Ventilation/Perfusion Matching: Of Myths, Mice, and Men

Abstract

Despite a huge range in lung size between species, there is little measured difference in the ability of the lung to provide a well-matched air flow (ventilation) to blood flow (perfusion) at the gas exchange tissue. Here, we consider the remarkable similarities in ventilation/perfusion matching between species through a biophysical lens and consider evidence that matching in large animals is dominated by gravity but in small animals by structure.

Introduction

The ability of the lungs to efficiently deliver oxygen from the environment to the blood depends critically on the “matched” delivery of oxygen-rich air and deoxygenated blood to the pulmonary alveoli (the site of gas exchange). At the whole-organ level, this matching is represented by the ratio of alveolar ventilation (V̇_A) to total lung perfusion (Q̇), where V̇_A is the rate at which air is delivered to the gas exchange region and Q̇ is cardiac output. Efficient gas exchange depends on whole-lung matching of V̇_A to Q̇ (i.e., the ratio V̇_A/Q̇), but—importantly—also depends on the distribution of V̇_A/Q̇ among thousands-to-millions of gas exchanging units in the mammalian lung. The lung’s vast gas exchange surface is distributed among many thousands of pulmonary acini (the exact number is species-dependent). In the intact lung, air and blood are supplied to the acini through asymmetrically branched airway and vascular networks that reside within a highly deformable lung tissue that has normal variation in its elastic properties, and the integrated air-blood-tissue system is subject to several mechanisms that are sensitive to gravity. As a consequence, both V̇_A and Q̇ distributions are quite heterogeneous. Despite this, in the healthy lung during normal breathing V̇_A/Q̇ is relatively narrowly distributed around the “ideal” mean of V̇_A/Q̇ = 1. This appears to be independent of species lung size across a wide range of mammals, with healthy rodents (1, 76), dogs (20, 78), pigs (32, 41), humans (27, 60, 80), horses (18, 31, 54), and even giraffes (55) having V̇_A and Q̇ distributions that are highly correlated with each other and with a fairly narrow V̇_A/Q̇ distribution. This is surprising because V̇_A/Q̇ matching has historically been proposed to depend on gravitational mechanisms and, more recently, on the resistance of the branching airway and pulmonary vascular geometries; it would therefore be reasonable to assume that it is also sensitive to species differences in lung height, as well as to the relative size of the airways and vessels with respect to the lung size.

It has been speculated that different mechanisms in large and small animals could explain their similarity of V̇_A/Q̇ distribution (24). Comparative physiology studies have identified allometric scaling laws that relate species body mass to many physiological parameters. Weibel and Taylor extended this to their hypothesis of “symmorphosis” (e.g., Refs. 83–85): that biological structures are economically designed to support function. Although symmorphosis is evident in some of the components of the oxygen pathway, it does not provide a framework to explain how the integrated lung provides relative consistency of V̇_A/Q̇ distribution with body size. Here, we consider the evidence for similar V̇_A/Q̇ regardless of animal size and the mechanisms that are thought to be important, and we use a theoretical analysis to propose that large and small animals differ considerably in the underlying mechanisms that dominate V̇_A/Q̇ matching. Understanding the size dependence of these mechanisms has implications for translation of animal experimental studies to human physiology and potentially to the very young human.

Biophysical Models to Test Mechanisms

Biophysical computational models of lung structure and function began to emerge in the early 2000s (7, 70, 73, 74) and have been shown to be a useful tool for examining the plausibility of hypotheses for lung structure-function interactions (12, 37, 66, 68). Biophysical models currently provide the only way for individual mechanisms to be theoretically analyzed in complete isolation from others. For example, V̇_A and Q̇ can be simulated with and without gravity, or without the influence of airway or blood vessel resistances (37). For example, using this approach, Clark et al. (12) concluded that both gravity and structure play a major role in determining the Q̇ distribution in the human lung (FIGURE 1). Vascular structure was shown to be important for inducing iso-gravitational heterogeneities and a central to peripheral gradient, the weight of the blood was shown to superimpose a gravitational gradient, and deformation of the lung tissue under its own weight exaggerated this gradient. Swan et al. (66) conducted a similar analysis of V̇_A in upright humans and concluded that, due to a relatively lower air than blood viscosity, airway structure plays a lesser role in determining V̇ distribution compared with the distribution of lung tissue compliance, which itself has a strong dependence on gravity. These analyses are summarized in FIGURES 2 AND 3, showing the additive contributions to the characteristic distributions of V̇_A and Q̇ in the human lung.

