Minimal model for calcium alternans due to SR release refractoriness

In the heart, rapid pacing rates may induce alternations in the strength of cardiac contraction, termed pulsus alternans. Often, this is due to an instability in the dynamics of the intracellular calcium concentration, whose transients become larger and smaller at consecutive beats. This alternation has been linked experimentally and theoretically to two different mechanisms: an instability due to (1) a strong dependence of calcium release on sarcoplasmic reticulum (SR) load, together with a slow calcium reuptake into the SR or (2) to SR release refractoriness, due to a slow recovery of the ryanodine receptors (RyR2) from inactivation. The relationship between calcium alternans and refractoriness of the RyR2 has been more elusive than the corresponding SR Ca load mechanism. To study the former, we reduce a general calcium model, which mimics the deterministic evolution of a calcium release unit, to its most basic elements. We show that calcium alternans can be understood using a simple nonlinear equation for calcium concentration at the dyadic space, coupled to a relaxation equation for the number of recovered RyR2s. Depending on the number of RyR2s that are recovered at the beginning of a stimulation, the increase in calcium concentration may pass, or not, over an excitability threshold that limits the occurrence of a large calcium transient. When the recovery of the RyR2 is slow, this produces naturally a period doubling bifurcation, resulting in calcium alternans. We then study the effects of inactivation, calcium diffusion, and release conductance for the onset of alternans. We find that the development of alternans requires a well-defined value of diffusion while it is less sensitive to the values of inactivation or release conductance.Postprint (author's final draft

Modeling Calcium Dynamics in Human Atria

Abstract Mathematical models of cardiac electrophysiology are an important tool to investigate the underlying mechanisms responsible of arrhythmias. In particular, an important question is the origin of atrial fibrillation (AF). Often, AF initiation is preceded by action potential duration (APD) alternans, i.e., beat to beat oscillations in the APD, that arise at slower rates in patients with persistent AF than in those without AF or with paroxymal AF. Most of these arrhythmias appear as a consequence of malfunctions in calcium dynamics that produce oscillations in intracellular calcium, inducing subsequent APD alternans through electromechanical coupling. The aim of this work is to present a human atrial mathematical model that gives insight into the presence of calcium alternans. For that the model by Nygren et al was modified in order to reproduce calcium alternans at high pacing rhythms, as has been observed in experiments. The model reproduces the nonlinear dependence of gain and fractional SR Ca release upon SR Ca load. At fast pacing rates it presents alternans, due to slow recovery from inactivation of the RyR. Finally, we compare the results from this new model with other human atrial models well established in the literature

Huge reduction of defibrillation thresholds four electrode defibrillators. 2014

In the absence of a better solution, ventricular fibrillation is treated by applying one or several large electrical shocks to the patient. The question of how to lower the energy required for a successful shock is still a current issue in both fundamental research and clinical practice. In the study presented here we will compare defibrillation applied through a four electrode device with the standard procedure using two electrodes. The method is tested through intensive numerical simulations. Here we have used a one dimensional geometry. At the level of the cardiac tissue, the bidomain and the modified Beeler-Reuter models were used. Three different shock waveforms are tested: monophasic and two types of biphasic shocks. The results are compared with those obtained with standard two electrode device. A significant reduction in defibrillation thresholds is achieved for all the three tested waveforms when we use a four electrode device

Dependency of Calcium Alternans on Ryanodine Receptor Refractoriness

<div><h3>Background</h3><p>Rapid pacing rates induce alternations in the cytosolic calcium concentration caused by fluctuations in calcium released from the sarcoplasmic reticulum (SR). However, the relationship between calcium alternans and refractoriness of the SR calcium release channel (RyR2) remains elusive.</p> <h3>Methodology/Principal Findings</h3><p>To investigate how ryanodine receptor (RyR2) refractoriness modulates calcium handling on a beat-to-beat basis using a numerical rabbit cardiomyocyte model. We used a mathematical rabbit cardiomyocyte model to study the beat-to-beat calcium response as a function of RyR2 activation and inactivation. Bi-dimensional maps were constructed depicting the beat-to-beat response. When alternans was observed, a novel numerical clamping protocol was used to determine whether alternans was caused by oscillations in SR calcium loading or by RyR2 refractoriness. Using this protocol, we identified regions of RyR2 gating parameters where SR calcium loading or RyR2 refractoriness underlie the induction of calcium alternans, and we found that at the onset of alternans both mechanisms contribute. At low inactivation rates of the RyR2, calcium alternans was caused by alternation in SR calcium loading, while at low activation rates it was caused by alternation in the level of available RyR2s.</p> <h3>Conclusions/Significance</h3><p>We have mapped cardiomyocyte beat-to-beat responses as a function of RyR2 activation and inactivation, identifying domains where SR calcium load or RyR2 refractoriness underlie the induction of calcium alternans. A corollary of this work is that RyR2 refractoriness due to slow recovery from inactivation can be the cause of calcium alternans even when alternation in SR calcium load is present.</p> </div

