Abstract
This is a model for the time-variation of helium concentrations in lung wash-out curves. The helium (or other inert gas) is in a spirometer, which is connected by a common dead space to two separate dead spaces, each of which leads into a chamber. The chambers expand and contract, thus taking in some helium at each “breath.” Equations for the changes in helium concentration in each part of the system are set up; in this way difference equations are derived for the amount of helium in the spirometer after each breath, in and out, and complete solutions when the initial concentration is zero in all parts of the system except the spirometer. A simple solution when the chambers do not essentially differ (“equal ventilation”) is compared with the general case. The concept of “unequal lung ventilation” is discussed critically in relation to the model; some physiological interpretations are also mentioned. Numerical examples are given to show the effect of changes in various constants, in particular tidal volumes, end volumes, and the common dead space.
Similar content being viewed by others
Literature
Bates, D. V., W. S. Fowler, and R. E. Forster. 1954. “Uniformity of Alveolar Ventilation at Different Lung Volumes.”J. Appl. Physiol.,6, 598–602.
Becklake, M. R. 1952. “A New Index of the Intrapulmonary Mixture of Inspired Air.”Thorax,7, 111, 123.
Bouhuys, A., K. E. Hagstam, and G. Lundin. 1956. “Efficiency of Pulmonary Ventilation During Rest and During Light Exercise.”Acta Physiol. Scand.,35, 289–304.
—, R. Jonson, and G. Lundin. 1957. “Influence of Added Dead Space on Pulmonary Ventilation.”Acta Physiol. Scand.,39, 105–120.
Cournand, A., R. L. Riley, A. Himmelstein, and R. Austrian. 1950. “Pulmonary Circulation and Alveolar Ventilation-Perfusion Relationships After Pneumonectomy.”J. Thoracic Surg.,19, 80–116.
Fowler, W. S. 1949. “Lung Function Studies, III. Uneven Pulmonary Ventilation in Normal Subjects and in Patients with Pulmonary Disease.”J. Appl. Physiol.,2, 283–299.
—, E. R. Cornish, and S. S. Kety. 1952a. “Lung Function Studies, VIII. Analysis of Alveolar Ventilation by PulmonaryN 2 Clearance Curves.”J. Clinical Invest.,31, 40–50.
Fowler, W. S. 1952b. “Intrapulmonary Distribution of Inspired Gas.”Physiol. Reviews,32, 1–20.
Gilson, J. C., P. Hugh-Jones, P. D. Oldham, and F. Meade. 1955.Lung Function in Coalworkers' Pneumoconiosis. Medical Research Council, Special Report Series. No. 290. London: H. M. Stationery Office.
Gordon, A. S., O. Prec, H. Wedell, M. S. Sadove, F. Raymon, J. T. Nelson, and A. C. Ivy. 1951. “Circulatory Studies During Artificial Respiration on Apneic Normal Adults, III.”J. Appl. Physiol.,4, 421–437.
Mundt, E., W. Schoedel, and H. Schwarz. 1941. “Über die Gleichmässigkeit der Lüngenbeluftung.”Plüger's Archiv.,244, 99–106.
Otis, A. B., C. B. McKerrow, R. A. Bartlett, J. Mead, M. B. McIlroy, N. J. Selverstone, and E. P. Radford. 1956. “Mechanical Factors in Distribution of Pulmonary Ventilation.”J. Appl. Physiol.,8, 427–43.
Rauwerda, P. E. 1946. “Unequal Ventilation of Different Parts of the Lung.” Thesis. Groningen, Holland.
Visser, B. F. 1957. “Clinical Gas Analysis.” Thesis. Kemink, Utrecht, Holland.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wise, M.E., Defares, J.G. A model for unequal ventilation of the lungs assuming a common dead space and two separate dead spaces. Bulletin of Mathematical Biophysics 21, 343–362 (1959). https://doi.org/10.1007/BF02477894
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02477894