Many biological mechanisms depend on the spatio -temporal distribution of intracellular Ca^2+. One fundamental example is the induction by Ca^2+ of postsynaptic long-term potentiation (LTP) in dendritic spines. To account for LTP one needs to be able to describe very precisely the 3D shape of each individual spine but also to calculate concomitantly the spatio -temporal distribution of Ca^2+ in a large number of spines connected to a same segment of a dendritic tree.

In our project we study the three dimensional reaction- diffusion problem arising in the mathematical modeling of calcium dynamics in the neurons. The solution of the problem necessitates very large 3D meshes due to its geometric complexity. A domain decomposition strategy was selected to overcome this. A Schwarz alternative method was applied to the nonlinear problem and a number of smaller nonlinear problems were solved per domain decomposition iteration. Inside each sub-domain we used a standard FEM package, FIDAP, which was modified for PVM parallelization and was supplemented by the options of time management introduced in our previous work. The computations we performed on SP2 machine. (Figure: Ca^2+ distribution in the spiny dendrite)

The short time special distribution of calcium in a dendrite.