery may lead to improved recovery of RV function and reduced stress/strain conditions in the patch area.

Change in conduction velocity due to fiber curvature in cultured neonatal rat ventricular myocytes

Computer modeling of cardiac propagation suggests that curvature of muscle fibers modulates conduction velocity (CV). The effect could be involved in arrhythmogenesis by altering the dynamics of reentrant wavefronts or by causing propagation block. To verify the existence of this effect experimentally, we measured CV in anisotropic neonatal rat ventricular myocyte monolayers. The orientation of the cells was directed by scratches machined into plastic coverslips. Each substrate contained a region in which scratch radius of curvature varied from 0.25 to 1.0 cm. The CV anisotropy ratio (longitudinal CV/transverse CV in straight fiber regions) was 2.3 +/- 0.3 (n = 38). We initiated wavefronts transverse to fibers with the fibers either curving toward or away from the wavefronts. Action potentials were recorded using a potentiometric dye and a video camera. Propagation was faster (p = 0.0003) when fibers curved toward wavefronts than when fibers curved in the opposite direction. The mean CV difference was 0.38 +/- 0.44 cm/s (n = 24), which is 3.5% of nominal straight fiber transverse CV (11.0 +/- 3.2 cm/s). The effect was also present (p = 0.07) when pacing was slowed from 350 to 500 ms (n = 6). In a control group (n = 8) with uncurved fibers, CV was the same in both directions (p = NS). We conclude that fiber curvature is a factor in modulating cardiac propagation.

Patient-specific MRI-based 3D FSI RV/LV/patch models for pulmonary valve replacement surgery and patch optimization

A patient-specific right/left ventricle and patch (RV/LV/patch) combination model with fluid-structure interactions (FSIs) was introduced to evaluate and optimize human pulmonary valve replacement/insertion (PVR) surgical procedure and patch design. Cardiac magnetic resonance (CMR) imaging studies were performed to acquire ventricle geometry, flow velocity, and flow rate for healthy volunteers and patients needing RV remodeling and PVR before and after scheduled surgeries. CMR-based RV/LV/patch FSI models were constructed to perform mechanical analysis and assess RV cardiac functions. Both pre- and postoperation CMR data were used to adjust and validate the model so that predicted RV volumes reached good agreement with CMR measurements (error <3%). Two RV/LV/patch models were made based on preoperation data to evaluate and compare two PVR surgical procedures: (i) conventional patch with little or no scar tissue trimming, and (ii) small patch with aggressive scar trimming and RV volume reduction. Our modeling results indicated that (a) patient-specific CMR-based computational modeling can provide accurate assessment of RV cardiac functions, and (b) PVR with a smaller patch and more aggressive scar removal led to reduced stress/strain conditions in the patch area and may lead to improved recovery of RV functions. More patient studies are needed to validate our findings.

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.

Molecular mechanisms and global dynamics of fibrillation: an integrative approach to the underlying basis of vortex-like reentry

Art Winfree's scientific legacy has been particularly important to our laboratory whose major goal is to understand the mechanisms of ventricular fibrillation (VF). Here, we take an integrative approach to review recent studies on the manner in which nonlinear electrical waves organize to result in VF. We describe the contribution of specific potassium channel proteins and of the myocardial fiber structure to such organization. The discussion centers on data derived from a model of stable VF in the Langendorff-perfused guinea pig heart that demonstrates distinct patterns of organization in the left (LV) and right (RV) ventricles. Analysis of optical mapping data reveals that VF excitation frequencies are distributed throughout the ventricles in clearly demarcated domains. The highest frequency domains are found on the anterior wall of the LV at a location where sustained reentrant activity is present. The optical data suggest that a high frequency rotor that remains stationary in the LV is the mechanism that sustains VF in this model. Computer simulations predict that the inward rectifying potassium current (IK1) is an essential determinant of rotor stability and frequency, and patch-clamp results strongly suggest that the outward component of IK1 of cells in the LV is significantly larger than in the RV. Additional computer simulations and analytical procedures predict that the filaments of the reentrant activity (scroll waves) adopt a non-random configuration depending on fiber organization within the ventricular wall. Using the minimal principle we have concluded that filaments align with the trajectory of least resistance (i.e. the geodesic) between their endpoints. Overall, the data discussed have opened new and potentially exciting avenues of research on the possible role played by inward rectifier channels in the mechanism of VF, as well as the organization of its reentrant sources in three-dimensional cardiac muscle. Such an integrative approach may lead us toward an understanding of the molecular and structural basis of VF and hopefully to new preventative approaches.

