## Abstract

Early measurements of autopsied lungs from infants, children, and adults suggested that the ratio of peripheral to central airway resistance was higher in infants than older children and adults. Recent measurements of forced expiration suggest that infants have high flows relative to lung volume. We employed a computational model of forced expiratory flow along with physiological and anatomic data to evaluate whether the infant lung is a uniformly scaled-down version of the adult lung. First, we uniformly scaled an existing computational model of adult forced expiration to estimate forced expiratory flows (FEF) and density dependence for an 18-mo-old infant. The values obtained for FEF and density dependence were significantly lower than those reported for healthy 18-mo-old infants. Next, we modified the model for the infant lung to reproduce standard indexes of expiratory flow [forced expiratory volume in 0.5 s (FEV_{0.5}), FEFs after exhalation of 50 and 75% forced vital capacity, FEF between 25 and 75% expired volume] for this age group. The airway sizes obtained for the infant lung model that produced accurate physiological measurements were similar to anatomic data available for this age and larger than those in the scaled model. Our findings indicate that the airways in the infant lung model differ from those in the scaled model, i.e., middle and peripheral airway sizes are larger than result from uniform downscaling of the adult lung model. We show that the infant lung model can be made to reproduce individual flow-volume curves by adjusting lumen area generation by generation.

- flow volume
- airway mechanics
- maximal expiratory flow-volume curve

early measurements of central and peripheral airways resistances of autopsied lungs from infants, children, and adults found that the ratio of peripheral to central airway resistances was higher in infants than in older children and adults (7). This finding of proportionately greater peripheral airway resistance in the infant has often been proposed as an explanation of why infants with lower respiratory illnesses have more severe respiratory symptoms than older children and adults. However, on the basis of anatomic measurements of airway size from autopsy specimens of infants, Hislop et al. (6) suggested that the infant airway tree is “a miniature version of the adult” and that “this pattern persists during post-natal growth.” During the past two decades, forced expiratory flows have been measured in infants, initially by using partial expiratory flow volume maneuvers and more recently with full maneuvers (4, 8, 16). These studies have indicated that infants have higher forced expiratory flows relative to the size of their lungs than adults and that infants have values of density dependence of forced expiratory flow that are similar to those for older children and adults (3).

A computational model has previously been developed to analyze adult forced expiratory flow-volume curves (9-12). This was based on available data about airway size and compliance in adults. Until now, no model has existed for studying forced expiratory flow in infants. We were interested in finding what changes to the adult model would be necessary for an adequate model prediction of infant flows. The specific objectives of our study were first to test the hypothesis that shrinking the adult model uniformly accurately predicts forced flows and density dependence in infants. In the event that this scaling does not adequately explain the forced flow measurements obtained from infants, the second objective was to modify the model parameters and obtain an infant model that accurately predicts forced flows and density dependence in infants. The distribution of airway properties needed for the infant model can be compared with airway sizes reported by Hislop et al. (6) as well as with the distribution in the adult model. The development of an infant model also offers the potential to infer airway properties of an individual infant from measurements of forced expiratory flows.

## METHODOLOGY

The computational model we use for forced expiratory flows has previously been described in detail (12), but the main points of the model are briefly summarized here. This model is based on Weibel's model A (17), and there are 17 generations of dichotomously branching airways. The mechanical behavior of each generation is specified by an area-pressure curve normalized to the maximal value of lumen area (*A*_{i}^{*}). Each generation has a specified curve; a representative curve, that for *generation 8*, is illustrated in Fig. 1. Each curve is described by two hyperbolas matched for intercept and slope at a transmural pressure (P) equal to 0 cmH_{2}O; the shape of these curves is described by the intercept (α_{0}) and slope (α′_{0}) at P = 0, as well as two shape-changing constants (*n*_{1}, *n*_{2}). Similar equations are used to specify the pressure-volume curve of the lung.

A given tracheal flow is distributed evenly among the airways in each generation. The pressure distribution in the airway tree for this flow is calculated by integrating (from the alveolus) the expression for the pressure gradient along an airway to the next (proximal) junction and then solving the Bernoulli equation in the junction. The procedure is repeated to the end of the intrathoracic trachea. Flow is then increased, and the pressure integration is repeated for the new flow. Maximum flow is identified as either the flow for which flow speed at some point in the airways is within 0.2% of wave speed at that point or the pressure at the end of the trachea reaches a preset limiting value.

