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 entropic spring similar to 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, ΔS, is related to the hysteresis area, ΔA, enclosed by the P–V curve during a breathing cycle, namely, ΔS=ΔA∕T, where T is the body temperature. Although ΔA is highly dependent on the disease, such formula applies to healthy as well as diseased lungs, regardless of the disease stage. Finally, we use an ansatz to predict analytically the entropy produced by the fibrotic and emphysematous lungs.
Highlights
The laws of thermodynamics are based on empirical evidence derived from the behavior of macroscopic systems (Fermi, 1956), and in this respect share similarities with much of our knowledge about biological systems
We have developed a thermodynamic model of the mechanics of breathing that gives a central role to entropic changes in the lung tissue
We applied the Clausius formalism to the transpulmonary pressure–volume (P–V) curves of a healthy lung and consider the lung tissue to behave as an entropic spring similar to rubber
Summary
The laws of thermodynamics are based on empirical evidence derived from the behavior of macroscopic systems (Fermi, 1956), and in this respect share similarities with much of our knowledge about biological systems. The connectivity of the brain has been studied in the framework of complex networks (Reis et al, 2014) as well as the maximization of entropy production (Seely et al, 2014) These advances often rely on extensive numerical computation because of the highly non-linear interactions involved between the myriad components in these complex systems. In the present study we propose a simple thermodynamic model of the pressure–volume (P–V) relationship of the lung We use this model to calculate the entropy produced in the lung during normal breathing, and examine how this production is altered in pulmonary fibrosis and emphysema. The Young’s modulus of rubber is proportional to absolute temperature, an intriguing property that causes rubber to release heat when stretched as a result of a corresponding decrease in entropy, and to
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