A Novel Mathematical Equation for a Noninvasive Determination of the Number of Alveoli of the Human Lung

Background: There had always been a spirited effort in understanding the transport of air or molecular oxygen plus other gases from alveolar air space into the pulmonary capillaries and from the latter back into the former using mathematical models; the determination of the number of alveoli using cadaver and invasive and partially noninvasive methods have been made. There is a need for a noninvasive method of mathematical nature, with evaluative, diagnostic, and prognostic application.

Objectives: The objectives of this research were to derive a mathematical equation for the noninvasive determination of the number of alveoli during rest and physical activity and elucidate the usefulness and advantage of the model over known methods.

Methods: Theoretical and computational (calculational) methods; data in the literature were substituted into the model mathematical equation for the computation of the number of alveoli in the human lungs.

Results and Discussion: The computed number (Nalv) of alveoli differed from one country or subcontinental region to another. The Nalv for the male were expectedly larger than for the female subjects.

Conclusion: The mathematical equation for totally noninvasive determination by computation is derivable and was derived. The total number (Nalv) of alveoli mobilised for function is a function of the width (d) of the nares (d 22/15), rate (Rv) of gas flow , and radius (ralv) of a functional alveolus . The equation has the potential to be of diagnostic, evaluative and prognostic value in medical practice. This new computational approach could be faster than other known approaches for the determination of the Nalv. A noninvasive approach by computation, relying on other noninvasively determined respiratory parameters, can eliminate the possibility of tissue damage.