Facilitating arrhythmia simulation: the method of quantitative cellular automata modeling and parallel running

Background

Many arrhythmias are triggered by abnormal electrical activity at the ionic channel and cell level, and then evolve spatio-temporally within the heart. To understand arrhythmias better and to diagnose them more precisely by their ECG waveforms, a whole-heart model is required to explore the association between the massively parallel activities at the channel/cell level and the integrative electrophysiological phenomena at organ level.

Methods

We have developed a method to build large-scale electrophysiological models by using extended cellular automata, and to run such models on a cluster of shared memory machines. We describe here the method, including the extension of a language-based cellular automaton to implement quantitative computing, the building of a whole-heart model with Visible Human Project data, the parallelization of the model on a cluster of shared memory computers with OpenMP and MPI hybrid programming, and a simulation algorithm that links cellular activity with the ECG.

Results

We demonstrate that electrical activities at channel, cell, and organ levels can be traced and captured conveniently in our extended cellular automaton system. Examples of some ECG waveforms simulated with a 2-D slice are given to support the ECG simulation algorithm. A performance evaluation of the 3-D model on a four-node cluster is also given.

Conclusions

Quantitative multicellular modeling with extended cellular automata is a highly efficient and widely applicable method to weave experimental data at different levels into computational models. This process can be used to investigate complex and collective biological activities that can be described neither by their governing differentiation equations nor by discrete parallel computation. Transparent cluster computing is a convenient and effective method to make time-consuming simulation feasible. Arrhythmias, as a typical case, can be effectively simulated with the methods described.

Electromechanical model of cardiac resynchronization in the dilated failing heart with left bundle branch block

Experimental studies have shown that biventricular pacing can improve systolic function in the failing heart with bundle branch block. The goal of this study was to develop and validate a three-dimensional computational model of the dilated failing heart with left bundle branch block to investigate how biventricular pacing can improve systolic mechanical performance and synchrony. In an anatomically detailed model of canine ventricular geometry, fiber architecture and Purkinje fiber network structure, a monodomain solution for anisotropic impulse conduction gave rise to electrical activation sequences that were consistent with experimentally observed patterns. Coupling this with regional myocardial mechanics computed for left branch bundle block and biventricular pacing showed good agreement with published regional fiber strains measured in dogs by using magnetic resonance imaging tagging. Biventricular pacing improved mechanical synchrony and systolic function in the computational model. The model may be a useful tool for investigating the pacing conditions required to achieve optimal mechanical improvement in the failing heart, especially because electrical synchrony does not correlate directly with mechanical synchrony and performance.

Relationship between regional shortening and asynchronous electrical activation in a three-dimensional model of ventricular electromechanics

INTRODUCTION

Asynchronous electrical activation can cause abnormalities in perfusion and pump function. An electromechanical model was used to investigate the mechanical effects of altered cardiac activation sequence.

METHODS AND RESULTS

We used an anatomically detailed three-dimensional computational model of the canine ventricular walls to investigate the relationship between regional electrical activation and the timing of fiber shortening during normal and ventricular paced beats. By including a simplified Purkinje fiber network and anisotropic impulse conduction in the model, computed electrical activation sequences were consistent with experimentally observed patterns. Asynchronous time courses of regional strains during beats stimulated from the left or right ventricular epicardium showed good agreement with published experimental measurements in dogs using magnetic resonance imaging tagging methods. When electrical depolarization in the model was coupled to the onset of local contractile tension development by a constant time delay of 8 msec, the mean delay from depolarization to the onset of systolic fiber shortening was 14 msec. However, the delay between the onset of fiber tension and initial shortening varied significantly; it was as late as 60 msec in some regions but was also as early as -50 msec (i.e., 42 msec before depolarization) in other regions, particularly the interventricular septum during free-wall pacing.

CONCLUSION

The large variation in delay times was attributable to several factors including local anatomic variations, the location of the site relative to the activation wavefront, and regional end-diastolic strain. Therefore, we conclude that these factors, which are intrinsic to three-dimensional ventricular function, make the regional sequence of fiber shortening an unreliable surrogate for regional depolarization or electromechanical activation in the intact ventricles.

