Respiratory tract, its implication, and the mathematical model for the determination of the radius of an alveolus.

The flow rate of air has been investigated which showed that rate decreases per tract from one generation to other. However, the physiological implication of the tapering respiratory tract is not adequately elucidated and a noninvasive mathematical model is unknown for the computation of an alveolar radius. The formulation of mathematical models that can account for the effect of tapering airways and calculation of the radius of the alveolus at each generation of respiratory tracts are the objectives of the research. The method of research is theoretical and computational. Known radii of all respiratory tracts except the alveolus were substituted into derived equation for the calculation of alveolar radius. The rate of gas flow, in metres per second, decreases with increasing number of tracts from one generation to another. However, the sum of the distance covered per unit time increases from one generation to another. The alveolar radius for an average adult lung is » 1.163 ± 0.080 (SD) exp (- 4) metre (df = 22 and coefficient of variation is » 6.879). Older adults have longer alveolar radius in male and female subjects. Although the rate of gas flow in metres per second increases for a while and then decreases, the total distance covered per unit time is increasingly high making the delivery of gas to the alveoli very rapid. The derived equations could be used for the computation of alveolar radius. There are gender, demographically and racially based differences in the radius of alveolus.