Slow pulse due to calcium current induces phase-2 reentry in heterogeneous tissue

Phase-2 reentry is a basic mechanism for the transition to VT and VF in the heart. It is thought to underly many causes of idiopathic ventricular arrhythmias as, for instance, those occurring in Brugada syndrome. Reentry is usually linked to heterogeneity in tissue repolarization. We study some circumstances under which a region of depolarized tissue can reexcite adjacent regions that exhibit shorter action potential duration (APD), eventually inducing reentry. Simulations are performed using a simplified ionic model that reproduces well the ventricular action potential (AP). We analyze first the conditions that lead to very short action potentials (APs). Then, we show that reexcitation takes place via a slow (calcium current induced) pulse that propagates into the region of short APs until it encounters excitable tissue. In two dimensions, this may give rise to reentry with the formation of counter-rotating spiral waves

Propagation malfunctions due to gap junction dysregulation

Gap junctions are membrane channels that connect the cytoplasm of adjacent cells allowing the cell-to-cell elec- trical coupling necessary for action potential propagation. Pathological conditions, such as malformations in connex- ins, mutations affecting phosphorylation of regulatory sites of connexins, alterations in gap junction organization, and type and quantity of connexin expression, can impede the normal electrical propagation. All these malfunctions can produce a dispersion of repolarization, implicated in ven- tricular arrhythmias. In fact, ventricular tachycardia and spontaneous ventricular arrhythmia occurred in more than twice as many connexin deficient hearts than wild-type hearts. We perform numerical simulations of a human ventric- ular model in order to mimic some of these pathological conditions. In particular, we consider a diminished Cx43 connexin expression, as well as altered connexin conduc- tance dynamics, i.e., modified maximum and minimum conductances gmax and gmin, half-inactivation voltage V1/2 and decay kinetics. Physiologically these modifica- tions can appear due to mutations or to different connexin configurations, i.e., forming heteromeric channels. Under these conditions we study the change in action potential duration (APD) and CV-restitution properties. We observe that, although CV diminishes with decreased connexin ex- pression, the APD remains almost constant up to the point of conduction block. Also, propagation differs for constant or time-dependent voltage conductance, conduction block occurring earlier for the former. While mutations result- ing in a stronger dependence of the delay time produced an appreciable change intercellular conductances, this ef- fect was not so important when the mutations affected the overall delay time. Thus, our results suggest that a correct description of gap junctional conductance is of big impor- tance for understanding action potential propagation un- der pathological conditions.Postprint (published version

Cardiac dynamics: modeling the Brugada syndrome

Este trabajo analiza mediante un modelo matemático reducido de corrientes ionicas la posibilidad de aparición de arritmias cardiacas

Propagation malfunctions due to gap junction dysregulation

Gap junctions are membrane channels that connect the cytoplasm of adjacent cells allowing the cell-to-cell electrical coupling necessary for action potential propagation. Pathological conditions, such as malformations in connexins, mutations affecting phosphorylation of regulatory sites of connexins, alterations in gap junction organization, and type and quantity of connexin expression, can impede the normal electrical propagation. All these malfunctions can produce a dispersion of repolarization, implicated in ventricular arrhythmias. In fact, ventricular tachycardia and spontaneous ventricular arrhythmia occurred in more than twice as many connexin deficient hearts than wild-type hearts. We perform numerical simulations of a human ventricular model in order to mimic some of these pathological conditions. In particular, we consider a diminished Cx43 connexin expression, as well as altered connexin conductance dynamics, i.e., modified maximum and minimum conductances gmax and gmin, half-inactivation voltage V1=2 and decay kinetics. Physiologically these modifications can appear due to mutations or to different connexin configurations, i.e., forming heteromeric channels. Under these conditions we study the change in action potential duration (APD) and CV-restitution properties. We observe that, although CV diminishes with decreased connexin expression, the APD remains almost constant up to the point of conduction block. Also, propagation differs for constant or time-dependent voltage conductance, conduction block occurring earlier for the former. While mutations resulting in a stronger dependence of the delay time produced an appreciable change intercellular conductances, this effect was not so important when the mutations affected the overall delay time. Thus, our results suggest that a correct description of gap junctional conductance is of big importance for understanding action potential propagation under pathological conditions.Postprint (published version

Phase-2 reentry in cardiac tissue: role of the slow calcium pulse

Phase-2 re-entry is thought to underlie many causes of idiopathic ventricular arrhythmias as, for instance, those occurring in Brugada syndrome. In this paper, we study under which circumstances a region of depolarized tissue can re-excite adjacent regions that exhibit shorter action potential duration (APD), eventually inducing reentry. For this purpose, we use a simplified ionic model that reproduces well the ventricular action potential. With the help of this model, we analyze the conditions that lead to very short action potentials (APs), as well as possible mechanisms for re-excitation in a cable. We then study the induction of re-entrant waves (spiral waves) in simulations of AP propagation in the heart ventricles. We show that re-excitation takes place via a slow pulse produced by calcium current that propagates into the region of short APs until it encounters excitable tissue. We calculate analytically the speed of the slow pulse, and also give an estimate of the minimal tissue size necessary for allowing reexcitation to take place.Peer ReviewedPostprint (published version