FIGURE 1.

Human lung model used for simulation of V̇_A/Q̇

Transverse sections are shown for the model with 1) structure, hydrostatics, and gravitational deformation; 2) no tissue deformation; 3) only tissue deformation; and 4) zero gravity. The table indicates logSDV and logSDQ calculated for each simulation, as well as the correlation (ρ) between V̇_A and Q̇. Some material is from Ref. 37, and used with permission from Journal of Applied Physiology.

FIGURE 2.

Perfusion distributions in dog and mouse lungs

Perfusion (Q̇) distributions in dog (top) and mouse (bottom) lungs, as simulated using the model of Clark et al. (12) with no gravitational effects (A); including hydrostatic effects and a linear gradient in elastic recoil pressure (B); same as in B but replacing the linear gradient in elastic recoil with deformation of the lung tissue under gravity and a distribution of elastic recoil pressures (C) predicted by the model of Tawhai et al. (68). The Q̇ distribution in dog responds considerably to the inclusion of gravitational factors, however the mouse Q̇ distribution is unchanged. D: summary of the dominating mechanisms.

FIGURE 3.

Ventilation distributions in dog and mouse lung models

Ventilation (V̇) distributions in dog (top) and mouse (bottom) lung models as simulated using the model of Swan et al. (66) with no gravitational effects (A; a constant elastic recoil pressure of 5 cmH₂O acting throughout the lung and a uniform distribution of acinar volumes/compliance at functional residual capacity); including a linear gradient in acinar volume at FRC, equivalent to a gradient in elastic recoil pressure of 0.25 cmH₂O/cm lung height (B); and including a deformation of lung tissue under gravity and a distribution of elastic recoil pressures predicted by the model of Tawhai et al. (68) (C). The V̇ distribution in dog responds considerably to the inclusion of gravitational factors, including a strong contribution from local tissue compliance. However, as with the Q̇ model results, the mouse V̇_A distribution is dependent predominantly on structure. D: summary of the dominating mechanisms.

The human airways and pulmonary blood vessels have more symmetrical branching with respect to branch dimensions and numbers of branch divisions in pathways from the trachea to the gas exchange surface than in most other mammalian species. Quadrupeds typically exhibit monopodial branching, which is characterized by main large and tapering pathways giving rise to many small lateral branches, which in turn taper and give rise to additional lateral branches in a self-similar manner (43). That is, at any branch division in a monopodial tree, the “child” branch with the smallest diameter will have a large branching angle, and the other child branch appears to be a tapering continuation of the parent. Aside from a single study showing that monopodial vascular structure results in greater heterogeneity in Q̇ distribution than in the human geometry (6), few computational studies have considered V̇_A/Q̇ matching in the species that have been most widely studied experimentally, i.e., rodents and dogs. Thus the relative contributions of gravity and structure in large and small mammals remains speculative. Potentially, the size and shape of the lung in these experimental animals influences the mechanisms of V̇_A/Q̇ matching and therefore the extrapolation of experimental and imaging results to humans.

