Cardiac cells stimulated with an axial current-like waveform reproduce electrophysiological properties of tissue fibers.

BACKGROUND AND OBJECTIVE: In silico electrophysiological models are generally validated by comparing simulated results with experimental data. When dealing with single-cell and tissue scales simultaneously, as occurs frequently during model development and calibration, the effects of inter-cellular coupling should be considered to ensure the trustworthiness of model predictions. The hypothesis of this paper is that the cell-tissue mismatch can be reduced by incorporating the effects of conduction into the single-cell stimulation current. METHODS: Five different stimulation waveforms were applied to the human ventricular O'Hara-Rudy cell model. The waveforms included the commonly used monophasic and biphasic (symmetric and asymmetric) pulses, a triangular waveform and a newly proposed asymmetric waveform (stimulation A) that resembles the transmembrane current associated with AP conduction in tissue. A comparison between single-cell and fiber simulated results was established by computing the relative difference between the values of AP-derived properties at different scales, and by evaluating the differences in the contributions of ionic conductances to each evaluated property. As a proof of the benefit, we investigated multi-scale differences in the simulation of the effects induced by dofetilide, a selective IKr blocker with high torsadogenic risk, on ventricular repolarization at different pacing rates. RESULTS: Out of the five tested stimulation waveforms, stimulation A produced the closest correspondence between cell and tissue simulations in terms of AP properties at steady-state and under dynamic pacing and of ionic contributors to those AP properties. Also, stimulation A reproduced the effects of dofetilide better than the other alternative waveforms, mirroring the 'beat-skipping' behavior observed at fast pacing rates in experiments with human tissue. CONCLUSIONS: The proposed stimulation current waveform accounts for inter-cellular coupling effects by mimicking cell excitation during AP conduction. The proposed waveform improves the correspondence between simulation scales, which could improve the trustworthiness of single-cell simulations without adding computational cost.

The heterogeneous effects of the great recession on informal care to the elderly.

This paper studies the role of unobserved factors to measure the impact of the economic downturn on informal care availability to the elderly in Europe. We use the Survey of Health, Ageing and Retirement in Europe (SHARE), which allows controlling for socio-demographic variables. Our results show that the impact of the Great Recession on care receipt depends not only on observed, but also on unobserved characteristics. For 21% of the sample, the effect is three to four times larger than the average effect for the entire sample. For 57% of the sample, there is no effect of the economic crisis, and this is related to unobservable factors. In our estimation process, we are able to characterize how this unobserved heterogeneity correlates with the observable variables. Moreover, we show that if the unobserved heterogeneity in the effect of the crisis is ignored, then we are not able to capture that there is no effect for more than half of the individuals, even if we allow for unobserved heterogeneity in the intercept of the model and for the heterogeneous effect of the crisis based on observables.

A response surface optimization approach to adjust ionic current conductances of cardiac electrophysiological models. Application to the study of potassium level changes.

Cardiac electrophysiological computational models are often developed from previously published models. The new models may incorporate additional features to adapt the model to a different species or may upgrade a specific ionic formulation based on newly available experimental data. A relevant challenge in the development of a new model is the estimation of certain ionic current conductances that cannot be reliably identified from experiments. A common strategy to estimate those conductances is by means of constrained non-linear least-squares optimization. In this work, a novel methodology is proposed for estimation of ionic current conductances of cardiac electrophysiological models by using a response surface approximation-based constrained optimization with trust region management. Polynomial response surfaces of a number of electrophysiological markers were built using statistical sampling methods. These markers included action potential duration (APD), triangulation, diastolic and systolic intracellular calcium concentration, and time constants of APD rate adaptation. The proposed methodology was applied to update the Carro et al. human ventricular action potential model after incorporation of intracellular potassium ([K+]i) dynamics. While the Carro et al. model was well suited for investigation of arrhythmogenesis, it did not allow simulation of [K+]i changes. With the methodology proposed in this study, the updated Carro et al. human ventricular model could be used to simulate [K+]i changes in response to varying extracellular potassium ([K+]o) levels. Additionally, it rendered values of evaluated electrophysiological markers within physiologically plausible ranges. The optimal values of ionic current conductances in the updated model were found in a notably shorter time than with previously proposed methodologies. As a conclusion, the response surface optimization-based approach proposed in this study allows estimating ionic current conductances of cardiac electrophysiological computational models while guaranteeing replication of key electrophysiological features and with an important reduction in computational cost with respect to previously published approaches. The updated Carro et al. model developed in this study is thus suitable for the investigation of arrhythmic risk-related conditions, including those involving large changes in potassium concentration.

DENIS: Solving cardiac electrophysiological simulations with volunteer computing.

Cardiac electrophysiological simulations are computationally intensive tasks. The growing complexity of cardiac models, together with the increasing use of large ensembles of models (known as populations of models), make extensive simulation studies unfeasible for regular stand-alone computers. To address this problem, we developed DENIS, a cardiac electrophysiology simulator based on the volunteer computing paradigm. We evaluated the performance of DENIS by testing the effect of simulation length, task deadline, and batch size, on the time to complete a batch of simulations. In the experiments, the time to complete a batch of simulations did not increase with simulation length, and had little dependence on batch size. In a test case involving the generation of a population of models, DENIS was able to reduce the simulation time from years to a few days when compared to a stand-alone computer. Such capacity makes it possible to undertake large cardiac simulation projects without the need for high performance computing infrastructure.