Wave front fragmentation due to ventricular geometry in a model of the rabbit heart

The role of the heart's complex shape in causing the fragmentation of activation wave fronts characteristic of ventricular fibrillation (VF) has not been well studied. We used a finite element model of cardiac propagation capable of simulating functional reentry on curved two-dimensional surfaces to test the hypothesis that uneven surface curvature can cause local propagation block leading to proliferation of reentrant wave fronts. We found that when reentry was induced on a flat sheet, it rotated in a repeatable meander pattern without breaking up. However, when a model of the rabbit ventricles was formed from the same medium, reentrant wave fronts followed complex, nonrepeating trajectories. Local propagation block often occurred when wave fronts propagated across regions where the Gaussian curvature of the surface changed rapidly. This type of block did not occur every time wave fronts crossed such a region; rather, it only occurred when the wave front was very close behind the previous wave in the cycle and was therefore propagating into relatively inexcitable tissue. Close wave front spacing resulted from nonstationary reentrant propagation. Thus, uneven surface curvature and nonstationary reentrant propagation worked in concert to produce wave front fragmentation and complex activation patterns. None of the factors previously thought to be necessary for local propagation block (e.g., heterogeneous refractory period, steep action potential duration restitution) were present. We conclude that the complex geometry of the heart may be an important determinant of VF activation patterns. (c) 2002 American Institute of Physics.

Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity

It has become widely accepted that the most dangerous cardiac arrhythmias are due to reentrant waves, i.e., electrical wave(s) that recirculate repeatedly throughout the tissue at a higher frequency than the waves produced by the heart's natural pacemaker (sinoatrial node). However, the complicated structure of cardiac tissue, as well as the complex ionic currents in the cell, have made it extremely difficult to pinpoint the detailed dynamics of these life-threatening reentrant arrhythmias. A simplified ionic model of the cardiac action potential (AP), which can be fitted to a wide variety of experimentally and numerically obtained mesoscopic characteristics of cardiac tissue such as AP shape and restitution of AP duration and conduction velocity, is used to explain many different mechanisms of spiral wave breakup which in principle can occur in cardiac tissue. Some, but not all, of these mechanisms have been observed before using other models; therefore, the purpose of this paper is to demonstrate them using just one framework model and to explain the different parameter regimes or physiological properties necessary for each mechanism (such as high or low excitability, corresponding to normal or ischemic tissue, spiral tip trajectory types, and tissue structures such as rotational anisotropy and periodic boundary conditions). Each mechanism is compared with data from other ionic models or experiments to illustrate that they are not model-specific phenomena. Movies showing all the breakup mechanisms are available at http://arrhythmia.hofstra.edu/breakup and at ftp://ftp.aip.org/epaps/chaos/E-CHAOEH-12-039203/ INDEX.html. The fact that many different breakup mechanisms exist has important implications for antiarrhythmic drug design and for comparisons of fibrillation experiments using different species, electromechanical uncoupling drugs, and initiation protocols. (c) 2002 American Institute of Physics.

Spatial heterogeneity in refractoriness as a proarrhythmic substrate: theoretical evaluation by numerical simulation

Spatial heterogeneity in the refractoriness of the ventricular myocardium due to a regionally prolonged refractory period has often been observed in patients with cardiovascular disease as the substrate for functional reentrant tachyarrhythmias. The present study sought to determine how functional reentrant activity could occur due to the spatial heterogeneity, using numerical simulation. Spatial heterogeneity in the refractoriness was introduced into a two-dimensional array by the regionally prolonged refractory period expressed as a square cluster. Double stimulation, conducted from a single source, was introduced into 4 types of matrices, which differed in their level of spatial heterogeneity. A pseudoelectrocardiogram was calculated from these matrices. Spiral waves were initiated in all the matrices except for the lowest heterogeneous matrix. A vulnerable window of the coupling interval, which induced spiral waves, was observed and was wider in proportion to the level of the heterogeneity. A higher level of heterogeneity and more limited range of coupling intervals were required to sustain the spiral waves. Furthermore, in the pseudoelectrocardiogram, sustained spiral waves exhibited a waveform like that in torsades de pointes (TdP) and their transformation into ventricular fibrillation (VF). Spatial heterogeneity in refractoriness due to a regionally prolonged refractory period could be a substrate for functional reentrant tachyarrhythmias, possibly including TdP and VF.

Dynamics of intramural scroll waves in three-dimensional continuous myocardium with rotational anisotropy

It has been suggested that reentrant activity in three-dimensional cardiac muscle may be organized as a scroll wave rotating around a singularity line called the filament. Experimental studies indicate that filaments are often concealed inside the ventricular wall and consequently, scroll waves do not manifest reentrant activity on the surface. Here we analyse how such concealed scroll waves are affected by a twisted anisotropy resulting from rotation of layers of muscle fibers inside the ventricular wall. We used a computer model of a ventricular slab (15x15x15 mm(3)) with a fiber twist of 120 degrees from endocardium to epicardium. The action potential was simulated using FitzHugh-Nagumo equations. Scroll waves with rectilinear filaments were initiated at various depths of the slab and at different angles with respect to fiber orientation. The analysis shows that independent of initial conditions, after a certain transitional period, the filament aligns with the local fiber orientation. The alignment of the filament is determined by the directional variations in cell coupling due to fiber rotation and by boundary conditions. Our findings provide a mechanistic explanation for the prevalence of intramural reentry over transmural reentry during polymorphic ventricular tachycardia and fibrillation.

