INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

The measurement of lung compliance and pulmonary resistance in infants and neonates has been helpful in predicting mortality and morbidity after the slow recovery from bronchopulmonary dysplasia, and in documenting the therapeutic effects of diuretics, bronchodilators, and corticosteroids on lung function (1).

The introduction of computerized commercially available pulmonary function systems has made the continuous and easy analysis of pulmonary mechanics available to the clinician and it has been suggested that these measurements may be helpful in the ventilatory management of infants with respiratory failure (7).

Most computerized systems use the equation of motion to derive compliance (C) and resistance (R) from the continuous recordings of airway flow (F), tidal volume (V), and transpulmonary pressure change (P) (8, 9):

P, V, and F are variables that change continuously during the respiratory cycle while C and R are assumed to remain constant. The equation describes a single compartment model of the lung, and the derived estimates of C and R are reliable and physiologically meaningful as long as the P/V and P/F relationships are linear during the respiratory cycle.

The P/V relationship is linear in infants with normal lungs who breathe within the tidal volume range, but is frequently nonlinear in infants with lung disease (10) and during mechanical ventilation when the linear range of the P/V relationship is exceeded (11). In this situation the equation of motion fails to give reliable values of C and R (14).

To improve the accuracy of analyzing breaths with nonlinear P/V and P/F relationships, algorithms that include volume-and/or flow-dependent terms for C and R have been used (15, 16). The best results were obtained by introducing a volume-dependent term of C into the equation of motion (17). Although the resulting algorithm may still not be ideal because not all breaths follow a pattern where C changes in proportion to V, it described an overdistention of the lungs in ventilated animals and infants better than the C20/C ratio described by Fisher and coworkers (18). These investigators observed a flattening of the P/V loop at the end of inspiration as a result of pulmonary overdistention (banana-shaped P/V loop) and compared the slope of the P/V loop during the last 20% of inspiration (C20) with the slope for the whole breath (C). A C20/C ratio of < 0.80 is indicative of pulmonary overdistention.

To overcome the limitations of presently used algorithms, a simple new technique to analyze C and R from the recordings of F, V, and P was developed. To avoid the interdependence of results inherent in the above methods, C and R were calculated using two different equations. R was calculated from the P/V loop by the method of Mead and Whittenberger at different levels of inflation (19). These R values were then introduced into the equation of motion together with the corresponding F, V, and P values, and the equation was solved for C. Thus multiple C values during inspiration and expiration could be obtained.

The purpose of this study was to evaluate this new technique in a lung model and in preterm infants, comparing the results to those obtained using the simple equation of motion and the equation of motion expanded by a volume-dependent term for C for analysis.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Equation of Motion

The basis for computer analysis of pulmonary mechanics is the equation of motion:

(1)

The transpulmonary pressure (P) measured at any point during the respiratory cycle is equal to the sum of the pressure required to overcome the elastic forces (V/C) and the pressure necessary to overcome the resistive forces (F · R).

Some investigators use an additional pressure term P₀ for the elastic recoil pressure of the lungs at end-expiration (9, 15). This is necessary when a positive end-expiratory pressure (PEEP) or inadvertent PEEP are present. In this study this term was omitted because the PEEP pressure present at the beginning of inspiration was subtracted from airway pressure changes, and none of the infants showed evidence of inadvertent PEEP. A pressure term for inertance was not included because it is negligible at low flow rates and does not improve the accuracy of C and R measurements (20, 21).

Linear Regression Analysis (LR)

From a large number of continuous data points of P, V, and F in the breathing cycle the two parameters C and R are derived by linear regression analysis.

This is a mathematical procedure where the difference between the observed P and the calculated P is squared, and the sum of all squares obtained from all the data points is made to reach a minimum. The calculated P is obtained from the equation of motion by inserting the best fit C and R values together with the measured F and V values.

