Use of static pressure-volume relations to estimate the total amount of pulmonary connective tissue--theoretical approach

Abstract

There is no accepted way to estimate the amount of connective tissue in the lungs in vivo. I propose an equation for estimating the total amount of pulmonary connective tissue from static pressure-volume relations. The stress-strain relations of pulmonary connective tissue were assumed to be describable by a non-linear exponential function: f = exp(ax)-1, where "f" is stress, "x" is strain, and "a" is Young's modulus of elasticity. The connective tissue elements were assumed to be distributed randomly in orientation within a pulmonary lobule, and the bodies of a pulmonary lobule were assumed to be packed in "equilibrium space division", as proposed by Suwa (1981). Stochastic geometry for elastic elements in the lung was used to obtain a set of equations describing the static pressure-volume relationship, such that P = (0.12 zeta 0/3V0) x [exp(ax)/(1 + x)2] and V = V0 (1 + x)3, where V0 is a reference lung volume in a perfectly relaxed state and zeta 0 is the total amount of connective tissue in the pulmonary parenchyma. This new model can accommodate static pressure-volume relations of human subjects in the range of relatively high lung volumes reported by Turner et al. (J App Physiol 25: 664, 1968), by Corbin et al. (Am Rev Respir Dis 120: 293, 1979), and by Finucane et al. (J App Physiol 26: 330, 1969). In conclusion, the total amount of connective tissue in lung parenchyma can be estimated with this new model of the static pressure-volume relationship at relatively high lung volumes.