INTRODUCTION

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INTEREST IN THE MECHANISMS by which airway inflammation produces airflow limitation in asthma (11) and the role of intrinsic airway disease vs. loss of recoil as a predictor of surgical response in emphysema (17) has contributed to a recent renewal of interest in lung mechanics. The concept of pulmonary resistance (RL) and dynamic compliance (Cdyn) or its reciprocal elastance (Edyn) implies that the pressure loss across the lung can be divided into a dissipative component in phase with the flow and into an elastic component in phase with the volume (6, 15). Classically, the dissipative component, or resistance, is considered to occur between the airway opening and the alveoli due to frictional pressure losses in the flow and convective acceleration, and the elastic component is considered to occur between the alveoli and the pleural surface (3, 8, 15, 20). It is known that this model is an approximation and that the pressure losses in the airways are different on inspiration and expiration, are dependent on lung volume, and are nonlinear functions of flow. Pulmonary compliance is also a function of volume, and a substantial part of total pressure difference occurs between the alveolar and pleural pressures and is caused by lung viscoelastic and viscoplastic behavior (5, 11). Nevertheless, measurements of RL and pulmonary compliance during spontaneous breathing are sensitive indexes of lung mechanics. However, with severe airway obstruction, maximal expiratory flow (E) in the normal tidal breathing volumes is inadequate for the subjects' ventilatory needs, and subjects develop dynamic hyperinflation (9) and intrinsic positive end-expiratory pressure (PEEP) (1). When this occurs, fitting RL and Cdyn by least squares from an entire breath produces a falsely low Cdyn. If separate inspiratory and expiratory RL (RL_i and RL_e, respectively) are determined, RL_i is overestimated and RL_e is underestimated. In this study, we present a new algorithm for analyzing quiet breathing that computes compliance and RL_i values which are not significantly different from these obtained from analyzing only the inspiratory portion of the breath and that detects a volume dependence of RL_e which is highly correlated with E limitation.

	METHODS

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Seven asthmatic subjects, seven healthy subjects, and 19 subjects with chronic obstructive pulmonary disease (COPD) caused by emphysema were studied. The asthmatic and normal subjects were included in a previous study (12). The subjects' anthropometric data are shown in Table 1. One normal subject and one asthmatic subject were moderate smokers. The illnesses of asthmatic and COPD subjects were diagnosed on the basis of the criteria of the American Thoracic Society (2). All subjects were clinically stable at the time of the study, and the asthmatic subjects had stopped use of bronchodilators for 24 h before tests were conducted. The protocol for normal and asthmatic subjects was approved by the Institutional Review Board, and each subject gave written consent. All COPD subjects had ceased smoking 6 mo before the study, and all were being evaluated for lung volume reduction or lung transplantation.

Measurements. Standard spirometry was obtained before the study. Lung mechanics were measured with the subjects seated in an air-conditioned, pressure-corrected, volume-displacement plethysmograph. The frequency response of this plethysmograph is adequate up to 10 Hz. Volume measurements were obtained by measurement of the pressure difference across a pneumotachograph located in the wall of the plethysmograph with an MP45 Validyne pressure transducer (±2 cmH₂O). To obtain volume, we then integrated and corrected this signal for the phase lag caused by the pneumatic capacitance of the plethysmograph. The characteristics of this type of plethysmograph are described elsewhere (10, 14). Flow was measured by a no. 3 Fleisch pneumotachograph connected to an MP45 Validyne pressure transducer (±2 cmH₂O). Transpulmonary pressure (Ptp) was measured by a 10-cm-long thin latex balloon positioned in the lower one-third of the esophagus, 38-45 cm from the nostril, and connected to a Statham 131 pressure transducer (5 psi). The balloon was filled with ~1 ml of air. Ptp was estimated as the difference between mouth and esophageal pressure. Placement of the balloon was considered correct if Ptp remained constant while subjects made gentle respiratory efforts against a small orifice. Oral pressure changes confirmed respiratory efforts. Signals of flow, volume, and Ptp were recorded on a strip-chart recorder (HP-7758A) and were digitally collected with a computer (DEC11/73) at a sample rate of 50 or 100 Hz for subsequent analysis. RL and Edyn were both estimated from data collected from at least eight breaths. Data from all irregular breaths, sighs, and swallows were discarded before analysis. Methods 1-4 for determination of RL and Edyn on a breath-by-breath basis are described below. Software was written and developed in MATLAB to compute the estimated parameters for each of the described methods (9a). The beginning of each breath is forced to zero volume to account for the integration drift. The estimated parameters are computed in a multiple linear regression by the method of least squares.

