Using the concepts of fractal scaling and constrained constructive optimization (CCO), a branching tree model, which has physiologically meaningful geometric properties, can be constructed [12-14]. A vascular branching tree model created in this way, although statistically correct in representing the vascular physiology, still does not possess a physiological correct arrangement of the major arteries. A distance-function based technique for staged growth of vascular models has been developed in this work to address this issue. Time-dependent constraints based on a signed-distance level set function have been added, so that the tree models will first be grown near the designated surface(s) and, then, gradually allowed to penetrate into the enclosed volume. The proposed technique has been applied to construct a model of the human cerebral vasculature, which is characterized by the above-mentioned distribution of the arteries.