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We consider Isogeometric Analysis (IGA) for the numerical solution of the electrophysiology of the atria, which in this work is modeled by means of the bidomain equations on thin surfaces. First, we consider the bidomain equations coupled with the Roger–McCulloch ionic model on simple slabs. Here, our goal is to evaluate the effects of the spatial discretization by IGA and the use of different B-spline basis functions on the accuracy of the approximation, in particular regarding the accuracy of the front velocity and the dispersion error. Specifically, we consider basis functions with high polynomial degree , p , and global high order continuity , C p − 1 , in the computational domain: our results show that the use of such basis functions is beneficial to the accurate approximation of the solution. Then, we consider a realistic application of the bidomain equations coupled with the Courtemanche–Ramirez–Nattel ionic model on the two human atria, which are represented by means of two NURBS surfaces.

Since myocardial fibers drive the electric signal propagation throughout the myocardium, accurately modeling their arrangement is essential for simulating heart electrophysiology (EP). Rule-Based-Methods (RBMs) represent a commonly used strategy to include cardiac fibers in computational models. A particular class of such methods is known as Laplace-Dirichlet-Rule-Based-Methods (LDRBMs) since they rely on the solution of Laplace problems. In this work we provide a unified framework, based on LDRBMs, for generating full heart muscle fibers. First, we review existing ventricular LDRBMs providing a communal mathematical description and introducing also some modeling improvements with respect to the existing literature. We then carry out a systematic comparison of LDRBMs based on meaningful biomarkers produced by numerical EP simulations. Next we propose, for the first time, a LDRBM to be used for generating atrial fibers. The new method, tested both on idealized and realistic atrial models, can be applied to any arbitrary geometries. Finally, we present numerical results obtained in a realistic whole heart where fibers are included for all the four chambers using the discussed LDRBMs. (C) 2020 Elsevier B.V. All rights reserved.

Bladder small DRG neurons, which are putative nociceptors pivotal to urinary bladder function, express more than a dozen different ionic membrane mechanisms: ion channels, pumps and exchangers. Small-conductance Ca2+-activated K+ (SKCa) channels which were earlier thought to be gated solely by intracellular Ca2+ concentration ([Ca]i) have recently been shown to exhibit inward rectification with respect to membrane potential. The effect of SKCa inward rectification on the excitability of these neurons is unknown. Furthermore, studies on the role of KCa channels in repetitive firing and their contributions to different types of afterhyperpolarization (AHP) in these neurons are lacking. In order to study these phenomena, we first constructed and validated a biophysically detailed single compartment model of bladder small DRG neuron soma constrained by physiological data. The model includes twenty-two major known membrane mechanisms along with intracellular Ca2+ dynamics comprising Ca2+ diffusion, cytoplasmic buffering, and endoplasmic reticulum (ER) and mitochondrial mechanisms. Using modelling studies, we show that inward rectification of SKCa is an important parameter regulating neuronal repetitive firing and that its absence reduces action potential (AP) firing frequency. We also show that SKCa is more potent in reducing AP spiking than the large-conductance KCa channel (BKCa) in these neurons. Moreover, BKCa was found to contribute to the fast AHP (fAHP) and SKCa to the medium-duration (mAHP) and slow AHP (sAHP). We also report that the slow inactivating A-type K+ channel (slow KA) current in these neurons is composed of 2 components: an initial fast inactivating (time constant ∼ 25-100 ms) and a slow inactivating (time constant ∼ 200-800 ms) current. We discuss the implications of our findings, and how our detailed model can help further our understanding of the role of C-fibre afferents in the physiology of urinary bladder as well as in certain disorders., Author summary The small dorsal root ganglion (DRG) neurons of the bladder carry information related to pain from the bladder to the spinal cord. The level of electrical activity of these neurons is generally low but rises in abnormal conditions such as bladder inflammation and spinal cord injury. In order to investigate the reasons for this hyperactivity, we constructed a model of the bladder small DRG neuron soma including its membrane ion channels and intracellular Ca2+ dynamics. One of the channels, the small-conductance Ca2+-activated K+ (SKCa) channel present in these neurons which was earlier thought to be activated solely by intracellular Ca2+ concentration was recently shown to exhibit inward rectification with respect to the neuron’s membrane potential. It was found that SKCa inward rectification can alter the repetitive firing of the bladder small DRG neurons. We also delineated the role SKCa and BKCa (large-conductance Ca2+-activated K+) channels to the complex afterhyperpolarization (AHP) of the neuron’s action potentials, shedding light on the mechanisms that govern repetitive firing in these sensory neurons. Our findings have implications for the normal biophysics and dysfunctional states of urinary bladder arising from changes in sensory axon function, and these are discussed.

