ABSTRACT
The plateau phase of a human ventricular myocyte is analysed. The plateau duration is a function of the time required for a myocyte's transmembrane voltage to decrease by a certain voltage, DeltaV. The timing of the plateau is shown to be controlled by two slowly changing gate variables, the inactivation gate that controls the inward/depolarizing L-type calcium current and the inactivation gate that controls the outward/repolarizing slow rectifier potassium current. The amount of current controlled by these variables is a function of the net conductivity of the corresponding sodium and potassium channels. An equation is derived that relates action potential duration to these net conductivities and the time dependence of the slowly moving variables. This equation is used to estimate plateau duration for a given value of DeltaV. The initial conditions of the slowly moving inactivation variables are shown to affect plateau duration. These initial conditions depend on the amount of time that has elapsed between a previous repolarization and a current depolarization (diastolic interval). The analysis thus helps to quantify the characteristics of action potential duration restitution.
Subject(s)
Action Potentials/physiology , Computer Simulation , Ion Channel Gating/physiology , Models, Cardiovascular , Myocytes, Cardiac/metabolism , Ventricular Function/physiology , Calcium/metabolism , Calcium Channels, L-Type/metabolism , Heart Ventricles , Humans , Potassium Channels/metabolismABSTRACT
The results of a geometric model of cardiac tissue, used to compute the bidomain conductivity tensors during three phases of ischaemia, are described. Ischaemic conditions were simulated by model parameters being changed to match the morphological and electrical changes of three phases of ischaemia reported in literature. The simulated changes included collapse of the interstitial space, cell swelling and the closure of gap junctions. The model contained 64 myocytes described by 2 million tetrahedral elements, to which an external electric field was applied, and then the finite element method was used to compute the associated current density. In the first case, a reduction in the amount of interstitial space led to a reduction in extracellular longitudinal conductivity by about 20%, which is in the range of reported literature values. Moderate cell swelling in the order of 10-20% did not affect extracellular conductivity considerably. To match the reported drop in total tissue conductance reported in experimental studies during the third phase of ischaemia, a ten fold increase in the gap junction resistance was simulated. This ten-fold increase correlates well with the reported changes in gap junction densities in the literature.
Subject(s)
Heart Conduction System/physiopathology , Models, Cardiovascular , Myocardial Ischemia/physiopathology , Electric Conductivity , Gap Junctions/physiology , Humans , Myocytes, Cardiac/physiologyABSTRACT
The paper describes a spherical harmonic-based finite element scheme for solving Poisson-type equations throughout volumes characterised by irregularly shaped inner and outer surfaces. The inner and outer surfaces are defined by spherical harmonics, and the volume in between these surfaces is divided into nested shells that are weighted averages of the inner and outer surfaces. The resulting mesh comprises hexahedral elements, wherein each hexahedral element is defined by inner and outer shells in the radial direction and divisions in the polar and azimuthal directions. The spacing between shells can be set to any desired value. Similarly, the size of the polar and azimuthal divisions can be specified. A test of the scheme on an anisotropic sphere, meshed with 720 nodes, yielded a relative error of 0.78% on the sphere's surface. As a comparison, a previously published combined finite element/boundary element scheme with a 946-node mesh produced a corresponding error of 3.57%.