Why V̇_A/Q̇ Matching Matters

Disruption to the normal V̇_A/Q̇ distribution has a profound impact on arterial oxygen levels. Data acquired from small to very large mammals show that measured arterial oxygen partial pressure (Pao₂) can be predicted with good accuracy from the lung’s underlying V̇_A/Q̇ distribution, indicating its influence on the efficiency of lung gas exchange (48, 58). V̇_A/Q̇ is impaired in virtually every lung pathology, and its variability increases (slightly) in older age (8). But in addition to V̇_A/Q̇ itself, its spatial distribution is also important: individuals with the same quantity of structural abnormality due to disease (e.g., local reduction in Q̇ in pulmonary embolism) can have a quite different functional response to their pathology depending on where their disease is located (11). For example, occlusion of gravitationally dependent tissue is likely to have a greater effect on pulmonary artery pressure than occlusion of non-gravitationally dependent tissue, since blood must redistribute “against gravity” when these regions are occluded. However, mid-lung occlusions appear to have the greatest effect on oxygen exchange (and so V̇_A-Q̇ matching). Therapies to treat lung disease or to support lung function are effectively seeking to re-normalize V̇_A/Q̇. Thus understanding the underlying mechanisms that determine the V̇_A/Q̇ distribution in the healthy lung over the human lifespan and its disruption in disease is critical to improved disease diagnosis and management.

Additionally, pre-clinical research relies on animal models, so species differences must be accounted for to enable successful translation of mechanistic insights derived from animal models to the human condition. Large animals with lung size similar to humans have been used extensively to understand basic lung physiology, but smaller animals are cheaper, more convenient, and offer well-studied genetic models of disease or aging. However, there have been issues in translating data obtained from animal models to human physiology for a number of respiratory diseases (35, 44, 47, 61, 77), and the implications of animal lung size must be considered alongside other factors when attempting to translate animal models to human.

Size-Independent V̇_A/Q̇ Matching

There are many experimental and imaging studies that have measured V̇_A or Q̇, but here we focus specifically on those that have investigated both in the same animals. That is, studies that specifically address the matching of V̇_A and Q̇ rather than investigate one or the other in isolation.

The majority of evidence for similar V̇_A/Q̇ distributions across mammalian species comes primarily from multiple inert gas elimination technique (MIGET) studies. In MIGET, a number (typically six) of inert gases are injected into the bloodstream, and their concentration in both the blood and expired air are monitored over time (81, 82). A 50-unit model (with each unit assigned a unique V̇_A/Q̇ value ranging from dead space to shunt) is fit to the data to provide an estimate of the distribution of V̇_A/Q̇. Reported metrics that have been derived from MIGET are usually consistent between studies within the same species: several typical metrics are reported in Table 1 (listed from approximately smallest to largest species lung size). Two particularly important metrics are the log SDQ (the dispersion of Q̇) and log SDV (the dispersion of V̇_A) (33). The majority of studies in Table 1 report similar log SDV and log SDQ values, the exceptions being rat, rabbit, sheep, and giraffe (that is, the smallest, a mid-sized, and the largest animal), which have much higher values. Note that, although the natural posture of all of the listed non-human species is prone, data in Table 1 were acquired in supine, prone, and lateral-decubitus positions, and some studies report awake data, whereas animals were anesthetized in others. Both posture and anesthetization affect lung mechanics, hence some variability in the data is expected. However, no relationship between animal/lung size and any index of V̇_A/Q̇ matching is apparent. The relative consistency between healthy subjects across species is a strong indication that V̇_A/Q̇ distributions are not dependent on the size of the lung.

Table 1.

