Action potential morphology heterogeneity in the atrium and its effect on atrial reentry: a two-dimensional and quasi-three-dimensional study

2006 ◽  
Vol 364 (1843) ◽  
pp. 1349-1366 ◽  
Author(s):  
Samuel R Kuo ◽  
Natalia A Trayanova
Keyword(s):  
Action Potential ◽  
Action Potentials ◽  
Three Dimensional ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Two Dimensional ◽  
Crista Terminalis ◽  
Wave Dynamics ◽  
Continuous Surface ◽  
The Right

Atrial fibrillation (AF) is believed to be perpetuated by recirculating spiral waves. Atrial structures are often characterized with action potentials of varying morphologies; however, the role of the structure-dependent atrial electrophysiological heterogeneity in spiral wave behaviour is not well understood. The purpose of this study is to determine the effect of action potential morphology heterogeneity associated with the major atrial structures in spiral wave maintenance. The present study also focuses on how this effect is further modulated by the presence of the inherent periodicity in atrial structure. The goals of the study are achieved through the simulation of electrical behaviour in a two-dimensional atrial tissue model that incorporates the representation of action potentials in various structurally distinct regions in the right atrium. Periodic boundary conditions are then imposed to form a cylinder (quasi three-dimensional), thus allowing exploration of the additional effect of structure periodicity on spiral wave behaviour. Transmembrane potential maps and phase singularity traces are analysed to determine effects on spiral wave behaviour. Results demonstrate that the prolonged refractoriness of the crista terminalis (CT) affects the pattern of spiral wave reentry, while the variation in action potential morphology of the other structures does not. The CT anchors the spiral waves, preventing them from drifting away. Spiral wave dynamics is altered when the ends of the sheet are spliced together to form a cylinder. The main effect of the continuous surface is the generation of secondary spiral waves which influences the primary rotors. The interaction of the primary and secondary spiral waves decreased as cylinder diameter increased.

Cardiac electrical restitution properties and stability of reentrant spiral waves: a simulation study

1999 ◽  
Vol 276 (1) ◽  
pp. H269-H283 ◽  
Author(s):  
Zhilin Qu ◽  
James N. Weiss ◽  
Alan Garfinkel
Keyword(s):  
Action Potential ◽  
Antiarrhythmic Drugs ◽  
Cardiac Tissue ◽  
Potential Model ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Two Dimensional ◽  
Recovery From Inactivation ◽  
Main Determinants ◽  
The Stability

Spiral wave breakup is a proposed mechanism underlying the transition from ventricular tachycardia to fibrillation. We examined the importance of the restitution of action potential duration (APD) and of conduction velocity (CV) to the stability of spiral wave reentry in a two-dimensional sheet of simulated cardiac tissue. The Luo-Rudy ventricular action potential model was modified to eliminate its restitution properties, which are caused by deactivation or recovery from inactivation of K+, Ca2+, and Na+ currents ( I K, I Ca, and I Na, respectively). In this model, we find that 1) restitution of I Ca and I Na are the main determinants of the steepness of APD restitution; 2) for promoting spiral breakup, the range of diastolic intervals over which the APD restitution slope is steep is more important than the maximum steepness; 3) CV restitution promotes spiral wave breakup independently of APD restitution; and 4) “defibrillation” of multiple spiral wave reentry is most effectively achieved by combining an antifibrillatory intervention based on altering restitution with an antitachycardia intervention. These findings suggest a novel paradigm for developing effective antiarrhythmic drugs.

scholarly journals Induced drift of scroll waves in the Aliev–Panfilov model and in an axisymmetric heart left ventricle

2020 ◽  
Vol 35 (5) ◽  
pp. 273-283 ◽  
Author(s):  
Sergei F. Pravdin ◽  
Timofei I. Epanchintsev ◽  
Timur V. Nezlobinskii ◽  
Alexander V. Panfilov
Keyword(s):  
Left Ventricle ◽  
Low Voltage ◽  
Three Dimensional ◽  
Spiral Wave ◽  
Spiral Waves ◽  
High Frequency Stimulation ◽  
Two Dimensional ◽  
Anatomical Model ◽  
Paroxysmal Tachycardia ◽  
Scroll Waves

AbstractThe low-voltage cardioversion-defibrillation is a modern sparing electrotherapy method for such dangerous heart arrhythmias as paroxysmal tachycardia and fibrillation. In an excitable medium, such arrhythmias relate to appearance of spiral waves of electrical excitation, and the spiral waves are superseded to the electric boundary of the medium in the process of treatment due to high-frequency stimulation from the electrode. In this paper we consider the Aliev–Panfilov myocardial model, which provides a positive tension of three-dimensional scroll waves, and an axisymmetric model of the left ventricle of the human heart. Two relations of anisotropy are considered, namely, isotropy and physiological anisotropy. The periods of stimulation with an apical electrode are found so that the electrode successfully entrains its rhythm in the medium, the spiral wave is superseded to the base of the ventricle, and disappears. The results are compared in two-dimensional and three-dimensional media. The intervals of effective stimulation periods are sufficiently close to each other in the two-dimensional case and in the anatomical model. However, the use of the anatomical model is essential in determination of the time of superseding.

