Abstract
An efficient numerical algorithm based on the convolution of functions and on finite difference approximations for the diffusion equation is utilized to determine the quantity of calcium ions (Ca
2+
) participating in unitary Ca
2+
release events, termed "Ca
2+
sparks", in heart muscle. Output images of localized increases in cytosolic Ca
2+
concentration ([Ca
2+
]), due predominantly to Ca
2+
release from intracellular storage sites, are obtained using fluorescent calcium indicators and confocal microscopy. To obtain the quantity of Ca
2+
underlying these localized increases of cytosolic [Ca
2+
], one-dimensional output images are deconvolved with a point spread function that describes the optical properties of the microscope. The resulting input image is then reconstructed, assuming symmetry, in a threedimensional image of [Ca
2+
] and all Ca
2+
-bound species. Temporal information about free and bound Ca
2+
species can be obtained by performing convolutions on a series of output images recorded in time and then accounting for the kinetics of Ca
2+
interactions with the fluorescent calcium indicator and other Ca
2+
binding species. The effect of microscope imaging properties on measurements of local [Ca
2+
] and the ability to reconstruct the underlying changes in Ca
2+
species during a Ca
2+
spark are presented.