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

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 = d₁ ^x + d₂ ^x, and λ in length l_p ^λ = l_l ^λ + l₂ ^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.