Mathematical model of electrotonic interactions during excitation and repolarisation of myocardial tissue

A discrete model has been developed which reproduces the intercellular electrophysiological processes within a block of myocardial tissue. The behaviour of individual elements is introduced in the form of the digitised physiologic and premature action potentials which are comprehended as series of jumps between discrete polarisation levels. For each cellular element, the model introduces the excitation threshold as the minimum electric flow in the surrounding which can excite the cell, and the sensitivity towards the electronic interactions which can advance or slow down the depolarisation and repolarisation processes of the cell. The excitation threshold and the electronic sensitivity are dependent on the current polarity of the element. The numerical solution of the model does not use a fixed time slicing integration but is based on discrete planning of asynchronous events. The time increments are dynamically computed according to the chosen precision of the discrete polarity levels. The model enables efficient stimulation of the electrophysiological properties in three-dimensional models of the myocardial tissue. The paper presents a detailed formal description of the model.