Neuronal growth and the Steiner problem

In this paper we conjecture that neuronal networks develop following an optimality principle. We point out that a neuronal outgrowth in culture may be seen as the solution of a classical optimization problem: the "Steiner Problem". A neuron might grow minimizing a "cost", which may be determined by the viscoelastic properties of the neuron cytoplasm. We then discuss the role of chemiotactic factors such as the Nerve Growth Factor (NGF) in an optimized neuronal development in vivo. Finally we suggest, with some mathematical arguments, that the optimization of the elastic forces in the growing neuron may give rise to a "fractal" structure.