The metabolic dissipation in Murrays minimum energy hypothesis includes only the blood metabolism. The metabolic dissipation of the vascular tree, however, should also include the metabolism of passive and active components of the vessel wall. Here, we extend the metabolic dissipation to include blood metabolism, as well as passive and active components of the vessel wall. The analysis is extended to the entire vascular arterial tree rather than a single vessel as in Murrays formulation. The calculations are based on experimentally measured morphological data of coronary artery network and the longitudinal distribution of blood pressure along the tree. While the model includes multiple dissipation sources, the total metabolic consumption of a complex vascular tree is found to remain approximately proportional to the cumulative arterial volume of the unit. This implies that the previously described scaling relations for the various morphological features (volume, length, diameter, flow) remain unchanged under the generalized condition of metabolic requirements of blood and blood vessel wall.