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Calculation of regional deposition of aerosol in the respiratory tract

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Abstract

The removal of air-borne particles in the respiratory tract is treated to enable regional deposition to be inferred from measurement of expired aerosol as well as predicted from theory of the primary removal processes. The analysis uses the analogy of a continuous tubular filter-bed and includes consideration of respiratory pauses and the mechanical mixing of gas flow. Derived equations relate regional deposition, distribution of aerosol in the expired air, and efficiency of removal at different depths in the respiratory tract.

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Abbreviations

a n :

coefficients of power series expansion ofP (x), equation (16)

A n (ve):

defined by equation (17b)

b n :

coefficients of a polynomial approximation ofC (ve), equation (24)

B n (k′):

defined in equation (20)

C(ve):

expired concentration measured at the mouth after volumev ehas been expired

C t :

average concentration in total expiration

f i(x) orf e (x):

During inspiration (or expiration)f i (x)dx (orf e (x) dx) is the probability that a particle reaching a lung element of volumedx at depthx is removed at that place

F i (x) orF e (x):

During inspiration (or expiration)F i (x) (orF e (x)) is the probability that a particle can be carried from entrance to depthx (or from depthx to entrance) without being removed

F (x) :

denotesF i (x)=Fe (x) when these are equal

h i (x) orh e (x):

During the respiratory pause following inspiration (or expiration)h i (x) (orh e (x)) is the probability that a particle in lung element at depthx is removed there

k, k′ :

mixing parameters introduced in equations (14), (19)

L (x), £ (x) :

fraction of total deposition that is deposited distal to depthx in the cases where there is no mixing and where there is mixing, respectively

M (v, x) :

mixing function defined in the text before equation (14) is introduced, with partal derivativesM v (v, x) andM x (v, x)

P (x) :

probability that a particle can be carried down to depthx, remain suspended during the pause and carried out again without being removed

P L (x):

average value ofP (y) withy ≧x

PU (x):

average value ofP (y) withy ≦x

R (x) :

concentration remaining at depthx at start of inspiration

s (x) :

normalized slope of penetration functionP (x), defined by equation (12)

£:

total deposition expressed as a fraction of the amount of aerosol inhaled

U (x), U (x) :

fraction of total deposition deposited proximal to depthx in the cases where there is no mixing and where there is mixing, respectively

v :

variable denoting volume of respiratory gas

v e :

expiratory volume

v i :

inspiratory tidal volume

v t :

tidal volume

x :

variable denoting volume of lung depth

Literature

  • Altshuler, B., E. D. Palmes, L. Yarmus, and N. Nelson, 1959. “Intrapulmonary Mixing of Gases Studied with Aerosols.”J. Appl. Physiol.,14, 321–27.

    Google Scholar 

  • —, L. Yarmus, E. D. Palmes, and N. Nelson, 1957. “Aerosol Deposition in the Human Respiratory Tract.”A.M.A. Arch. of Indust. Health,15, 293–303.

    Google Scholar 

  • Brown, J. H., K. M. Cook F. G. Ney, and T. Hatch. 1950. “Influence of Particle Size upon the Retention of Particulate Matter in the Human Lung.”Am. J. Pub. Health,40, 450–58.

    Article  Google Scholar 

  • Findeisen, W. 1935. “Uber das Absetzen kleiner, in der Luft suspendierter Teilchen in der menschlichen Lunge bei der Atmung.”Arch. ges. Physiol.,236, 367–78.

    Article  Google Scholar 

  • Gormley, P. G. and M. Kennedy. 1949. “Diffusion from a Stream Flowing through a Cylinder Tube.”Proc. Royal Irish Acad., Section A,52, 163–69.

    MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • —, T. N. Tracewell, and W. H. Lassen. 1951. “On the Retention of Air-Borne Particulates in the Human Lung: II.”A.M.A. Arch. Indust. Hyg.,3, 359–66.

    Google Scholar 

  • ——, and W.H. Lassen. 1952. “Retention of Air-Borne Particulates in the Human Lung: III.”6, 508–511.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Industrial Medicine, New York University-Bellevue Medical Center, New York, USA

    Bernard Altshuler

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  1. Bernard Altshuler
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Altshuler, B. Calculation of regional deposition of aerosol in the respiratory tract. Bulletin of Mathematical Biophysics 21, 257–270 (1959). https://doi.org/10.1007/BF02477914

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  • DOI: https://doi.org/10.1007/BF02477914

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