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A Simplified Approach for the Estimation of the Ventilatory Compensation Point


Medicine & Science in Sports & Exercise: April 2012 - Volume 44 - Issue 4 - p 716–724
doi: 10.1249/MSS.0b013e318237fb5f

Incremental cardiopulmonary exercise test with gas exchange measurement is the gold standard for the identification of the ventilatory compensation point (VCP). It has previously been demonstrated that the change in the slope of increment of minute ventilation over HR (ΔE/ΔHR) can be used alternatively to the ventilatory equivalent for CO2 (E/V˙CO2) method for detection of VCP in healthy subjects undergoing cycle ergometer (C) incremental exercise. The same evaluation during treadmill (T) incremental exercise and comparison between C and T have not yet been performed.

Purpose We analyzed, during both C and T incremental exercises, the E/HR and the respiratory rate (RR)/HR relationships, expressed either as slope or as an absolute value. We hypothesized that changes in the slope of increment of the two relationships could represent a reliable method for VCP detection, regardless of exercise mode and protocol.

Methods Fourteen healthy male subjects (age = 31 ± 7 yr (mean ± SD)) underwent two T incremental exercises—fast (FT) and slow (ST) protocols (8 km·h−1, 2% (FT) and 1% (ST) grade per minute)—and one C incremental exercise (30 W·min−1). O2 uptake (V˙O2), V˙CO2, E, HR, and RR were measured breath by breath.

Results A good between-method agreement in the detection of VCP by the ΔE/ΔV˙CO2, ΔE/ΔHR, and the ΔRR/ΔHR slope changes was found in both T protocols and C. No differences (C vs T and FT vs ST) were found in the slope of the ΔE/ΔHR and ΔRR/ΔHR relationships after the VCP and in the E/HR and RR/HR absolute values at VCP.

Conclusions In healthy young males, the ΔE/ΔHR and ΔRR/ΔHR relationships during T and C incremental exercises can be reliably used to detect the VCP as an alternative to the ventilatory equivalent method.

Supplemental digital content is available in the text.

1Laboratory of Respiratory Pathophysiology, Department of Public Health and Infectious Diseases, Sapienza University of Rome, Rome, ITALY; 2Laboratory of Respiratory Pathophysiology, Research Team ER10, University of Paris 6, Pierre and Marie Curie Faculty of Medicine (site Pitié-Salpêtrière), Paris, FRANCE; 3Service of Pneumology and Intensive Care, Pitié-Salpêtrière Hospital Group, Paris, FRANCE; and 4Eleonora Spencer Lorillard Cenci Foundation, Rome, ITALY

Address for correspondence: Paolo Onorati, M.D., Laboratory of Respiratory Pathophysiology, Department of Public Health and Infectious Diseases, Sapienza University of Rome, Viale dell’Università 37, 00185 Rome, Italy; E-mail:

Submitted for publication May 2011.

Accepted for publication September 2011.

Supplemental digital content is available for this article. Direct URL citations appear in the printed text and are provided in the HTML and PDF versions of this article on the journal’s Web site (

Incremental cardiopulmonary exercise testing (CPET) is the gold standard for the assessment of physiological (or pathophysiological) limits of exercise tolerance and for appropriate design of training programs either in sport medicine or in chronic disease rehabilitation. For the latter, work intensity prescription should preferably rely on gas exchange measurements for determination of exercise thresholds (i.e., lactic acidosis threshold or LAT, ventilatory compensation point or VCP) (2,9,22,37). Unfortunately, the knowledge and application of the CPET in sport and clinical medicine are still limited because of the fact that equipments (i.e., gas exchange analyzers) used are expensive and often cumbersome. For these reasons, practical and (in some instances) simpler approaches for estimation of exercise thresholds have been evaluated in the past by different authors to facilitate the prescription of training programs. Therefore, several strategies have been proposed; some were based either on ventilatory (minute ventilation E) or on respiratory rate (RR) responses (6,16,26,27), whereas others were based on HR response or on HR variability (3,7,14,18), all of them being expressed as a function of time (or work rate). Of interest, the reliability of some of these methods has been largely debated (5,6,8,15,17,20,21,29,35).

