Numerical Simulations of Fractionated Electrograms and Pathological Cardiac Action Potential

The aim of this work is twofold. First we focus on the complex phenomenon of electrogram fractionation, due to the presence of discontinuities in the conduction properties of the cardiac tissue in a bidomain model. Numerical simulations of paced activation may help to understand the role of the membrane ionic currents and of the changes in cellular coupling in the formation of conduction blocks and fractionation of the electrogram waveform. In particular, we show that fractionation is independent ofINAalterations and that it can be described by the bidomain model of cardiac tissue. Moreover, some deflections in fractionated electrograms may give nonlocal information about the shape of damaged areas, also revealing the presence of inhomogeneities in the intracellular conductivity of the medium at a distance.The second point of interest is the analysis of the effects of space–time discretization on numerical results, especially during slow conduction in damaged cardiac tissue. Indeed, large discretization steps can induce numerical artifacts such as slowing down of conduction velocity, alteration in extracellular and transmembrane potential waveforms or conduction blocks, which are not predicted by the continuous bidomain model. Several possible numerical and physiological explanations of these effects are given. Essentially, the discrete system obtained at the end of the approximation process may be interpreted as a discrete model of the cardiac tissue made up of isopotential cells where the effective intracellular conductivity tensor depends on the space discretization steps; the increase of these steps results in an increase of the effective intracellular resistance and can induce conduction blocks if a certain critical value is exceeded

Towards dynamical network biomarkers in neuromodulation of episodic migraine

Computational methods have complemented experimental and clinical neursciences and led to improvements in our understanding of the nervous systems in health and disease. In parallel, neuromodulation in form of electric and magnetic stimulation is gaining increasing acceptance in chronic and intractable diseases. In this paper, we firstly explore the relevant state of the art in fusion of both developments towards translational computational neuroscience. Then, we propose a strategy to employ the new theoretical concept of dynamical network biomarkers (DNB) in episodic manifestations of chronic disorders. In particular, as a first example, we introduce the use of computational models in migraine and illustrate on the basis of this example the potential of DNB as early-warning signals for neuromodulation in episodic migraine.Comment: 13 pages, 5 figure

Mathematical Analysis of the Role of Heterogeneous Distribution of Excitable and Non-excitable Cells on Early Afterdepolarizations

Early afterdepolarizations (EADs) are abnormal oscillations during the plateau phase of the cardiac action potential and have been linked to cardiac arrhythmias. At the cellular level, EADs can be caused by reactivation of the L-type calcium (Ca2+) channels, spontaneous Ca2+ releases from the sarcoplasmic reticulum, or both. In tissue, these EADs can trigger action potentials in neighboring cells, which may propagate as a nonlinear wave. In this scenario, EADs are attributed to cellular/subcellular/channel properties. In this study, we show a novel mechanism of EADs due to heterogeneous distribution of excitable and non-excitable cells in tissue, using a physiologically detailed computational model and mathematical analysis. In tissue, excitability of cells depends on the cell type and physiological and pathological conditions. Non-excitable cells create a non-excitable gap in tissue, which has been thought to be a cause of slow waves and reflected waves. Here, we show that the non-excitable gap also can be responsible for EAD generation. However, EADs occur only when the non-excitable gap size is optimal. If the gap size is too small, no EADs occur. If the gap size is too large, the action potential wave cannot propagate through the gap region. We also demonstrate that EADs caused by the non-excitable gap can initiate reentry in tissue, which has been linked to ventricular tachycardia and fibrillation. Thus, the non-excitable gap can lead to both focal and reentrant arrhythmias. EADs shown in this study are spatial phenomena and require tissue heterogeneity. Our study sheds light on the role of tissue heterogeneity on focal and reentrant arrhythmias

Neurophysiology

Contains reports on seven research projects.National Institutes of Health (Grant 5 RO1 EY01149-02)Bell Telephone Laboratories, Inc. (Grant)National Institutes of Health (Grant 1 TO1 EY00090-01

Front Solutions for Bistable Differential-Difference Equations with Inhomogeneous Diffusion

We consider a bistable differential-difference equation with inhomogeneous diffusion. Employing a piecewise linear nonlinearity, often referred to as McKean\u27s caricature of the cubic, we construct front solutions which correspond, in the case of homogeneous diffusion, to monotone traveling front solutions or, in the case of propagation failure, to stationary front solutions. A general form for these fronts is given for essentially arbitrary inhomogeneous discrete diffusion, and conditions are given for the existence of solutions to the original discrete Nagumo equation. The specific case of one defect is considered in depth, giving a complete understanding of propagation failure and a grasp on changes in wave speed. Insight into the dynamic behavior of these front solutions as a function of the magnitude and relative position of the defects is obtained with the assistance of numerical results

Front Solutions for Bistable Differential-Difference Equations with Inhomogeneous Diffusion

This is the published version, also available here: http://dx.doi.org/10.1137/100807156.We consider a bistable differential-difference equation with inhomogeneous diffusion. Employing a piecewise linear nonlinearity, often referred to as McKean's caricature of the cubic, we construct front solutions which correspond, in the case of homogeneous diffusion, to monotone traveling front solutions or, in the case of propagation failure, to stationary front solutions. A general form for these fronts is given for essentially arbitrary inhomogeneous discrete diffusion, and conditions are given for the existence of solutions to the original discrete Nagumo equation. The specific case of one defect is considered in depth, giving a complete understanding of propagation failure and a grasp on changes in wave speed. Insight into the dynamic behavior of these front solutions as a function of the magnitude and relative position of the defects is obtained with the assistance of numerical results

Actions and interactions of high pressure and general anaesthetics in rat hippocampal Ca1 neurones

The thesis is divided into two experimental sections: the first concerns the actions of general anaesthetics on rat hippocampal CA1 neurones at atmospheric pressure. The second investigates some properties of CA1 neurones under high helium pressure. The general anaesthetics studied at one atmosphere were enflurane, isoflurane, halothane, ketamine and methohexitone. Antidromic field potential measurements were taken in the absence and presence of the anaesthetics in order to assess changes in axonal/somatic excitability. Accommodation behaviour of CA1 neurones was also investigated in intracellular experiments with the above anaesthetics. The principal findings were that the anaesthetics studied decreased the amplitude of the antidromic field potential and induced hyperpolarization, with the exception of ketamine which enhanced antidromic responses at low concentration and had mixed effects upon the resting potential. Halothane also induced a second antidromic population spike. The inhalation anaesthetics (enflurane, isoflurane, halothane) all blocked accommodation. Ketamine was found to slightly compromise accommodation, whilst methohexitone had mixed effects. A voltage-clamp study indicated that enflurane reduced the M-current of CA1 neurones. CA1 neurone responses to helium pressure (up to 13.3MPa) were investigated using a purpose built pressure chamber designed to facilitate intracellular recording. In field potential experiments antidromic and orthodromic responses (to both single and paired pulses) were studied at one atmosphere and following compression. Responses were found to be mixed at elevated pressure. Some preparations were found to be unaffected by pressure whilst others became more excitable. Ketamine and methohexitone were found to have similar actions at 10MPa to their actions at 0.1 MPa. Intracellular measurements were made at pressure (5MPa and 10MPa). Resting membrane potential, input resistance and threshold potential were found to be unaffected by pressure. High pressure was found to block accommodation and reduce the associated AHP in CA1 neurones