Pulmonary vascular resistance variability/reactivity in terms of a quantized/continuum fractal network

S. H. Bennett, M. W. Eldridge, Jay M Milstein, B. W. Goetzman, M. J. Woldenberg

Research output: Contribution to journalArticle

Abstract

Resistance, rin, follows a 3/4 allometric scaling law from a fractal architecture, but an explanation for biological variability is lacking. For an asymmetric fractal branching tree of Horsfield order N with degree of asymmetry, Δ = 0,1,2 ...; k orders of arteries with branching ratio, Rb1; N-k small arteries/capillaries with branching ratio Rb2 ;bifurcation design a, where 1/a = 4/x - 1/λ, x is a scaling exponent in the diameter law dp x = d1 x + d2 x, and λ in length lp λ = ll λ + l2 λ, rin = rc/Rb2 N(Rb2 k/R b1 k/a(1 - κk/1 - κ) + N - k) where κ = (Formula Presented) and 0 < κ < ∞. Unlike a symmetric tree, rin is not bounded by κ ≤ 1, but varies continuously with a and is quantized according to Δ. From morphometric data and the slope of pressure-flow curves from dog, cat and human, this model demonstrates a conjugate mapping between structure and function, and a quantum/continuum variance in resistance influenced by individual differences in branching asymmetry and/or arterial design.

Original languageEnglish (US)
JournalFASEB Journal
Volume12
Issue number5
StatePublished - Mar 20 1998

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Biochemistry
  • Cell Biology

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    Bennett, S. H., Eldridge, M. W., Milstein, J. M., Goetzman, B. W., & Woldenberg, M. J. (1998). Pulmonary vascular resistance variability/reactivity in terms of a quantized/continuum fractal network. FASEB Journal, 12(5).