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Dynamic Distribution of Gas Flow

L. A. Engel

10.1002/cphy.cp030332

Source: Supplement 12: Handbook of Physiology, The Respiratory System, Mechanics of Breathing

Originally published: 1986

Published online: January 2011

Full Article on Wiley Online Library



Abstract

The sections in this article are:

1 Gas Flow
1.1 Distribution of Convection (Bulk Flow)
1.2 Distribution of Gas Concentrations
2 Regional Distribution of Gas Flow
2.1 Gas Distribution at Constant Flow Rate
2.2 Ventilation Distribution During Quiet Breathing
2.3 Ventilation Distribution At Higher Flow Rates
2.4 Mechanisms in Upright Posture
2.5 Mechanisms in Horizontal Posture
2.6 Lung‐Chest Wall Interaction
3 Intraregional Distribution of Gas Flow
3.1 Frequency Dependence
3.2 Convection‐Diffusion Interactions
4 Cardiogenic Gas Flow and Mixing
4.1 Mechanisms
4.2 Consequences
Figure 1.

Distribution of inhaled bolus of 133Xe between apical and caudal lung regions as function of inspiratory now. Bolus is inhaled at identical lung volume in both upright and supine postures (upright functional residual capacity). Note large interindividual variability, linear relationship with flow in upright posture, and greater flow dependence of craniocaudal distribution in supine posture. alv, alveolar ventilation.

From Sybrecht et al. 119
Figure 2.

Influence of breathing frequency on regional and mouth washout of 133Xe. Abscissa: volume expired (corrected for dead space) during time required to halve initial count rates (VA½) at 12 breaths/min (Δ) and 57 breaths/min (○). Note all regional VA½ increased with frequency (P < 0.005) in parallel fashion; mean mouth VA½ identical at two frequencies.

From Forkert et al. 44
Figure 3.

Regional distribution of 133Xe bolus inhaled at 0.4 liter/s from functional residual capacity in 1 subject. Top: inspiration with predominantly intercostal and accessory muscles (IC). Bottom: inspiration with enhanced abdominal motion (Ab). Symbols indicate duplicate measurements. Abscissa is normalized alveolar 133Xe concentration. Note preferential distribution of 133Xe to basal regions after Ab inspiration and to upper midzones after IC inspiration.

From Roussos et al. 107
Figure 4.

Influence of different breathing patterns on rib cage shape. Cross section of upper and lower rib cage in arbitrary units adjusted to give equal deflections during relaxation from total lung capacity to functional residual capacity (dotted line). During quiet breathing, at 60 breaths/min, and during exercise, the loops are parallel to the relaxation line. Single rapid inspiration (dashed line) causes relatively greater expansion of upper rib cage.
Figure 5.

Model analyses of ratio of tidal volume distribution to upper and lower lung regions as function of inspiratory flow in upright lungs. A: single constant‐flow inhalation of 850 ml. B: sinusoidal breathing at frequency (f) of 15 breaths/min. Note flow dependence of single‐breath distribution and flow independence of tidal breathing.

A from Connolly et al. 18; B from Chang and Shykoff 15 © 1982, with permission from Pergamon Press, Ltd
Figure 6.

Models of lung‐chest wall interaction assuming that change in transpulmonary pressure (ΔPL(t)] is sole determinant of flow and lung expansion (A) or assuming that ΔPL(t) is partly determined by lung mechanical properties (B).
Figure 7.

Concentration of inspired gas [F(x,t)] plotted against distance from alveoli during 1‐liter breath at constant flow of 1 liter/s in symmetrical trumpet model. Curves 1-10 are solutions of Eq. 1 with diffusion coefficient of 0.225 cm2/s at 0.2‐s intervals from start of inspiration to end of expiration. Note relatively stationary diffusion front at end inspiration (curves 2-5).

From Paiva and Engel 92
Figure 8.

Lung model of two trumpet‐shaped units (V1 and V2) with common stem joining at branch point. S, S1, and S2 represent total cross‐sectional area including alveoli; s, s1, and s2 refer to cross‐sectional areas of conducting airways only. Geometrical asymmetry represented by shorter axial length of one unit (V2), which extends from branch point to dashed circle whose position can vary.

From Paiva and Engel 92
Figure 9.

Left: two‐trumpet model representing asymmetrical branching distal to respiratory bronchioles. Asymmetry quantitated by unequal volumes of two units (V1 > V2) subtended at branch point (BP). Dichotomous branching results in identical cross sections at BP (A1 = A2). Right: concentration profiles of inspired gas concentration at end inspiration (curve 5) and at equal intervals during expiration at constant flow (curves 6-10) in model as function of distance from end of larger trumpet. Vertical dashed line, terminal end of smaller trumpet; dashed curves, concentration profiles within smaller trumpet.
Figure 10.

Concentration profiles of O2 at end inspiration (top) and end expiration (bottom) during single breath of O2 in asymmetrically branching model of alveolar ducts (shown in inset). Locations A‐E and P‐S correspond to nodes in model. Despite homogeneous expansion, substantial concentration differences are established between parallel pathways and persist at end expiration.

