arXiv subjects
Publications and source records attributed to Lars Petter Endresen.
We give an algorithm for efficient step size control in numerical integration of non-stiff initial value problems, based on a formula tailormade to methods where the numerical solution is compared with a solution of lower order.
In recent decades, several mathematical models describing the pacemaker activity of the rabbit sinoatrial node have been developed. We demonstrate that it is not possible to establish the existence, uniqueness, and stability of a limit cycle oscillation in those models. Instead we observe an infinite number of limit cycles. We then display numerical results from a new model, with a limit cycle that can be reached from many different initial conditions.
We give an explicit formula for the membrane potential of cells in terms of the intracellular and extracellular ionic concentrations, and derive equations for the ionic currents that flow through channels, exchangers and electrogenic pumps based on simple energy considerations and conservation laws. We demonstrate that the work done by the pump is equal to the potential energy of the cell plus the energy loss due to the downhill ionic fluxes through the channels and the exchanger. Our equations predict osmotic pressure variations. The theory is illustrated in a simple model of spontaneously active cells in the cardiac pacemaker. The simulated action potential and the five currents in the model are in excellent agreement with experiments. The model predicts the experimental observed intracellular ionic concentration of potassium, calcium and sodium. We do not see any drift of the values for the concentrations in a long time simulation, instead we can obtain the same asymptotic values starting with equal intracellular and extracellular ionic concentrations.