Influence of cardiac tissue anisotropy on re-entrant activation in computational models of ventricular fibrillation

The aim of this study was to establish the role played by anisotropic diffusion in (i) the number of filaments and epicardial phase singularities that sustain ventricular fibrillation in the heart, (ii) the lifetimes of filaments and phase singularities, and (iii) the creation and annihilation dynamics of filaments and phase singularities. A simplified monodomain model of cardiac tissue was used, with membrane excitation described by a simplified 3-variable model. The model was configured so that a single re-entrant wave was unstable, and fragmented into multiple re-entrant waves. Re-entry was then initiated in tissue slabs with varying anisotropy ratio. The main findings of this computational study are: (i) anisotropy ratio influenced the number of filaments Sustaining simulated ventricular fibrillation, with more filaments present in simulations with smaller values of transverse diffusion coefficient, (ii) each re-entrant filament was associated with around 0.9 phase singularities on the surface of the slab geometry, (iii) phase singularities were longer lived than filaments, and (iv) the creation and annihilation of filaments and phase singularities were linear functions of the number of filaments and phase singularities, and these relationships were independent of the anisotropy ratio. This study underscores the important role played by tissue anisotropy in cardiac ventricular fibrillation

Early afterdepolarisations and ventricular arrhythmias in cardiac tissue: a computational study

Afterdepolarisations are associated with arrhythmias in the heart, but are difficult to study experimentally. In this study we used a simplified computational model of 1D and 2D cardiac ventricular tissue, where we could control the size of the region generating afterdepolarisations, as well as the properties of the afterdepolarisation waveform. Provided the size of the afterdepolarisation region was greater than around 1 mm, propagating extrasystoles were produced in both 1D and 2D. The number of extrasystoles produced depended on the amplitude, period, and duration of the oscillatory EAD waveform. In 2D, re-entry was also initiated for specific combinations of EAD amplitude, period, and duration, with the afterdepolarisation region acting as a common pathway. The main finding from this modelling study is therefore that afterdepolarisations can act as potent sources of propagating extrasystoles, as well as a source of re-entrant activation

Filament behavior in a computational model of ventricular fibrillation in the canine heart

The aim of this paper was to quantify the behavior of filaments in a computational model of re-entrant ventricular fibrillation. We simulated cardiac activation in an anisotropic monodomain with excitation described by the Fenton-Karma model with Beeler-Reuter restitution, and geometry by the Auckland canine ventricle. We initiated re-entry in the left and right ventricular free walls, as well as the septum. The number of filaments increased during the first 1.5 s before reaching a plateau with a mean value of about 36 in each simulation. Most re-entrant filaments were between 10 and 20 mm long. The proportion of filaments touching the epicardial surface was 65%, but most of these were visible for much less than one period of re-entry. This paper shows that useful information about filament dynamics can be gleaned from models of fibrillation in complex geometries, and suggests that the interplay of filament creation and destruction may offer a target for antifibrillatory therap

Dispersion of cardiac action potential duration and the initiation of re-entry: A computational study

BACKGROUND: The initiation of re-entrant cardiac arrhythmias is associated with increased dispersion of repolarisation, but the details are difficult to investigate either experimentally or clinically. We used a computational model of cardiac tissue to study systematically the association between action potential duration (APD) dispersion and susceptibility to re-entry. METHODS: We simulated a 60 × 60 mm 2 D sheet of cardiac ventricular tissue using the Luo-Rudy phase 1 model, with maximal conductance of the K+ channel gKmax set to 0.004 mS mm-2. Within the central 40 × 40 mm region we introduced square regions with prolonged APD by reducing gKmax to between 0.001 and 0.003 mS mm-2. We varied (i) the spatial scale of these regions, (ii) the magnitude of gKmax in these regions, and (iii) cell-to-cell coupling. RESULTS: Changing spatial scale from 5 to 20 mm increased APD dispersion from 49 to 102 ms, and the susceptible window from 31 to 86 ms. Decreasing gKmax in regions with prolonged APD from 0.003 to 0.001 mS mm-2 increased APD dispersion from 22 to 70 ms, and the susceptible window from <1 to 56 ms. Decreasing cell-to-cell coupling by changing the diffusion coefficient from 0.2 to 0.05 mm2 ms-1 increased APD dispersion from 57 to 88 ms, and increased the susceptible window from 41 to 74 ms. CONCLUSION: We found a close association between increased APD dispersion and susceptibility to re-entrant arrhythmias, when APD dispersion is increased by larger spatial scale of heterogeneity, greater electrophysiological heterogeneity, and weaker cell-to-cell coupling