Method 1. Whole-breath RL. This method examines a complete breath from the start of inspiratory flow (I) to the end of E. The start of I is determined by searching back from a definite inspiration to the first point that is >0. End E is taken as the last point <0 in the expiratory phase of the breath. After the zero flow points are determined, the data are fit to the equation

(1)

where PL_FRC is Ptp at functional residual capacity (FRC), V is volume relative to FRC, and is the flow in all methods.

Method 2. RL of two half breaths. This method examines each breath, split into an inspiratory and an expiratory component. The end of I is determined as the last point >0 in the breath. Start of E is determined as the first point <0. After determining the zero points, the data are fitted to the equations

(2)

(3)

where Edyn_i is the dynamic elastance during inspiration. For Eq. 3, Edyn_e is the dynamic elastance during expiration.

Method 3. Whole-breath RL_i + RL_e. This method examines the whole breath with one elastance term and a separate RL_i and RL_e. After determining the zero-flow points, the I is forced to zero during expiration, the E is forced to zero during inspiration, and the data are fitted to the equation

(4)

Method 4. Whole-breath RL_i + RL_e + RL'_e . This method examines the whole breath, as in method 3, with the addition of a RL'_e term. This additional term will account for the increasing resistance during expiration in subjects with dynamic hyperinflation. The RL'_e term measures an interaction between volume and resistance during expiration. After determining the zero-flow points, the data are fit to the equation

(5)

For comparison, a zero-elastance method is also included. This method looks only at the inspiratory portion of the breath. A pressure-volume (PV) relationship is determined between the points of zero flow at the beginning of inspiration and end of inspiration. This elastance volume is then subtracted from the inspiratory pressure to give a pressure-flow curve. This leads to the equation

(6)

Again, the least squares method is used to determine the RL_i, and the intercept term is forced to zero by reflecting the data around the intercept.

Inhalation challenge. Subjects from both the normal and asthmatic groups were requested to undergo bronchial challenges with methacholine (MCh). After diluent, MCh was delivered in doubling concentrations through a dosimeter (Rosenthal) with a manually triggered solenoid valve that was electronically controlled to deliver compressed air at 20 psi for 1 s. Each dose of aerosol was delivered during five breaths taken from FRC to total lung capacity. The starting concentrations of agents were 0.125-0.5 mg/ml for asthmatic subjects and 1-5 mg/ml for normal subjects. The challenge ended when maximal flow at 50% vital capacity (VC) was decreased by 60% or at a concentration of MCh of 320 mg/ml.

	RESULTS

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A typical breath from three subjects is displayed in Figs. 1-3. Each of these figures contains four subplots for the same breath of one subject as determined by using the different methods of estimation for the RL and Edyn. Figure 1A shows data from a 58-yr-old normal male, and Fig. 1B shows data from the same subject after a MCh challenge. Figure 2A is a typical breath from a 24-yr-old asthmatic male subject during an asymptomatic period, and Fig. 2B is the same individual after a MCh challenge. Figure 3 shows data from a 52-yr-old female with severe hyperinflation and airway obstruction that were predominantly caused by emphysema.

