Atrial Flutter Mechanism Detection Using Directed Network Mapping

Atrial flutter (AFL) is a common atrial arrhythmia typically characterized by electrical activity propagating around specific anatomical regions. It is usually treated with catheter ablation. However, the identification of rotational activities is not straightforward, and requires an intense effort during the first phase of the electrophysiological (EP) study, i.e., the mapping phase, in which an anatomical 3D model is built and electrograms (EGMs) are recorded. In this study, we modeled the electrical propagation pattern of AFL (measured during mapping) using network theory (NT), a well-known field of research from the computer science domain. The main advantage of NT is the large number of available algorithms that can efficiently analyze the network. Using directed network mapping, we employed a cycle-finding algorithm to detect all cycles in the network, resembling the main propagation pattern of AFL. The method was tested on two subjects in sinus rhythm, six in an experimental model of in-silico simulations, and 10 subjects diagnosed with AFL who underwent a catheter ablation. The algorithm correctly detected the electrical propagation of both sinus rhythm cases and in-silico simulations. Regarding the AFL cases, arrhythmia mechanisms were either totally or partially identified in most of the cases (8 out of 10), i.e., cycles around the mitral valve, tricuspid valve and figure-of-eight reentries. The other two cases presented a poor mapping quality or a major complexity related to previous ablations, large areas of fibrotic tissue, etc. Directed network mapping represents an innovative tool that showed promising results in identifying AFL mechanisms in an automatic fashion. Further investigations are needed to assess the reliability of the method in different clinical scenarios.

A myofibre model for the study of uterine excitation-contraction dynamics

As the uterus remodels in preparation for delivery, the excitability and contractility of the uterine smooth muscle layer, the myometrium, increase drastically. But when remodelling proceeds abnormally it can contribute to preterm birth, slow progress of labour, and failure to initiate labour. Remodelling increases intercellular coupling and cellular excitability, which are the main targets of pharmaceutical treatments for uterine contraction disorders. However, the way in which electrical propagation and force development depend on intercellular coupling and cellular excitability is not fully understood. Using a computational myofibre model we study the dependency of electrical propagation and force development on intercellular coupling and cellular excitability. This model reveals that intercellular coupling determines the conduction velocity. Moreover, our model shows that intercellular coupling alone does not regulate force development. Further, cellular excitability controls whether conduction across the cells is blocked. Lastly, our model describes how cellular excitability regulates force development. Our results bridge cellular factors, targeted by drugs to regulate uterine contractions, and tissue level electromechanical properties, which are responsible for delivery. They are a step forward towards understanding uterine excitation-contraction dynamics and developing safer and more efficient pharmaceutical treatments for uterine contraction disorders.

A COMPLEX ORDER MODEL OF ATRIAL ELECTRICAL PROPAGATION FROM FRACTAL POROUS CELL MEMBRANE

Cardiac tissue is characterized by structural and cellular heterogeneities that play an important role in the cardiac conduction system. Under persistent atrial fibrillation (persAF), electrical and structural remodeling occur simultaneously. The classical mathematical models of cardiac electrophysiological showed remarkable progress during recent years. Among those models, it is of relevance the standard diffusion mathematical equation, that considers the myocardium as a continuum. However, the modeling of structural properties and their influence on electrical propagation still reveal several limitations. In this paper, a model of cardiac electrical propagation is proposed based on complex order derivatives. By assuming that the myocardium has an underlying fractal process, the complex order dynamics emerges as an important modeling option. In this perspective, the real part of the order corresponds to the fractal dimension, while the imaginary part represents the log-periodic corrections of the fractal dimension. Indeed, the imaginary part in the derivative implies characteristic scales within the cardiac tissue. The analytical and numerical procedures for solving the related equation are presented. The sinus rhythm and persAF conditions are implemented using the Courtemanche formalism. The electrophysiological properties are measured and analyzed on different scales of observation. The results indicate that the complex order modulates the electrophysiology of the atrial system, through the variation of its real and imaginary parts. The combined effect of the two components yields a broad range of electrophysiological conditions. Therefore, the proposed model can be a useful tool for modeling electrical and structural properties during cardiac conduction.

Electrical propagation of vasodilatory signals in capillary networks

A computational model is developed to study electrical propagation of vasodilatory signals and arteriolar regulation of blood flow depending on the oxygen tension and agonist distribution in capillary network. The involving key parameters of endothelial cell-to-cell electrical conductivity and plasma membrane area per unit volume were calibrated with the experimental data on an isolated endothelial tube of mouse skeletal feeding arteries. The oxygen saturation parameters in terms of ATP release from erythrocytes are estimated from the data of a left anterior descending coronary blood perfusion of dog. In regard to the acetylcholine induced upstream conduction, our model shows that spatially uniform superfusion of acetylcholine attenuates the electrical signal propagation, and blocking calcium activated potassium channels suppresses that attenuation. On the other hand, local infusion of acetylcholine induces enhanced electrical propagation that corresponds to physiological relevance. In the integration of the endothelial tube and the lumped arterioles vessel model, we show that endothelial purinergic oxygen sensing of ATP released from erythrocytes and local infusion of acetylcholine are all individually effective to induce vasodilatory signals to regulate blood flow in arterioles. We have recapitulated the upstream vasomotion in arterioles from the elevated oxygen tension in the downstream capillary domain. This study is a foundation for characterizing effective pharmaceutical strategies for ascending vasodilation and oxygenation.

Non-ohmic tissue conduction in cardiac electrophysiology: upscaling the non-linear voltage-dependent conductance of gap junctions

Gap junctions are key mediators of the intercellular communication in cardiac tissue, and their function is vital to sustain normal cardiac electrical activity. Conduction through gap junctions strongly depends on the hemichannel arrangement and transjunctional voltage, rendering the intercellular conductance highly non-Ohmic. Despite this marked non-linear behavior, current tissue-level models of cardiac conduction are rooted on the assumption that gap-junctions conductance is constant (Ohmic), which results in inaccurate predictions of electrical propagation, particularly in the low junctional-coupling regime observed under pathological conditions. In this work, we present a novel non-Ohmic multiscale (NOM) model of cardiac conduction that is suitable for tissue-level simulations. Using non-linear homogenization theory, we develop a conductivity model that seamlessly upscales the voltage-dependent conductance of gap junctions, without the need of explicitly modeling gap junctions. The NOM model allows for the simulation of electrical propagation in tissue-level cardiac domains that accurately resemble that of cell-based microscopic models for a wide range of junctional coupling scenarios, recovering key conduction features at a fraction of the computational complexity. A unique feature of the NOM model is the possibility of upscaling the response of non-symmetric gap-junction conductance distributions, which result in conduction velocities that strongly depend on the direction of propagation, thus allowing to model the normal and retrograde conduction observed in certain regions of the heart. We envision that the NOM model will enable organ-level simulations that are informed by sub- and inter-cellular mechanisms, delivering an accurate and predictive in-silico tool for understanding the heart function.Author summaryThe heart relies on the propagation of electrical impulses that are mediated gap junctions, whose conduction properties vary depending on the transjunctional voltage. Despite this non-linear feature, current mathematical models assume that cardiac tissue behaves like an Ohmic (linear) material, thus delivering inaccurate results when simulated in a computer. Here we present a novel mathematical multiscale model that explicitly includes the non-Ohmic response of gap junctions in its predictions. Our results show that the proposed model recovers important conduction features modulated by gap junctions at a fraction of the computational complexity. This contribution represents an important step towards constructing computer models of a whole heart that can predict organ-level behavior in reasonable computing times.