We present an approach to generate 3-D arterial tree models based on physiological principles while at the same time certain morphological properties are enforced at construction time. The driving force of the construction is a simplified angiogenesis model incorporating case-specific information about the metabolic demand within the considered domain. The vascular tree is constructed iteratively by successively adding new segments in chemotactic response to angiogenic growth factors secreted by ischemic cells. Morphometrically confirmed bifurcation statistics of vascular networks are incorporated to optimize the synthetic vasculature. The proposed method is able to generate artificial, yet physiologically plausible, arterial tree models that match the metabolic demand of the embedding tissue and fulfill the prescribed morphological properties at the same time. The proposed tree generation approach is applied in a simulation setup based on the metabolic configuration and anatomy of the macaque visual cortex. We analyze the generated tree models with respect to morphological and physiological aspects including fluid-dynamic simulations. The comparison of our results with the findings of different studies on the structure of cerebral vasculatures demonstrates the plausibility of our method.