Entropy Production and the Pressure-Volume Curve of the Lung

TL;DR

This paper analytically examines entropy production during breathing in healthy and diseased lungs, linking it to pressure-volume hysteresis and lung tissue properties, with implications for understanding lung mechanics in health and disease.

Contribution

It introduces an analytical framework connecting lung P-V curves, entropy production, and disease-related changes, extending thermodynamic analysis to pulmonary disorders.

Findings

Entropy production relates to hysteresis area in P-V curves.

Increased bulk modulus in fibrosis correlates with higher entropy production.

The model predicts entropy changes in fibrotic and emphysematous lungs.

Abstract

We investigate analytically the production of entropy during a breathing cycle in healthy and diseased lungs. First, we calculate entropy production in healthy lungs by applying the laws of thermodynamics to the well-known transpulmonary pressure-volume ($P-V$) curves of the lung under the assumption that lung tissue behaves as an entropy spring-like rubber. The bulk modulus, $B$, of the lung is also derived from these calculations. Second, we extend this approach to elastic recoil disorders of the lung such as occur in pulmonary fibrosis and emphysema. These diseases are characterized by particular alterations in the $P-V$ relationship. For example, in fibrotic lungs $B$ increases monotonically with disease progression, while in emphysema the opposite occurs. These diseases can thus be mimicked simply by making appropriate adjustments to the parameters of the $P-V$ curve. Using Clausius's formalism, we show that entropy production, $\Delta S$, is related to the hysteresis area, $\Delta A$, enclosed by the $P-V$ curve during a breathing cycle, namely, $\Delta S=\Delta A/T$, where $T$ is the body temperature. Although $\Delta A$ is highly dependent on the disease, such formula applies to healthy as well as diseased lungs, regardless of the disease stage. Finally, we use {\it ansatzs} to predict analytically the entropy produced by the fibrotic and emphysematous lungs.