View larger version (29K): [in this window] [in a new window]   Fig. 1.   Pressure-volume relationship in normal subject. A: baseline; B: after maximal dose of methacholine (MCh). For each plot, y-axis is transpulmonry pressure (Ptp; in cmH2O) and x-axis is volume (in liters) relative to functional residual capacity (FRC). RL, pulmonary resistance; RLi, RLe, inspiratory and expiratory RL, respectively; RL'e, volume interaction term. Top left: whole-breath method (method 1); top right: half-breath method (method 2). Bottom left: whole-breath method RLi + RLe method (method 3); bottom right: whole-breath RLi + RLe + RL'e method (method 4). , Recorded data; solid line through the , estimated pressure fit; * , zero-flow points; dashed line, connects zero-flow points at start of inspiration to end of inspiration. Thick solid line, estimated elastance from each method, as described above. For the half-breath method, thick solid line represents elastance of inspiration; dotted line represents elastance of expiration. In this normal individual, all methods fit the data well, and elastic pressure computed from dynamic elastance does not differ greatly from line connecting zero-flow points. After MCh (B), amplitude of pressure-volume loop doubles. Two elastances determined from half-breath method are quite different. Inspiratory pressure-volume relationship from half-breath method and from other three methods closely approximates line connecting zero-flow points. Dynamic elastance fit is still quite good.

View larger version (33K): [in this window] [in a new window]   Fig. 2.   Pressure-volume relationship in asthmatic subject. A: baseline; B: after maximal dose of MCh. Symbols are same as in Fig. 1. A: dynamic elastance during inspiration in method 2 and methods 1, 3, and 4 is very similar to dashed line connecting zero-flow points. Computed elastic pressure-volume relationship is displaced toward expiratory side of loop in single-resistance method 1 but passes through zero-flow points in method 3 from which RLe is greater than RLi. B: computed elastic pressures are quite different during inspiration and expiration with the half-breath method 2. Elastic pressure with method 3 is significantly different from line connecting zero-flow points, causing a higher RLi and lower RLe. Method 4 fits data well. Elastic pressure computed from method 4 differs slightly in this breath from line connecting points of zero flow, but it was not different when averaged across several breaths. Ptp at FRC is increased, because this subject had substantial increase in FRC during MCh-induced bronchoconstriction.

View larger version (35K): [in this window] [in a new window]   Fig. 3.   Pressure-volume relationship in patient with emphysema. Symbols are same as in Fig. 1. Methods 1 and 3, while fitting to the pressure-volume data reasonably well, overestimate width of loop at high lung volumes and underestimate it at low lung volumes. Elastance is much greater than slope of dashed line connecting zero-flow points because of reduced estimate of elastic recoil at FRC. Data from inspiratory half-breath method fit data well. Expiratory half-breath method fits pressure-volume data better than methods 1 or 3, but elastance is much greater than from inspiratory half breath, predicting a reduced elastic recoil at FRC. Method 4, with volume dependence during expiration, fits data quite well during inspiration and expiration and predicts elastic pressure-volume relationship similar to inspiratory half-breath method.

Summary data are given in Table 2 and Figs. 4 and 5. The RL_i computed by the zero-elastance method is underestimated compared with computation by method 2. The relationships between RL_i from the inspiratory half breath (method 2) to the RL of method 1 and RL_i of methods 3 and 4 are shown in Fig. 4, A-C, respectively. The relationships between inspiratory elastance from the inspiratory half breath (method 2) and elastance from methods 1, 3, and 4 are shown in Fig. 5, A-C, respectively.

View larger version (13K): [in this window] [in a new window]   Fig. 4.   Resistance of each subject by other methods compared with inspiratory half-breath method. , Normal subjects; *, normal subjects after MCh; , subjects with chronic obstructive pulmonary disease (COPD); , asthmatic subjects; , asthmatic subjects after MCh. Dashed line is line of identity. Both x- and y-axes are in units of cmH2O · l1 · s. A: method 1 (whole-breath RL). B: method 3 (whole-breath RLi and RLe). C: method 4 (whole-breath RLi + RLe + RL'e).

