A space-fractional bidomain framework for cardiac electrophysiology: 1D alternans dynamics

Observers-based event-triggered adaptive fuzzy backstepping synchronization of uncertain fractional order chaotic systems

In this paper, for a class of uncertain fractional order chaotic systems with disturbances and partially unmeasurable states, an observer-based event-triggered adaptive fuzzy backstepping synchronization control method is proposed. Fuzzy logic systems are employed to estimate unknown functions in the backstepping procedure. To avoid the explosion of the complexity problem, a fractional order command filter is designed. Simultaneously, in order to reduce the filter error and improve the synchronization accuracy, an effective error compensation mechanism is devised. In particular, a disturbance observer is devised in the case of unmeasurable states, and a state observer is established to estimate the synchronization error of the master-slave system. The designed controller can ensure that the synchronization error converges to a small neighborhood around the origin finally and all signals are semiglobal uniformly ultimately bounded, and meanwhile, it is conducive to avoiding Zeno behavior. Finally, two numerical simulations are given to verify the effectiveness and accuracy of the proposed scheme.

Sensitivity Analysis of Cardiac Alternans and Tachyarrhythmia to Ion Channel Conductance Using Population Modeling

Action potential duration (APD) alternans, an alternating phenomenon between action potentials in cardiomyocytes, causes heart arrhythmia when the heart rate is high. However, some of the APD alternans observed in clinical trials occurs under slow heart rate conditions of 100 to 120 bpm, increasing the likelihood of heart arrhythmias such as atrial fibrillation. Advanced studies have identified the occurrence of this type of APD alternans in terms of electrophysiological ion channel currents in cells. However, they only identified physiological phenomena, such as action potential due to random changes in a particular ion channel’s conductivity through ion models specializing in specific ion channel currents. In this study, we performed parameter sensitivity analysis via population modeling using a validated human ventricular physiology model to check the sensitivity of APD alternans to ion channel conductances. Through population modeling, we expressed the changes in alternans onset cycle length (AOCL) and mean APD in AOCL (AO meanAPD) according to the variations in ion channel conductance. Finally, we identified the ion channel that maximally affected the occurrence of APD alternans. AOCL and AO meanAPD were sensitive to changes in the plateau Ca²⁺ current. Accordingly, it was expected that APD alternans would be vulnerable to changes in intracellular calcium concentration.

Balancing conduction velocity error in cardiac electrophysiology using a modified quadrature approach

Conduction velocity error is often the main culprit behind the need for very fine spatial discretizations and high computational effort in cardiac electrophysiology problems. In light of this, a novel approach for simulating an accurate conduction velocity in coarse meshes with linear elements is suggested based on a modified quadrature approach. In this approach, the quadrature points are placed at arbitrary offsets of the isoparametric coordinates. A numerical study illustrates the dependence of the conduction velocity on the spatial discretization and the conductivity when using different quadrature rules and calculation approaches. Additionally, examples using the modified quadrature in coarse meshes for wave propagation demonstrate the improved accuracy of the conduction velocity with this method. This novel approach possesses great potential in reducing the computational effort required but remains limited to specific linear elements and experiences a reduction in accuracy for irregular meshes and heterogeneous conductivities. Further research can focus on developing an adaptive quadrature and extending the approach to other element formulations in order to make the approach more generally applicable.

Simulation of atrial fibrillation in a non-ohmic propagation model with dynamic gap junctions

Gap junctions exhibit nonlinear electrical properties that have been hypothesized to be relevant to arrhythmogenicity in a structurally remodeled tissue. Large-scale implementation of gap junction dynamics in 3D propagation models remains challenging. We aim to quantify the impact of nonlinear diffusion during episodes of arrhythmias simulated in a left atrial model. Homogenization of conduction properties in the presence of nonlinear gap junctions was performed by generalizing a previously developed mathematical framework. A monodomain model was solved in which conductivities were time-varying and depended on transjunctional potentials. Gap junction conductances were derived from a simplified Vogel-Weingart model with first-order gating and adjustable time constant. A bilayer interconnected cable model of the left atrium with 100  μm resolution was used. The diffusion matrix was recomputed at each time step according to the state of the gap junctions. Sinus rhythm and atrial fibrillation episodes were simulated in remodeled tissue substrates. Slow conduction was induced by reduced coupling and by diffuse or stringy fibrosis. Simulations starting from the same initial conditions were repeated with linear and nonlinear gap junctions. The discrepancy in activation times between the linear and nonlinear diffusion models was quantified. The results largely validated the linear approximation for conduction velocities >20 cm/s. In very slow conduction substrates, the discrepancy accumulated over time during atrial fibrillation, eventually leading to qualitative differences in propagation patterns, while keeping the descriptive statistics, such as cycle lengths, unchanged. The discrepancy growth rate was increased by impaired conduction, fibrosis, conduction heterogeneity, lateral uncoupling, fast gap junction time constant, and steeper action potential duration restitution.

Optical Ultrastructure of Large Mammalian Hearts Recovers Discordant Alternans by In Silico Data Assimilation

Understanding and predicting the mechanisms promoting the onset and sustainability of cardiac arrhythmias represent a primary concern in the scientific and medical communities still today. Despite the long-lasting effort in clinical and physico-mathematical research, a critical aspect to be fully characterized and unveiled is represented by spatiotemporal alternans patterns of cardiac excitation. The identification of discordant alternans and higher-order alternating rhythms by advanced data analyses as well as their prediction by reliable mathematical models represents a major avenue of research for a broad and multidisciplinary scientific community. Current limitations concern two primary aspects: 1) robust and general-purpose feature extraction techniques and 2) in silico data assimilation within reliable and predictive mathematical models. Here, we address both aspects. At first, we extend our previous works on Fourier transformation imaging (FFI), applying the technique to whole-ventricle fluorescence optical mapping. Overall, we identify complex spatial patterns of voltage alternans and characterize higher-order rhythms by a frequency-series analysis. Then, we integrate the optical ultrastructure obtained by FFI analysis within a fine-tuned electrophysiological mathematical model of the cardiac action potential. We build up a novel data assimilation procedure demonstrating its reliability in reproducing complex alternans patterns in two-dimensional computational domains. Finally, we prove that the FFI approach applied to both experimental and simulated signals recovers the same information, thus closing the loop between the experiment, data analysis, and numerical simulations.