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 language||English (US)|
|State||Published - Mar 20 1998|
ASJC Scopus subject areas
- Agricultural and Biological Sciences (miscellaneous)
- Biochemistry, Genetics and Molecular Biology(all)
- Cell Biology