scholarly journals Rapid Fabrication of Continuous Surface Fresnel Microlens Array by Femtosecond Laser Focal Field Engineering

Micromachines ◽  
2020 ◽  
Vol 11 (2) ◽  
pp. 112 ◽  
Author(s):  
Linyu Yan ◽  
Dong Yang ◽  
Qihuang Gong ◽  
Yan Li
Keyword(s):  
Femtosecond Laser ◽  
Three Dimensional ◽  
Fresnel Lens ◽  
Two Dimensional ◽  
Direct Writing ◽  
Lens Array ◽  
Two Photon ◽  
Rapid Fabrication ◽  
Continuous Surface ◽  
Two Photon Polymerization

Femtosecond laser direct writing through two-photon polymerization has been widely used in precision fabrication of three-dimensional microstructures but is usually time consuming. In this article, we report the rapid fabrication of continuous surface Fresnel lens array through femtosecond laser three-dimensional focal field engineering. Each Fresnel lens is formed by continuous two-photon polymerization of the two-dimensional slices of the whole structure with one-dimensional scan of the corresponding two-dimensional engineered intensity distribution. Moreover, we anneal the lens array to improve its focusing and imaging performance.

Separation of the 3D stress state of a loaded plate into two-dimensional tasks: bending and symmetric compression of the plate

2021 ◽  
Vol 103 (3) ◽  
pp. 53-62
Author(s):  
Victor Revenko ◽  
Andrian Revenko
Keyword(s):  
Boundary Conditions ◽  
Harmonic Functions ◽  
Three Dimensional ◽  
Partial Solution ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Normal Stresses ◽  
Equilibrium Equations ◽  
Dimensional Boundary ◽  
The Right

The three-dimensional stress-strain state of an isotropic plate loaded on all its surfaces is considered in the article. The initial problem is divided into two ones: symmetrical bending of the plate and a symmetrical compression of the plate, by specified loads. It is shown that the plane problem of the theory of elasticity is a special case of the second task. To solve the second task, the symmetry of normal stresses is used. Boundary conditions on plane surfaces are satisfied and harmonic conditions are obtained for some functions. Expressions of effort were found after integrating three-dimensional stresses that satisfy three equilibrium equations. For a thin plate, a closed system of equations was obtained to determine the harmonic functions. Displacements and stresses in the plate were expressed in two two-dimensional harmonic functions and a partial solution of the Laplace equation with the right-hand side, which is determined by the end loads. Three-dimensional boundary conditions were reduced to two-dimensional ones. The formula was found for experimental determination of the sum of normal stresses via the displacements of the surface of the plate.

scholarly journals LOCALIZATION OF RESPONSE FUNCTIONS OF SPIRAL WAVES IN THE FITZHUGH–NAGUMO SYSTEM

2006 ◽  
Vol 16 (05) ◽  
pp. 1547-1555 ◽  
Author(s):  
I. V. BIKTASHEVA ◽  
A. V. HOLDEN ◽  
V. N. BIKTASHEV
Keyword(s):  
External Force ◽  
Wave Solution ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Two Dimensional ◽  
Response Functions ◽  
Space And Time ◽  
Wave Drift ◽  
Linearized Problem ◽  
Small Periodic

Dynamics of spiral waves in perturbed, e.g. slightly inhomogeneous or subject to a small periodic external force, two-dimensional autowave media can be described asymptotically in terms of Aristotelean dynamics, so that the velocities of the spiral wave drift in space and time are proportional to the forces caused by the perturbation. The forces are defined as a convolution of the perturbation with the spirals Response Functions, which are eigenfunctions of the adjoint linearized problem. In this paper we find numerically the Response Functions of a spiral wave solution in the classic excitable FitzHugh–Nagumo model, and show that they are effectively localized in the vicinity of the spiral core.

THREE-DIMENSIONAL ASPECTS OF RE-ENTRY IN EXPERIMENTAL AND NUMERICAL MODELS OF VENTRICULAR FIBRILLATION

1999 ◽  
Vol 09 (04) ◽  
pp. 695-704 ◽  
Author(s):  
V. N. BIKTASHEV ◽  
A. V. HOLDEN ◽  
S. F. MIRONOV ◽  
A. M. PERTSOV ◽  
A. V. ZAITSEV
Keyword(s):  
Ventricular Fibrillation ◽  
Numerical Simulations ◽  
Numerical Models ◽  
Three Dimensional ◽  
Spiral Waves ◽  
Excitable Media ◽  
Ventricular Wall ◽  
Two Dimensional ◽  
Key Features ◽  
Scroll Waves

Ventricular fibrillation is believed to be produced by the breakdown of re-entrant propagation waves of excitation into multiple re-entrant sources. These re-entrant waves may be idealized as spiral waves in two-dimensional, and scroll waves in three-dimensional excitable media. Optically monitored, simultaneously recorded endocardial and epicardial patterns of activation on the ventricular wall do not always show spiral waves. We show that numerical simulations, even with a simple homogeneous excitable medium, can reproduce the key features of the simultaneous endo- and epicardial visualizations of propagating activity, and so these recordings may be interpreted in terms of scroll waves within the ventricular wall.