Including all data points of a respiratory cycle into the analysis gives total compliance (C_t) and total resistance (R_t). Including only the data points recorded during inspiration or expiration gives inspiratory and expiratory compliance (C_i, C_e), and inspiratory and expiratory resistance (R_i, R_e), respectively.

Multiple Linear Regression (MLR)

If C is not constant but changes during inspiration, the above equation will only give a weighted mean of C. For more accurate analysis of how C changes during the breath, a volume-dependent term for C can be added to the equation of motion.

(2)

C₁ represents the compliance for the linear and C₂ the compliance for the nonlinear, volume-dependent part of the P/V relationship. The three parameters C₁, C₂, and R, can be calculated by applying multiple linear regression analysis (MLR) to the large number of data points P, V, and F during each breath using the least square fitting procedure described previously. The actual C at different levels of inflation can be calculated by the following equation.

(3)

Analysis of P/V Relationship Under Condition of Nonlinearity (APVNL)

The newly developed algorithm for the analysis of nonlinear P/V relationships (APVNL) uses two different equations to calculate C and R at increasing and decreasing levels of V. First, the total R was calculated at different levels of inflation volume using the method of Mead and Whittenberger (19).

(4)

The pressure difference between inspiratory pressure (P_ins) and expiratory pressure (P_exp) was obtained for each step of volume change from the P/V loop. This value was divided by the sum of inspiratory (F_ins) and expiratory flow (|F_exp|) measured at the same level of volume to obtain R. Then C_i and C_e were calculated at different levels of inflation and deflation by entering the corresponding V, P, F, and R values into the equation of motion:

(5)

A mechanical lung model consisting of two latex balloons of equal compliance and resistance was created. The balloons were covered with a nonelastic cylinder (plastic syringe) restricting their expansion after a certain level of inflation was reached. The values of C and R of the model were determined by static measurements. To obtain C, air was injected into the model by a syringe in 1-ml increments up to a volume of 10 ml, and the pressure at each volume step was measured. To obtain R, pressure was measured at increasing flows (1 to 5 L/min) through the tubes and adapters of the model after removal of the balloons.

The test lung was ventilated with a Sechrist IV-100B SAVI pressure-controlled ventilator (Sechrist Industries, Inc., Anaheim, CA). Inspiratory and expiratory times were 0.3 and 0.6 s, respectively, imitating the breathing pattern of preterm infants, whose lungs have a short time constant. To achieve a V of 10 ml a peak inspiratory pressure of 40 cm H₂O was necessary. The recordings of P, F, and V were analyzed by the LR, MLR, and APVNL methods, and the results of the dynamic C and R measurements were compared with the static C and R characteristics of the lung model.

Infants

The recordings of flow, esophageal, and airway pressure of 22 premature infants who had been studied for different reasons were reviewed. Ten to 15 breaths were selected and analyzed in each infant with the LR, MLR, and APVNL methods.

The following criteria for breath selection were used: (1) tidal volume  8.0 ml/kg; (2) inspiratory and expiratory volume within 10% of each other, to eliminate breaths with large air leaks around the endotracheal (ET) tube; (3) esophageal pressure at the same level in the beginning and end of a breath, thus avoiding periods of swallowing and esophageal spasm; (4) regular phasic breathing with normal ratio between inspiratory and expiratory time thus excluding sighs, expiratory braking, and breath holding; (5) the P/V loop without inversions or figure eight crossovers. However, banana-shaped P/V loops indicating a decrease in C during inspiration were included in the analysis.

Visual inspection of the P/V loops of an infant's breaths was used to separate the infants into two groups, one with mostly linear (elliptical P/V loop), and the other with clearly nonlinear P/V relationship (banana-shaped P/V loop) (18).

