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Use of a heat transfer analogy for a mathematical model of respiratory tract deposition

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Abstract

Mathematical models predicting the aerosol deposition in the respiratory tract are reviewed. Data in the literature indicated not only that the air flow in the trachea and major bronchi may not be laminar, but also that the entrance effect of the tube or airway has not been considered. A new approach to a mathematical model of respiratory tract deposition, based on the analogy of the heat and mass transfer, is discussed.

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Literature

  • Akiyama, M. and K. C. Cheng. 1971. “Boundary Vorticity Method for Laminar Forced Convection Heat Transfer in Curved Pipes.”Int. J. Heat Mass Transfer,14 (10), 1659–1675.

    Article  MATH  Google Scholar 

  • Alavi, S. M., T. E. Keats and W. M. O'Brien. 1970. “The Angle of Tracheal Bifurcation: Its Normal Measuration.”Am. J. Roentgenol.,108, 546–549.

    Google Scholar 

  • Altshuler, B. 1959. “Calculation of Regional Deposition of Aerosol in the Respiratory Tract.”Bull. Math. Biophysics,21, 257–270.

    Google Scholar 

  • Angus, G. E. and W. M. Thurlbeck. 1972. “Number of Alveoli in the Human Lung.”J. Appl. Physiol.,32, 483–485.

    Google Scholar 

  • Beeckmans, J. M. 1965a. “The Deposition of Aerosols in the Respiratory Tract: I. Mathematical Analysis and Comparison with Experimental Data.”Canad. J. Physiol. and Pharm.,43, 157–172.

    Google Scholar 

  • — 1965b. “Correction Factor for Size-Selective Sampling Results. Based on a New Computed Alveolar Deposition Curve.”Am. Occup. Hyg.,8, 221–231.

    Google Scholar 

  • Boelta, L. M. K., G. Young and H. W. Iverson. 1948. Cited inFluid Dynamics and Heat Transfer, Knudsen, J. G. and D. L. Katz. New York: McGraw-Hill, p. 403.

    Google Scholar 

  • Davies, C. N. 1961. “A Formalized Anatomy of the Human Respiratory Tract.” InInhaled Particles and Vapours, Davies, C. N., ed. London: Pergamon Press, pp. 82–87.

    Google Scholar 

  • —, editor. 1966.Aerosol Science. London: Academic Press.

    Google Scholar 

  • Engel, S. 1959. “The Lobulation of the Mammalian Lung.”Anatomischer Anzeiger,106, 86–89.

    Google Scholar 

  • — 1964. “Comparative Anatomy and Pulmonary Air-Cleaning Mechanisms in Man and Certain Experimental Animals.”Health Phys.,10, 967–971.

    Article  Google Scholar 

  • Findeisen, W. 1935. “Uber das Absetzen Kleiner, in der Luft Suspendierten Teilchen in der menschlichen Lunge bei der Atmung.”Arch. Ges. Physiol.,236, 367–379.

    Article  Google Scholar 

  • Friedlander, S. K. 1964. “Particle Deposition by Diffusion in the Lower Lung: Application of Dimensional Analysis.”Am. Ind. Hyg. Ass. J.,25, 37–42.

    Google Scholar 

  • Fuchs, N. A. 1964.The Mechanics of Aerosols. New York: Pergamon Press.

    Google Scholar 

  • Gracuto, Shiela M. 1971. “Master Thesis.” University of Chicago.

  • Gussman, R. A. and J. M. Beeckmans. 1970. “Theoretical Consideration for Pulmonary Deposition in High Pressure Environments: A Model.”British Occupational Hygiene Society, 3rd International Symposium on Inhaled Particles, London, September 16–23, pp. 1.8.1–1.8.8.

    Google Scholar 

  • Hausen, H. 1943. Cited inHeat and Mass Transfer, Eckert, E. R. G. and R. M. Drake, Jr. New York: McGraw-Hill, p. 212.

    Google Scholar 

  • Horsfield, K. and G. Cumming. 1967. “Angles of Branching and Diameters of Branches in the Human Bronchial Tree.”Bull. Math. Biophysics,29, 245–259.

    Google Scholar 

  • — and —. 1968. “Morphology of the Bronchial Tree in Man.”J. Appl. Physiol.,24, 373–383.

    Google Scholar 

  • Jacobi, W. and D. Martin. 1970. “Diffusion Deposition of Inhaled Particles in the Upper Bronchial Tree.” Paper presented on the 2nd International IRPA-Congress in Brighton, May 3–8.

  • Kliment, V., J. Libich and V. Kaudersova. 1972. “Geometry of Guinea-pig Respiratory Tract and Application of Landahl's Model of Deposition of Aerosol Particles.”J. Hyg. Epidemiol. Microbiol. Immunol.,16, 107–114.

    Google Scholar 

  • Landahl, H. D. 1950a. “On the Removal of Air-borne Droplets by the Human Respiratory Tract: I. The Lung.”Bull. Math. Biophysics,12, 43–56.

