TITLE:
From Pressure-Volume Relationship to Volume-Energy Relationship: A Thermo-Statistical Model for Alveolar Micromechanics
AUTHORS:
Kyongyob Min
KEYWORDS:
Thermo-Statistic Entropy, Thermodynamic Temperature, Sigmoid Pressure-Volume Curve, Logistic Equation, Volume-Energy Relationship
JOURNAL NAME:
Applied Mathematics,
Vol.11 No.11,
November
13,
2020
ABSTRACT: The connective tissue fiber system and the surfactant system are essential and interdependent components of lung elasticity. Despite considerable efforts over the last decades, we are still far from understanding the quantitative roles of either the connective tissue fiber or the surfactant systems. Through thermo-statistic considerations of alveolar micromechanics, the author introduced a thermo-statistic state function “entropy” to analyze the elastic property of pulmonary parenchyma based on the origami model of alveolar polyhedron. By use of the entropy for alveolar micromechanics, from the logistic equation for the static pressure (P)-volume (V) curves including parameters a, b, c, and k (V - a = b/[1+ exp{-k (P - c)}]), a set of equations was obtained to define the internal energy of lungs (UL) and its corresponding lung volume (VL). Then, by use of parameters a, b, c, and k, an individual volume-internal energy (VL - UL) diagram was constructed from reported data in patients on mechanical ventilation. Each VL - UL diagram constructed was discussed that its minimal value Uo = c (a + b/2) and its shape parameter b/k represent quantitatively the energy of tissue force and the energy of surface force. Furthermore, by use of the VL - UL relationship, the hysteresis of lungs estimated by entropy production was discussed as dependent on the difference in the number of contributing pulmonary lobules. That is, entropy production might be a novel quantitative indicator to estimate the dynamics of the bronchial tree. These values obtained by combinations of parameters of the logistic P-V curve seem useful indicators to optimize setting a mechanical ventilator. Thus, it is necessary to develop easy tools for fitting the individual sigmoid pressure-volume curve measured in the intensive care unit to the logistic equation.