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 language | English (US) |
|---|---|
| Journal | FASEB Journal |
| Volume | 12 |
| Issue number | 5 |
| State | Published - Mar 20 1998 |
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ASJC Scopus subject areas
- Agricultural and Biological Sciences (miscellaneous)
- Biochemistry, Genetics and Molecular Biology(all)
- Biochemistry
- Cell Biology
Cite this
Pulmonary vascular resistance variability/reactivity in terms of a quantized/continuum fractal network. / Bennett, S. H.; Eldridge, M. W.; Milstein, Jay M; Goetzman, B. W.; Woldenberg, M. J.
In: FASEB Journal, Vol. 12, No. 5, 20.03.1998.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Pulmonary vascular resistance variability/reactivity in terms of a quantized/continuum fractal network
AU - Bennett, S. H.
AU - Eldridge, M. W.
AU - Milstein, Jay M
AU - Goetzman, B. W.
AU - Woldenberg, M. J.
PY - 1998/3/20
Y1 - 1998/3/20
N2 - 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.
AB - 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.
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M3 - Article
VL - 12
JO - FASEB Journal
JF - FASEB Journal
SN - 0892-6638
IS - 5
ER -