The physical characteristics of the infants in the two groups are given in Table 1. Infants with nonlinear P/V relationships had a lower study and birthweight, lower gestational age, a more frequent need for mechanical ventilation, and more frequent clinical evidence of pulmonary disease than the infants with linear P/V relationships. This observation is consistent with the causes of a nonlinear P/V curve in preterm infants, alveolar overdistention secondary to mechanical ventilation (4 of 11), atelectasis secondary to surfactant deficiency (5 of 11), alveolar recruitment during inspiration and collapse during expiration in hyaline membrane disease (5 of 11), and areas of different time constants in bronchopulmonary dysplasia (2 of 11).

Technical Equipment

The flows were measured with a hot wire anemometer (Bear NVM-1; Bear Medical System Inc., Riverside, CA). The flow signal was calibrated using known flows measured with an electronic flow meter (Matheson 2800; Gas Products, Secaucus, NJ). The hot wire anemometer was placed between the ventilator circuit and the ET tube or attached to nasal prongs when the infant was not intubated. It added 0.6 ml of deadspace. The tidal volume was obtained by digital integration of the flow signal.

The esophageal pressure was measured through a size 8.0 Fr water-filled feeding tube placed into the lower part of the esophagus. The airway pressure was acquired from the side port of the ET tube connectors or the nasal prongs. Esophageal pressure and airway pressure (including the pressure of the lung model) were sensed by pressure transducers (Statham ID P23XL; Statham Instruments Inc., Osnard, CA) connected to transducer couplers (Gould, Inc., Cleveland, OH). Calibration was done with a water manometer.

There was no phase shift between flow and pressure signals and no over- or underdamping of the signals up to 10 Hz. All signals were digitized at 100 Hz and stored on a computer disk for further analysis (Vectra 486; Hewlett Packard, Palo Alto, CA). Transpulmonary pressure was obtained by the computer as the difference between airway and esophageal pressures. Transpulmonary pressure was used in the three different algorithms (LR, MLR, APVNL) to calculate C and R. The results therefore reflect pulmonary C and pulmonary R. 

Statistical Analysis

C_i and C_e at tidal volume levels of 2, 4, 6, and 8 ml/kg, and R were determined from the recordings of the P, F, and V by the MLR and APVNL methods. A single value of C_i and C_e was obtained for each breath by the LR method. Means and coefficient of variation (CV) for the measurements were determined for each infant. For groups of infants the medians of the means and their ranges together with the medians and ranges of CV are given.

To decide how well the observed and calculated pressures correlated, the coefficient of correlation (r) for the two pressures was obtained for each breath. Furthermore, the squared difference between the observed and calculated pressure curves was integrated over time and the results were used as an arbitrary measure of fitting (area difference, AD). Calculated pressure was obtained at 10-ms intervals throughout the respiratory cycle by inserting the appropriate measurements of F and V together with the C and R values obtained for this phase of the respiratory cycle, into the equation used to calculate C and R. Means and CV for r and AD were calculated for each infant. For groups of infants the medians of the means and their ranges are given.

The mean values of CV, r, and AD obtained from the measurements in each infant were used as indicators of how well the three different methods described the pulmonary mechanics in the infants. The Sign Test of Dixon and Mood (22) was used to detect significant differences (p < 0.05) in the CV, r, and AD of the measurements generated by the three methods of analysis.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Test Lung

The changes in C of the lung model obtained by static measurments and by dynamic measurements with the APVNL, MLR, and LR methods are given in Figure 1.

View larger version (16K): [in this window] [in a new window]   Figure 1.   Changes in static and dynamic compliance obtained by the LR, MLR, and APVNL methods over the tidal volume range of the lung model.

C_i obtained by the APVNL method was very close to the static measurements. In contrast, C_i obtained by the MLR method severely underestimated true C especially in the beginning of inspiration, but approximated the static measurements in the last third of inflation.

The LR method only gave a single value of C_i for the whole breath which was close to the values obtained by the MLR and APVNL methods at the end of inspiration.

