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Vascular metabolic dissipation in Murray's law

Departments of ¹Biomedical Engineering, ²Cellular and Integrative Physiology, and ³Surgery, Indiana University Purdue University, Indianapolis, Indiana

Submitted 22 August 2006 ; accepted in final form 16 November 2006

The metabolic dissipation in Murray's 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. In this study, 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 Murray's formulation. The calculations are based on experimentally measured morphological data of coronary artery network and the longitudinal distribution of blood pressure along the tree. Whereas 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, and flow) remain unchanged under the generalized condition of metabolic requirements of blood and blood vessel wall.

vessel wall; vascular tree; scaling laws

This article has been cited by other articles:

				Y. Liu, C. Dang, M. Garcia, H. Gregersen, and G. S. Kassab Surrounding tissues affect the passive mechanics of the vessel wall: theory and experiment Am J Physiol Heart Circ Physiol, December 1, 2007; 293(6): H3290 - H3300. [Abstract] [Full Text] [PDF]