Our interest was to develop new and alternative strategies to those considered standards, such as the ventilatory equivalent for carbon dioxide expressed either as slope (ΔE/ΔV˙CO2) or as a ratio (E/V˙CO2) as a function of time or oxygen uptake (V˙O2) (36), for determination of exercise thresholds. In this regard, we have previously demonstrated that the ΔE/ΔHR relationship can be used as an alternative to the ventilatory equivalent for CO2 method for estimation of VCP in healthy untrained subjects undergoing a cycle ergometer (C) incremental exercise (28). More specifically, we have pointed out that the ΔE/ΔHR relationship was best described by a bilinear response during C exercise, a finding that was in accordance with previous studies on rate-adaptive pacemakers (32,34). In contrast, we found that change of steepness of this bilinear response consistently corresponded to VCP but not to LAT (28). One plausible explanation for this finding was that a more evident increase in the steepness of E (expressed as a function of V˙O2 or time) would be expected at the VCP than at the LAT (36,41), whereas the HR response could either maintain the same linearity presented at moderate work intensities (13) or, in some instances (depending on exercise performance and protocol), depart from it (i.e., HR deflection point (HRDP) or HR threshold), decreasing its rate of increment with respect to work rate (5,20,21,31).

In the present study, we hypothesized that changes in the slope (“break point”) of the ΔE/ΔHR and the ΔRR/ΔHR relationships can be used during treadmill (T) and C incremental exercises as an alternative to the well-standardized ΔE/ΔV˙CO2 method for identification of VCP. We were also interested in evaluating possible differences in VCP estimation by these alternative methods (ΔE/ΔHR and ΔRR/ΔHR) potentially related to a) a different design of T incremental exercise protocols (i.e., different speeds of work rate increment), as already ruled out for the ΔE/ΔHR method during C incremental exercise (28), and b) different exercise modes (i.e., running vs cycling). We anticipate that both the ΔE/ΔHR and ΔRR/ΔHR methods would be reliable as much as those standards for VCP determination during C and T. This would lead to the development of less expensive exercise equipments without gas analyzers that could be easily used in sport medicine and in a clinical exercise setting.

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Fourteen untrained healthy male subjects were recruited for the study. Exclusion criteria included medical history or clinical and/or laboratory findings of cardiorespiratory, metabolic, or neuromuscular diseases. Laboratory tests included resting ECG, spirometry, single-breath diffusing capacity of the lung for carbon monoxide, fasting glycemia, blood cell count, and serological analysis of renal, hepatic, and thyroidal function. Subjects’ characteristics are shown in Table 1. The study was approved by the ethics committee of the Sapienza University of Rome in accordance with the Declaration of Helsinki. Written informed consent was obtained from each participant before the initiation of the project.



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Study design.

On the enrollment day, each and every subject was familiarized with CPET equipment by performing at least one incremental exercise to volitional fatigue on both C and T.

On experimental days, all subjects underwent two step-incremental exercise protocols (both separated by a minimum of 48 h of interval) on a T (T170 De Med; COSMED, Rome, Italy). The T speed was set at a constant speed of 8 km·h−1, and protocols differed from each other on the speed of grade increments: 2%·min−1 and 1%·min−1 for the fast (FT) and slow (ST) protocols, respectively. On a separate day, all subjects also performed a 1-min step (30 W) incremental exercise on a C (ERG 551; Bosch, Germany). Each exercise test consisted of a) 2 min of rest, b) 1 min of warm-up (running at 8 km·h−1 and 0% of grade or cycling at 20 W), c) an incremental phase, and d) a 4-min recovery period. For C, participants were asked to cycle at a pedaling rate of 60 rpm. The tests were interrupted as soon as the subject was not able to keep the running speed of 8 km·h−1 and the pedaling frequency of 60 rpm, for T and C, respectively. The tests’ sequence was randomized.

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Gas exchange and exercise measurements.

Pulmonary gas exchange indexes were measured using a breath-by-breath apparatus (COSMED Quark b2; Rome, Italy). Subjects breathed through a facial mask connected to a photoelectric digital turbine (diameter = 28 mm, resolution = 4 mL). Expired gas was drawn from the distal part of the turbine using a special sampler capillary of polymer Nafion (Perma Pure LLC, Toms River, NJ); O2 and CO2 concentrations were determined by rapid response analyzers (O2 zirconium, CO2 infrared). Calibration of the system was performed immediately before each test, using a 3-L syringe to calibrate the turbine and a two-point calibration of the gas analyzers using room air and a gas mixture from a tank (O2 = 16%, CO2 = 5%, and N2 balance). Corrections for the transport delay, from the turbine to the sensor, and for the rise time of the analyzers during the calibrations procedure were taken into account (1). The following data were obtained breath by breath and averaged every 10 s for subsequent analysis: O2 uptake (V˙O2, STPD), CO2 output (V˙CO2, STPD), E (BTPS), RR, and end-tidal partial pressures for O2 and CO2 (PETCO2). HR was derived from R–R intervals measured from 12-lead ECG and recorded as a function of V˙O2.