The R_t obtained by the APVNL and MLR methods was 96.1 and 100.0 cm H₂O/L/s, respectively. Both values were close to the static measurements of resistance which was 96.8 cm H₂O/L/s. No reliable measurements of R_t could be obtained in the lung model with the LR method.

Infants

Figures 2-5 illustrate the application of the three methods of analysis to the recordings of P, F, and V. Figure 2 demonstrates a scalar trace of flow, esophageal pressure, airway pressure, and tidal volume during spontaneous breathing of one of the premature infants (weight at study time: 1,045 g; birthweight: 1,185 g; gestational age: 30 wk). The marked breath was selected for analysis. The breathing pattern of the infant was regular and the breaths fulfill the selection criteria.

View larger version (24K): [in this window] [in a new window]   Figure 2.   Scalar trace of flow, esophageal pressure, airway pressure, and tidal volume during spontaneous breathing in one of the infants. The marked breath was selected for further analysis of pulmonary function.

View larger version (20K): [in this window] [in a new window]   Figure 3.   P/V loop of the selected breath. The loop shows the typical "banana shape" indicating a decrease in compliance. The resistance values obtained from the loop at eight different steps of inflation are shown on the right.

View larger version (18K): [in this window] [in a new window]   Figure 4.   Compliance values of the selected breath measured during inspiration by APVNL and MLR method. Only at the end of inspiration are the measurements similar.

View larger version (27K): [in this window] [in a new window]   Figure 5.   Error of fitting for the selected breath calculated as area difference between measured and calculated pressure for LR, MLR, and APVNL methods. On the right, the correlation between observed and calculated pressure is depicted graphically. Heavy line = observed pressure. Dotted line = calculated pressure.

Figure 3 depicts the P/V loop of the selected breath. The loop shows a flattening with increasing pressure (banana shape) indicating a nonlinear P/V relationship. The R_t values calculated at eight different steps of inflation from the P/V loop by the Mead and Whittenberger (19) method are shown.

Figure 4 shows how the C_i values of the selected breath obtained by the APVNL and MLR methods change with inspiration. APVNL gives a C_i that increases initially, reaches a peak early during inspiration, and then decreases toward the end of inspiration. The MLR method shows a C_i that continuously decreases during inspiration. The two methods of analysis gave quite different C_i values in the beginning but became closer at the end of the breath.

Figure 5 demonstrates the difference between measured and calculated pressures for LR, MLR, and APVNL methods. Compared with the LR method the pressure curves show an improved fit with the MLR method but a nearly perfect fit with the APVNL method. This is reflected numerically by the error values for inspiration and expiration. They reflect the AD between the two curves which is smaller for the APVNL method than for the other two methods. The correlations between observed and calculated pressures are displayed on the right-hand side of the figure. The correlations show a similar trend as observed in the AD analysis with MLR and APVNL methods giving a better correlation than the LR method.

Table 2 shows the C of the 11 infants with linear P/V relationship at increasing steps of V for the three algorithms. C did not change significantly at increasing steps of V. This was expected because the elliptical P/V loops of the infants' breaths had indicated linear P/V relationships. The MLR method frequently yielded nonphysiological, often negative values, especially for the expiratory phase at lower levels of inflation. The range of measurements obtained with the MLR method was wider at low levels of inflation than for measurements done with the APVNL method. In consequence the CV for the different C measurements was significantly smaller for the APVNL method than for the MLR method up to a V of 4 ml/kg for the inspiration (p < 0.02) and up to a V of 6 ml/kg for the expiration (p < 0.05). However, the median C values obtained by the two methods were not significantly different.

Table 3 shows the C measurements at increasing steps of V obtained with the three methods of analysis in the 11 infants with nonlinear P/V relationships. Both the MLR and APVNL methods reflected a decrease in C with increasing inflation. This was expected because of the banana-shaped P/V loops of the infants' breaths which indicated nonlinear P/V relationships. Again, the MLR method yielded frequent nonphysiological, often negative C values at lower levels of inflation especially during the expiratory phase. The range of C measurements was wider for the MLR than for the APVNL method at low levels of inflation. The coefficients of variation of C were, therefore, significantly larger for the MLR method than for the APVNL method up to the V of 6 ml/kg for inspiration (p < 0.02) and expiration (p < 0.01). The MLR method gave significantly lower C values than the APVNL method at 4, 6, and 8 ml/kg during inspiration. Measurements during expiration were not significantly different between the methods.