The granule cell of the olfactory bulb was first described by Golgi in 1875 and Cajal and his contemporaries in the 1890s as an enigmatic cell without an axon, whose status as a nerve cell was questionable. Insight into its functions began in the 1960s with evidence that it acted as an interneuron to mediate powerful inhibition of mitral cells. The circuit was found to involve dendrodendritic synapses for activation by mitral cell lateral dendrites of the granule cell dendritic spines and inhibition of the same and neighboring mitral cell lateral dendrites. Subsequent studies established the roles of glutamatergic receptors and GABAergic receptors in this circuit. The lateral inhibition is believed to be involved in contrast enhancement between mitral cells responding to different odor molecules. Current studies are analysing how the lateral inhibition can be mediated over arbitrary distances between columns of granule cells through action potential propagation in the mitral cell secondary dendrites. Among other important properties, granule cells undergo neurogenesis from precursor cells throughout adult life. This originally enigmatic cell thus appears to play a critical role in olfactory processing.

Waveblock formation is the main cause of reentry. We have performed a comprehensive numerical modeling study of block formation due to anisotropy in Ten Tusscher and Panfilov (2006) ionic model for human ventricular tissue. We have examined the border between different areas of myocardial fiber alignment and have shown that blockage can occur for a wave traveling from a transverse fiber area to a longitudinal one. Such blockage occurs for reasonable values of the anisotropy ratio (AR): from 2.4 to 6.2 with respect to propagation velocities. This critical AR decreases by the suppression of I Na and I Ca, slightly decreases by the suppression of I Kr and I Ks, and substantially increases by the suppression of I K1. Hyperkalemia affects the block formation in a complex, biphasic way. We provide examples of reentry formation due to the studied effects and have concluded that the suppression of I K1 should be the most effective way to prevent waveblock at the areas of abrupt change in anisotropy.

One of the first and most important stages of odor processing occurs in the glomerular units of the olfactory bulb and most likely involves mitral cell synchronization. Using a detailed model constrained by a number of experimental findings, we show how the intercellular coupling mediated by intraglomerular gap junctions (GJs) in the tuft dendrites could play a major role in sychronization of mitral cell action potential output in spite of their distal dendritic location. The model suggests that the high input resistance and active properties of the fine tuft dendrites are instrumental in generating local spike synchronization and an efficient forward and backpropagation of action potentials between the tuft and the soma. The model also gives insight into the physiological significance of long primary dendrites in mitral cells, and provides evidence against the use of reduced single compartmental models to investigate network properties of cortical pyramidal neurons.

Cardiac fibroblasts, when coupled functionally with myocytes, can modulate the electrophysiological properties of cardiac tissue. We present systematic numerical studies of such modulation of electrophysiological properties in mathematical models for (a) single myocyte-fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for zero-, one-, and two-sided MF couplings. Our studies of MF units elucidate the dependence of the action-potential (AP) morphology on parameters such as [Formula: see text], the fibroblast resting-membrane potential, the fibroblast conductance [Formula: see text], and the MF gap-junctional coupling [Formula: see text]. Furthermore, we find that our MF composite can show autorhythmic and oscillatory behaviors in addition to an excitable response. Our 2D studies use (a) both homogeneous and inhomogeneous distributions of fibroblasts, (b) various ranges for parameters such as [Formula: see text], and [Formula: see text], and (c) intercellular couplings that can be zero-sided, one-sided, and two-sided connections of fibroblasts with myocytes. We show, in particular, that the plane-wave conduction velocity [Formula: see text] decreases as a function of [Formula: see text], for zero-sided and one-sided couplings; however, for two-sided coupling, [Formula: see text] decreases initially and then increases as a function of [Formula: see text], and, eventually, we observe that conduction failure occurs for low values of [Formula: see text]. In our homogeneous studies, we find that the rotation speed and stability of a spiral wave can be controlled either by controlling [Formula: see text] or [Formula: see text]. Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity. We also study the efficacy of a low-amplitude control scheme, which has been suggested for the control of spiral-wave turbulence in mathematical models for cardiac tissue, in our MF model both with and without heterogeneities.

