title: The fractal geometry of nutrient exchange surfaces does not provide an explanation for 3/4-power metabolic scaling.
abstract: BACKGROUND
  A prominent theoretical explanation for 3/4-power allometric scaling of metabolism proposes that the nutrient exchange surface of capillaries has properties of a space-filling fractal. The theory assumes that nutrient exchange surface area has a fractal dimension equal to or greater than 2 and less than or equal to 3 and that the volume filled by the exchange surface area has a fractal dimension equal to or greater than 3 and less than or equal to 4.
  
  
  RESULTS
  It is shown that contradicting predictions can be derived from the assumptions of the model. When errors in the model are corrected, it is shown to predict that metabolic rate is proportional to body mass (proportional scaling).
  
  
  CONCLUSIONS
  The presence of space-filling fractal nutrient exchange surfaces does not provide a satisfactory explanation for 3/4-power metabolic rate scaling.
authors.affiliation: Office of Environmental Health Hazard Assessment, California Environmental Protection Agency, Sacramento, California 95812, USA. ppainter@oehha.ca.gov
authors.forename: Page R
authors.initials: PR
authors.lastname: Painter
mesh_terms: D000818:Animals; D001158:Arteries / Q000502:physiology; D001669:Biochemical Phenomena; D015992:Body Mass Index; D004734:Energy Metabolism; D017709:Fractals; D006801:Humans; D008954:Models, Biological; D008962:Models, Theoretical