Typical metrics reported in MIGET studies, ordered approximately by animal size

	P(a-a)o2, Torr	Pao2, Torr	Shunt, %	Deadspace, %	Mean V̇/Q̇ of V̇	Mean V̇/Q̇ of Q̇	log SDV	log SDQ
Rat (1)	32.0 ± 4.0	87.0 ± 5.0	3.3 ± 1.3	13.0 ± 5.0	4.30 ± 0.60	1.40 ± 0.30	1.06 ± 0.11	1.06 ± 0.18
Rabbit (15)	12.9 ± 2.9		0.2 ± 0.2	45.0 ± 3.0			0.81 ± 0.06	0.95 ± 0.09
Dog (20)	22.8 ± 6.0	91.1 ± 8.4	2.8 ± 1.7	44.3 ± 5.5			0.36 ± 0.13	0.45 ± 0.14
Dog (78)	19.5	83.0	0.6	21.7.0			0.70	0.55
Pig (41) (young)	13.0 ± 1.0	91.0 ± 1.8		45.0 ± 1.4	1.13 ± 0.01	0.77 ± 0.03	0.58 ± 0.02	0.66 ± 0.05
Sheep A (17)		79.1 ± 9.7	0.7 ± 0.6	43.6 ± 9.5	1.76 ± 1.93	0.39 ± 0.08	1.29 ± 0.78	0.66 ± 0.17
Sheep B (17)		83.3 ± 9.7	1.4 ± 1.0	44.1 ± 11.2	1.51 ± 2.26	0.39 ± 0.07	1.04 ± 0.65	0.66 ± 0.12
Sheep (65)		101.0 ± 6.5	0.4 ± 0.5	33.9 ± 7.0	3.35 ± 1.41	0.96 ± 0.21	1.40 ± 0.56	0.76 ± 0.14
Human (80)	9.3 ± 5.4	92.0 ± 4.2	0.0	41.7 ± 3.2	1.03 ± 0.06	0.78 ± 0.12	0.33 ± 0.06	0.43 ± 0.14
Human (60)	3.1 ± 2.0	99.0 ± 2.0					0.40 ± 0.03	0.38 ± 0.03
Human (27)	10.5 ± 9.0	93.9 ± 12.8	0.5 ± 1.0	34.8 ± 14.1				0.67 ± 0.28
Horse*(trotter) (54)	0.0 ± 2.5	93.8 ± 2.2	0.9 ± 0.2		1.29 ± 0.09	1.16 ± 0.08	0.31 ± 0.02	0.32 ± 0.03
Horse† (18)	12.4 ± 1.2	100.6 ± 2.4	0.28 ± 0.09				0.38 ± 0.02	0.36 ± 0.02
Horse (46)		95.0 ± 4.0	1.0 ± 0.2	68.0 ± 6.0‡				0.28 ± 0.04
Giraffe (55)		70.0		33.0			1.02	1.07

Data from normal controls (at rest) were selected from each study, except for studies in horse, where at-rest data were typically not available (the slowest animal speed was instead selected). *Walking. ^†Short duration gallop. ^‡Dead space here is combined with high V̇/Q̇ (defined as 10 < V̇/Q̇ < 100).

A limitation of MIGET is that is does not provide spatial information. A direct, but invasive, way of obtaining spatial data is by inhalation or injection of fluorescent aerosols or microspheres into the airways and pulmonary circulation, respectively. These microscopic particles can be assumed to distribute in proportion to flow, and so can be used to assess the spatial correlation of V̇_A and Q̇. This method has been used to study (among others) rat (24, 62), goat (50), dog (9), and sheep (49). Microsphere studies are destructive and therefore are limited to animals, and so non-invasive (or less-invasive) imaging-based methods are also used, including positron emission tomography (PET) (48, 53, 75), computed tomography (e.g., using tracer gases) (42), and single-photon emission computed tomography (SPECT) (56, 57). Microsphere and imaging methods produce data that are quite different from MIGET, and this is reflected in the metrics that are typically derived from them, some of which are only applicable to spatially distributed data. The coefficient of variation (COV) of V̇_A, Q̇, and V̇_A/Q̇, and the correlation between V̇_A and Q̇ (typically Pearson’s R for a linear regression) are those most frequently reported. Although there is a trend toward standardization of reporting of V̇_A/Q̇ metrics, not all studies across species are directly comparable due to reporting and methodological differences. Typical COVs are on the order of ~40%, but it is difficult to compare between animals (or studies) because COV depends on the size of the regions that are sampled, which depends on the spatial resolution of the technique employed to quantify V̇_A and/or Q̇. Correlation between V̇_A and Q̇ is quite consistent in large animals. Microsphere studies have found R of ~0.9 in pigs (3), 0.81 in goats (50), and ~0.7 in sheep (49). Lower correlation (R = 0.49) has been found in rats when standard random sampling is used (62), but careful anatomical sampling at the near-acinar level gives R = 0.82 (24), which is consistent with the larger animals. Similar correlations have been found using PET in dogs [R = 0.69 prone and 0.81 supine for correlation of V̇_A and Q̇ per unit gas content, in perfused units only (75)].