Top and bottom from Davidson and Engel 24; inset adapted from Parker et al. 97
Figure 11.

Effect of heart motion on adjoining lung units. Cardiac pressure impulse produces transient deflation of lung units resulting in flow pulses whose magnitude depends on resistance (R) and compliance (C) product of units.


Figure 1.

Distribution of inhaled bolus of 133Xe between apical and caudal lung regions as function of inspiratory now. Bolus is inhaled at identical lung volume in both upright and supine postures (upright functional residual capacity). Note large interindividual variability, linear relationship with flow in upright posture, and greater flow dependence of craniocaudal distribution in supine posture. alv, alveolar ventilation.

From Sybrecht et al. 119


Figure 2.

Influence of breathing frequency on regional and mouth washout of 133Xe. Abscissa: volume expired (corrected for dead space) during time required to halve initial count rates (VA½) at 12 breaths/min (Δ) and 57 breaths/min (○). Note all regional VA½ increased with frequency (P < 0.005) in parallel fashion; mean mouth VA½ identical at two frequencies.

From Forkert et al. 44


Figure 3.

Regional distribution of 133Xe bolus inhaled at 0.4 liter/s from functional residual capacity in 1 subject. Top: inspiration with predominantly intercostal and accessory muscles (IC). Bottom: inspiration with enhanced abdominal motion (Ab). Symbols indicate duplicate measurements. Abscissa is normalized alveolar 133Xe concentration. Note preferential distribution of 133Xe to basal regions after Ab inspiration and to upper midzones after IC inspiration.

From Roussos et al. 107


Figure 4.

Influence of different breathing patterns on rib cage shape. Cross section of upper and lower rib cage in arbitrary units adjusted to give equal deflections during relaxation from total lung capacity to functional residual capacity (dotted line). During quiet breathing, at 60 breaths/min, and during exercise, the loops are parallel to the relaxation line. Single rapid inspiration (dashed line) causes relatively greater expansion of upper rib cage.



Figure 5.

Model analyses of ratio of tidal volume distribution to upper and lower lung regions as function of inspiratory flow in upright lungs. A: single constant‐flow inhalation of 850 ml. B: sinusoidal breathing at frequency (f) of 15 breaths/min. Note flow dependence of single‐breath distribution and flow independence of tidal breathing.

A from Connolly et al. 18; B from Chang and Shykoff 15 © 1982, with permission from Pergamon Press, Ltd


Figure 6.

Models of lung‐chest wall interaction assuming that change in transpulmonary pressure (ΔPL(t)] is sole determinant of flow and lung expansion (A) or assuming that ΔPL(t) is partly determined by lung mechanical properties (B).



Figure 7.

Concentration of inspired gas [F(x,t)] plotted against distance from alveoli during 1‐liter breath at constant flow of 1 liter/s in symmetrical trumpet model. Curves 1-10 are solutions of Eq. 1 with diffusion coefficient of 0.225 cm2/s at 0.2‐s intervals from start of inspiration to end of expiration. Note relatively stationary diffusion front at end inspiration (curves 2-5).

From Paiva and Engel 92


Figure 8.

Lung model of two trumpet‐shaped units (V1 and V2) with common stem joining at branch point. S, S1, and S2 represent total cross‐sectional area including alveoli; s, s1, and s2 refer to cross‐sectional areas of conducting airways only. Geometrical asymmetry represented by shorter axial length of one unit (V2), which extends from branch point to dashed circle whose position can vary.

From Paiva and Engel 92


Figure 9.

Left: two‐trumpet model representing asymmetrical branching distal to respiratory bronchioles. Asymmetry quantitated by unequal volumes of two units (V1 > V2) subtended at branch point (BP). Dichotomous branching results in identical cross sections at BP (A1 = A2). Right: concentration profiles of inspired gas concentration at end inspiration (curve 5) and at equal intervals during expiration at constant flow (curves 6-10) in model as function of distance from end of larger trumpet. Vertical dashed line, terminal end of smaller trumpet; dashed curves, concentration profiles within smaller trumpet.



Figure 10.

Concentration profiles of O2 at end inspiration (top) and end expiration (bottom) during single breath of O2 in asymmetrically branching model of alveolar ducts (shown in inset). Locations A‐E and P‐S correspond to nodes in model. Despite homogeneous expansion, substantial concentration differences are established between parallel pathways and persist at end expiration.

Top and bottom from Davidson and Engel 24; inset adapted from Parker et al. 97


Figure 11.

Effect of heart motion on adjoining lung units. Cardiac pressure impulse produces transient deflation of lung units resulting in flow pulses whose magnitude depends on resistance (R) and compliance (C) product of units.

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Article Title: Dynamic Distribution of Gas Flow
 

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L. A. Engel. Dynamic Distribution of Gas Flow. Compr Physiol 2011, Supplement 12: Handbook of Physiology, The Respiratory System, Mechanics of Breathing: 575-593. First published in print 1986. doi: 10.1002/cphy.cp030332