The study was approved by the Human Subjects Committee, Harbor/University of California at Los Angeles Medical Center.

Data from 474 healthy subjects (Table E1) from three laboratories were used: Harbor/University of California at Los Angeles Medical Center; El Camino College, Torrance, California; and Department of Physiology, University of León, Spain. The Harbor/University of California at Los Angeles Medical Center data included 80 men found to be normal after complete workup for asbestos exposure. These 80, ranging in age from 37 to 74 years, included 14 current smokers and 39 exsmokers with a median of 20 pack years of cigarette smoking. All other subjects were healthy nonsmoking students or community members without complaints. Subjects were familiarized with the apparatus, gave informed consent, and exercised to their maximum tolerance on the cycle and/or treadmill using incremental protocols of varying duration. Five automated gas exchange measurement systems were used: previously fabricated breath-by-breath (21–23) and MedGraphics (St. Paul, MN) systems at Harbor/University of California at Los Angeles Medical Center, breath-by-breath and mixing chamber systems SensorMedics (Yerba Buena, CA) at El Camino College, and a breath-by-breath MedGraphics system at the University of Leon.

In addition, to demonstrate the relationship between V̇e, V̇co₂, and Vd/Vt, prior data from 28 normal men with arterial blood measurements every 2 minutes (and incremental exercise of the same duration) were reanalyzed (1, 22). As detailed in the online data supplement, other studies were also performed.

To accurately determine ventilation as if the subject were not breathing with a mouthpiece and flow-measuring device, the mechanical dead space volume, determined by water displacement, was subtracted from each tidal volume, so that the V̇e reported represented the subject's ventilation excluding that of the apparatus dead space (23). The measured mechanical dead space volume, depending on the mouthpiece, flowmeter, and connections used, ranged from 75 to 95 ml for the Harbor/University of California at Los Angeles Medical Center-fabricated system, from 45 to 65 ml for the Medical Graphics systems, and from 90 to 110 ml for the SensorMedics system.

Gas exchange variables (1, 4, 5, 24) were calculated and summarized every 30 seconds. The AT was determined using the V-slope method (1, 25). Three relationships between V̇e and Vco₂ were evaluated in each subject as: (1) slope and intercept of V̇e versus V̇co₂ during exercise, excluding data above the ventilatory compensation point (10, 20), (2) V̇e/V̇co₂@AT averaged for 1 minute at and immediately after the AT, and (3) lowest V̇e/V̇co₂ determined by averaging the three lowest consecutive 0.5 minutes data points.

Microsoft Office-2000, SPSS-10, and Origin-6.0 computer software were used. All values were reported as mean ± SD except when specified. An α of p values less than 0.05 was considered significant. Comparisons in the same subjects used paired, 2-tailed t tests (26). Correlation and regression analyses used analysis of variance. Simple individual linear regression analyses helped calculate Pearson correlation coefficients (r). Multicolinearity stepwise analyses used age, sex, height, and weight as independent variables to predict ventilatory efficiency with multiple correlation coefficients (R) (27, 28).

We then assessed the influence of site, age, sex, fitness, and ergometer type on the lowest V̇e/V̇co₂ using the previously calculated reference formula.

As shown by the arterial blood gas measurements (Figure 1)

Figure 1. Pattern of change in ventilatory efficiency and associated variables during incremental exercise. Mean ± SD Pa_CO2, VD/VT, pH, and ratios of V̇E/V̇CO₂ and V̇E/V̇O₂ are plotted at rest and at 2-minute intervals from unloaded cycling to peak exercise and recovery in 28 normal, late middle-aged men (59 ± 3 years, 175 ± 6 cm, and 93 ± 10 kg). These men were selected from a larger population with blood gas measurements because each reached his AT and peak V̇O₂ at 9 to 11 and 13 to 15 minutes, respectively.