Mechanisms for V̇_A/Q̇ Matching

Gravity can affect the distributions of V̇_A and Q̇ in several additive ways (12, 66). Deformation of the lung under its own weight increases the density of capillaries in the dependent tissue, as well as increasing the compliance of the dependent tissue. The tissue compliance is the change in volume that results from a given change in transpulmonary pressure (which is the difference between pleural pressure and air pressure). Note that compliance is the inverse of elasticity (the change in pressure for a given change in volume). The gravitationally induced gradient in compliance contributes to a preferential distribution of ventilation, with the more compliant lung (basal regions when upright) undergoing a larger volume change than the less compliant lung (apical regions when upright). Gravity also acts on the weight of the blood internal to the pulmonary circulation, influencing its distribution through the larger vessels and the balance of blood and air pressures at the capillary level that determine the capillary flow (12). It used to be thought that gravity was the primary mechanism determining the V̇_A and Q̇ distributions and therefore their matching, but experimental and imaging studies have suggested that non-gravitational factors must play a major role. In fact, some studies suggest that gravity accounts for only up to half of the measured heterogeneity in V̇_A (45, 53) or Q̇ (26, 52, 59). Other mechanisms that have been suggested important are the “matched” geometries of the airways and arteries (2, 25), and active control (including hypoxic pulmonary vasoconstriction and hypercapnic bronchodilation). However, the latter has been suggested to not contribute significantly (22) or to make a small contribution (5) to V̇_A/Q̇ matching under baseline conditions in healthy subjects.

The conducting airway tree in mammals is “matched” by an accompanying arterial tree that branches in concert with the airways to supply the same regions of tissue. Some have speculated that this anatomical matching could provide the simplest explanation for V̇_A and Q̇ to be well-matched (23), and—if correct—it would also explain the similarity of V̇_A/Q̇ distribution regardless of animal size, and the lack of a complete inversion of V̇_A and Q̇ gradients with an inversion of posture. However, our recent work using a model constrained by basic physical laws (37) showed that, in the supine adult human (i.e., the posture most frequently examined in imaging studies), matching of V̇_A/Q̇ cannot be explained by matched airway and artery geometries. The model that was used for this evaluation is an integration of our previous models of airway and blood vessel geometries (7, 70), soft tissue mechanics (68), ventilation (66) and perfusion distributions (12), and steady-state gas transfer (39). The geometries of the airway and pulmonary vascular models consist of imaging (computed tomography)-based large airways/vessels, with additional branches generated using a volume-filling branching algorithm (7, 70). This provides morphometrically consistent one-dimensional (1D) branching networks (with associated diameter information) for the conducting airways and accompanying pulmonary vessels down to the level of the pulmonary acini; these are spatially distributed within a three-dimensional (3D) model of the lung volume. The airway and vascular tree models are tethered to a model for lung soft tissue mechanics (68), which assumes that the tissue is a compressible, nonlinearly hyperelastic material that undergoes large deformations (i.e., volume and/or shape changes) during breathing or a change in posture (i.e., due to the weight of the lung and the direction of gravity). The model is constrained to remain in contact with a “chest wall” against which the lung is free to slide. The tissue mechanics model predicts the displacement of the airways and vessels as the tissue moves, the local tethering pressures (that act on the airways and vessels), and acinar volume. The ventilation model (66) uses an equation at each acinus (or larger units of tissue) that represents the nonlinear relationship between tissue volume and compliance, along with equations for airway resistance and flow conservation, to predict the distribution of ventilation (and therefore V̇_A). Because the ventilation model includes the effect of gravitational deformation on acinus volume and a nonlinear pressure-volume relationship for the tissue, it predicts regional ventilation behavior similar to the classic “onion-skin” model of Milic-Emili et al. (51). Under normal tidal breathing conditions, the model correctly predicts that the distribution of ventilation is strongly dependent on the tissue compliance with a small contribution from the resistance of the airways (66). Q̇ is approximated using a steady-state blood flow model in the full pulmonary circulation (the arteries, capillaries, veins) to calculate Q̇ at each acinus (12). The model assumes Poiseuille flow with gravity acting on the blood in the larger vessels, combined with Fung and Sobin’s classic “sheet flow” model in recruitable and distensible pulmonary capillary sheets that are configured within a ladder-like geometry for the intra-acinar arteriole-capillary-venule pathways (10). The resultant prediction of V̇_A/Q̇ at each acinus can be used with a steady-state model of gas transfer (39) to predict the regional and systemic arterial partial pressures of oxygen. To evaluate the contributions of matched structure and other mechanisms associated with gravity to V̇_A/Q̇ matching, we considered artificial scenarios where various mechanisms were switched on or off. We considered tissue deformation (of a tissue with uniform specific compliance), hydrostatic effects (the weight of the blood, the presence of the pleural pressure gradient), and the resistance of the branching structures.

