Impedance matching at arterial bifurcations

Abstract

Reflections of pulse waves will occur in arterial bifurcations unless the impedance is matched continuously through changing geometric and elastic properties. A theoretical model is presented which minimizes pulse wave reflection through bifurcations. The model accounts for the observed linear changes in area within the bifurcation, generalizes the theory to asymmetrical bifurcations, characterizes changes in elastic properties from parent to daughter arteries, and assesses the effect of branch angle on the mechanical properties of daughter vessels. In contradistinction to previous models, reflections cannot be minimized without changes in elastic properties through bifurcations. The theoretical model predicts that in bifurcations with area ratios (β) less than 1.0 Young's moduli of daughter vessels may be less than that in the parent vessel if the Womersley parameter α in the parent vessel is less than 5. Larger area ratios in bifurcations are accompanied by greater increases in Young's moduli of branches. For an idealized symmetric aortic bifurcation (α = 10) with branching angles θ = 30° (opening angle 60°) Young's modulus of common iliac arteries relative to that of the distal abdominal aorta has an increase of 1.05, 1.68 and 2.25 for area ratio of 0.8, 1.0 and 1.15, respectively. These predictions are consistent with the observed increases in Young's moduli of peripheral vessels. Young's moduli of branches relative to that of the parent vessel are predicted to increase with larger branching angles, though this has yet to be confirmed experimentally (i.e. for α = 10, β = 1.0, Young's moduli of branches relative to that of the parent vessel increases from 1.68 to 3.77 for an increase in θ from 30 to 45°). In conclusion, reflections are minimized in bifurcations where mechanical properties of the arterial wall change continuously with changes in geometry.