Intercellular spiral waves of calcium.

Intercellular calcium waves have been observed in a large number of cell types, and are known to result from a variety of stimuli, including mechanical or hormonal stimulation. Recently, spiral intercellular waves of calcium have been observed in slices of hippocampal tissue. We use an existing model to study the properties of spiral intercellular calcium waves. Although intercellular spiral waves are well known in the context of cardiac muscle, due to the small value of the calcium diffusion coefficient intercellular calcium waves have fundamentally different properties. We show that homogenisation techniques give a good estimate for the plane wave speed, but do not describe spiral behaviour well. Using an expression for the effective diffusion coefficient we estimate the intercellular calcium permeability in liver. For the bistable equation, we derive an analytic estimate for the value of the intercellular permeability at which wave propagation fails. In the calcium wave model, we show numerically that the spiral period is first a decreasing, then an increasing, function of the intercellular permeability. We hypothesise that this is because the curvature of the spiral core is unimportant at low permeability, the period being approximately set instead by the speed of a plane wave along a line of coupled cells in one dimension.