Branching asymmetry in the lung airway tree

Arnab Majumdar
Center for Polymer Studies, Dept. of Physics and Dept of Bio

Adriano M. Alencar
Center for Polymer Studies, Boston University

Sergey V. Buldyrev
Center for Polymer Studies, Boston University

Zoltán Hantos
Department of Medical Informatics and Engineering, and Institute of Surgical Research, University of Szeged, Hungary

H. Eugene Stanley
Center for Polymer Studies and Dept. of Physics, Boston University

Béla Suki
Dept of Biomedical Engineering, Boston University

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     Last modified: May 12, 2006

Abstract
We study the distribution P(N,D) of diameters D as a function of a generation N in asymmetric airway trees of lungs from four mammalian species. We find that the airway bifurcations are self-similar in each species such that the ratios of diameters of the major and minor daughters to their parent, kmaj and kmin respectively, are constants independent of N until a cut-off diameter Dc is reached. We show that this is consistent with a model of the airway tree based on an asymmetric division of flow at each bifurcation. We derive the family of distributions P(N,D), which are truncated log-normal distributions, in good agreement with experimental data. We also show that the Poiseuille flow resistance of our model airway tree is related to the asymmetry parameter r and only weakly depends on the size parameter Qc. Our findings suggest that the primary determinant of the observed heterogeneity is an underlying regular branching asymmetry.