In this study, we present an innovative mathematical modeling approach that allows detailed characterization of Ca 2+ movement within the three-dimensional volume of an atrial myocyte. Essential aspects of the model are the geometrically realistic representation of Ca 2+ release sites and physiological Ca 2+ flux parameters, coupled with a computationally inexpensive framework. By translating nonlinear Ca 2+ excitability into threshold dynamics, we avoid the computationally demanding time stepping of the partial differential equations that are often used to model Ca 2+ transport. Our approach successfully reproduces key features of atrial myocyte Ca 2+ signaling observed using confocal imaging. In particular, the model displays the centripetal Ca 2+ waves that occur within atrial myocytes during excitation-contraction coupling, and the effect of positive inotropic stimulation on the spatial profile of the Ca 2+ signals. Beyond this validation of the model, our simulation reveals unexpected observations about the spread of Ca 2+within an atrial myocyte. In particular, the model describes the movement of Ca 2+ between ryanodine receptor clusters within a specific z disk of an atrial myocyte. Furthermore, we demonstrate that altering the strength of Ca 2+ release, ryanodine receptor refractoriness, the magnitude of initiating stimulus, or the introduction of stochastic Ca 2+ channel activity can cause the nucleation of proarrhythmic traveling Ca 2+ waves. The model provides clinically relevant insights into the initiation and propagation of subcellular Ca 2+ signals that are currently beyond the scope of imaging technology.
Thul, R., Coombes, S., Roderick, H. L., & Bootman, M. D. (2012). Subcellular calcium dynamics in a whole-cell model of an atrial myocyte. Proceedings of the National Academy of Sciences, 109(6), 2150-2155. https://doi.org/10.1073/pnas.1115855109