We constructed a simple model of lung distensibility in which the relationship between pressure (P) and volume (V) is of the exponential form obtained empirically: V = a+ becP , where a, b, and c are constants, and e is the base of the natural logarithm. The model lung is idealized as a frictionless diaphragm moving in a cylinder. Diaphragm movement is impeded by a variable force (F). By assuming that the rate of change of F is proportional to the inverse of the distance of the diaphragm from a maximal distance, the pressure-volume relationship assumes the above exponential form. The model was applied to 14 randomly selected patients, seven with increased lung compliance and seven with decreased lung compliance. For all but three of the patients, the model accounted for over 99% of the variability of the data; for all patients this value was greater than 96%. Correlations were calculated among both traditional measures of lung elasticity and parameters introduced by construction of the model. In general, the various measures correlated poorly with one another. It is argued that the concept of "lung elasticity" will remain imprecisely defined until the relationship between lung structure and lung function is better understood.
Benish, William; Harper, Peggy; Ward, Joseph; and Popovich, John Jr.
"A Mathematical Model of Lung Static Pressure-Volume Relationships: Comparison of Clinically Derived Parameters of Elasticity,"
Henry Ford Hospital Medical Journal
: Vol. 36
Available at: https://scholarlycommons.henryford.com/hfhmedjournal/vol36/iss1/12