Endogenous driving and synchronization in cardiac and uterine virtual tissues: bifurcations and local coupling

Cardiac and uterine muscle cells and tissue can be either autorhythmic or excitable. These behaviours exchange stability at bifurcations produced by changes in parameters, which if spatially localized can produce an ectopic pacemaking focus. The effects of these parameters on cell dynamics have been identified and quantified using continuation algorithms and by numerical solutions of virtual cells. The ability of a compact pacemaker to drive the surrounding excitable tissues depends on both the size of the pacemaker and the strength of electrotonic coupling between cells within, between, and outside the pacemaking region. We investigate an ectopic pacemaker surrounded by normal excitable tissue. Cell–cell coupling is simulated by the diffusion coefficient for voltage. For uniformly coupled tissues, the behaviour of the hybrid tissue can take one of the three forms: (i) the surrounding tissue electrotonically suppresses the pacemaker; (ii) depressed rate oscillatory activity in the pacemaker but no propagation; and (iii) pacemaker driving propagations into the excitable region. However, real tissues are heterogeneous with spatial changes in cell–cell coupling. In the gravid uterus during early pregnancy, cells are weakly coupled, with the cell–cell coupling increasing during late pregnancy, allowing synchronous contractions during labour. These effects are investigated for a caricature uterine tissue by allowing both excitability and diffusion coefficient to vary stochastically with space, and for cardiac tissues by spatial gradients in the diffusion coefficient

Correction: Bayesian Sensitivity Analysis of a Cardiac Cell Model Using a Gaussian Process Emulator.

There are multiple errors in S1 Text. Please view the correct S1 Text below. Supporting Information S1 Text. Additional mathematical details. Detailed description of the Gaussian process emu-lator, how the design data were used to fit the emulator, how the emulator was evaluated, and how it was used for variance based sensitivity analysis. (PDF

Variance Based Sensitivity Analysis of IKrIKr in a Model of the Human Atrial Action Potential Using Gaussian Process Emulators

Cardiac cell models have become valuable research tools, but biophysically detailed models embed large numbers of parameters, which must be fitted from experimental data. The provenance of these parameters can be difficult to establish, and so it is important to understand how parameter values influence model behaviour. In this study we examined how model parameters influence the repolarising current I Kr in the Courtemenache-Ramirez-Nattel model of the human atrial action potential. We used a statistical approach in which Gaussian processes (GP) are used to emulate the model outputs. A GP emulator can treat model inputs and outputs as uncertain, and so can be used to directly calculate sensitivity indices. We found that 3 of the 10 parameters influencing I Kr had a strong influence on AP D 70 , AP D 90 , and Dome V m . These three parameters scale the magnitude of the I Kr gating variable time constant and the voltage dependence of the steady state activation curve, and these mechanisms act to modify the amplitude of I Kr during repolarisation. This study highlights the potential value of statistical approaches for investigating cardiac models, and that uncertainties or errors in parameters resulting from attempts to fit experimental data during model development can ultimately affect model behaviour

Dispersion of Recovery and Vulnerability to Re-entry in a Model of Human Atrial Tissue With Simulated Diffuse and Focal Patterns of Fibrosis

