Modelling calcium transients in cardiac myocytes

Abstract

We develop a three-dimensional model of the calcium dynamics in a half-sarcomere of a cardiac myocyte. We use the model to investigate the cardiac calcium transient, and the effect of choices made during model construction on the simulated calcium dynamics. We first construct a compartmental model of the calcium dynamics in a non-excitable cell, to investigate the effect of including a model of a SERCA pump which acts as a calcium buffer. We also look at the issue of futile cycling across the membrane of the endoplasmic reticulum when the cell is at rest. We develop a technique of grid refinement which enables an alternating direction implicit algorithm to be solved over a domain which contains multiple levels of grid spacing, while conserving the quantity being modelled. This is useful when the solution changes rapidly in some regions of the domain, but not elsewhere, as in a cardiac cell half-sarcomere. We have only developed the grid-refinement technique in two-dimensions, and so it is not used in the three-dimensional model. The three-dimensional half-sarcomere model couples homogenised and non-homogenised schemes. Near the cell membrane the geometry of the sarcoplasmic reticulum (SR) is important, and we model it explicitly. Further from the membrane the SR forms a complex network. The geometry here is not well known, and complicated to model, so homogenisation is used to avoid explicitly modelling the structure. The model is again used to investigate the effect of including a buffering SERCA pump model. It is also used to investigate the effect of shifting the location of the sodium calcium exchangers, which is not well known, and to assess the accuracy of the assumption that there are not significant spatial calcium gradients in given compartments which is used when building compartmental models. We add dynamic models of the ryanodine receptors to the three-dimensional model and then investigate the effect of changing the position of the L-type calcium channels, and the effect of increasing the depth of the diadic cleft. We then reduce the three dimensional model into a compartmental model to determine how the loss of spatial information will impact the results.