  We introduce a mesoscopic model for natural network formation processes,
acting as a bridge between the discrete and continuous network approach
proposed by Hu and Cai. The models are based on a common approach where the
dynamics of the conductance network is subject to pressure force effects. We
first study topological properties of the discrete model and we prove that if
the metabolic energy consumption term is concave with respect to the
conductivities, the optimal network structure is a tree (i.e., no loops are
present). We then analyze various aspects of the mesoscopic modeling approach,
in particular its relation to the discrete model and its stationary solutions,
including discrete network solutions. Moreover, we present an alternative
formulation of the mesoscopic model that avoids the explicit presence of the
pressure in the energy functional.
