Constitutive Equation of Lung Tissue Elasticity

Abstract

A constitutive equation for the lung tissue elasticity is formulated under the hypotheses of a simplified alveolar geometry and a pseudo-strain-energy function for the interalveolar septa. The resulting equation contains four material constants. The theoretical result has been tested against published data on uniaxial and triaxial loadings, and is tested critically here with respect to new experimental results on biaxial loading. Comparison between theory and experiments shows that a general agreement is obtained in an approximate sense. The model fits our biaxial experimental data with most correlation coefficients above 0.995. Some details not predicted by the theory are discussed. Since the theory is derived for triaxial loading and the biaxial test is a severe one, the formula should be applicable to the triaxial case at least to the same degree of approximation. The form of the theoretical formula is convenient to use in analytic studies of lung mechanics. Additional key words: mechanical behavior of the lung; stress-strain relationship; strain energy; alveolus model; distortion; interdependence; pressure volume curves.