Multi-scale models of local control of calcium induced calcium release

Calcium-induced-calcium-release in cardiac myocytes is the release of Ca(2+) from the sarcoplasmic reticulum (SR) triggered by Ca(2+) entering the cell through L-type Ca(2+) channels. The Ca(2+) is released through ryanodine receptors which 'sense' local [Ca(2+)] in the small region (the diadic space) positioned between the t-tubules and the SR. The length-scale of a single diad is of the order of 10nm and the diffusion time-scale is of order of 1 micros with each cell containing approximately 10,000 diadic spaces which act independently. However, typically one is interested in Ca(2+) currents at the whole cell level and higher. This is a multi-scale problem and cannot be solved by direct computation. In this paper we develop a general framework for deriving approximate solutions of these models.