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Similarly, for the total 474 subjects (Figure 2)

Figure 2. V̇E/V̇CO₂ and V̇E/V̇O₂ at 30-second intervals in 474 subjects during incremental exercise before and after the AT. Before the AT, the V̇E/V̇CO₂ progressively decreased (p < 0.05) while V̇E/V̇O₂ stabilized (p > 0.05). After the AT, V̇E/V̇CO₂ stabilized (p > 0.05) for several minutes while V̇E/V̇O₂ rose progressively (p < 0.001).

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Table 1

The upper panel of Figure 3

Figure 3. Lowest V̇E/V̇CO₂ during exercise is compared with the V̇E versus V̇CO₂ (upper) and V̇E/V̇CO₂@AT (lower) obtained in the same tests in 474 normal subjects. Reasons for the wider scatter of the V̇E versus V̇CO₂ slopes are noted in the DISCUSSION.

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Age, sex, and height influence the relationship of V̇e and V̇co₂ ratios as shown in Table 2

As detailed in Sections E2, Figure E1, and Table E2 in the online data supplement, duplicate studies showed similar values for the V̇e/V̇co₂@AT and the lowest V̇e/V̇co₂ whether on the treadmill or cycle as well as better reproducibility than the V̇e versus V̇co₂ slope. Table E3 shows the absence of the effect of laboratory site, ergometer, sex, and age on the reference formula but a small effect of exceptional physical fitness.

The relationships of these parameters are shown graphically in Figure 4

Figure 4. Comparison of V̇E versus V̇CO₂ slopes in three normal subjects (upper panels) and the V̇E/V̇CO₂ ratios as related to time in the same three studies (lower panels). Data points are shown every 0.5 minutes during progressively increasing cycle ergometer exercise. The open symbols occur after the ventilatory compensation points (VCP) and are thus not used for calculation of the slopes (straight solid lines) and intercepts of V̇E versus V̇CO₂. The V̇E/V̇CO₂ values (lower panels) reach a broad, nearly constant nadir between the AT and ventilatory compensation point arrows. Subject 1 is typical of an average response; Subject 2 has a large positive intercept for V̇E versus V̇CO₂ slope, and Subject 3, an intercept close to zero. Although the V̇E versus V̇CO₂ slopes for Subjects 1 and 2 are similar, their Y-axis intercepts differ, causing the lowest V̇E/V̇CO₂ and V̇E/V̇CO₂@AT ratios of Subject 1 to differ markedly from those of Subject 2. For Subjects 2 and 3, although the lowest V̇E/V̇CO₂ and V̇E/V̇CO₂@AT ratios are similar, the V̇E versus V̇CO₂ slopes differ markedly.

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The mean values for all three parameters of ventilatory efficiency are relatively similar (Table 1). The V̇e versus V̇co₂ slope measurement has the advantage of familiarity in evaluating the severity of heart failure. However, it is less reproducible than both ratios in sequential testing (Figure E1); the slope value becomes improperly high when data above the ventilatory compensation point are used in the linear regression; and the slope value may be inappropriately low because of early transient hyperventilation. Such hyperventilation soon after the start of exercise tests, which is often observed whether studying normal subjects or patients, probably accounts for some variability in the V̇e versus V̇co₂ slope (Figure E1) and the number of exceptionally low values for the slope (Figure 3).

From the mathematical derivation of V̇e/V̇co₂ (V̇e/V̇co₂ = k/[{Pa_CO2} × {1 − Vd/Vt}]), it is evident that this ratio depends on both Pa_CO2 and Vd/Vt (7, 29–31). Because an increase in V̇e/V̇co₂ ratios or V̇e versus V̇co₂ slope may be due to either a low Pa_CO2, an abnormally high dead space fraction (increased Vd/Vt), or both, measurement of Pa_CO2 and calculation of Vd/Vt are required to precisely quantify ventilatory efficiency.