Our scaling of the adult lung to the infant lung requires that all structures in the lung change size uniformly; airway lengths must be multiplied by a scale factor of the cube root of the ratio of infant (i) to adult (a) total lung volumes (TLV) (TLV_{i}/TLV_{a})^{1/3}, and airway areas must be multiplied by a scale factor of (TLV_{i}/TLV_{a})^{2/3}. We chose to scale to an 18-mo-old infant for which published anatomic and physiological data exist (1, 6, 8). Infant total lung capacity was chosen as 800 ml with a tissue volume of 186 ml for a TLV of 986 ml (1). The adult model has a total lung capacity of 4,840 ml and tissue-plus-blood volume of 1,200 ml for a TLV of 6,040 ml. Thus the scale factor for length is 0.547 and for area is 0.299.

Maximal expiratory flow-volume curves were calculated from the scaled model for air and a mixture of 80% helium and 20% oxygen (heliox). Maximal flow was calculated at 18 values of forced vital capacity from 85 to 0% of expired vital capacity (VC_{e}). The sensitivity of the model to its parameters was assessed by making large variations (±50%) in the following parameters: *A*_{i}^{*}, α_{0}, and α′_{0} of each airway area-pressure curve at 0 cmH_{2}O. The analysis was performed by adjusting these parameters for airways divided into three zones: peripheral, middle, and central, corresponding to Weibel generations 16-8, 7-4, and 3-0, respectively (10).

To obtain a baseline infant model, bronchial lengths were kept at the scaled model lengths, whereas the airway cross-sectional areas (*A*_{i}^{*}) of the scaled model were adjusted generation by generation until the flow-volume curve obtained yielded values of forced expiratory volume in 0.5 s, forced expiratory flows after exhalation of 50 and 75% forced vital capacity, and forced expiratory flow between 25 and 75% expired volume that were very close to the reference values in Table 1.

## RESULTS

*Scaling of adult model.* The flow-volume curves for air and heliox generated from the scaled model are illustrated in Fig. 2; these curves are noticeably scooped at low lung volumes. The variables calculated from the flow-volume curve with air are much lower than the 50th percentile values for an 18-mo-old infant (Table 1) (8). The calculated flow-volume curve for heliox has higher flows than the calculated curve for air at lung volumes above 74% VC_{e} (Fig. 2). However, the calculated values for the density dependence of flow at 50% VC_{e} (DD_{50}) and at 75% VC_{e} (DD_{75}) are lower, and the point at which air and heliox flows become equal, the volume of isoflow (V_{isoV̇}), occurs at a higher lung volume than in infants of this age (Table 1) (2).

*Infant lung model.* The flow-volume curves obtained for air and heliox by use of the infant model (Fig. 3*A*) are similar in appearance to curves obtained in healthy infants. In addition, the values for V_{isoV̇}, DD_{50}, and DD_{75} calculated from this infant model are similar to the physiologically measured values from healthy infants (Table 1). The peripheral movement of the choke point as expiration progresses is also shown in Fig. 3*A*.

Isovolume pressure flow curves simulated with air were constructed with the infant lung model (Fig. 3*B*). Flow limitation, as indicated by a plateau in flow, was achieved at all lung volumes used. The onset of a plateau occurred at higher values of driving pressure (pressure drop from alveolus to the downstream end of the intrathoracic trachea) at higher lung volumes; however, the highest driving pressures required to achieve flow limitation were <40 cmH_{2}O.

Table 2 lists the airway areas vs. generation number for the adult model, the scaled model, the infant lung model, and anatomic values reported for 18-mo-old and 19-mo-old infants. The airway sizes obtained for the infant model are larger than those obtained for the scaled model but are similar to the anatomic values. These values are compared in Fig. 4, where the airway area vs. generation for the scaled model, infant lung model, and the raw anatomic data (as read from the published graph) are normalized to the adult values. The airway sizes for the middle and peripheral airways of the scaled model were smaller than both the airway sizes of the infant lung model and the anatomic data.

*Sensitivity of infant lung model.* Flow-volume curves obtained by adjusting the parameters in the infant lung model for the central, middle, and peripheral airway zones are illustrated in Fig. 5. These simulations illustrate that the model is much more sensitive to changes in *A*_{i}^{*} and the α_{0} than to changes in the α′_{0}. In addition, the effects on the flow-volume curve are similar for changes in *A*_{i}^{*} and α_{0}. Decreasing either the maximal airway area or the resting airway area at *P* = 0 cmH_{2}O decreases the forced expiratory flow, and their effects are most prominent in the central and mid airways. However, decreasing these parameters in the central airways produces a more flattened flow-volume curve at higher lung volumes, which is consistent with tracheomalacia, whereas the effect of decreasing these parameters in the mid zone produces a flow-volume curve similar to bronchopulmonary dysplasia, asthma, or cystic fibrosis (2, 5, 13-15).

