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Research Papers

Numerical Modelling and Analysis of Peripheral Airway Asymmetry and Ventilation in the Human Adult Lung

[+] Author and Article Information
F. S. Henry1

Molecular and Integrative Physiological Sciences, Harvard School of Public Health, Boston, MA 02115fhenry@hsph.harvard.edu

C. J. Llapur, R. S. Tepper

James Whitcomb Riley Hospital for Children,  Indiana University, Indianapolis, IN 46202–5225

A. Tsuda

Molecular and Integrative Physiological Sciences, Harvard School of Public Health, Boston, MA 02115

1

Corresponding author.

J Biomech Eng 134(6), 061001 (Jun 08, 2012) (12 pages) doi:10.1115/1.4006809 History: Received August 12, 2011; Revised April 26, 2012; Posted May 11, 2012; Published June 08, 2012; Online June 08, 2012

We present a new one-dimensional model of gas transport in the human adult lung. The model comprises asymmetrically branching airways, and heterogeneous interregional ventilation. Our model differs from previous models in that we consider the asymmetry in both the conducting and the acinar airways in detail. Another novelty of our model is that we use simple analytical relationships to produce physiologically realistic models of the conducting and acinar airway trees. With this new model, we investigate the effects of airway asymmetry and heterogeneous interregional ventilation on the phase III slope in multibreath washouts. The model predicts the experimental trend of the increase in the phase III slope with breath number in multibreath washout studies for nitrogen, SF6 and helium. We confirm that asymmetrical branching in the acinus controls the magnitude of the first-breath phase III slope and find that heterogeneous interregional ventilation controls the way in which the slope changes with subsequent breaths. Asymmetry in the conducting airways appears to have little effect on the phase III slope. That the increase in slope appears to be largely controlled by interregional ventilation inhomogeneities should be of interest to those wishing to use multibreath washouts to detect the location of the structural abnormalities within the lung.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Schematic of upper and lower lung regions and asymmetrically branching conducting airway model

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Figure 2

Branching notation

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Figure 3

Schematic of a typical asymmetrically branching airway model acinus (shown without alveoli for clarity) (a); the number of ducts in each generation for all model acini (c); the frequency distribution of terminal ducts, or sacs, in the model acini (b); and volumes of the model acini at FRC in the upper (dark gray) and lower (light gray) egions of the lung (d)

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Figure 9

Predicted variation of SnIII with breath number for nitrogen, helium and SF6 (―•―, φ = 0.5 and no gas exchange; ―▾―, φ = 0.5 and gas exchange;

, φ = 1.0 and no gas exchange) compared to the experimental data of Crawford [8] (□) and of Grönkvist [18] (Δ), and the predictions of Verbanck and Paiva [9] (― ― ―) (taken from Fig. 6 of that publication) and Tawhai and Hunter [10] (― · ―) (taken from Fig. 3 of that publication and representing their LPA-ACA model with gas exchange). See text for definition of φ.

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Figure 12

The gridded interface intact (a) and separated along the interface (b)

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Figure 13

Boundary treatment at the east face of the parent duct

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Figure 14

Boundary treatment at the west face of daughter duct 2

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Figure 15

Prediction, using the standard model, of the variation over exhalation of the concentration of nitrogen at the inlet to generation 0 (the trachea).

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Figure 4

The effect of changes in bifurcation model parameters r and η (see Eq. 9) on the average asymmetry (see text for definition) of the model acinus

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Figure 5

Volumes of and flow rates into the upper (solid line) and lower lung (broken line) regions for VFRC = 3700ml and VT = 1000ml α = 0.581, β = 0.4 and γ = 0.425

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Figure 6

Variation of first-breath phase III slope, S1III , for nitrogen, helium and SF6 with φ, the fraction of the area associated with the alveolar volume, which is added to the duct flow area. See text for definition of φ.

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Figure 7

The effect of changes in bifurcation model parameters r and η (see Eq. 9) on the predicted value of the first-breath phase III slope, S1III , for nitrogen, helium, and SF6. Included for reference are the experimental values of S1III due to Crawford [8]

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Figure 8

Effect of various combinations of ventilation parameters on SnIII with breath number for nitrogen. α=(VU)FRC/VFRC, where (VU)FRC is the volume of the upper lung region at FRC; β=(VU)T/VT, where (VU)T is the tidal volume entering the upper lung region; and FSU/L  = flow sequence factor between the upper and lower regions (see Eq. 4. [□] = experimental data of Crawford [8]

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Figure 10

Predicted variation of SnIII with breath number for nitrogen for various configurations of the model. (a) -▴- asymmetric conducting airways (r = 0.326, η = 3), asymmetric acinar airways (r = 0.326, η = 7.5), and heterogeneous interregional ventilation (α = 0.581, β = 0.4 and γ = 0.425); i.e., the standard model. (b) -Δ- asymmetric conducting airways (r = 0.326, η = 3), asymmetric acinar airways (r = 0.326, η = 7.5), and homogeneous ventilation (α=β=γ=0.5). (c) -▪- asymmetric conducting airways(r = 0.326, η = 3), symmetric acinar airways (r = 0.5, η = 7.5) and heterogeneous interregional ventilation (α = 0.581, β = 0.4 and γ = 0.425). (d) -□- asymmetric conducting airways (r = 0.326, η = 3), symmetric acinar airways (r = 0.5, η = 7.5) and homogeneous ventilation (α=β=γ=0.5). (e) -¯- symmetric conducting airways (r = 0.5, η = 3), symmetric acinar airways (r = 0.5, η = 7.5) and homogeneous interregional ventilation (α=β=γ=0.5). Experimental data (□) taken from Fig. 3 of Crawford [8]. (All above predictions had φ = 0.5 and no gas exchange.)

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Figure 11

Typical duct of length lD and one-dimensional grid (a) and detail of a grid cell (b). Dummy cells are used to implement boundary conditions and transfer data from neighboring ducts.

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