American Journal of Respiratory and Critical Care Medicine

When evaluating dyspnea in patients with heart or lung disease it is useful to measure the quantity of ventilation needed to eliminate metabolically produced CO2 (i.e., the ventilatory efficiency). Mathematically, the relationship between ventilation (V̇E) and CO2 output is determined by the arterial CO2 pressure and the physiologic dead space–tidal volume ratio. We decided to determine how age, sex, size, fitness, and the type of ergometer influenced ventilatory efficiency in normal subjects. Three methods were compared for expressing this relationship: (1) the V̇E versus CO2 output slope below the ventilatory compensation point, commonly used by cardiologists for estimating the severity of heart failure; (2) the V̇E/CO2 output ratio at the anaerobic threshold, commonly used by pulmonologists; and (3) the lowest V̇E/CO2 output ratio during exercise, the latter parameter not previously reported. We studied 474 healthy adults, between 17 and 78 years of age during incremental cycle and treadmill cardiopulmonary exercise tests at three test sites, correcting the total V̇E for the equipment dead space. The lowest V̇E/CO2 output ratio was insignificantly different from the ratio at the anaerobic threshold, less variable than that for the slope relationship, and unaffected by the site, ergometer, and gas exchange measurement systems. The regression equation for the lowest V̇E/CO2 output ratio was 27.94 + 0.108 × age + (0.97 = F, 0.0 = M) − 0.0376 × height, where age is in years and height is in centimeters. We conclude that the lowest V̇E/CO2 output ratio is the preferred noninvasive method to estimate ventilatory inefficiency.

Measurements of ventilatory efficiency have been found to be useful in assessing the presence and severity of both heart (115) and lung (1, 46, 1618) diseases. The ideal (most efficient) lung at a regulated arterial Pco2 (PaCO2, Pco2 set point) is one in which there is uniform matching of lung ventilation (V̇e) to perfusion. With mismatching, efficiency of lung gas exchange is reduced, necessitating an increase in ventilation for a given CO2 output (V̇co2) and PaCO2. Such mismatching contributes to the exercise dyspnea found in patients with primary disease of the pulmonary circulation or secondary effects on the pulmonary vasculature by left ventricular failure or lung diseases (19).

Necessarily, V̇e is closely linked to V̇co2 at all times. During rest or very mild exercise, the relationship between V̇e and V̇co2 can vary widely, predominantly because of psychogenic factors and differences in the PaCO2 and dead space–tidal volume ratio (Vd/Vt) (1). During heavy and very heavy exercise, i.e., above the anaerobic threshold (AT), the increase in V̇e relative to V̇co2 is variable and dependent on the decrease in pH and PaCO2 induced by the lactic acidosis (19). However, during moderate exercise, before the onset of ventilatory compensation for the exercise-induced lactic acidosis, the relationship of V̇e to V̇co2 is normally relatively stable and uniform. We initially planned to compare two previously described methods relating V̇e to V̇co2 in the midwork rate range: (1) the V̇e versus V̇co2 slope from start of exercise to the ventilatory compensation point for metabolic acidosis (V̇e versus V̇co2) (914, 20) and (2) the V̇e/V̇co2 ratio, i.e., the ventilatory equivalent for CO2 at the AT (V̇e/V̇co2@AT) (1, 46, 15). In the process of comparing these two methods in a large healthy population on the cycle and treadmill, we found that a third method using the lowest V̇e/V̇co2 ratio during exercise had significant advantages over the other two. In this study, we report the normal V̇e to V̇co2 relationship expressed by all three methods, and describe the effect of subject sex, age, height, fitness, and form of ergometry on these parameters of ventilatory efficiency.

Subjects, Locale, Equipment, and Protocols

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 (2123) 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.

Statistical Analysis

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.

Pattern of Change in V̇E/V̇CO2 and V̇E/V̇O2 as Related to VD/VT, PaCO2, and pH during Increasing Exercise

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

, the Vd/Vt, the ideal but invasive measurement of ventilatory inefficiency, has the least variability at the AT. Although the PaCO2 pH and Vd/Vt decline somewhat above the AT, the V̇e/V̇co2, which has reached its nadir at the AT, stabilizes for the next 2 minutes. In contrast, V̇e/V̇o2 concurrently increases at and above the AT. Both V̇e/V̇o2 and V̇e/V̇co2 increase late in exercise and early recovery, due to the acidemia-induced hyperventilation, manifested by the further decreases in pH and PaCO2.

Similarly, for the total 474 subjects (Figure 2)

, V̇e/V̇co2 stabilizes at and above the AT whereas V̇e/V̇o2 stabilizes briefly below and at the AT and then progressively increases. Because V̇e/V̇co2 values decrease very little for some time after the AT and are more stable than V̇e/V̇o2 for a longer time, we analyzed ventilatory efficiency during exercise not only as the V̇e versus V̇co2 slope (914, 20) and V̇e/V̇co2@AT (1, 46, 15), but also as the lowest V̇e/V̇co2.