FIGURE 1 shows the human model from Kang et al. (37) and acinar V̇_A/Q̇ in transverse sections under four different scenarios: 1) with structure, hydrostatics, and gravitational deformation (“full model”); 2) with no tissue deformation; 3) with only tissue deformation; and 4) with zero gravity. The branching airway and vascular trees contributed the majority of iso-gravitational heterogeneity in V̇_A and Q̇ in this model with uniform tissue compliance, but they did not contribute to V̇_A/Q̇ matching: in our study, gravity was the determining mechanism. We found that, when structure was effectively removed by randomizing V̇_A and Q̇ within iso-gravitational sections, the correlation between V̇_A and Q̇ was reduced only minimally. We further note that, in the intact lung, we expect that normal variation in tissue compliance would contribute far more significantly to V̇_A heterogeneity than the airway resistance.

The adult human has a mid-sized lung compared with others in Table 1 but with more symmetrical shape and branching than typical laboratory animals (non-primates). It is possible that increased branching asymmetry could be important for V̇_A/Q̇ in other species. We also suggested (37) that tree matching could be more important (gravity less important) in the neonatal lung or small laboratory animals, but this has not been tested.

A Theoretical Examination of Mouse and Dog

To understand how species differences in lung size could contribute to V̇_A/Q̇ matching, here we address some basic theoretical considerations. The distributions of both V̇_A and Q̇ are clearly dependent on the branching structure of the airways, arteries, and veins (albeit with far less sensitivity in the airways than vessels). However, in the intact lung, the contribution of resistance to flow is interdependent with the compliance of the alveolar tissue at the distal ends of the airway tree. The airways and vessels contribute directly to the distributions of V̇_A and Q̇ via their resistance, where resistance depends on 1) their size and 2) the physical properties of the fluid that is flowing within them. For example, if we assume a Poiseuille resistance, R_P, in each conducting airway and blood vessel, then $R_P=8\mu L/\pi r^4$, where μ is the viscosity of fluid in the airway or vessel, and L and r are airway or vessel length and radius, respectively. This means that to achieve a perfectly uniform V̇_A/Q̇ distribution, we would require a lung with exactly matched branching structure and identical change in dimensions during ventilation and perfusion, as well as the absence of gravity. Even in the absence of gravity, the compliant airways and blood vessels change in dimension in response to transmural pressure (Ptm; the difference between air or blood pressure internally, and tethering pressure from the surrounding tissue externally). Any difference in airway and arterial wall radius, compliance, or Ptm will therefore result in a different resistance of the anatomically matched airways and vessels. The viscosity of air and blood differ ~100-fold (air ~2 × 10⁻⁵ Pa·s, blood ~3 × 10⁻³ Pa·s). On top of this, the compliant tissue distal to the major airways has an influence on air flow distribution, and the capillary vessels tethered to this tissue have an influence on blood flow distribution. So, even if the vessel dimensions were exactly the same as the airway dimensions, each vascular pathway is ~100 times more resistive to flow than the corresponding airway pathway. This immediately implies a far greater sensitivity of Q̇ distribution to structure than V̇_A distribution (relative to the influence of other factors, such as compliance), since resistance of the airways is much smaller than that of the blood vessels. Resistance is inversely proportional to the fourth power of radius. It therefore makes physical sense that V̇_A and Q̇ distributions in smaller animals could be relatively more sensitive to airway and blood vessel size.

