Spiral waves within a bistability parameter region of an excitable medium

Spiral waves are a well-known and intensively studied dynamic phenomenon in excitable media of various types. Most studies have considered an excitable medium with a single stable resting state. However, spiral waves can be maintained in an excitable medium with bistability. Our calculations, performed using the widely used Barkley model, clearly show that spiral waves in the bistability region exhibit unique properties. For example, a spiral wave can either rotate around a core that is in an unexcited state, or the tip of the spiral wave describes a circular trajectory located inside an excited region. The boundaries of the parameter regions with positive and "negative" cores have been defined numerically and analytically evaluated. It is also shown that the creation of a positive or "negative" core may depend on the initial conditions, which leads to hysteresis of spiral waves. In addition, the influence of gradient flow on the dynamics of the spiral wave, which is related to the tension of the scroll wave filaments in a three-dimensional medium, is studied.

Why Is Only Type 1 Electrocardiogram Diagnostic of Brugada Syndrome? Mechanistic Insights From Computer Modeling

Background: Three types of characteristic ST-segment elevation are associated with Brugada syndrome but only type 1 is diagnostic. Why only type 1 ECG is diagnostic remains unanswered. Methods: Computer simulations were performed in single cells, 1-dimensional cables, and 2-dimensional tissues to investigate the effects of the peak and late components of the transient outward potassium current (I to ), sodium current, and L-type calcium current (I Ca,L ) as well as other potassium currents on the genesis of ECG morphologies and phase 2 reentry (P2R). Results: Although a sufficiently large peak I to was required to result in the type 1 ECG pattern and P2R, increasing the late component of I to converted type 1 ECG to type 2 ECG and suppressed P2R. Increasing the peak I to promoted spiral wave breakup, potentiating the transition from tachycardia to fibrillation, but increasing the late I to prevented spiral wave breakup by flattening the action potential duration restitution and preventing P2R. A sufficiently large I Ca,L conductance was needed for P2R to occur, but once above the critical conductance, blocking I Ca,L promoted P2R. However, selectively blocking the window and late components of I Ca,L suppressed P2R, countering the effect of the late I to . Blocking either the peak or late components of sodium current promoted P2R, with the late sodium current blockade having the larger effect. As expected, increasing other potassium currents potentiated P2R, with ATP-sensitive potassium current exhibiting a larger effect than rapid and slow component of the delayed rectifier potassium current. Conclusions: The peak I to promotes type 1 ECG and P2R, whereas the late I to converts type 1 ECG to type 2 ECG and suppresses P2R. Blocking the peak I Ca,L and either the peak or the late sodium current promotes P2R, whereas blocking the window and late I Ca,L suppresses P2R. These results provide important insights into the mechanisms of arrhythmogenesis and potential therapeutic targets for treatment of Brugada syndrome.

On the dynamics of the torus around the kicked black hole

There is a special interest to understand the dynamical properties of the accretion disk created around the newly formed black hole due to the supermassive black hole binaries which merge inside the gaseous disk. The newly formed black hole would have a kick velocity up to thousands of km/s that drives a perturbation on a newly accreted torus around the black hole. Some of the observed supermassive black holes at the center of the Active Galactic Nucleus (AGN) move with a certain velocity relative to its broader accretion disk. In this paper, the effects of the kicked black holes onto the infinitesimally thin accreted torus are studied by using the general relativistic hydrodynamical code, focusing on changing the dynamics of the accretion disk during the accretion disk–black hole interaction. We have found that the non-axisymmetric global mode [Formula: see text] inhomogeneity, which causes a spiral-wave-structure, is excited on the torus due to kicked black hole. The higher the perturbation velocity produced by the kicked black hole, the longer the time the torus takes to reach the saturation point. The created spiral density waves which rapidly evolve into the spiral shocks are also observed from the numerical simulations. The spiral shock is responsible for accreting matter toward the black hole. First, the spiral-wave-structure is developed and the accretion through the spiral arms is stopped around the black hole. At the later time of simulation, the formed spiral shocks partly cause the angular momentum loss across the torus.

