Effectiveness of numerical techniques for calculating the quantity of Ca²⁺species during calcium sparks in heart muscle

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 (Ca2+) participating in unitary Ca2+ release events, termed “Ca2+sparks”, in heart muscle. Output images of localized increases in cytosolic Ca2+ concentration ([Ca2+]), due predominantly to Ca2+ release from intracellular storage sites, are obtained using fluorescent calcium indicators and confocal microscopy. To obtain the quantity of Ca2+ underlying these localized increases of cytosolic [Ca2+], 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 [Ca2+] and all Ca2+-bound species. Temporal information about free and bound Ca2+ species can be obtained by performing convolutions on a series of output images recorded in time and then accounting for the kinetics of Ca2+ interactions with the fluorescent calcium indicator and other Ca2+ binding species. The effect of microscope imaging properties on measurements of local [Ca2+] and the ability to reconstruct the underlying changes in Ca2+ species during a Ca2+ spark are presented.