Table 4 shows the R measurements of the 11 infants with linear and with nonlinear P/V relationships. R_t values obtained by the three methods were similar regardless of P/V relationship. In infants with linear P/V relationship the R_e values obtained with the MLR method were lower than the measurements with the LR method and were often in an unphysiologically low or negative range. In the infants with nonlinear P/V relationship R_i values measured with the LR method were nonphysiologically low or negative while R_e values were too high. CV for R_i and R_e measurements was significantly larger when obtained by MLR method than by the LR method regardless of P/V relationship. Table 5 gives the R_t values obtained by the APVNL method at increasing levels of inflation. There were no significant changes in R_t during the breath in either infants with linear or nonlinear P/V relationships.

Finally, AD and r between observed and calculated pressures were evaluated for the three methods of analysis.

Table 6 displays the medians and ranges of AD for the three methods of analysis. AD was significantly lower for the APVNL method than for the other two methods regardless of P/V relationship. There was no significant difference in AD between the LR and MLR methods.

Table 7 presents correlation coefficients, r, for calculated and measured pressures obtained by the three methods of analysis; r was significantly higher for the APVNL method than for the other two methods regardless of P/V relationship. The LR and MLR methods did not show significantly different r values.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

The newly developed APVNL method of analysis properly described the nonlinear P/V relationship and the R of a lung model. In contrast, the MLR method largely underestimated the model's C especially in the beginning of inspiration. Similar observations were made in infants. Furthermore the APVNL method consistently showed a lower variability of C_i and C_e measurements in the first half of a breath than the MLR method regardless of P/V relationship.

The AD between observed and calculated pressure was significantly smaller and the correlation between the pressures significantly better for the APVNL method than for the MLR method. Even in infants with nonlinear P/V relationships the MLR method did not improve the fitting of the two pressures significantly above the fitting provided by the LR method.

It must be concluded from these findings that the MLR method is not reliable in describing nonlinear P/V relationships in small infants, and that the APVNL method offers a simple, more accurate solution to the challenge of analyzing breaths with nonlinear P/V relationships. The APVNL method may become an important clinical tool in detecting lung overdistention in mechanically ventilated infants, which is evident from decreasing C measurements at the end of inspiration. In addition, changes in C at lower levels of inflation reflecting alveolar recruitment during inspiration and collapse during expiration can be identified with the APVNL method and used to adjust the PEEP to prevent alveolar collapse (23, 24).

The observed variability of the C measurements in the beginning of the breath may be the result of alveolar recruitment, the degree of which may vary from breath to breath. In addition, methodological problems may have contributed to this variability. Flow and pressure increase rapidly in the beginning of the breath. Digitizing these values at a frequency of 100 Hz may result in more variable flow and pressure measurements closer to the 2 than to the 8 ml/kg volume point.

The APVNL method assumes that R_t is equal to R_i and R_e. This assumption is necessary because R_i and R_e cannot be measured accurately by the Mead and Whittenberg method in the presence of a nonlinear P/V relationship (14). This assumption results in a small error in the calculation of C_i and C_e because R_i is normally smaller than R_e, and R_t is in between the two. The resulting error is small because in the neonate respiratory failure is mainly characterized by alveolar disease and in consequence a low C (25, 26). Airway problems are rare and only become more frequent after the first month in infants with bronchopulmonary dysplasia. Furthermore, pulmonary resistance if compared with weight or lung size is lower in the neonate than in infants or children because of dysanaptic lung development (27, 28). Consequently, the pressure necessary to overcome the resistive forces during a breath is small compared with the pressure necessary to overcome the elastic forces. The error made by replacing R_i and R_e by R_t, therefore, only has a negligible effect on the calculation of C_i and C_e. That these assumptions are reasonable is supported by the accuracy with which the APVNL method describes the lung model, and the improved reproducibility of C measurements, and the better model fit achieved with the APVNL method in infants. In patients with elevated R_t and a large difference between R_i and R_e, but relatively normal C, the APVNL method may not work as well.