scholarly journals Making Anaglyphs in Photoshop

2005 ◽  
Vol 13 (3) ◽  
pp. 36-39 ◽  
Author(s):  
Jerry Sedgewick
Keyword(s):  
Imaging System ◽  
Three Dimensional ◽  
Ct Scans ◽  
Two Dimensional ◽  
The Right ◽  
Two Dimensional Images

In order to achieve a three dimensional appearance to a pair of two dimensional images, two off-axis images can be produced and colorized. These can be overlayed slightly apart and then viewed through glasses with two differently colored sides, one color for the left eye and another for the right eye in combinations containing red, green or blue colors. These off-axis and colorized images are referred to as anaglyphs.Off-axis images can be achieved through the use of a tilting stage on a microscope, by physically changing the position of a camera in relation to a still object, or through changing the axis of an optical stack of sections, such as what is created by confocal/CT scans. Some images lend themselves more to a 3D look both by virtue of inherent three dimensionality limited by the resolution of the imaging system.

scholarly journals The interaction of atoms and molecules with solid surfaces XII—Critical phenomena in a two-dimensional gas

1937 ◽  
Vol 163 (912) ◽  
pp. 132-138 ◽  
Keyword(s):  
Critical Temperature ◽  
Equation Of State ◽  
Critical Phenomena ◽  
Three Dimensional ◽  
Inert Gases ◽  
Two Dimensional ◽  
Lennard Jones ◽  
Low Concentrations ◽  
High Concentrations ◽  
The Right

In a paper recently published by Professor Lennard-Jones and the author (Lennard-Jones and Devonshire 1937) the equation of state of a gas at high concentrations has been calculated in terms of the interatomic fields. The equation found had the right kind of properties and, in particular, using the interatomic fields previously determined from the observed equation of state at low concentrations (Lennard-Jones 1931), the critical temperature was given correctly to within a few degrees for the inert gases. In this paper we shall apply the same method to determine the equation of state of a two-dimensional gas. Although such a gas cannot strictly be obtained in practice, an inert gas adsorbed on a surface (or in fact any gas held by van der Waals’ forces only) would probably behave very much like one, the fluctuations of the potential field over the surface not being of much importance. In confirmation of this it may be noted that the specific heat of argon adsorbed on charcoal was found by Simon (Simon 1935) to be equal to that of a perfect two-dimensional gas down to 60° K. A gas adsorbed on a liquid would be an even better representation of a two-dimensional one. Some measurements on the adsorption of krypton and xenon on liquid mercury have been made by Cassel and Neugebauer (Cassel and Neugebauer 1936), and they found no trace of any critical phenomena though they worked at temperatures considerably below the critical temperature of xenon. Our results are in agreement with this, for they show that the critical temperature of a two-dimensional gas should be about half that of the corresponding three-dimensional one.

scholarly journals Intracellular calcium dynamics at the core of endocardial stationary spiral waves in Langendorff-perfused rabbit hearts

2008 ◽  
Vol 295 (1) ◽  
pp. H297-H304 ◽  
Author(s):  
Liang Tang ◽  
Gyo-Seung Hwang ◽  
Hideki Hayashi ◽  
Juan Song ◽  
Masahiro Ogawa ◽  
...  
Keyword(s):  
Intracellular Calcium ◽  
Transmembrane Potential ◽  
Spiral Wave ◽  
In Vitro Models ◽  
Spiral Waves ◽  
Calcium Dynamics ◽  
The Core ◽  
Intracellular Calcium Dynamics ◽  
The Right

In vitro models of sustained monomorphic ventricular tachycardia (MVT) are rare and do not usually show spiral reentry on the epicardium. We hypothesized that MVT is associated with the spiral wave in the endocardium and that this stable reentrant propagation is supported by a persistently elevated intracellular calcium (Cai) transient at the core of the spiral wave. We performed dual optical mapping of transmembrane potential ( Vm) and Cai dynamics of the right ventricular (RV) endocardium in Langendorff-perfused rabbit hearts ( n = 12). Among 64 induced arrhythmias, 55% were sustained MVT (>10 min). Eighty percent of MVT showed stationary spiral waves (>10 cycles, cycle length: 128 ± 14.6 ms) in the endocardial mapped region, anchoring to the anatomic discontinuities. No reentry activity was observed in the epicardium. During reentry, the amplitudes of Vm and Cai signals were higher in the periphery and gradually decreased toward the core. At the core, maximal Vm and Cai amplitudes were 42.95 ± 5.89% and 43.95 ± 9.46%, respectively, of the control ( P < 0.001). However, the trough of the Vm and Cai signals at the core were higher than those in the periphery, indicating persistent Vm and Cai elevations during reentry. BAPTA-AM, a calcium chelator, significantly reduced the maximal Cai transient amplitude and prevented sustained MVT and spiral wave formation in the mapped region. These findings indicate that endocardial spiral waves often anchor to anatomic discontinuities causing stable MVT in normal rabbit ventricles. The spiral core is characterized by diminished Vm and Cai amplitudes and persistent Vm and Cai elevations during reentry.

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