A low Pa_CO2 set point could be due to hypoxemia, chronic respiratory alkalosis, or chronic metabolic acidosis. Ordinarily, however, a high V̇e/V̇co₂ or V̇e versus V̇co₂ slope reveals the likelihood of high dead space ventilation due to poor perfusion of ventilated alveoli. Acute anxiety hyperventilation with a low Pa_CO2 is more likely to affect the V̇e versus V̇co₂ slope than the ratios.

Another confounding situation would be the presence of an abnormally high Vd/Vt in a patient who has chronic hypoventilation (high Pa_CO2), as might occur in a patient with a compensated chronic respiratory acidosis or metabolic alkalosis. In such a case, the two abnormalities might offset each another, resulting in normal values for the V̇e/V̇co₂ ratios and V̇e versus V̇co₂ slope. Thus although these noninvasive measurements are valuable parameters to assess gas exchange efficiency and to determine if Vd/Vt is likely elevated, they need to be put into the clinical context.

Despite these confounding situations, noninvasive measurements of ventilatory efficiency can be very helpful in identifying or grading severity of disease. For example, Kleber and colleagues (9) found that 46% of 142 patients with consecutive heart failure had a V̇e versus V̇co₂ slope exceeding 35; that the median value was 128% of predicted and that the V̇e versus V̇co₂ slope correlated with the AT, peak V̇o₂, and New York Heart Association class. In 53 patients with primary pulmonary hypertension, we found that the V̇e/V̇co₂@AT were 172 ± 52% of normal predicted and that 49 of the 53 patients had values exceeding the 95% confidence limits (4).

It is often important to consider the ventilatory response over the entire exercise test. Theoretically, it is reasonable, as others have done (32), to quantify ventilatory efficiency by normalizing V̇e to V̇o₂ rather than V̇co₂. However, it is evident from Figures 1 and 2 that there is less variability in V̇e/V̇co₂ than V̇e/V̇o₂ during moderate intensity exercise because of the sensitivity of the ventilatory control mechanism to Pa_CO2 and arterial pH in the physiologic ranges (19, 33–35). Furthermore, the V̇e/V̇o₂ changes rapidly just after the AT, whereas the V̇e/V̇co₂ usually remains stable for several minutes after the AT is reached during an incremental exercise test (Figures 1, 2, and 4).

To obtain a universal predicting equation for multiple gas exchange systems it is necessary to subtract the rebreathed volume of the experimental apparatus (instrument dead space) times the breathing frequency from the actual ventilation (1, 23). This rebreathed volume includes the mouthpiece exterior to the mouth, connectors, and flow transducer or breathing valve. When this volume times breathing frequency was subtracted from total V̇e using different volumes in repeated tests, V̇e/V̇co₂ ratios were not influenced, but V̇e versus V̇co₂ slopes and intercepts were changed (see Table E4 in the online data supplement).

Formulae have been derived to predict V̇e versus V̇co₂ slope and V̇e/V̇co₂@AT and lowest V̇e/V̇co₂ ratios during exercise for the noninvasive measurement of ventilatory efficiency. Because the lowest V̇e/V̇co₂ and V̇e/V̇co₂@AT are so similar, and the AT may be uncertain in some patients, it is sensible and clinically practical to use the lowest V̇e/V̇co₂. Values derived from the formulae in this series are reasonably similar to those derived from smaller populations previously reported (V̇e/V̇co₂@AT formula for cycle ergometry [1, 22]; V̇e versus V̇co₂ slope formulae for treadmill [20] or cycling tests [30, 31]). This series is the only one using multilinear correlation analysis in which sex, age, and height all emerge as significant predictors. However the number of elderly normal subjects is not large. The normal distribution of the values about the mean allow the use of 1.66× the SD to calculate the upper 95% confidence limits for adults. The derived predicting equation for lowest V̇e/V̇co₂ during exercise was quite robust in that it was not affected by type of ergometer, despite differences in age (20, 30, 36–38), sex (20), height, equipment, and locale. This study supports the use of a single reference formula for lowest V̇e/V̇co₂ to noninvasively assess ventilatory efficiency in adult patients.