Different groups of investigators have tried to improve the performance of lung models and techniques used to describe the characteristics of lung or respiratory system in patients. The dynamic measurements have the advantage of not requiring special ventilatory patterns (constant inspiratory flow) or interruption of the respiratory cycle (airway occlusion) in patients with respiratory failure who are easily agitated. The dynamic measurements are based on the analysis of the continuously changing variables of P, F, and V during a respiratory cycle. The equation of motion describes these changes well in infants with normal lungs (14). In situations where the fitting between observed and calculated pressures remains poor, the expansion of the equation of motion by volume- or flow- dependent terms of elastance and resistance can improve the goodness of fit, but frequently provides unrealistic values of the additional coefficients (15). We have made a similar experience with the MLR method in our preterm infants. Even in situations with documented nonlinear P/V relationships the MLR method did not improve AD in most infants compared with the basic, first-order model of the LR method, and frequently the results were in the nonphysiologic range.

Results obtained by the MLR method are frequently unreliable because the MLR algorithm forces the results into a pattern where C either increases or decreases in relation to V, a pattern not always seen in the clinical situation. For example, a C that changes at a different rate in the beginning than at the end of inflation or a C that increases in the beginning and decreases at the end of a breath cannot be analyzed correctly by the MLR method (see Figures 1 and 4).

Although the C values obtained by the LR or MLR methods were often inaccurate (as shown during measurements done in the lung model) or showed nonphysiologic results, the correlation between observed and calculated pressures was good. This observation has been made before and illustrates that r cannot be used to judge the accuracy of the measurements (17). Therefore, we used the area difference between the two pressure curves (AD), which changes much more dramatically with better or worse fitting of the two curves than r does. However, even that measure does not prove that the C values are accurate in a physiological sense.

The reproducibility of the measurements obtained by the three methods of analysis in each infant was compared by the CV. The variance of the measurements is not only determined by true breath-to-breath changes in the analyzed coefficients (intrapatient variability) but also by errors introduced into the measurements by imperfect algorithms that are not suited to describe certain pulmonary conditions. Because the same breaths were analyzed by the three methods, intrapatient variability should be the same and differences in CV of the measurements obtained must indicate differences in modeling accuracy between the three methods. The APVNL method showing the smallest CV, therefore, must model the pulmonary condition of the infants most accurately.

The LR and MLR methods allow the independent calculation of R_i and R_e. These results are accurate when using the LR method as long as the P/V relationship of the breath analyzed is linear. Large errors, however, are introduced into the calculation of R_i and R_e when analyzing breaths with nonlinear P/V relationships (14). Because C_i and C_e cannot be determined accurately in this situation, R_i and R_e which are interrelated with C_i and C_e by the equation of motion, are also inaccurate. Because in the neonate most of the transpulmonary pressure changes are needed to overcome the elastic properties of the lungs, small errors in the calculation of C_i and C_e lead to large errors in R_i and R_e. The same limitations observed for the LR method in determining R_i and R_e, appear to be true for the MLR method, because C_i and C_e values also show a high variability and many are in an unphysiological low range. Only the R_t values regardless of P/V relationship or method of analysis appear to be reproducible and in the normal range.

In summary, for the determination of C at the end of inspiration all three methods of analysis give similar results. However, when the changes in C during lung inflation or deflation are of interest, the APVNL method gives more accurate and reproducible results than the MLR method.