Multifunctional cork - alkali-activated fly ash composites: A sustainable material to enhance buildings' energy and acoustic performance

This work evaluates, for the first time, the possibility of producing multifunctional alkali-activated composites combining ultra-low density, low thermal conductivity, high acoustic absorption, and good moisture buffering capacity. The composites were prepared using cork as a lightweight aggregate. This novel material might promote energy savings and tackle the CO2 emissions of the building sector, while simultaneously improve the comfort for inhabitants (e.g. humidity levels regulation and sound pollution reduction). The composites apparent density (as low as 168 kg/m3 ) and thermal conductivity (as low as 68 mW/m K) are amongst the lowest ever reported for alkali-activated materials (AAM) composites and foams, while their sound absorption ability is comparable to the best performing AAM foams reported to date, but in addition these eco-friendly composites also show good ability to passively adjust the humidity levels inside buildings. The multifunctional properties shown by the cork - AAM composites set them apart from other conventional building materials and might contribute to the global sustainability of the construction sector

Conductance heterogeneities induced by multistability in the dynamics of coupled cardiac gap junctions

In this paper, we study the propagation of the cardiac action potential in a one-dimensional fiber, where cells are electrically coupled through gap junctions (GJs). We consider gap junctional gate dynamics that depend on the intercellular potential. We find that different GJs in the tissue can end up in two different states: a low conducting state and a high conducting state. We first present evidence of the dynamical multistability that occurs by setting specific parameters of the GJ dynamics. Subsequently, we explain how the multistability is a direct consequence of the GJ stability problem by reducing the dynamical system's dimensions. The conductance dispersion usually occurs on a large time scale, i.e., thousands of heartbeats. The full cardiac model simulations are computationally demanding, and we derive a simplified model that allows for a reduction in the computational cost of four orders of magnitude. This simplified model reproduces nearly quantitatively the results provided by the original full model. We explain the discrepancies between the two models due to the simplified model's lack of spatial correlations. This simplified model provides a valuable tool to explore cardiac dynamics over very long time scales. That is highly relevant in studying diseases that develop on a large time scale compared to the basic heartbeat. As in the brain, plasticity and tissue remodeling are crucial parameters in determining the action potential wave propagation's stability. (C) 2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)

Cardiac dynamics: a simplified model for action potential propagation

<p>Abstract</p> <p>This paper analyzes a new semiphysiological ionic model, used recently to study reexitations and reentry in cardiac tissue [I.R. Cantalapiedra <it>et al</it>, PRE <b>82</b> 011907 (2010)]. The aim of the model is to reproduce action potencial morphologies and restitution curves obtained, either from experimental data, or from more complex electrophysiological models. The model divides all ion currents into four groups according to their function, thus resulting into fast-slow and inward-outward currents. We show that this simplified model is flexible enough as to accurately capture the electrical properties of cardiac myocytes, having the advantage of being less computational demanding than detailed electrophysiological models. Under some conditions, it has been shown to be amenable to mathematical analysis. The model reproduces the action potential (AP) change with stimulation rate observed both experimentally and in realistic models of healthy human and guinea pig myocytes (TNNP and LRd models, respectively). When simulated in a cable it also gives the right dependence of the conduction velocity (CV) with stimulation rate. Besides reproducing correctly these restitution properties, it also gives a good fit for the morphology of the AP, including the notch typical of phase 1. Finally, we perform simulations in a realistic geometric model of the rabbit’s ventricles, finding a good qualitative agreement in AP propagation and the ECG. Thus, this simplified model represents an alternative to more complex models when studying instabilities in wave propagation.</p