    MathSciNet  Google Scholar 

  • — 1950b. “On the Removal of Air-borne Droplets by the Human Respiratory Tract: II. The Nasal Passages.”,12, 161–169.

    MathSciNet  Google Scholar 

  • — 1963. “Particle Removal by the Respiratory System. Note on the Removal of Airborne Particulates by the Human Respiratory Tract with Particular Reference to the Role of Diffusion.”,25, 29–39.

    Google Scholar 

  • Leveque, J. 1928. Cited inFluid Dynamics and Heat Transfer, Knudsen, J. G. and D. L. Katz. New York: McGraw-Hill, p. 367.

    Google Scholar 

  • Matsuba, K. and W. M. Thurlbeck. 1971. “The Number and Dimensions of Small Airways in Nonemphysematous Lungs.”Am. Rev. Respirat. Dis.,104, 516–524.

    Google Scholar 

  • McLaughlin, R. F., W. S. Tyler and R. O. Canada. 1961a. “A study of the Subgross Pulmonary Anatomy in Various Mammals.”Am. J. Anat.,108, 149–165.

    Article  Google Scholar 

  • —— and —. 1961b. “Subgross Pulmonary Anatomy in Various Mammals and Man.”J. Am. Med. Ass.,175, 694–697.

    Google Scholar 

  • —— and —. 1966. “Subgross Pulmonary Anatomy of the Rabbit, Rat and Guinea-pig with Additional Notes on the Human Lung.”Am. Rev. Respirat. Dis.,94, 380–387.

    Google Scholar 

  • Mitchell, R. I. 1971. “Aerosol Retention in the Lungs as a Function of Respiration Rate and Particle Size.”Ph.D. Thesis, The Ohio State University.

  • Nusselt, W. 1917. Cited inFluid Dynamics and Heat Transfer, Knudsen, J. G. and D. L. Katz. New York: McGraw-Hill, p. 401.

    Google Scholar 

  • Parker, H., K. Horsfield and G. Cumming. 1971. “Morphology of Distal Airways in the Human Lung.”J. Appl. Physiol.,31, 386–391.

    Google Scholar 

  • Prandtl, L. 1910, 1928. Cited inHeat and Mass Transfer, Eckert, E. R. G. and R. M. Drake, Jr. New York: McGraw-Hill, p. 207.

    Google Scholar 

  • Schlichting, H. 1960.Boundary Layer Theory, 4th edn. New York: McGraw-Hill.

    MATH  Google Scholar 

  • Schroter, R. C. and M. F. Sudlow. 1969. “Flow Patterns in Models of the Human Bronchial Airways.”Resp. Physiol.,7, 341–355.

    Article  Google Scholar 

  • Sudlow, M. F., D. E. Olsen and R. C. Schroter. 1970. “Fluid Mechanics of Bronchial Air-Flow.”British Occupational Hygiene Society, 3rd International Symposium on Inhaled Particles, London, September 16–23, pp. 1.7.1–1.7.6.

    Google Scholar 

  • Task Group on Lung Dynamics. 1966. “Deposition and Retention Models for Internal Dosimetry of the Human Respiratory Tract.”Health. Phys.,12, 173–208.

    Google Scholar 

  • Taylor, G. I. 1916. Cited inHeat and Mass Transfer, Eckert, E. R. G. and R. M. Drake, Jr. New York: McGraw-Hill, p. 207.

    Google Scholar 

  • Tenney, S. M. and J. E. Remmers. 1963. “Comparative Quantitative Morphology of the Mammalian Lung: Diffusing Area.”Nature,197, 54–56.

    Article  Google Scholar 

  • — and D. Bartlett, Jr. 1967. “Comparative Quantitative Morphology of the Mammalian Lung: Trachea.”Resp. Physiol.,3, 130–135.

    Article  Google Scholar 

  • Weibel, E. R. and D. H. Gomez. 1962. “Architecture of the Human Lung.”Science,137, 577–585.

    Google Scholar 

  • — 1963.Morphometry of the Human Lung. New York: Academic Press.

    Google Scholar 

  • — 1972. “Morphometric Estimation of Pulmonary Diffusion Capacity. V. Comparative Morphometry of Alveolar Lungs.”Resp. Physiol.,14, 26–43.

    Article  Google Scholar 

  • West, J. B. 1961. “Observations on Gas Flow in the Human Bronchial Tree.” InInhaled Particles and Vapours, Davies, C. N., ed. London: Pergamon Press, pp. 3–8.

    Google Scholar 

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  1. Lovelace Foundation for Medical Education and Research, 5200 Gibson Boulevard, S.E., 87108, Albuquerque, New Mexico

    Hsu-Chi Yeh

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Yeh, HC. Use of a heat transfer analogy for a mathematical model of respiratory tract deposition. Bltn Mathcal Biology 36, 105–116 (1974). https://doi.org/10.1007/BF02458596

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  • DOI: https://doi.org/10.1007/BF02458596

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