To shed further light on this, we consider as examples the models of Clark et al. (12) and Swan et al. (66) applied in representative geometries obtained from a small rodent (mouse), and a well-studied species with lungs closer to human dimensions (dog). Geometric models of the lungs, lobes, blood vessels, and airways were created for the two animals (7, 73), with airways, arteries, and veins to the acinar level. The models were based on volumetric CT of normal dog lung obtained during static breath hold at 5 cmH₂O (36) and micro-CT of mouse during breath hold at 25 cmH₂O and scaled to a representative FRC of 0.3 ml. Dimensions of major airways and blood vessels were measured from imaging. The dog model has 24,964 acini, and the mouse model has 3,705, which is consistent with experimental estimates in each species (24, 63, 64). In dog, cardiac output was set to 4.9 l/min and tidal volume at 375 ml, respiratory rate was set to 15 breaths/min. In mouse, the corresponding boundary conditions were cardiac output of 17 ml/min, tidal volume of 0.15 ml, and respiratory rate of 120 breaths/min. The anatomical models of each species were embedded in the finite element model of lung tissue deformation that was previously described (68), assuming that specific compliance of the lung is the same in both species (where specific compliance is the compliance divided by the lung volume). V̇_A and Q̇ models were coupled to the tissue deformation model and solved as previously described for humans (12, 66).

Human and dog airway and vessel radii range from ~0.1 (peripheral) to 10 mm (proximal), whereas the equivalent diameters in mouse or rat are ~0.01–0.1 mm, and so the per-vessel resistance to flow is far higher in these small mammals. It could therefore be expected that airway and vascular resistance are more important determinants of both Q̇ and V̇_A distribution in small compared with large mammals. However, it has been (conversely) suggested that, because small mammals have fewer and shorter airways and blood vessels, the heterogeneity in their V̇_A and Q̇ is likely smaller (55). Without a computational model, it would be extremely difficult to assess whether the fewer number of vessels outweighs the contribution of their smaller size to heterogeneity. Similarly, the height of the lung (gravitational head) in dogs and humans is ~15–30 cm, whereas equivalent dimensions in rat or mouse are <2 cm. On this basis alone, one would expect gravitational influences to be more dominant in larger mammals. FIGURE 2 shows simulation of Q̇ in dog and mouse lung models in 1) zero gravity at FRC with a constant 5 cmH₂O elastic recoil pressure, 2) with hydrostatic effects of gravity only (no tissue deformation, but a linear gradient in elastic recoil pressure and including the weight of blood internal to the vessels), and 3) with combined hydrostatics and tissue deformation (68). The dog model is consistent with previous models of Q̇ distribution in humans: vascular asymmetry contributes to heterogeneity and to decreases in Q̇ in the extremities; the hydrostatic pressure gradient acts 1) directly on blood to drive it preferentially to the dependent lung and 2) contributes to the “zonal model” (87) constraint at the capillary level; and deformation of the lung tissue establishes a gravitational gradient of vessel density [also known as the “Slinky” effect (34)], enhancing the Q̇ gradient (12, 69). Simulations in mice differ considerably. The vasculature of the mouse is much more highly resistive than that of the dog, which increases Q̇ heterogeneity, and the considerably smaller gravitational head of the mouse lung means that hydrostatic and gravitational effects are negligible. The Q̇ distribution in the mouse lung in FIGURE 2 is thus almost entirely determined by its vascular structure.