View larger version (13K): [in this window] [in a new window]   Fig. 5.   Elastance of each subject by other methods compared with inspiratory half-breath method. A: method 1 (whole-breath RL). B: method 3 (whole-breath RLi and RLe). C: method 4 (whole-breath RLi + RLe + RL'e). Symbols are same as in Fig. 4.

In the normal and the asthmatic subjects before MCh, all methods gave similar results for both resistance and elastance. After MCh, the normal individuals whose resistance increased to >10 cmH₂O · l¹ · s and all the asthmatic subjects tended to have a lower total RL or RL_i by all methods other than the half-breath RL_i. In contrast, in normal and asthmatic subjects, the elastance values, as determined by methods 2 and 3, were fairly comparable, although the fit was best with method 4. Table 3 gives the mean R² for the fits obtained by each model in each group of subjects.

The COPD patients tended to have higher RL and dramatically higher elastance with methods 1 and 3 than with the half-breath method. Method 4 provides good agreement with the half-breath elastance. The RL_i tends to be lower than with the half-breath method. However, RL_i by method 4 agrees much better with the zero-elastance method (Table 2).

None of the normal or asthmatic subjects at baseline was flow limited, as determined by the partial flow-volume curve, and their values for RL'_e were small and variable. Normal subjects whose partial flows after MCh impinged on the control tidal breathing flow-volume relationship increased their FRC, as evidenced by significant decrease in inspiratory capacity, and they had substantial decreases in RL'_e, as shown in Fig. 6. Two of the asthmatic subjects had RL'_e at baseline of less than 5 cmH₂O · l² · s, and all subjects had decreases in inspiratory capacity (IC) and RL'_e after MCh. An increasing magnitude of RL'_e is associated with increasing dynamic hyperinflation, as shown by the correlation with decreasing IC.

View larger version (30K): [in this window] [in a new window]   Fig. 6.   Relationship between RL'e and dynamic hyperinflation in normal and asthmatic subjects; x-axis, additional RL'e term from method 4 for each subject; y-axis, %control inspiratory capacity for each subject. , Normal subjects; *, normal subjects after MCh; , asthmatic subjects; , asthmatic subjects after MCh.

	DISCUSSION

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The model of a constant RL and elastance is a useful approximation of the respiratory system properties which are sensitive to changes in lung mechanics (6, 15). Resistive pressure drop is close to the magnitude of cardiogenic oscillation in Ptp; therefore, the R² for normal subjects is lower than during bronchoconstriction. The R² by all methods was between 0.61 and 0.96 in normal subjects. In all others, the linear regression models reported in this study give R² values in excess of 0.80. Method 4, which has the most parameters to fit consistently, gave the highest values of R² (>0.95) during bronchoconstriction, so it would be difficult to get a substantially better fit by adding additional terms to address the known nonlinearities in the pressure-flow and PV curves (18). The use of regression analysis to fit an elastance for the entire PV in normal individuals yields the same data as the ratio of the difference in pressure and volume at points of zero flow but is less variable than the two-point method, which is more sensitive to cardiogenic oscillations in the pressure.

During airway obstruction, flow limitation causes varying nonlinear pressure-flow relationships which affect the estimate of elastance and the partitioning of RL_i and RL_e when using least squares curve fitting. We arbitrarily chose to use a regression equation fitted to the inspiratory half-breath as our standard for comparison rather than use the elastic PV relationship from the zero-flow method and fit a resistance to the pressure difference from that PV relationship. In the normal and asthmatic subjects before MCh, the derived elastic PV relationships were essentially the same as the line connecting zero-flow points (Figs. 1A and 2A). However, during severe bronchoconstriction in both the normal subjects and, more dramatically, in the asthmatic subjects, nonlinearities in the pressure-flow relationships (15) are accommodated by an elastance from the half-breath method, which may be similar to that derived by the two-point method, but a PV relationship is consistently displaced toward the expiratory side of the PV loop (Figs. 1B and 2B). Therefore, those normal subjects who had large increases in RL_i after MCh (and all asthmatic subjects after MCh) had an overestimate of their RL_i when calculated by the half-breath method (Fig. 4).