Effect of Sex and Age

Table 1

TABLE 1. Ventilatory efficiency during cardiopulmonary exercise tests by age and sex




Lowest V̇E/V̇CO2

V̇E versus V̇CO2 Slope

V̇E versus V̇CO2 Intercept
< 204623.5 ± 2.023.2 ± 2.022.9 ± 2.82.0 ± 2.6
21–309024.2 ± 2.123.9 ± 2.123.6 ± 2.82.7 ± 2.1
31–404925.3 ± 2.625.0 ± 2.723.9 ± 3.13.0 ± 1.9
41–503726.2 ± 2.226.1 ± 2.225.2 ± 2.92.5 ± 1.7
51–605428.2 ± 2.828.0 ± 2.927.2 ± 3.02.6 ± 2.7
> 603429.4 ± 2.229.4 ± 2.327.5 ± 3.13.2 ± 4.3
Average25.7 ± 3.125.5 ± 3.224.7 ± 3.42.6 ± 2.6
< 202925.5 ± 1.725.4 ± 1.825.2 ± 2.71.7 ± 1.7
21–305025.8 ± 2.325.4 ± 2.224.1 ± 2.12.3 ± 1.7
31–402727.9 ± 2.127.7 ± 2.326.9 ± 3.22.1 ± 1.5
41–502826.7 ± 2.626.5 ± 2.625.8 ± 2.71.5 ± 1.4
51–602028.5 ± 3.228.0 ± 3.326.5 ± 3.42.7 ± 2.6
> 601029.4 ± 2.529.3 ± 2.628.7 ± 3.10.3 ± 1.0
Average16426.8 ± 2.726.5 ± 2.725.6 ± 3.02.0 ± 1.8
26.1 ± 3.0
25.9 ± 3.0
25.0 ± 3.3
2.4 ± 2.4

Definition of abbreviations: AT = anaerobic threshold; V̇CO2 = carbon dioxide output; V̇E = ventilation.

describes the effect of age and sex on the three parameters relating V̇e to V̇co2. All values progressively increase with age and tend to be slightly lower in men than in women. For any age and sex the V̇e/V̇co2@AT and the lowest V̇e/V̇co2 are virtually identical but slightly higher than the V̇e versus V̇co2 slope.

Comparisons of Three Measurements of Ventilatory Efficiency

The upper panel of Figure 3

shows a good correlation between V̇e versus V̇co2 slope and the lowest V̇e/V̇co2 (r = 0.85 and SD = 1.77); the lower panel shows the excellent correlation between V̇e/V̇co2@AT and the lowest V̇e/V̇co2 (r = 0.99, SD = 0.45, Y = 1.00 ± 0.97X). In assessing the V̇e versus V̇co2 slope, the intercepts on the Y-axis were positive 90%, negative 5%, and very near zero 5% of the time.

Multicolinearity Analyses and Reference Formulae

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

TABLE 2. Predicting equations for ventilatory efficiency during cardiopulmonary exercise tests

Constant and Dependent Parameters

Statistical Analysis
Independent Parameters
Age (yr)
Sex (M = 0, F = 1)
Height (cm)
Standard Deviation
p Value
V̇E/V̇CO2@AT47428.250.1051.00−0.03752.390.607< 0.0001
Lowest V̇E/V̇CO247427.940.1080.97−0.03762.430.605< 0.0001
V̇E versus V̇CO2

< 0.0001

Definition of abbreviations: AT = anaerobic threshold; V̇CO2 = CO2 output; V̇E = ventilation; V̇E/V̇CO2@AT = ventilatory equivalent for CO2 at the AT.

. The V̇e/V̇co2 ratios are less variable than the V̇e versus V̇co2 slope, as evidenced by the higher R values and lower SDs in the ratio reference equations. The 95% confidence limit for the upper limit of normal adds approximately four units to the ratio means and five units to the slope mean.

Other Findings

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.

Ventilatory efficiency decreases, i.e., ventilation–perfusion relationships are impaired, in proportion to the reduction in exercise capacity in chronic heart failure (7, 8), primary pulmonary hypertension (46), and most lung diseases (1618). In the case of chronic heart failure, the V̇e versus V̇co2 slope is commonly used to grade severity (9, 10). Characteristically in heart failure, the Vd/Vt is increased (7), but hypoxemia is absent. Because ventilatory efficiency decreases as exercise capacity decreases in chronic heart failure (2, 3, 710) and probably most diseases involving the pulmonary circulation, knowledge of normal values allows the clinician to distinguish between mild disease and normalcy.

Relationship between the V̇E versus V̇CO2 Slope and V̇E/V̇CO2 Ratios

The relationships of these parameters are shown graphically in Figure 4

. Although the V̇e versus V̇co2 slope has been equated to the V̇e/V̇co2 ratio (29), they are equal only when the intercept of the V̇e versus V̇co2 plot goes through the origin, which takes place only 5% of the time.

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).

Clinical Use of the V̇E and V̇CO2 Relationships

From the mathematical derivation of V̇e/V̇co2 (V̇e/V̇co2 = k/[{PaCO2} × {1 − Vd/Vt}]), it is evident that this ratio depends on both PaCO2 and Vd/Vt (7, 2931). Because an increase in V̇e/V̇co2 ratios or V̇e versus V̇co2 slope may be due to either a low PaCO2, an abnormally high dead space fraction (increased Vd/Vt), or both, measurement of PaCO2 and calculation of Vd/Vt are required to precisely quantify ventilatory efficiency.

A low PaCO2 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 PaCO2 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 PaCO2), 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).

Why V̇E/V̇CO2 Is Preferable to V̇E/V̇O2

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 PaCO2 and arterial pH in the physiologic ranges (19, 3335). 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).

Mechanical Dead Space Volume

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, 3638), 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.

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Correspondence and requests for reprints should be addressed to Karlman Wasserman, M.D., Ph.D., Division of Respiratory and Critical Care Physiology and Medicine, Research and Education Institute, Harbor-UCLA Medical Center, Box 405, St. John's Cardiovascular Research Center, 1000 West Carson Street, Torrance, CA 90509-2910. E-mail:


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