The infant lung model was applied to physiological measurements obtained from two healthy 18-mo-old infants who had forced expiratory maneuvers obtained from the standard airway inflation pressure of 30 cmH_{2}O (8). The airway area for each generation was adjusted to obtain a visual fit to the measured flow-volume curves (Fig. 6). The infant lung model provided an excellent match to these curves.

## DISCUSSION

Our results indicate that uniform scaling of the adult lung to the volume of the infant lung produces forced expiratory flow-volume curves by using air and heliox with flows that are significantly lower than those obtained from physiological measurements in this young age group. The low predicted flows and the low density dependence from the scaled model result from airways that are too small relative to the lung volume. The pronounced scooping of the flow-volume curve (as well as the low values of density dependence) indicates narrow peripheral airways. However, increasing the size of the airways in the computational model to obtain forced expiratory flows and density dependence consistent with physiological data in infants removed scooping from the flow-volume curve and yielded airway sizes that were also consistent with anatomic data in infants. These findings suggest that infants have large airways relative to the lung volume they serve and that the lung does not grow uniformly from infancy to adulthood.

We obtained our infant lung model by adjusting only the *A*_{i}^{*} parameter in the scaled adult model so that the flow-volume curve we obtained matched the physiological reference values. It is interesting to note that the infant values of *A*_{i}^{*} in the peripheral airways, although less than in the adult model, are not dramatically less. For instance, in *generation 16*, the adult model has 180 cm^{2}, whereas in our infant model the corre sponding value is 133 cm^{2} and the value given by scaling is 53.8 cm^{2}. It is apparent from Fig. 5 that the model is most sensitive to maximal *A*_{i}^{*} and the resting area of the area-pressure curve at 0 cmH_{2}O (α_{0}). The sensitivities of the model to these two parameters are similar; hence, generating a model to produce a maximal expiratory flow-volume curve can be done by adjusting only one of these parameters; we chose to use *A*_{i}^{*} with the same normalized pressure area curves in all models.

The isovolume pressure-flow curves in Fig. 3*B* demonstrate plateaus, which are in qualitative accord with the data obtained in healthy infants (4). Forced maneuvers are generated in healthy infants by inflating a jacket around the infant's chest and abdomen that applies pressures between 80 and 120 cmH_{2}O to the body surface. Because it has been estimated that ∼50% of this applied pressure may be transmitted to the airway, the transpulmonary pressure generated during the forced expiratory maneuver may range between 40 and 60 cmH_{2}O. Our model results support the conclusion drawn by Feher et al. (4) that adequate jacket pressure is transmitted to the lungs to achieve flow limitation from 40% VC_{e} to full expiration. The isovolume pressure-flow curves demonstrate that at low lung volumes the plateau in flow is reached at values of driving pressure much less than those required for achieving wave speed limitation. This is because the airways, especially those in the periphery, are so narrowed that small increases in flow require large increases in driving pressure to overcome the viscous pressure dissipation. That is, flow at low lung volumes is effectively limited by dissipative loss mechanisms, as is the case with the adult model (12). The peripheral movement of the flow-limiting segment as expiration progresses is similar in this model to the earlier adult model.

The predicted values for the density dependence of maximal flow by the infant lung model are comparable to but greater than the reported physiological values obtained in this age group, whereas the model value of the V_{isoV̇} is very similar (Table 1). The greater than observed values of density dependence suggest that the model values of *A*_{i}^{*} for peripheral airways may be somewhat larger than occurs in infants.

We adjusted the infant lung model to match individual forced expiratory flow-volume curves obtained from two 18-mo-old infants with different forced expiratory flow-volume curves. The model provided satisfactory fits to both and generated different area distributions. These results must be approached with considerable caution. We have used the same normalized area-pressure curves in the infant model as were used in the adult model. No data exist, as far as we are aware, on which to make any other assumption. These curves have no volume dependence; the lumen area changes solely as a function of transmural pressure. The model airways follow a symmetrical dichotomous branching pattern, whereas real airway trees do not. The area distribution, almost certainly, is not unique. Variation of other parameters or combinations of parameters may well have achieved the same result. We did not investigate this possibility. Although it is not reasonable to try to identify an airway generation in a real lung with one in the model, the interpretation may be valid in terms of central, middle, and peripheral airways. In summary, using a computational model of forced expiratory flow, along with physiological and anatomic data, we have demonstrated that the infant lung is not a scaled-down version of the adult lung. We have developed a computational model that predicts lung function indexes that match those for an 18-mo-old infant that may prove to be useful in obtaining airway area information from flow-volume curves in infants.

## GRANTS

This research was funded by National Heart, Lung, and Blood Institute Grant 54062.

## Footnotes

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- Copyright © 2004 the American Physiological Society