Entropy Production and the Pressure–Volume Curve of the Lung

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.

From Pressure-Volume Relationship to Volume-Energy Relationship: A Thermo-Statistical Model for Alveolar Micromechanics

“…Classically static PV relationships of which is measured by the area of PV loop and described as the entropy production (D) of Oliveria et al [16] as follows:…”

Perspectives on Complexity, Chaos and Thermodynamics in Environmental Pathology

“…As stressed by Schrödinger, they have to export the entropy they generate to the outer environment in order to live [ 52 ]. Interestingly, anatomical structures involved in this “entropy purge” (e.g., lung) show fractal organization [ 53 , 54 ]. Referring to the pathological context, morpho-functional alteration at the different integration scales of living organisms (from subcellular to organismic level) may affect the original complexity and the “entropy purge” needed to maintain the organism far from equilibrium, thus healthy and ultimately alive [ 20 , 55 ].…”

“…Examples of interfaces at the tissue/organ level include lungs, gills, kidney and intestine. Very interestingly, these interfaces display fractal properties and are implied in entropy purge from organisms [ 53 , 54 ], their integrity and functionality being critical for maintaining organisms far from thermodynamic equilibrium [ 35 , 52 ].…”

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“…Both scenarios indicate a lower compliance and greater pressure required to increase the lung volume in the region of operating pressure. In certain pathological situations such as ARDS, a sigmoidal representation of V A ( P el ) with a low compliance region at low P el [ 28 , 31 – 34 ] could be captured in the parameterization of F rec .…”