FIGURE 3 shows estimation of V̇_A in dog and mouse in 1) zero gravity with a uniform distribution of elastic recoil pressure (5 cmH₂O) at FRC, 2) with a linear gravitational distribution of tissue compliance but no tissue deformation, and 3) a complete model with tissue deformation under gravity included. Again, the dog and mouse models show different mechanisms determining their V̇_A distributions. As with Q̇ in both species, airway path asymmetry contributes to heterogeneity of resistance and therefore V̇_A, and to decrease in V̇_A in the extremities; however, this is to a lesser extent than Q̇ because air is less viscous than blood. Variation in acinus compliance induces a gravitational gradient in V̇_A, and deformation of the tissue accentuates this gradient (66). Again, the relative contribution of mechanisms determining V̇_A distribution in the mouse are predicted to be different to those in the dog, with airway structure dominating in the mouse because of its much smaller size (higher resistance).

Although V̇_A /Q̇ matching is more gravitationally driven in the dog model [and in human models (37), consistent with West (86)] and structurally driven in the mouse model, the models have a remarkably similar distribution of V̇_A/Q̇ (FIGURE 4). Thus, although this theoretical analysis suggests that the relative contributions of mechanisms are different, the V̇_A/Q̇ matching and gas exchange function are very comparable, which reconciles well with the experimental evidence that V̇_A/Q̇ matching is largely independent of animal size.

FIGURE 4.

V̇_A/Q̇ distributions in dog and mouse lung models

V̇_A/Q̇ distributions in dog (A) and mouse (C) lung models. Although the mechanisms driving V̇_A/Q̇ matching do not have the same relative influence between the species, there is remarkable similarity in the distribution of V̇_A/Q̇ through the lung models, and so the relative distribution of each is not significantly different. These distributions can be formulated in the form of a standard MIGET log plot for dog (B) and mouse (C), and show distributions typical of those obtained experimentally.

The Implications

Approaching the question of the impact of size on function from the point of view of the physics that govern fluid flows and tissue deformation allows us to tease apart the contributions of gravity and structure to V̇_A, Q̇, and their matching. Gravity is still routinely taught to be the primary determinant of the V̇_A and Q̇ distributions and V̇_A/Q̇ matching, but data acquired over the past 30 or so years has strongly indicated that non-gravitational factors are also important. The theoretical considerations presented here suggest that V̇_A/Q̇ matching is dominated by different mechanisms depending on the size of the animal in question. In particular, the smaller the animal, the more likely that the shared anatomical branching structure of the pulmonary airways and blood vessels determines V̇/Q̇ matching. This may be of considerable importance when translating results of pre-clinical and physiological studies to the human context.

The question of size is not limited to comparisons between species: we speculate that matched structure will be more important in the very young human lung compared with adult; however, this is entirely untested. Adult physiological data and treatment strategies do not necessarily translate to children or infants (4, 19, 40), which might be due in part to the immaturity of their alveolar structure (29, 30) but might also be influenced by the mechanisms of V̇_A/Q̇ matching that relate to size. There is a wealth of imaging data describing V̇_A/Q̇ matching in the adult lung, but the relevance of this data to young children is understudied. This is understandable, since young children are often uncooperative, and there are fewer justifiable techniques for imaging a healthy child’s lung than there are in adults (21, 40). MRI techniques to estimate V̇_A/Q̇ that have been tested on adults also hold promise for imaging infants and children (28). Translation of these methods to estimate V̇_A/Q̇ in the much smaller human lung would be enhanced by an understanding of the relative importance of the underlying mechanisms.

The human infant lung is larger than that of the mouse but smaller than that of the dog (the two species considered here); if the theoretical analysis discussed here holds true with lung size, then the infant lung should see greater influence of matched tree branching than the adult lung but more influence from gravity than in the mouse. However, infants also have more compliant chest walls than adults, which adds additional complexity to understanding the mechanisms that are most important in their V̇_A/Q̇ matching. Some aspects of the very young lung can be considered to be like a “small adult”: for example, the conducting airways and accompanying vasculature are all present at birth (16, 29). However, although their branching geometry is essentially the same as in adults, their size could be an important contributor to overall lung function: as in small animals, vascular and airway resistance would be a stronger determinant of V̇_A/Q̇ distributions in an infant than in an adult lung, and this could impact on diagnostic tests and drug delivery strategies in early life.