Fractal analysis reveals functional unit of ventilation in the lung

Sam Bayat, Ludovic Broche, Loïc Dégrugilliers, Liisa Porra, Manuel Paiva, Sylvia Verbanck

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Ventilation is inhomogeneous in the lungs across species. It has been hypothesized that ventilation inhomogeneity is largely determined by the design of the airway branching network. Because exchange of gases at the alveolar barrier is more efficient when gas concentrations are evenly distributed at subacinar length scales, it is assumed that a 'functional unit' of ventilation exists within the lung periphery, where gas concentration becomes uniform. On the other hand, because the morphology of pulmonary airways and alveoli, and the distribution of inhaled fluorescent particles show self-similar fractal properties over a wide range of length scales, it has been predicted that fractal dimension of ventilation approaches unity within an internally homogeneous functional unit of ventilation. However, the existence of such a functional unit has never been demonstrated experimentally due to lack of in situ gas concentration measurements of sufficient spatial resolution in the periphery of a complex bifurcating network. Here, using energy-subtractive synchrotron radiation tomography, we measured the distribution of an inert gas (Xe) in the in vivo rabbit lung during Xe wash-in breathing manoeuvres. The effects of convective flow rate, diffusion and cardiac motion were also assessed. Fractal analysis of resulting gas concentration and tissue density maps revealed that fractal dimension was always smaller for Xe than for tissue density, and that only for the gas, a length scale existed where fractal dimension approached unity. The length scale where this occurred was seen to correspond to that of a rabbit acinus, the terminal structure comprising only alveolated airways. KEY POINTS: Gas ventilation is inhomogeneous in the lung of many species. However, it is not known down to what length scales this inhomogeneity persists. It is generally assumed that ventilation becomes homogeneous at subacinar length scales, beyond the spatial resolution of commonly available imaging techniques, hence this has not been demonstrated experimentally. Here we measured the distribution of inhaled Xe gas in the rabbit lung using synchrotron radiation energy-subtractive imaging and used fractal analysis to show that ventilation becomes internally uniform within regions about the size of rabbit lung acini.

Original languageEnglish
Pages (from-to)5121-5132
Number of pages12
JournalJournal of Physiology
Issue number22
Publication statusPublished - Nov 2021

Bibliographical note

© 2021 The Authors. The Journal of Physiology © 2021 The Physiological Society.


  • fractal analysis
  • pulmonary ventilation
  • synchrotrons
  • xenon


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