Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that are triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media and their application to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact in cardiac arrhythmias.Peer ReviewedPreprin

Sideband instabilities and defects of quasipatterns

Quasipatterns have been found in dissipative systems ranging from Faraday waves in vertically vibrated fluid layers to nonlinear optics. We describe the dynamics of octagonal, decagonal and dodecagonal quasipatterns by means of coupled Ginzburg–Landau equations and study their stability to sideband perturbations analytically using long-wave equations as well as by direct numerical simulation. Of particular interest is the influence of the phason modes, which are associated with the quasiperiodicity, on the stability of the patterns. In the dodecagonal case, in contrast to the octagonal and the decagonal case, the phase modes and the phason modes decouple and there are parameter regimes in which the quasipattern first becomes unstable with respect to phason modes rather than phase modes. We also discuss the different types of defects that can arise in each kind of quasipattern as well as their dynamics and interactions. Particularly interesting is the decagonal quasipattern, which allows two different types of defects. Their mutual interaction can be extremely weak even at small distances.Peer ReviewedPreprin

Computational Model of Calcium Signaling in Cardiac Atrial Cells at the Submicron Scale

In cardiac cells, calcium is the mediator of excitation-contraction coupling. Dysfunctions in calcium handling have been identified as the origin of some cardiac arrhythmias. In the particular case of atrial myocytes, recent available experimental data has found links between these dysfunctions and structural changes in the calcium handling machinery (ryanodine cluster size and distribution, t-tubular network, etc). To address this issue, we have developed a computational model of an atrial myocyte that takes into account the detailed intracellular structure. The homogenized macroscopic behavior is described with a two-concentration field model, using effective diffusion coefficients of calcium in the sarcoplasmic reticulum (SR) and in the cytoplasm. The model reproduces the right calcium transients and dependence with pacing frequency. Under basal conditions, the calcium rise is mostly restricted to the periphery of the cell, with a large concentration ratio between the periphery and the interior. We have then studied the dependence of the speed of the calcium wave on cytosolic and SR diffusion coefficients, finding an almost linear relation with the former, in agreement with a diffusive and fire mechanism of propagation, and little dependence on the latter. Finally, we have studied the effect of a change in RyR cluster microstructure. We find that, under resting conditions, the spark frequency decreases slightly with RyR cluster spatial dispersion, but markedly increases when the RyRs are distributed in clusters of larger size, stressing the importance of RyR cluster organization to understand atrial arrhythmias, as recent experimental results suggest (Macquaide et al., 2015).Peer ReviewedPostprint (published version

Influence of the tubular network on the characteristics of calcium transients in cardiac myocytes

Transverse and axial tubules (TATS) are an essential ingredient of the excitation-contraction machinery that allow the effective coupling of L-type Calcium Channels (LCC) and ryanodine receptors (RyR2). They form a regular network in ventricular cells, while their presence in atrial myocytes is variable regionally and among animal species We have studied the effect of variations in the TAT network using a bidomain computational model of an atrial myocyte with variable density of tubules. At each z-line the t-tubule length is obtained from an exponential distribution, with a given mean penetration length. This gives rise to a distribution of t-tubules in the cell that is characterized by the fractional area (F.A.) occupied by the t-tubules. To obtain consistent results, we average over different realizations of the same mean penetration length. To this, in some simulations we add the effect of a network of axial tubules. Then we study global properties of calcium signaling, as well as regional heterogeneities and local properties of sparks and RyR2 openings. In agreement with recent experiments in detubulated ventricular and atrial cells, we find that detubulation reduces the calcium transient and synchronization in release. However, it does not affect sarcoplasmic reticulum (SR) load, so the decrease in SR calcium release is due to regional differences in Ca2+ release, that is restricted to the cell periphery in detubulated cells. Despite the decrease in release, the release gain is larger in detubulated cells, due to recruitment of orphaned RyR2s, i.e, those that are not confronting a cluster of LCCs. This probably provides a safeguard mechanism, allowing physiological values to be maintained upon small changes in the t-tubule density. Finally, we do not find any relevant change in spark properties between tubulated and detubulated cells, suggesting that the differences found in experiments could be due to differential properties of the RyR2s in the membrane and in the t-tubules, not incorporated in the present model. This work will help understand the effect of detubulation, that has been shown to occur in disease conditions such as heart failure (HF) in ventricular cells, or atrial fibrillation (AF) in atrial cells.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 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

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

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

Digital skills, no matter what

Even if we may consider that young university students are digital natives, it is not clear that they posses the skills corresponding to the level demanded as professionals with a university degree. To assess the level of digital skills of the student body and also of the teaching staff in the Bachelor’s degree in Architectural Technology and Building Construction at the Barcelona School of Building Construction (EPSEB-UPC), a study was carried out connected to a Final Degree Project in these studies. Based on the results obtained, an implementation strategy and improvement of the level of skills in digital, information and communication technologies (ICT) was defined. For this, we took advantage of a change in the Degree’s curriculum and the implementation of the Workshop subjects, taught in every semester and designed with the key objective of promoting transversality among the different disciplines of the Degree. The COVID-19 situation has somewhat hindered the work planned for the 2020/21 academic year, but without any doubt it has shown us, in a forceful way, that digital skills are essential in university education and that the appropriate mechanisms must be established to guarantee their assimilation throughout the entire learning process. [SPANISH] Aunque podamos considerar que los jóvenes universitarios son nativos digitales, quedaría por demostrar que dispusieran de las habilidades correspondientes al nivel que precisan como profesionales con titulación de grado superior. Para evaluar el nivel en competencias digitales del estudiantado y también del profesorado que imparte docencia en el Grado en Arquitectura Técnica y Edificación de la Escuela Politécnica Superior de la Edificación de Barcelona (EPSEB-UPC) se realizó un estudio vinculado a un Trabajo Final de Grado de la propia titulación. A partir de los resultados obtenidos, se definió una estrategia de implementación y mejora del nivel en competencias digitales que incluyen las técnologías de la información y la comunicación (TIC) aprovechando la circunstancia de un cambio de Plan de Estudios y la aparición de las asignaturas Taller, ubicadas en cada cuatrimestre y diseñadas con el objetivo clave de promover la transversalidad entre las diferentes disciplinas del Grado. Las circunstancias COVID-19 han dificultado en cierta manera los trabajos previstos para el curso 2020/21, pero sin ninguna duda nos han demostrado, de manera contundente, que las competencias digitales son imprescindibles en la docencia universitaria y que deben establecerse los mecanismos adecuados para garantizar su asunción a lo largo de todo el proceso de aprendizaje.Peer ReviewedPostprint (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