We introduce a preconditioner for the solution of the Bidomain system governing the propagation of action potentials in the myocardial tissue. The Bidomain model is a degenerate parabolic set of nonlinear reaction-diffusion equations. The nonlinear term describes the ion flux at the cellular level. The degenerate nature of the problem results in a severe ill conditioning of its discretization. Our preconditioning strategy is based on a suitable adaptation of the Monodomain model, a simplified version of the Bidomain one, which is by far simpler to solve, nevertheless is unable to capture significant features of the action potential propagation. The Monodomain preconditioner application to a non-symmetric formulation of the Bidomain system results at the algebraic level in a lower block-triangular preconditioner. We prove optimality of the preconditioner with respect to the mesh size, and corroborate our theoretical results with 3D numerical simulations both on idealized and real ventricle geometries. (C) 2009 Elsevier Inc. All rights reserved.

The distribution of cellular source-sink relationships plays an important role in cardiac propagation. It can lead to conduction slowing and block as well as wave fractionation. It is of great interest to unravel the mechanisms underlying evolution in wavefront geometry. Our goal is to investigate the role of the source-sink relationship on wavefront geometry using computer simulations. We analyzed the role of variability in the microscopic source-sink relationship in driving changes in wavefront geometry. The electrophysiological activity of a homogeneous isotropic tissue was simulated using the ten Tusscher and Panfilov 2006 action potential model and the source-sink relationship was characterized using an improved version of the Romero et al. safety factor formulation (SFm2). Our simulations reveal that non-uniform dispersion of the cellular source-sink relationship (dispersion along the wavefront) leads to alterations in curvature. To better understand the role of the source-sink relationship in the process of wave formation, the electrophysiological activity at the initiation of excitation waves in a 1D strand was examined and the source-sink relationship was characterized using the two recently updated safety factor formulations: the SFm2 and the Boyle-Vigmond (SFVB) definitions. The electrophysiological activity at the initiation of excitation waves was intimately related to the SFm2 profiles, while the SFVB led to several counterintuitive observations. Importantly, with the SFm2 characterization, a critical source-sink relationship for initiation of excitation waves was identified, which was independent of the size of the electrode of excitation, membrane excitability, or tissue conductivity. In conclusion, our work suggests that non-uniform dispersion of the source-sink relationship alters wavefront curvature and a critical source-sink relationship profile separates wave expansion from collapse. Our study reinforces the idea that the safety factor represents a powerful tool to study the mechanisms of cardiac propagation in silico, providing a better understanding of cardiac arrhythmias and their therapy., This work was partially supported by the "VI Plan Nacional de Investigacion Cientifica, Desarrollo e Innovacion Tecnologica'' from the Ministerio de Economia y Competitividad of Spain (TIN2012?37546?C03?01) and the European Commission (European Regional Development Funds - ERDF ? FEDER), Plan Nacional de Investigacion Cientifica, Desarrollo e Innovacion Tecnologica, Plan Avanza en el marco de la Accion Estrategica de Telecomunicaciones y Sociedad de la Informacion del Ministerio de Industria Turismo y Comercio of Spain (TSI?020100?2010?469), Programa de Apoyo a la Investigacion y Desarrollo (PAID?06?11?2002) de la Universidad Politecnica de Valencia, Direccion General de Politica Cientifica de la Generalitat Valenciana (GV/2013/119) and Programa Prometeo (PROMETEO/2012/030) de la Conselleria d'Educacio Formacio I Ocupacio, Generalitat Valenciana. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.