Nonlinearities due to refractoriness in SR Ca release

Calcium alternans is a pro-arrhytmic cardiac dysfunction related to beat-to-beat changes in the amplitude of intracellular calcium transient, that typically occurs at rapid pacing rates. Although oscillations in sarcoplasmic reticulum (SR) content have been related with calcium alternans, the experimental appearance of alternans without these oscillations suggests that another mechanism related with refractoriness of SR calcium release might be key, at least, under certain conditions. We investigate how RyR2 refractoriness modulates calcium handling on a beat-to-beat basis using a numerical rabbit cardiomyocyte model. We find that a slow recovery from inactivation of the RyR2 might be crucial. On one hand, a steep relation between sarcoplasmic reticulum (SR) load and calcium release makes regular calcium cycling unstable at high SR calcium load and/or fast pacing rates, in agreement with previous explanation when RyR2 inactivation is not important. On the other hand, we show that calcium release can also depend strongly on the number of RyR2 ready to open if an important number of RyR2s inactivate after the release. This gives rise to a steep nonlinear relation between the calcium release and the level of recovered RyR2, so that a small change in the later produces big changes in calcium release. A conclusion of this result is that RyR2 refractoriness can be the main nonlinearity behind alternans even when alternation in SR-Ca load is present.Peer ReviewedPostprint (published version

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

Effects of small conductance calcium activated potassium channels in atrial myocytes

Among the different potassium channels present in cardiac myocytes, the small conductance Ca2+ activated potassium channels (SK channels) are particular because they are affected by changes in intracellular calcium. The functional role of these channels in cardiac electrophysiology is still under intense debate. While they do not seem to play an important role in healthy hearts – their associated current, IKCa, is smaller than other potassium currents -, there is increasing evidence that they may become relevant under pathological conditions. In fact, both pro- and anti-arrhythmic effects have been assigned to these channels, depending on the clinical situation. In this work, we have incorporated the current through SK channels, IKCa, into an electrophysiological ionic model of human atria myocyte. This allows us to evaluate changes in the action potential under different parameters affecting the kinetics of these channels. We observe a large dependence of the action potential duration with the conductance and gate dynamics of the channel. The dependence of SK channels with changes in intracellular calcium dynamics helps decreasing the proarrhythmic effect of spontaneous calcium release eventsPeer ReviewedPostprint (published version

Calcium alternans is a global order-disorder phase transition: robustness on ryanodine receptor release dynamics

Electromechanical alternans is a beat-to-beat alterna- tion in the strength of contraction of a cardiac cell which appears often due to an instability of calcium cycling. The global calcium signal in cardiomyocytes is the result of the combined effect of several thousand micron scale domains called Calcium Release Units (CaRU), coupled through diffusion, where the flow of calcium among different cell compartments is regulated by stochastic signaling involv- ing the ryanodine receptor (RyR). Recently, numerical sim- ulations have suggested that the transition from regular Ca cycling to alternans is an order-disorder phase transition consistent with the Ising universality class. Inside the cell, groups of CaRU form transient areas within the cell where alternans appear. However, global alternans appears only as a result of the synchronization of the oscillation phase among different subunits. We show here that this transi- tion is indeed robust and universal upon changes in the behavior of the RyR. Using three different set of parame- ters for the transition rates among open, closed and inacti- vated states in the RyR, we show that different RyR behav- ior leads to the same type of order-disorder transition.Postprint (published version

Slow pulse due to calcium current induces phase-2 reentry in heterogeneous tissue

Phase-2 reentry is a basic mechanism for the transition to VT and VF in the heart. It is thought to underly many causes of idiopathic ventricular arrhythmias as, for instance, those occurring in Brugada syndrome. Reentry is usually linked to heterogeneity in tissue repolarization. We study some circunstances under which a region of depolarized tissue can reexcite adjacent regions that exhibit shorter action potential duration (APD), eventually inducing reentry. Simulations are performed using a simplified ionic model that reproduces well the ventricular action potential (AP). We analyze first the conditions that lead to very short action potentials (APs). Then, we show that reexcitation takes place via a slow (calcium current induced) pulse that propagates into the region of short APs until it encounters excitable tissue. In two dimensions, this may give rise to reentry with the formation of counter-rotating spiral wavesPostprint (published version