Understanding the relationship between shape and function of dendritic spines is an elusive topic. Several modelling approaches have been used to investigate the interplay between spine geometry, calcium diffusion and electric signalling. We here use a second order finite element method to solve the Poisson–Nernst–Planck equations and describe electrodiffusion in dendritic spines. With this, we obtain relationships between dendritic geometry and calcic as well as electric responses to synaptic events. Our findings support the hypothesis that spine geometry plays a role shaping the electrical responses to synaptic events. Our method was also able to reveal the fine scale distribution of calcium in spines with irregular shapes.

了解树突棘的形状和功能之间的关系是一个难以捉摸的话题。几种建模方法已用于研究脊柱几何形状，钙扩散和电信号传导之间的相互作用。我们在这里使用二阶有限元方法来求解Poisson-Nernst-Planck方程并描述树突棘中的电扩散。由此，我们获得了树突状几何形状与钙之间的关系以及对突触事件的电响应。我们的发现支持这样的假说，即脊柱几何形状在影响对突触事件的电反应中起着重要作用。我们的方法还能够揭示不规则形状的棘中钙的精细分布。