Computational Analysis of Mapping Catheter Geometry and Contact Quality Effects on Rotor Detection in Atrial Fibrillation

Atrial fibrillation (AF) is the most common cardiac arrhythmia and catheter mapping has been proved to be an effective approach for detecting AF drivers to be targeted by ablation. Among drivers, the so-called rotors have gained the most attention: their identification and spatial location could help to understand which patient-specific mechanisms are acting, and thus to guide the ablation execution. Since rotor detection by multi-electrode catheters may be influenced by several structural parameters including inter-electrode spacing, catheter coverage, and endocardium-catheter distance, in this study we proposed a tool for testing the ability of different catheter shapes to detect rotors in different conditions. An approach based on the solution of the monodomain equations coupled with a modified Courtemanche ionic atrial model, that considers an electrical remodeling, was applied to simulate spiral wave dynamics on a 2D model for 7.75 s. The developed framework allowed the acquisition of unipolar signals at 2 KHz. Two high-density multipolar catheters were simulated (Advisor™ HD Grid and PentaRay®) and placed in a 2D region in which the simulated spiral wave persists longer. The configuration of the catheters was then modified by changing the number of electrodes, inter-electrodes distance, position, and atrial-wall distance for assessing how they would affect the rotor detection. In contact with the wall and at 1 mm distance from it, all the configurations detected the rotor correctly, irrespective of geometry, coverage, and inter-electrode distance. In the HDGrid-like geometry, the increase of the inter-electrode distance from 3 to 6 mm caused rotor detection failure at 2 mm distance from the LA wall. In the PentaRay-like configuration, regardless of inter-electrode distance, rotor detection failed at 3 mm endocardium-catheter distance. The asymmetry of this catheter resulted in rotation-dependent rotor detection. To conclude, the computational framework we developed is based on realistic catheter shapes designed with parameter configurations which resemble clinical settings. Results showed it is well suited to investigate how mapping catheter geometry and location affect AF driver detection, therefore it is a reliable tool to design and test new mapping catheters.

Anatomical Model of Rat Ventricles to Study Cardiac Arrhythmias under Infarction Injury

Species-specific computer models of the heart are a novel powerful tool in studies of life-threatening cardiac arrhythmias. Here, we develop such a model aimed at studying infarction injury in a rat heart, the most common experimental system to investigate the effects of myocardial damage. We updated the Gattoni2016 cellular ionic model by fitting its parameters to experimental data using a population modeling approach. Using four selected cellular models, we studied 2D spiral wave dynamics and found that they include meandering and break-up. Then, using an anatomically realistic ventricular geometry and fiber orientation in the rat heart, we built a model with a post-infarction scar to study the electrophysiological effects of myocardial damage. A post-infarction scar was simulated as an inexcitable obstacle surrounded by a border zone with modified cardiomyocyte properties. For cellular models, we studied the rotation of scroll waves and found that, depending on the model, we can observe different types of dynamics: anchoring, self-termination or stable rotation of the scroll wave. The observed arrhythmia characteristics coincide with those measured in the experiment. The developed model can be used to study arrhythmia in rat hearts with myocardial damage from ischemia reperfusion and to examine the possible arrhythmogenic effects of various experimental interventions.

Detecting spiral wave tips using deep learning

The chaotic spatio-temporal electrical activity during life-threatening cardiac arrhythmias like ventricular fibrillation is governed by the dynamics of vortex-like spiral or scroll waves. The organizing centers of these waves are called wave tips (2D) or filaments (3D) and they play a key role in understanding and controlling the complex and chaotic electrical dynamics. Therefore, in many experimental and numerical setups it is required to detect the tips of the observed spiral waves. Most of the currently used methods significantly suffer from the influence of noise and are often adjusted to a specific situation (e.g. a specific numerical cardiac cell model). In this study, we use a specific type of deep neural networks (UNet), for detecting spiral wave tips and show that this approach is robust against the influence of intermediate noise levels. Furthermore, we demonstrate that if the UNet is trained with a pool of numerical cell models, spiral wave tips in unknown cell models can also be detected reliably, suggesting that the UNet can in some sense learn the concept of spiral wave tips in a general way, and thus could also be used in experimental situations in the future (ex-vivo, cell-culture or optogenetic experiments).

