Please enter verification code
Quantitative Relationship Between Expiratory Airflow Limitation and Dynamic Hyperinflation: A Thermo-statistical Model
International Journal of Theoretical and Applied Mathematics
Volume 6, Issue 4, August 2020, Pages: 46-52
Received: Oct. 2, 2020; Accepted: Oct. 26, 2020; Published: Nov. 11, 2020
Views 133      Downloads 26
Kyongyob Min, Internal Medicine, Ueda-Shimotanabe Hospital, Osaka, Japan
Article Tools
Follow on us
Clinical assessment of expiratory flow limitation (EFL) is important for diagnosing chronic pulmonary disease (COPD). Either EFL or dynamic hyperinflation (DH) in COPD has been understood based on wave speed theory, which is widely accepted as the standard concept. However, a theoretical perspective on the relationship between EFL and DH may require another approach. This article proposed another explanation for EFL with the introduction of pulmonary entropy with thermo-statistical considerations on choke state of the pulmonary system. According to Gibbs' thermodynamic equilibrium theory, the choke state of the pulmonary system was characterized by a critical pressure (Pc) emergence in the pulmonary parenchyma, which was proportional to the elastic recoil pressure (Pel) and the slope of maximal flow-volume curve (σ). Thermodynamic balance between energies (supplied from the body as heat, stored as the entropy of lungs, and dissipated in the respiratory system) explained the work of breathing (WOB), by which it was explained that an intrinsic PEEP (PEEPi) was emerging as a difference between sufficient and insufficient WOB for energy demands of the body. It was concluded that EFL would limit the WOB into less than demanded during exercise, and that the difference between demand and performance would induce a product of PEEPi and DH in volume.
Thermo-statistical Model, Entropy Elasticity, Expiratory Airflow Limitation (FEL), Dynamic Hyperinflation (DH), Intrinsic Positive End-expiratory Pressure (PEEPi), Work of Breathing (WOB)
To cite this article
Kyongyob Min, Quantitative Relationship Between Expiratory Airflow Limitation and Dynamic Hyperinflation: A Thermo-statistical Model, International Journal of Theoretical and Applied Mathematics. Vol. 6, No. 4, 2020, pp. 46-52. doi: 10.11648/j.ijtam.20200604.11
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Pride NB and Mimic-Emili. Lung mechanics, in Chronic Ostructive Lung Disease, Clverly and Pride NB, Eds, pp. 135-160, Chapman Hall, London, UK, 1995.
Fry DL and Hyatt RE. Pulmonary mechanics. A unified analysis of the relationship between pressure, volume and gasflow in the lungs of normal and diseased human subjects. Am J Med. 1960, 29 (4): 672-689.
Tiffeneau R and Pinelli A. Air circulant et air captive dans l’exporation de la function ventillatoire pulmonaire. Paris Med. 1947, 133: 624-631.
Dawson, SV, Elliott, EA. Wave-speed limitation on expiratory-a unifying concept. J Appl Physiol 1997, 43: 498-515, doi /10.1152/jappl.1977.43.3.498.
Min KY, Hosoi K, Kinoshita Y, Hara S, Degami H, Takada T, Nakamura T. Use of fractal geometry to propose a new mechanism of airway-parenchymal interdependence. Open Journal of Molecular and Integrative Physiology, 2012, 2; 14-20 doi: 10.4236/ojmip.2012.21003.
Webb, WR. Thin-Section CT of the secondary pulmonary lobule: Anatomy and the image—The 2004 Fleischner Lecture 1. Radiology 2006, 239 (2): 322-38 doi: 10.1148/radiol.2392041968.
Kitaoka, H, Carlos A M Hoyos, Ryuji Takaki. Origami Model for Breathing Alveoli. Adv Exp Med Biol 2010, 669: 49-52. doi: 10.1007/978-1-4419-5692-7_10.
Lanczos, C. Introduction in The variational principle of mechanics. 4hth Edition, Dover Publications, New York, p. 1, 1986.
Tantucci C. Expiratory Flow Limitation Definition, Mechanisms, Methods, and Significance. Pulmonary Med. 2013, article ID749860, 6pages, doi. 10.1155/2013/749860.
Kittel C, Kroemer H. Entropy and temperature. In: Thermal Physics, 2nd Edn. WH Freeman and Company (1980). pp 27-54.
Min KY. Entropy change of lungs: determinant of the static properties of the lungs. Applied Mathematics, 2015, 6; 1200-1207. 10.4236/am.2015.68111.
Mead J, Turner JM, Macklem PT, Little JB. Significance of the relationship between lung recoil and maximum expiratory flow. J Appl Physiol. 1967, 22 (1): 95-108, doi/10.1152/jappl.1967.22.1.95.
Leaver DG and Pride NB. Contributions of Loss of Lung Recoil and of Enhanced Airways Collapsibility to Airflow Obstruction of Chronic Bronchitis and Emphysema. J Clin Invest.1973, 52: 2117-2128, doi: 10.1172/JCI107396.
Kenny, JES 2019. Campbell’s diagram
Tomonaga Shin-itiro. Quantum Mecahnics Vol. II New Quantum Theory, Amsterdam: North-Holland Pub. Co.; New York: Interscience Publishers, 1966/ Japanese version, Misuzu-shobou, 1997, Appendix VIII, pp 286-287.
Calverley PMA and Koulouris NG. Flow limitation and dynamic hyperinflation: key concepts in modern respiratory phyiology. Eur Respir J. 2005, 25 (1): 186-199, doi: 10.1183/09031936.04.00113204.
Tantucci C, Duguet A, Similowski T, Zelter M, Derenne JP, and Milic-Emili J. Effect of salbutamol on dynamic hyperinflation in chronic obstructive pulmonary disease patients. Eur Respir J 1998, 12 (4): 799-804, doi: 10.1183/09031936.98.12040799.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186