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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.

Local Ca2+ spark releases are essential to the Ca2+ cycling process. Thus, they play an important role in ventricular and atrial cell contraction, as well as in sinoatrial cell automaticity. Characterizing their properties in healthy cells from different regions in the heart can reveal the basic biophysical differences among these regions. We designed a semi-automatic Matlab Graphical User Interface (called Sparkalyzer) to characterize parameters of Ca2+ spark release from any major cardiac tissue, as recorded in line-scan mode with a confocal laser-scanning microscope. We validated the algorithm on experimental images from rabbit sinoatrial, atrial, and ventricular cells loaded with Fluo-4 AM. The program characterizes general image parameters of Ca2+ transients and sparks: spark duration, which indicates for how long the spark provides Ca2+ to the closed intracellular mechanisms (typical value: 25±1, 23±1, 26±1ms for sinoatrial, atrial, and ventricular cells, respectively); spark amplitude, which indicates the amount of Ca2+ released by a single spark (1.6±0.1, 1.6±0.2, 1.4±0.1F/F0 for sinoatrial, atrial, and ventricular cells, respectively); spark length, which is the length of the Ca2+ wavelets fired out of a row of ryanodine receptors (5±0.1, 5±0.2, 3.4±0.3μm for sinoatrial, atrial, or ventricular cells, respectively) and number of sparks (0.14±0.02, 0.025±0.01, 0.02±0.01 for 1μm in 1s for sinoatrial, atrial, and ventricular cells, respectively). This method is reliable for Ca2+ spark analysis of sinoatrial, atrial, or ventricular cells. Moreover, by examining the average value of Ca2+ spark characteristics and their scattering around the mean, atrial, ventricular and sinoatrial cells can be differentiated.

Regulation of cardiac electrical and mechanical activities are highly dependent on L-type calcium current (I CaL ). Moreover, the phenomenon of I CaL . inactivation plays a crucial role in adjusting action potential repolarization. This paper investigates the relationship between extracellular calcium concentration, [Ca+2]o, and action potential (AP). In particular, calcium-dependent inactivation (CDI) of I CaL has been analyzed to quantify its dependence on [Ca+2] o and its impact on AP duration. We have analyzed three human atrial cell models (hAM) by testing benchmarks like AP, I CaL , and I Ncx (sodium-calcium exchange current) with the variation of [Ca+2]o. The role of CDI was assessed by simulating the AP-clamp technique followed by 1) running the baseline model under normal CDI mechanism and 2) running the model without the CDI mechanism. The comparison of three hAMs shows that besides the contribution of CDI, driving force (DF), and I NCX current should also be considered while studying the relationship between AP duration (APD) and [Ca+2] o. None of the hAMs reproduced in a physiologically correct way the effects of [Ca+2]o on APD, therefore our results call for a new hAM able to reproduce correctly the [Ca+2]o effect

Heart failure (HF) is associated with cardiac arrhythmias, which impairs cardiac electromechanics that causes dysfunction of cardiac muscle contraction leading to increased risks of morbidity and mortality. Previous studies have revealed that HF causes alteration to the electrophysiological and structural properties of the atria. The aim of this study was to investigate the primary factor of HF-induced remodelling on the dynamical behaviours of electrical excitation waves in sheep atria. The biophysically detailed model of sheep atrial action potentials developed by Butters et al was modified to incorporate experimental data of HF-induced remodelling on ion channels. The developed atrial cell models in HF were then incorporated into the 3D anatomical sheep atria model developed in our previous study. The 3D model considered both electrical heterogeneity and tissue anisotropy. At the cellular level, HF shortened the action potential duration at 90% of repolarisation (APD 90 ). At 3D organ level, activation time of the whole atria was prolonged due to the downregulation of expression of gap junction proteins (Cx43). Consequently, the wavelength of excitation waves was abbreviated, which may help to sustain re-entrant excitation waves in the atria. This study provides mechanistic insights into the pro-arrhythmic effect of HF-induced remodeling on ion channels, Ca2+ handling and intercellular coupling in the sheep atria.

Exposure to air pollutants agents, like sulfur dioxide (SO 2 ), has significant effects on the cardiovascular system. Studies have shown that SO 2 blocks $I_{CaL}$ and increases the $I_{Na}, I_{K1}$ and $I_{to}$ currents, which implies action potential duration (APD) decrease, favoring the initiation of atrial arrhythmias. This study aims to assess the effects of the $SO_{2}$ at different concentrations on human atrial action potential, using computational simulation. For this, based on experimental data, we developed concentration-dependent equations to simulate the $SO_{2}$ effects on the currents. They were incorporated in the Courtemanche model of human atrial cell and in a 2D model of atrial tissue. S1-S2 cross-field protocol was applied to initiate a rotor. $SO_{2}$ concentrations from 0 to 100 $\mu M$ were implemented. Our results are in agreement with results from non-human in vitro and in vivo studies. The $SO_{2}$ causes APD shortening and loss of plateau phase in a fraction that increases as the concentration increases. In the 2D model, a rotor can be generated from 50 $\mu M$ of $SO_{2}$ concentration, showing a pro-arrhythmic effect.