Fibrosis in atrial tissue can act as a substrate for persistent atrial fibrillation, and can be focal or diffuse. Regions of fibrosis are associated with slowed or blocked conduction, and several approaches have been used to model these effects. In this study a computational model of 2D atrial tissue was used to investigate how the spatial scale of regions of simulated fibrosis influenced the dispersion of action potential duration (APD) and vulnerability to re-entry in simulated normal human atrial tissue, and human tissue that has undergone remodeling as a result of persistent atrial fibrillation. Electrical activity was simulated in a 10 × 10 cm square 2D domain, with a spatially varying diffusion coefficient as described below. Cellular electrophysiology was represented by the Courtemanche model for human atrial cells, with the model parameters set for normal and remodeled cells. The effect of fibrosis was modeled with a smoothly varying diffusion coefficient, obtained from sampling a Gaussian random field (GRF) with length scales of between 1.25 and 10.0 mm. Twenty samples were drawn from each field, and used to allocate a value of diffusion coefficient between 0.05 and 0.2 mm2 /ms. Dispersion of APD was assessed in each sample by pacing at a cycle length of 1,000 ms, followed by a premature beat with a coupling interval of 400 ms. Vulnerability to re-entry was assessed with an aggressive pacing protocol with pacing cycle lengths decreasing from 450 to 250 ms in 25 ms intervals for normal tissue and 300–150 ms for remodeled tissue. Simulated fibrosis at smaller spatial scales tended to lengthen APD, increase APD dispersion, and increase vulnerability to sustained re-entry relative to fibrosis at larger spatial scales. This study shows that when fibrosis is represented by smoothly varying tissue diffusion, the spatial scale of fibrosis has important effects on both dispersion of recovery and vulnerability to re-entry

Fitting two human atrial cell models to experimental data using Bayesian history matching

Cardiac cell models are potentially valuable tools for applications such as quantitative safety pharmacology, but have many parameters. Action potentials in real cardiac cells also vary from beat to beat, and from one cell to another. Calibrating cardiac cell models to experimental observations is difficult, because the parameter space is large and high-dimensional. In this study we have demonstrated the use of history matching to calibrate the maximum conductance of ion channels and exchangers in two detailed models of the human atrial action potential against measurements of action potential biomarkers. History matching is an approach developed in other modelling communities, based on constructing fast-running Gaussian process emulators of the model. Emulators were constructed from a small number of model runs (around 10 2 ), and then run many times (>10 6) at low computational cost, each time with a different set of model parameters. Emulator outputs were compared with experimental biomarkers using an implausibility measure, which took into account experimental variance as well as emulator variance. By repeating this process, the region of non-implausible parameter space was iteratively reduced. Both cardiac cell models were successfully calibrated to experimental datasets, resulting in sets of parameters that could be sampled to produce variable action potentials. However, model parameters did not occupy a small range of values. Instead, the history matching process exposed inputs that can co-vary across a wide range and still be consistent with a particular biomarker. We also found correlations between some biomarkers, indicating a need for better descriptors of action potential shape

Bayesian sensitivity analysis of a 1D vascular model with Gaussian process emulators

One-dimensional models of the cardiovascular system can capture the physics of pulse waves, but involve many parameters. Since these may vary among individuals, patient-specific models are difficult to construct. Sensitivity analysis can be used to rank model parameters by their effect on outputs, and to quantify how uncertainty in parameters influences output uncertainty. This type of analysis is often conducted with a Monte Carlo method, where large numbers of model runs are used to assess input-output relations. The aim of this study was to demonstrate the computational efficiency of variance based sensitivity analysis of 1D vascular models using Gaussian process emulators, compared to a standard Monte Carlo approach. The methodology was tested on four vascular networks of increasing complexity to analyse its scalability. The computational time needed to perform the sensitivity analysis with an emulator was reduced by the 99.96% compared to a Monte Carlo approach. Despite the reduced computational time, sensitivity indices obtained using the two approaches were comparable. The scalability study showed that the number of mechanistic simulations needed to train a Gaussian process for sensitivity analysis was of the order math formula, rather than math formula needed for Monte Carlo analysis (where d is the number of parameters in the model). The efficiency of this approach, combined with capacity to estimate the impact of uncertain parameters on model outputs, will enable development of patient-specific models of the vascular system, and has the potential to produce results with clinical relevance