Effects of electroporation on the transmembrane potential distribution in a two-dimensional bidomain model of cardiac tissue

INTRODUCTION

Defibrillation shocks, when delivered through internal electrodes, establish transmembrane potentials (Vm) large enough to electroporate the membrane of cardiac cells. The effects of such shocks on the transmembrane potential distribution are investigated in a two-dimensional rectangular sheet of cardiac muscle modeled as a bidomain with unequal anisotropy ratios.

METHODS AND RESULTS

The membrane is represented by a capacitance Cm, a leakage conductance g(l) and a variable electroporation conductance G, whose rate of growth depends exponentially on the square of Vm. The stimulating current Io, 0.05-20 A/m, is delivered through a pair of electrodes placed 2 cm apart for stimulation along fibers and 1 cm apart for stimulation across fibers. Computer simulations reveal three categories of response to Io: (1) Weak Io, below 0.2 A/m, cause essentially no electroporation, and Vm increases proportionally to Io. (2) Strong Io, between 0.2 and 2.5 A/m, electroporate tissue under the physical electrode. Vm is no longer proportional to Io; in the electroporated region, the growth of Vm is halted and in the region of reversed polarity (virtual electrode), the growth of Vm is accelerated. (3) Very strong Io, above 2.5 A/m, electroporate tissue under the physical and the virtual electrodes. The growth of Vm in all electroporated regions is halted, and a further increase of Io increases both the extent of the electroporated regions and the electroporation conductance G.

CONCLUSION

These results indicate that electroporation of the cardiac membrane plays an important role in the distribution of Vm induced by defibrillation strength shocks.

Incidence, evolution, and spatial distribution of functional reentry during ventricular fibrillation in pigs

Functional reentry has been hypothesized to be an underlying mechanism of ventricular fibrillation (VF); however, its contribution to activation patterns during fully developed VF is unclear. We applied new quantitative pattern analysis techniques to mapping data acquired from a 21 x 24 unipolar electrode array (2-mm spacing) located on the ventricular epicardium of 7 open-chest, unsupported pigs. Data epochs 4 seconds long beginning 1, 10, 20, 30, and 40 seconds after electrical induction were analyzed. Reentrant circuits were automatically identified and quantified. We found that 2.3% of activation pathways could unambiguously be classified as reentrant. From scaling analysis, an additional 28% of the pathways may also have been reentrant. Reentry was short-lived with 1.5+/-1.5 (mean+/-SD) complete cycles per circuit. The fraction of reentrant pathways, number of cycles per circuit, cycle duration, and area and perimeter of the cores all increased significantly as VF progressed. Core drift speed decreased significantly. Neither the orientation of the cores nor the direction of drift was well predicted by the epicardial fiber orientation (r2=0.108 and 0.138, respectively, by linear regression). Reentrant circuits were clustered in regions of the epicardium. We conclude the following: (1) Epicardial reentry is relatively uncommon and short-lived during VF, suggesting either that sustained reentry is transmural or that mechanisms governing sustained reentry are relatively unimportant to the dynamics of VF. (2) Reentrant circuits become more common, larger, and longer-lived as VF progresses, which may explain a recently observed increase in VF organization during the first minute of VF. (3) The conditions necessary to induce and sustain reentry are distributed nonuniformly.

Modeling defibrillation: effects of fiber curvature

The goal of this modeling study is to demonstrate extinguishing of a spiral wave reentry in a sheet of myocardium that incorporates curved fibers. The tissue is represented as a homogeneous bidomain with unequal anisotropy ratios. The spiral wave is initiated via cross-field stimulation of the bidomain sheet. The defibrillation shock is delivered via two line electrodes that occupy opposite tissue boundaries. Simulation results demonstrate that large-scale regions of depolarization are induced under the cathode as well as at locations in the vicinity of the anode. For high shock strengths, the new wavefronts generated from the regions of induced depolarization restrict the spiral wave pathway and render the tissue too refractory to further maintain the reentry. Weak shocks leave large portions of the sheet unaffected allowing the spiral wave to find recovered tissue and thus survive.

