### Abstract

Resistance, r_{in}, 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, R_{b1}; N-k small arteries/capillaries with branching ratio R_{b2} ;bifurcation design a, where 1/a = 4/x - 1/λ, x is a scaling exponent in the diameter law d_{p}
^{x} = d_{1}
^{x} + d_{2}
^{x}, and λ in length l_{p}
^{λ} = l_{l}
^{λ} + l_{2}
^{λ}, r_{in} = r_{c}/R_{b2}
^{N}(R_{b2}
^{k}/R _{b1}
^{k/a}(1 - κ^{k}/1 - κ) + N - k) where κ = (Formula Presented) and 0 < κ < ∞. Unlike a symmetric tree, r_{in} 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 |

### ASJC Scopus subject areas

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

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## Cite this

*FASEB Journal*,

*12*(5).