Pressure Losses on Realistic Geometry of Tracheobronchial Tree

Real bronchial tree is very complicated piping system.
Analysis of flow and pressure losses in this system is very difficult.
Due to the complex geometry and the very small size in the lower
generations is examination by CFD possible only in the central part
of bronchial tree. For specify the pressure losses of lower generations
is necessary to provide a mathematical equation. Determination of
mathematical formulas for calculation of pressure losses in the real
lungs is time consuming and inefficient process due to its complexity
and diversity. For these calculations is necessary to slightly simplify
the geometry of lungs (same cross-section over the length of
individual generation) or use one of the idealized models of lungs
(Horsfield, Weibel). The article compares the values of pressure
losses obtained from CFD simulation of air flow in the central part of
the real bronchial tree with the values calculated in a slightly
simplified real lungs by using a mathematical relationship derived
from the Bernoulli and continuity equations. The aim of the article is
to analyse the accuracy of the analytical method and its possibility of
use for the calculation of pressure losses in lower generations, which
is difficult to solve by numerical method due to the small geometry.

• Michaela Chovancova
• Jakub Elcner

• Pressure gradient
• airways resistance
• real geometry of bronchial tree
• breathing.

[1] J. B. West, “Respiratory physiology: The essentials,” Lippincott Williams and Wilkins, Philadalphia, 2008.
[2] R. M. Schwartzstein, M. J. Parker, “Respiratory physiology: A clinical approach,” Lippincott Williams and Wilkins, Philadalphia, 2006.
[3] Schmidt A., Zidowitz S., Kriete A., Denhard T., Krass S., Peitgen H.O. (2004) A digital reference model of the human bronchial tree, Computerized Medical Imaging and Graphics, vol. 28, 203-211
[4] Menter, F. R., Langtry, R. B., Likki, S. R., Suzen, Y. B., Huang, P. G., &Völker, S. (2006). A Correlation-Based Transition Model Using Local Variables—Part I: Model Formulation. Journal of Turbomachinery, 128(3), 413. doi:10.1115/1.2184352
[5] Tan, F. P. P., Soloperto, G., Bashford, S., Wood, N. B., Thom, S., Hughes, A., &Xu, X. Y. (2008). Analysis of flow disturbance in a stenosed carotid artery bifurcation using two-equation transitional and turbulence models. Journal of Biomechanical Engineering, 130(6), 061008. doi:10.1115/1.2978992
[6] W. O. Feen, H. Rahn, “Handbook of Physiology: Respiration,” American Physiological Society, Washington, D.C., 1964.
[7] R. A. Rhoades, D. R. Bell, “Medical Physiology,” Lippincott Williams and Wilkins, Philadalphia, 2008
[8] F. G. Hoppin Jr., J. Hildebrandt, “Mechanical properties of the Lung,” In West, J.B. (Ed.), New York, 1977.
[9] K. Horsfield, G. Cumming “Morphology of the bronchial tree in man,” Journal of applied physiology, page 373, 1968.