Realization of fully biological restoration of cardiac rhythm: a computational translational exploration

Background Recently it was demonstrated how the heart itself could be enabled to quickly restore its rhythm by realizing a biologically-integrated cardiac defibrillator (BioICD) through modification and subsequent expression of ion channels in cardiomyocytes [1]. By incorporating these frequency-dependent depolarizing ion channels, abnormal cardiac rhythm could be rapidly detected and terminated to restore sinus rhythm in a fully biological and shock-free manner. However, from a translational point of view, it remains unclear how such rhythm restoration can be realized via ion channel gene therapy. Purpose To explore and understand the importance of the distribution and number of BioICD-expressing cardiomyocytes in realizing fully biological restoration of cardiac rhythm. Methods To this purpose, two different realistic gene therapy configurations, i.e. those corresponding to systemic and local transgene delivery, were tested in human ventricular virtual cardiac monolayers. For the systemic delivery group, BioICD-expressing cells were homogeneously distributed (10 random variations) over the tissue with fixed total expression percentage (14 percentages). For the local delivery group, circular areas (7 radii) were given BioICD-expressing cells randomly patterned (10 variations) in a Gaussian distribution with 3 fixed total expression percentages. For both groups, spiral waves were initiated (9 locations) and studied for the following 10 seconds for each test condition, thereby equaling 1260 and 1890 conditions, respectively. Results For systemic delivery, normal rhythm was restored in all cases for >50% BioICD expressing cells, with time till termination being inversely related to the percentage, resulting in only 4.3s and 2.5s for 50% and 100%, respectively. Regarding termination, it was observed that conduction blocks appeared throughout the tissue and subsequently connected to force arrhythmic waves to terminate, while this process remained incomplete in the <50% groups. Local delivery, on the other hand, resulted in islands of ionic heterogeneity, causing attraction and anchoring of the spiral waves in a size and distance-dependent manner. Hence, BioICD-based self-termination was not observed in any of the investigated conditions, leaving spiral waves to persist. Conclusion This study reveals that wide-spread distribution of BioICD-expressing cardiomyocytes is required for the realization of fully biological self-restoration of cardiac rhythm, of which the efficiency is dosage-dependent. Local expression, however, results in stabilization of spiral wave activity. Further exploration of this emerging concept of biological cardioversion may not only expand our understanding of cardiac arrhythmias, but also pave the way to breakthrough advances in arrhythmia management. FUNDunding Acknowledgement Type of funding sources: Public grant(s) – EU funding. Main funding source(s): European Research Council (Starting grant 716509) to D.A. Pijnappels.

Emergence of Stripe-Core Mixed Spiral Chimera on a Spherical Surface of Nonlocally Coupled Oscillators

We report on a stripe-core mixed spiral chimera in a system of nonlocally coupled phase oscillators, located on the spherical surface, where the spiral wave consisting of phase-locked oscillators is separated by a stripe-type region of incoherent oscillators into two parts. We analyze the existence and stability of the stripe-core mixed spiral chimera state rigorously, on the basis of the Ott–Antonsen reduction theory. The stability diagram for the stationary states including the spiral chimeras as well as incoherent state is presented. Our stability analysis reveals that the stripe-core mixed spiral chimera state emerges as a unique attractor and loses its stability via the Hopf bifurcation. We verify our theoretical results using direct numerical simulations of the model system.

Formation of spiral waves in cylindrical containers under orbital excitation

The lowest swirling wave mode arising in upright circular cylinders as a response to circular orbital excitation has been widely studied in the last decade, largely due to its high practical relevance for orbitally shaken bioreactors. Our recent theoretical study (Horstmann et al., J. Fluid Mech., vol. 891, 2020, A22) revealed a damping-induced symmetry breaking mechanism that can cause spiral wave structures manifested in the so far widely disregarded higher rotating wave modes. Building on this work, we develop a linear criterion describing the degree of spiralisation and classify different spiral regimes as a function of the most relevant dimensionless groups. The analysis suggests that high Bond numbers and shallow liquid layers favour the formation of coherent spiral waves. This result paved the way to find the predicted wave structures in our interfacial sloshing experiment. We present two sets of experiments, with different characteristic damping rates, verifying the formation of both coherent and overdamped spiral waves in conformity with the theoretical predictions.