When an atrial cell is paced rapidly, calcium (Ca) waves can form on the cell boundary and propagate to the cell interior. These waves are referred to as “triggered waves” because they are initiated by Ca influx from the L-type Ca channel and occur during the action potential. However, the consequences of triggered waves in atrial tissue are not known. Here, we develop a phenomenological model of Ca cycling in atrial myocytes that accounts for the formation of triggered waves. Using this model, we show that a fundamental requirement for triggered waves to induce abnormal electrical activity in tissue is that these waves must be synchronized over large populations of cells. This is partly because triggered waves induce a long action potential duration (APD) followed by a short APD. Thus, if these events are not synchronized between cells, then they will on average cancel and have minimal effects on the APD in tissue. Using our computational model, we identify two distinct mechanisms for triggered wave synchronization. The first relies on cycle length (CL) variability, which can prolong the CL at a given beat. In cardiac tissue, we show that CL prolongation leads to a substantial amplification of APD because of the synchronization of triggered waves. A second synchronization mechanism applies in a parameter regime in which the cell exhibits stochastic alternans in which a triggered wave fires, on average, only every other beat. In this scenario, we identify a slow synchronization mechanism that relies on the bidirectional feedback between the APD in tissue and triggered wave initiation. On large cables, this synchronization mechanism leads to spatially discordant APD alternans with spatial variations on a scale of hundreds of cells. We argue that these spatial patterns can potentially serve as an arrhythmogenic substrate for the initiation of atrial fibrillation.

Cardiac simulations play an important role in studies involving understanding and investigating the mechanisms of cardiac arrhythmias. Today, studies of arrhythmogenesis and maintenance are largely being performed by creating simulations of a particular arrhythmia with high accuracy comparable to the results of clinical experiments. Atrial fibrillation (AF), the most common arrhythmia in the United States and many other parts of the world, is one of the major field where simulation and modeling is largely used. AF simulations not only assist in understanding its mechanisms but also help to develop, evaluate and improve the computer algorithms used in electrophysiology (EP) systems for ablation therapies. In this paper, we begin with a brief overeview of some common techniques used in simulations to simulate two major AF mechanisms – spiral waves (or rotors) and point (or focal) sources. We particularly focus on 2D simulations using Nygren et al.s mathematical model of human atrial cell. Then, we elucidate an application of the developed AF simulation to an algorithm designed for localizing AF rotors for improving current AF ablation therapies. Our simulation methods and results, along with the other discussions presented in this paper is aimed to provide engineers and professionals with a working-knowledge of application-specific simulations of spirals and foci.

AimAtrial fibrillation is the most common persistent cardiac arrhythmia, and it is not well controlled by present drugs. Because some resin acids open voltage-gated potassium channels and reduce neuronal excitability, we explored the effects of the resin acid isopimaric acid (IPA) on action potentials and ion currents in cardiomyocytes. MethodsSpontaneously beating mouse atrial HL-1 cells were investigated with the whole-cell patch-clamp technique. Results1-25 mol L-1 IPA reduced the action potential frequency by up to 50%. The effect of IPA on six different voltage-gated ion channels was investigated; most voltage-dependent parameters of ion channel gating were shifted in the negative direction along the voltage axis, consistent with a hypothesis that a lipophilic and negatively charged compound binds to the lipid membrane close to the positively charged voltage sensor of the ion channels. The major finding was that IPA inactivated sodium channels and L- and T-type calcium channels and activated the rapidly activating potassium channel and the transient outward potassium channel. Computer simulations of IPA effects on all of the ion currents were consistent with a reduced excitability, and they also showed that effects on the Na channel played the largest role to reduce the action potential frequency. Finally, induced arrhythmia in the HL-1 cells was reversed by IPA. ConclusionLow concentrations of IPA reduced the action potential frequency and restored regular firing by altering the voltage dependencies of several voltage-gated ion channels. These findings can form the basis for a new pharmacological strategy to treat atrial fibrillation. Funding Agencies|Swedish Research Council; Swedish Heart-Lung Foundation; Swedish Brain Foundation; ALF

Cardiac tissue conduction velocity (CV) is a relevant variable in the maintenance and stability of atrial fibrillation (AF). The main goal of this work is to investigate modulation of CV in human chronic AF by inter-subject variability in ionic channel properties, cellular environmental factors and tissue coupling, by using a population of mathematical models. A monodomain tissue model was developed on the basis of the Skibsbye human atrial cell model. In this model, nine parameters are varied leading to a total number of 500 tissue models (8×156 cells). Among these simulations, 126 models are found within the experimental physiological range of biomarkers obtained from 149 chronic AF patients. The resulting population of 126 tissue models covers the variability in the biomarkers observed in the experimental recordings. The specific balance between sodium current and diffusion coefficient modulates the CV, critical for arrhythmia inducibility. The developed population of tissue models establishes the basis for further research in ionic mechanisms that facilitate AF maintenance and in-silico evaluation of personalised drug treatments.