ABSTRACT
Optical mapping from the cut surface of a "wedge preparation" allows observation inside the heart wall, below the epicardium or endocardium. We use numerical simulations based on the bidomain model to illustrate how the transmembrane potential is influenced by the cut surface. The distribution of transmembrane potential around a unipolar cathode depends on the fiber angle. For intermediate angles, hyperpolarization appears on only one side of the electrode, and is large and widespread.
Subject(s)
Action Potentials/physiology , Body Surface Potential Mapping/methods , Cardiac Pacing, Artificial/methods , Electric Stimulation Therapy/methods , Heart Conduction System/physiology , Models, Cardiovascular , Tissue Culture Techniques/methods , Animals , Artifacts , Cells, Cultured , Computer Simulation , Diagnosis, Computer-Assisted/methods , Humans , Membrane Potentials/physiology , Myocytes, Cardiac/physiologyABSTRACT
Simulating the electrocardiogram requires specifying the transmembrane potential distribution within the heart and calculating the potential on the surface of the body. Often, such calculations are based on the bidomain model of cardiac tissue. A subtle but fundamental problem arises when considering the boundary between the cardiac tissue and the surrounding volume conductor. In general, one finds that two potentials--the extracellular potential in the tissue and the potential in the surrounding bath--obey three boundary conditions, implying that the potentials are overdetermined. In this paper, we derive a general method for handling bidomain boundary conditions that eliminates this problem. The gist of the method is that we add an additional term to the transmembrane potential that falls exponentially with depth into the tissue. The purpose of this term is to satisfy the third boundary condition. Then, we take the limit as the length constant associated with this extra term goes to zero. Our result is two boundary conditions that approximately account for the full set of three boundary conditions at the tissue surface.
Subject(s)
Action Potentials/physiology , Diagnosis, Computer-Assisted/methods , Electrocardiography/methods , Heart Conduction System/physiology , Models, Biological , Animals , Computer Simulation , HumansABSTRACT
The bidomain model can be used for calculating the electrical potential in the heart during defibrillation. However, this model consists of a coupled system of two partial differential equations that are, in general, difficult and time consuming to solve. In this paper, we present an approximate, iterative method of solving the bidomain equations. After working out the general method, we apply it to four problems: (i) a cylindrical strand in a uniform electric field, (ii) a nonuniform electric field applied to tissue with straight fibers, (iii) a spherical heart in a uniform electric field, and (iv) a two-dimensional sheet of cardiac tissue with curving fibers. Finally, we analyze the general case of three dimensions.
Subject(s)
Action Potentials , Arrhythmias, Cardiac/physiopathology , Arrhythmias, Cardiac/therapy , Electric Countershock/methods , Models, Cardiovascular , Myocytes, Cardiac , Therapy, Computer-Assisted/methods , Animals , Heart Conduction System/physiopathology , Humans , Membrane Potentials , Models, Neurological , Treatment OutcomeABSTRACT
INTRODUCTION: Anodal excitation of cardiac tissue occurs by two mechanisms: "make" and "break." Anodal strength-interval curves are divided into two sections, with break excitation occurring at short intervals and make at long intervals. Our goal is to determine how an elevated extracellular potassium ion concentration, [K]o, affects the mechanism of anodal excitation and influences the anodal strength-interval curve. METHODS AND RESULTS: Computer simulations of unipolar stimulation were performed using the bidomain model, with membrane kinetics governed by the Luo-Rudy model. The diastolic threshold for anodal stimulation first decreased and then increased with increasing [K]o, reaching a minimum value at [K]o = 12 mM. The mechanism for diastolic anodal excitation was make for all [K]o values except 13.3 mM, in which case it was break. For low [K]o (4 and 8 mM) the break section of the anodal strength-interval contained a "dip," but for high [K]o (12 and 13 mM), the dip disappeared. CONCLUSION: High [K]o predisposes cardiac tissue to break excitation, which is thought to play an important role in reentry induction and defibrillation. Because fibrillation raises extracellular [K]o levels, break excitation may play a more important role in defibrillation than is suggested by simulations and experiments using normal [K]o values.