Three-dimensional analysis of regional cardiac function: a model of rabbit ventricular anatomy

The three-dimensional geometry and anisotropic properties of the heart give rise to nonhomogeneous distributions of stress, strain, electrical activation and repolarization. In this article we review the ventricular geometry and myofiber architecture of the heart, and the experimental and modeling studies of three-dimensional cardiac mechanics and electrophysiology. The development of a three-dimensional finite element model of the rabbit ventricular geometry and fiber architecture is described in detail. Finally, we review the experimental results, from the level of the cell to the intact organ, which motivate the development of coupled three-dimensional models of cardiac electromechanics and mechanoelectric feedback.

Purkinje-muscle reentry as a mechanism of polymorphic ventricular arrhythmias in a 3-dimensional model of the ventricles

Multiple electrode mapping of the ventricles during complex tachyarrhythmias has revealed focal subendocardial activation whose mechanism remains unexplained. We hypothesized that reentry involving the Purkinje-muscle junctions (PMJs) may be a mechanism for such focal excitations. We have constructed an anatomically appropriate computerized 3-dimensional model of the mammalian ventricles that includes the Purkinje conduction system and 214 PMJs distributed throughout the endocardium. Isochronal maps during normal excitation, as well as during right or left bundle branch block, resembled experimental measurements and compared well with isochronal maps of propagation in the human heart. Activity observed at both sides of a PMJ in the model showed that propagation from Purkinje fibers to muscle was slower than in the opposite direction. Under these realistic and normal conditions, the evolution of reentrant activity involving muscle and the Purkinje network was simulated. The reentry pattern was independent of the initiation site. It evolved with drifting epicardial breakthroughs and transformed on the endocardium from focal activity to figure-of-8 reentry. In addition, the ECG amplitude undulated during the evolution, and decrease in the cycle period, apparent wavelength, and propagation velocity were observed. Finally, the reentry was terminated if the Purkinje system was disconnected from the muscle before it reached a relative steady state. The simulation results suggest the following: (1) Epicardial breakthroughs and endocardial focal activity may originate at the PMJs. (2) The ECG amplitude may decrease as the reentry stabilizes and the excitation wavelength decreases. (3) The Purkinje system may have a double role in the evolution of reentry: first, it is essential to the reentry at the initial stage; second, it may lead to the establishment of intramyocardial reentry, at which time the Purkinje system becomes irrelevant.

Anisotropy, fiber curvature, and bath loading effects on activation in thin and thick cardiac tissue preparations: simulations in a three-dimensional bidomain model

INTRODUCTION

A modeling study is presented to explore the effects of tissue conductivity, fiber orientation, and presence of an adjoining extracellular volume conductor on electrical conduction in cardiac muscle. Simulated results are compared with those of classical in vitro experiments on superfused thin layer preparations and on whole hearts.

METHODS AND RESULTS

The tissue is modeled as a three-dimensional bidomain block adjoining an isotropic bath. In the thin layer model, the fibers are assumed parallel. In the thick block model, fiber rotation, curvature, and tipping are incorporated. Results from the thin layer model explain experimental observations that the rate of rise of the entire action potential upstroke is faster and the magnitude of the extracellular potential is smaller across fibers than along fibers in a uniformly propagating front. The simulation identified that this behavior only arises in tissue with unequal anisotropy in the two spaces and adjoining an extracellular bath. Simulated conduction and potential distributions in the thick block model are shown to well approximate experimental maps. The potentials are sensitive to changes in the fiber orientations. A slight 5 degrees tipping of intramural fibers out of the planes parallel to the epicardium and endocardium will lead to an asymmetry of the magnitudes of the positive regions. In addition, the introduction of fiber curvature leads to more realistic isochrone and extracellular potential distributions. The orientation of the central negative region of the extracellular potential is shown to be determined by the average of the fiber direction at the plane of pacing and the plane of recording.

CONCLUSIONS

The simulations demonstrate the sensitivity of spread of activation and potential time courses and distributions to the underlying electrical properties in both thick and thin slabs. The bidomain model is shown to be a useful representation of cardiac tissue for interpreting experimental data of activation.

Imaging myocardial fiber architecture in vivo with magnetic resonance

Methods are presented to image the fiber architecture of the human myocardium in vitro and in vivo. NMR images are obtained of the diffusion anisotropy tensor, indicative of local myofiber orientation. Studies of cardiac necropsy specimens demonstrate classic features of ventricular myoarchitecture including the continuous endocardial to epicardial variation of fiber helix angles (angles to the ventricular circumferential direction) of approximately +1.3 to -1.3 radians. Cross-fiber anisotropy is also observed. In the beating heart, NMR diffusion data must be corrected for the effects of myocardial deformation during the cardiac cycle. This correction can be performed using an independent MRI method to map the strain-rate tensor field of the myocardium through time. Combining fiber orientation with local myocardial strain rate, local rates of myocardial fiber shortening may be computed.