E limitation causes a very nonlinear pressure-flow relationship. One might expect that expiration would be best fit by a resistance like the Rohrer equation, in which pressure drop was proportional to both and squared (16). However, in severe airway obstruction, particularly in COPD patients in whom RL_i was relatively low and maximal was very low, the area of the loop which represents flow-resistive work was wider near FRC, when is low, than near end inspiration, when is high. These individuals were flow limited during most of their tidal breath. They were dynamically hyperinflated, with substantial intrinsic PEEP. The slope of the expiratory pressure-flow curve near zero flow may be the same as that of the inspiratory pressure-flow curve. However, the positive pleural pressure produced by the passive recoil of their hyperinflated chest wall, plus any expiratory muscle activity, may be 5-7 cmH₂O near end expiration, which exceeds the maximal pressure required to achieve maximal . When this pressure is divided by the maximal E of 0.1-0.2 l/s, the apparent RL ranges from 25 to 70 cmH₂O · l¹ · s. The RL'_e term in the emphysema patients was large and negative, so that RL_e (RL_e + RL'_e · V) was very large near end expiration and decreased dramatically to approximate RL_i at the beginning of expiration. Using least squares regression, Peslin and associates (13) found, in subjects who were not flow limited, that adding nonlinear pressure-flow, or PV relationships, or volume dependence of resistance did not materially improve the fit obtained with only resistance and compliance. None of their methods fits data from flow-limited patients, but they did not test a term for volume dependence of only RL_e.

When the RL'_e term is not employed, the computed pressure-elastic volume curve is biased toward positive pleural pressure values near end expiration. This produces an overestimate of elastance and RL_i and is more marked in the patients with end-stage COPD, who have high levels of intrinsic PEEP, than in asthmatic subjects during MCh challenge who have high resistance but are only encroaching on maximal flow near FRC. Thus asthmatic subjects have lower values of RL'_e during bronchoconstriction (see Table 2).

In normal and mildly bronchoconstricted individuals, RL'_e is not significantly different from zero. In a previous study (12) describing the response to MCh in the same asthmatic subjects who participated in the present study, we reported that, during severe bronchoconstriction, asthmatic subjects had higher RL_i than RL_e. We attributed that result to the bronchodilatory effect of tidal inspiration that reduced bronchoconstriction on the subsequent expiration. These individuals also had marked increases in elastance. At that time, we considered the possibility that our computed elastance was biased toward the chest wall PV curve near end expiration, thus artificially increasing both the elastance and the RL_i. Using method 4 in the present study, we recomputed the RL_i and RL_e in those subjects who had RL in excess of 10 cmH₂O · l¹ · s after MCh. This analysis (Table 2) confirms a dramatic increase in elastance with bronchoconstriction and an RL_i greater than the RL_e at midtidal volume (VT) In subjects with induced bronchoconstriction, maximal is very sensitive to end I (4, 11, 21). Standard partial flow-volume curves initiated from 70% VC are usually above end-inspiratory volume, which may result in bronchodilatation that underestimates the amount of flow limitation on the previous tidal respiration (11). Flow limitation can be documented by suddenly applying a negative pressure at the mouth (7) or by inducing a brief voluntary increase in expiratory effort, as we did with the emphysema patients in this study. However, our experience to date suggests that a substantial negative RL'_e term is indicative of E limitation and intrinsic PEEP. Determination of RL'_e requires no additional manipulation in patients who have an esophageal balloon in place. These data also demonstrate the potential of overestimating the Edyn in the presence of flow limitation if the expiratory portion of the breath is included without adjustment for the volume dependence of RL_e.