Elasticity of the Pulmonary Alveolar Sheet

Abstract

An analysis of experimental data on the pulmonary alveolar sheet of the cat shows: (1) As far as elasticity in the plane of the sheet is concerned, the alveolar sheet may be regarded as uniform; the compliance of the posts is the same as that of the membranes. (2) Within a physiological range of positive transmural pressure, the mean thickness of the sheet varies linearly with the pressure. Also, the stress distribution in the alveolar-capillary membrane is nonuniform and nonisotropic. A theoretical sheet thickness-pressure relationship is derived in which the effect of stress resultants (sum of elastic stress and surface tension) is explicitly linked to the compliance of the sheet thickness. The sheet-flow theory then shows that average flow is very sensitive to the arteriole pressure. The flow per alveolar sheet is (1/ C ) ( h a 4 -- h v 4 ). Here h a and h v are equal to alveolar sheet thickness at the arteriole and venule, respectively. When art > alv , h a = h 0 + α( art - alv ), where art is the blood pressure in the sheet at the arteriole, alv is the gas pressure in the alveolus, α is the compliance constant for the sheet thickness, and h 0 is the thickness at Δ = 0. The constant C = 4µf Lα/ (SA), where µ is the coefficient of viscosity of blood, f is a friction parameter (on the order of 4, depending on the post geometry), L is the average length of the streamlines in the sheet, S is the vascular space-tissue ratio (on the order of 0.9), and A is the sheet area. Comparison of this formula with the experimental results of Roos et al., using h 0 and α values from Glazier et al., shows reasonable agreement.