Assessing the origin and velocity of Ca2+ waves in three-dimensional tissue: Insights from a mathematical model and confocal imaging in mouse pancreas tissue slices

Many tissues are gap-junction-coupled syncytia that support cell-to-cell communication via propagating calcium waves. This also holds true for pancreatic islets of Langerhans, where several thousand beta cells work in synchrony to ensure proper insulin secretion. Two emerging functional parameters of islet function are the location of wave initiator regions and the velocity of spreading calcium waves. High-frequency confocal laser-scanning imaging in tissue slices is one of the best available methods to determine these markers, but it is limited to two-dimensional cross-sections of an otherwise three-dimensional islet. Here we show how mathematical modeling can significantly improve this limitation. Firstly, we analytically determine the shape of velocity profiles of spherical excitation waves in the focal plane of a homogeneous three-dimensional space. Secondly, we introduce a mathematical model consisting of coupled excitable cells that considers cellular heterogeneities to approach more realistic conditions by means of numerical simulations. We demonstrate the effectiveness of our approach on experimentally recorded waves from an islet that was stimulated with 9 mM glucose. Furthermore, we show that calcium waves were primarily triggered by a specific region located 30 µm bellow the focal plane at the periphery of the islet. Additionally, we show that the velocity of the calcium wave was around 80 µm/s. We discuss the importance of our approach for the correct determination of the origin and velocity of calcium waves from experimental data, as well as the pitfalls that are due to improper procedural simplifications.