Limitations in electrophysiological model development and validation caused by differences between simulations and experimental protocols.

Models of ion channel dynamics are usually built by fitting isolated cell experimental values of individual parameters while neglecting the interaction between them. Another shortcoming regards the estimation of ionic current conductances, which is often based on quantification of Action Potential (AP)-derived markers. Although this procedure reduces the uncertainty in the calculation of conductances, many studies evaluate electrophysiological AP-derived markers from single cell simulations, whereas experimental measurements are obtained from tissue preparations. In this work, we explore the limitations of these approaches to estimate ion channel dynamics and maximum current conductances and how they could be overcome by using multiscale simulations of experimental protocols. Four human ventricular cell models, namely ten Tusscher and Panfilov (2006), Grandi et al. (2010), O'Hara et al. (2011), and Carro et al. (2011), were used. Two problems involving scales from ion channels to tissue were investigated: 1) characterization of L-type calcium voltage-dependent inactivation ICa,L; 2) identification of major ionic conductance contributors to steady-state AP markers, including APD90, APD75, APD50, APD25, Triangulation and maximal and minimal values of V and dV/dt during the AP (Vmax, Vmin, dV/dtmax, dV/dtmin). Our results show that: 1) ICa,L inactivation characteristics differed significantly when calculated from model equations and from simulations reproducing the experimental protocols. 2) Large differences were found in the ionic currents contributors to APD25, Triangulation, Vmax, dV/dtmax and dV/dtmin between single cells and 1D-tissue. When proposing any new model formulation, or evaluating an existing model, consistency between simulated and experimental data should be verified considering all involved effects and scales.

In silico simulations of experimental protocols for cardiac modeling.

A mathematical model of the AP involves the sum of different transmembrane ionic currents and the balance of intracellular ionic concentrations. To each ionic current corresponds an equation involving several effects. There are a number of model parameters that must be identified using specific experimental protocols in which the effects are considered as independent. However, when the model complexity grows, the interaction between effects becomes increasingly important. Therefore, model parameters identified considering the different effects as independent might be misleading. In this work, a novel methodology consisting in performing in silico simulations of the experimental protocol and then comparing experimental and simulated outcomes is proposed for parameter model identification and validation. The potential of the methodology is demonstrated by validating voltage-dependent L-type calcium current (ICaL) inactivation in recently proposed human ventricular AP models with different formulations. Our results show large differences between ICaL inactivation as calculated from the model equation and ICaL inactivation from the in silico simulations due to the interaction between effects and/or to the experimental protocol. Our results suggest that, when proposing any new model formulation, consistency between such formulation and the corresponding experimental data that is aimed at being reproduced needs to be first verified considering all involved factors.

A human ventricular cell model for investigation of cardiac arrhythmias under hyperkalaemic conditions.

In this study, several modifications were introduced to a recently proposed human ventricular action potential (AP) model so as to render it suitable for the study of ventricular arrhythmias. These modifications were driven by new sets of experimental data available from the literature and the analysis of several well-established cellular arrhythmic risk biomarkers, namely AP duration at 90 per cent repolarization (APD(90)), AP triangulation, calcium dynamics, restitution properties, APD(90) adaptation to abrupt heart rate changes, and rate dependence of intracellular sodium and calcium concentrations. The proposed methodology represents a novel framework for the development of cardiac cell models. Five stimulation protocols were applied to the original model and the ventricular AP model developed here to compute the described arrhythmic risk biomarkers. In addition, those models were tested in a one-dimensional fibre in which hyperkalaemia was simulated by increasing the extracellular potassium concentration, [K(+)](o). The effective refractory period (ERP), conduction velocity (CV) and the occurrence of APD alternans were investigated. Results show that modifications improved model behaviour as verified by: (i) AP triangulation well within experimental limits (the difference between APD at 50 and 90 per cent repolarization being 78.1 ms); (ii) APD(90) rate adaptation dynamics characterized by fast and slow time constants within physiological ranges (10.1 and 105.9 s); and (iii) maximum S1S2 restitution slope in accordance with experimental data (S(S1S2)=1.0). In simulated tissues under hyperkalaemic conditions, APD(90) progressively shortened with the degree of hyperkalaemia, whereas ERP increased once a threshold in [K(+)](o) was reached ([K(+)](o)≈6 mM). CV decreased with [K(+)](o), and conduction was blocked for [K(+)](o)>10.4 mM. APD(90) alternans were observed for [K(+)](o)>9.8 mM. Those results adequately reproduce experimental observations. This study demonstrated the value of basing the development of AP models on the computation of arrhythmic risk biomarkers, as opposed to joining together independently derived ion channel descriptions to produce a whole-cell AP model, with the new framework providing a better picture of the model performance under a variety of stimulation conditions. On top of replicating experimental data at single-cell level, the model developed here was able to predict the occurrence of APD(90) alternans and areas of conduction block associated with high [K(+)](o) in tissue, which is of relevance for the investigation of the arrhythmogenic substrate in ischaemic hearts.