A mathematical model for electrical activity in pig atrial tissue

Atrial fibrillation (AF) is the most common sustained form of cardiac arrhythmia occurring in humans. Its effective treatment requires a detailed understanding of the underlying mechanisms at the genetic, molecular, cellular, tissue and organ levels. To study the complex mechanisms underlying the development, maintenance and termination of cardiac arrhythmias, we need preclinical research models. These models range from in vitro cell cultures to in vivo small and large animal hearts. However, translational research requires that the results of these animal experiments are understood in the context of human subjects. Currently, this is achieved through simulations with state-of-the-art mathematical models for human and animal heart tissue. In the context of AF, a model that is extensively used by experimentalists, is that of the pig atria. However, until now, an ionically detailed mathematical model for pig atrial tissue has been lacking, and researchers have been forced to rely on mathematical models from other animal species to understand their experimental observations. In this paper, we present the first ionically detailed mathematical model of porcine atrial electrophysiology. To build the model, we first fitted experimental patch-clamp data from literature to describe the individual currents flowing across the cell membrane. Later, we fine-tuned the model by fitting action potential duration restitution (APDR) curves for different repolarisation levels. The experimental data for the APDR studies was produced in N. Voigt’s lab. We extended our model to the tissue level and demonstrated the ability to maintain stable spiral waves. In agreement with previous experimental results, our model shows that early repolarisation is primarily driven by a calcium-mediated chloride current, IClCa, which is completely inactivated at high pacing frequencies. This is a condition found only in porcine atria. The model shows spatiotemporal chaos with reduced repolarisation.

Unifying turbulent dynamics framework distinguishes different brain states

Recently, significant advances have been made by identifying the levels of synchronicity of the underlying dynamics of a given brain state. This research has demonstrated that unconscious dynamics tend to be more synchronous than those found in conscious states, which are more asynchronous. Here we go beyond this dichotomy to demonstrate that the different brain states are always underpinned by spatiotemporal chaos but with dissociable turbulent dynamics. We investigated human neuroimaging data from different brain states (resting state, meditation, deep sleep, and disorders of consciousness after coma) and were able to distinguish between them using complementary model-free and model-based measures of turbulent information transmission. Our model-free approach used recent advances describing a measure of information cascade across spatial scales using tools from turbulence theory. Complementarily, our model-based approach used exhaustive in silico perturbations of whole-brain models fitted to the empirical neuroimaging data, which allowed us to study the information encoding capabilities of the brain states. Overall, the current framework demonstrates that different levels of turbulent dynamics are fundamental for describing and differentiating between brain states.

Integrated Time-Fractional Diffusion Processes for Fractional-Order Chaos-Based Image Encryption

The purpose of this paper is to explore a novel image encryption algorithm that is developed by combining the fractional-order Chua’s system and the 1D time-fractional diffusion system of order α∈(0,1]. To this end, we first discuss basic properties of the fractional-order Chua’s system and the 1D time-fractional diffusion system. After these, a new spatiotemporal chaos-based cryptosystem is proposed by designing the chaotic sequence of the fractional-order Chua’s system as the initial condition and the boundary conditions of the studied time-fractional diffusion system. It is shown that the proposed image encryption algorithm can gain excellent encryption performance with the properties of larger secret key space, higher sensitivity to initial-boundary conditions, better random-like sequence and faster encryption speed. Efficiency and reliability of the given encryption algorithm are finally illustrated by a computer experiment with detailed security analysis.

Suppression of fibrillation consisting of stable rotors by periodic pacing

Recent experimental studies have shown that a sequence of low-energy electrical far-field pulses is able to terminate fibrillation with substantially lower per-pulse energy than a single high-energy electric shock (see S. Luther et al. Nature 475 (7355), 235-239). During this low-energy antifibrillation pacing (LEAP) procedure only tissue near sufficiently large conduction heterogeneities, such as large coronary arteries, is activated. In order to understand the mechanism behind LEAP, We have carried out a statistical study of resetting a medium filled by one or more stable spirals (“rotors”) in a two-dimensional electrophysiological model of cardiac tissue perforated by blood vessels to the resting state (“defibrillation”). We found the highest success probabilities for this defibrillation for underdrive pacing with periods 10 – 20 percent larger than the dominant period of the stable rotors in the unperturbed dynamics. If a sufficiently large number pulses is applied and an optimal pacing period chosen, the energy per pulse required for successful defibrillation is about 75 - 80 percent lower than the energy needed for single-shock defibrillation. Optimal conditions to control and suppress fibrillation based on stable rotors, hence, are similar to the ones in found for the case of an electrophysiological model displaying spatiotemporal chaos (“electrical turbulence”) in an earlier study (see P. Buran et al. Chaos 27, 113110 (2017)). The optimal pacing period is found to increase with increasing strength of the electrical field strength used in the model. The success probability also increases strongly until the fourth or fifth pulse administered, which is strongly correlated to an observed increase of the fraction of re-excitable tissue with each subsequent pulse. Monitoring the fraction of excitable tissue in the model as key quantity of the excitable medium, moreover, enabled us to successfully predict the optimal pacing period for defibrillation.

Identification of the Gray–Scott Model via Deterministic Learning

Gray–Scott model is one of the most well-known reaction–diffusion models which has a wealth of spatiotemporal chaos behavior. It is commonly used to study spatiotemporal chaos. In the paper, a novel method is proposed for the identification of the Gray–Scott model via deterministic learning and interpolation. The method mainly consists of two phases: the local identification phase and the global identification phase. Local identification is achieved using the finite difference method and deterministic learning. Based on the local identification results, the interpolation method is employed to obtain global identification. Numerical experiments show the feasibility and effectiveness of the proposed method.