Thermodynamic modelling of the lung mechanics

Abstract

From a thermodynamic point of view, we obtain a general expression of the distortion energy of the lung. From a Maxwell relation of this energy expression, we obtain a relation between the recoil pressure and the surface tension. By using the properties of partial derivatives, we derive a general thermodynamic expression for the surface area. For the two separate cases: (1) fluid-filled lungs (with constant surface tension) and; (2) air-filled lungs (with variable surface tension), we provide explicit expressions for the surface area, the distortion energy and the mechanical work by obtaining the fitting parameters upon comparing the model to the experimental data. In all situations the model predictions are in good agreement with the experimental data. Different from other existing lung models, our model employs the intrinsic relationships of thermodynamics, e.g. Maxwell relations, which provide additional equations and hence reduce the number of the unknowns. Only in obtaining the final explicit expressions, are experimental data used for finding certain parameters in the functional relationships. And this is the only subjectivity of our model.