Transport in Porous Media

, Volume 11, Issue 3, pp 281–295 | Cite as

Mechanical model of lung parenchyma as a two-phase porous medium

  • Piotr Kowalczyk


The anatomy and geometry of the lung at the micro- and macroscopic level have been described briefly. A notion of lung parenchyma — a macroscopically continuous medium whose mechanical properties result from those of microstructural components — has been adapted. Simplifying assumptions propounded in the constitutive model have been discussed. Two phases have been distinguished in the medium: the solid phase — a highly deformable, nonlinearly elastic skeleton in the form of a thin-walled tissue structure on the micro-scale — and the fluid phase — perfect gas (air) filterating through the structure. General constitutive relations for both phases and their mechanical interactions have ben formulated. Further, the fundamental set of differential equations of the quasi-static coupled problem has been developed. Large deformations, material nonlinearities, and dependence of permeability on skeleton deformation have been included. Matrix formulation of the problem has been presented from the point of view of the finite element method. An implicit iterative time integration scheme has been proposed. The algorithm has been illustrated with results of simple numerical tests.

Key words

Finite element method implicit time integration quasi-static analysis tissue-gas interaction large deformations two-phase porous medium constitutive modelling lung mechanics biomechanics 


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  1. Frankus, A. and Lee, G. C., 1974, A theory of distortion studies of lung parenchyma based on alveolar membrane properties,J. Biomech. 7, 101–107.Google Scholar
  2. Fung, Y. C., 1974, A theory of elasticity of the lung,Trans. ASME, J. Appl. Mech. 41, 8–14.Google Scholar
  3. Fung, Y. C., Tong, P. and Patitucci, P., 1978, Stress and strain in the lung,J. Engng. Mech. Div. (Proc. ASCE) 104, 201–223.Google Scholar
  4. Fung, Y. C., 1980,Biomechanics. Mechanical Properties of Living Tissues, Springer-Verlag, New York.Google Scholar
  5. Hoppin, F. G., Lee, G. C. and Dawson, S. V., 1975, Properties of lung parenchyma in distortion,J. Appl. Physiol. 39, 742–751.Google Scholar
  6. Lee, G. C. and Frankus, A., 1975, Elasticity properties of lung parenchyma derived from experimental distortion data,Biophys. J. 15, 481–493.Google Scholar
  7. Liu, J. T. and Lee, G. C., 1978, Static finite deformation analysis of the lung,J. Engng Mech. Div. (Proc. ASCE) 104, 225–238.Google Scholar
  8. Mead, J., Takishima, T. and Leith, D., 1970, Stress distribution in lungs: A model of pulmonary elasticity,J. Appl. Physiol. 28, 596–608.Google Scholar
  9. Weibel, E. R., 1963,Morphometry of the Human Lung, Academic Press, New York.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Piotr Kowalczyk
    • 1
  1. 1.Institute of Fundamental Technological ResearchPolish Academy of SciencesWarsawPoland

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