Two authors, experts in CPET, independently evaluated the exercise thresholds (automatic detection by the software was not taken into account) using two user-controlled rulers available in the software; the authors were blinded with respect to the type of exercise and the test protocol. In the presence of disagreement, a third expert took the final decision between the two possible options.

The LAT was detected individually using the V-slope method (2) and verified against other points, i.e., the V˙O2 at which the E/V˙O2 and end-tidal partial pressure for O2 began to increase systematically, whereas E/V˙CO2 and PETCO2 remained stable. The VCP was identified where E started to change out of proportion of V˙CO2 with the increase of E/V˙CO2 and the consequent decline of PETCO2 (36,41).

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VCP estimation by the analysis of the E and HR and the RR and HR relationships.

For VCP detection, the relationships between E and HR and between RR and HR were analyzed as E and RR plotted against HR (ΔE/ΔHR and ΔRR/ΔHR).

In our study, the VCP detection on the ΔE/ΔHR and ΔRR/ΔHR plots was evaluated using the aforementioned dedicated software and was estimated by visually applying a “best line fit” (S2 line) from the end of exercise to submaximal data. VCP was detected where E and RR departed from linearity. A second linear fit (S1 line) was drawn through submaximal data from VCP to the end of the warm-up phase; if discernible, LAT was defined as the level where E and RR also departed from linearity.

For the assessment of the VCP according to each method (ΔE/ΔV˙CO2, ΔE/ΔHR, and ΔRR/ΔHR), the authors followed the same procedure as described for exercise threshold evaluation.

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Statistical analysis.

Group data are presented as mean ± SD. The Pearson product–moment correlation coefficient was used to detect correlation among criterion variables. Differences among measured variables were determined by ANOVA followed by the Bonferroni correction; the level of statistical significance was set at P < 0.01. The limits of agreement between the ventilatory equivalent for the CO2, the ΔE/ΔHR, and the ΔRR/ΔHR methods for the estimation of VCP were evaluated by the Bland–Altman analysis, where the individual differences are plotted against their respective means. The independency between the variability and the magnitude of the measurement (i.e., a between-method difference not proportional to mean value) was previously assessed by plotting the absolute differences versus subjects’ means and using the Spearman rank correlation (i.e., correlation coefficient close to zero). Thus, the mean bias and the 95% limits of agreement were calculated as mean ± 1.96 SD; if correlation was present between the variability and the magnitude of the measurement (i.e., correlation coefficient close to 1), a logarithmic transformation of data was performed to try to solve the problem (4). In addition, for the evaluation of the observers’ reliability in exercise threshold detection, we used the Bland–Altman method for the analysis of the interrater agreement.

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Exercise data and comparisons between the C, FT, and ST protocols are presented in Table 2. As expected, significant lower values were observed during C compared with T for peak exercise value of V˙O2 or V˙O2peak (P < 0.01), LAT-V˙O2 (P < 0.001), V˙Epeak (P < 0.01), HRpeak (P < 0.01), and V˙O2 at VCP (V˙O2@VCP) (for each method of detection) (P < 0.01), whereas similar values were obtained for FT versus ST. During T, LAT-V˙O2 did not reach a statistical difference between protocols as well as V˙O2peak; the maximal grade reached during the FT resulted significantly higher compared with ST (P < 0.001).



The ΔE/ΔHR and the ΔRR/ΔHR relationships before and after the VCP were best described by a linear fitting (see S1 and S2 linear regression coefficients (R2) in Table 2 and in Figs. 1, 2, and 3, panels A and C).







In the ΔE/ΔHR plot (Figs. 1A, 2A, and 3A), a change in the slope (“break point”) was clearly discernable in each and every subject during C and both FT and ST protocols; in the ΔRR/ΔHR plot (Figs. 1C, 2C, and 3C), a clear break point was discernable in each and every subject during C and the ST protocol and in 13 (93%) of 14 subjects during the FT protocol; these break points corresponded to the VCP detected using the ΔE/ΔV˙CO2 and the E/V˙CO2 versus V˙O2 plots (Figs. 1, 2, and 3, panels B and D).

A good interrater agreement was observed in VCP determination, especially applying the ΔE/ΔV˙CO2 and ΔE/ΔHR methods (Table, Supplemental Digital Content 1, and Figure, Supplemental Digital Content 2,; for all of the subjects and for each exercise protocol, the difference in V˙O2@VCP and the coefficient of variation between observers become less than 100 mL·min−1 and 4%, respectively, by applying the three experimental methods (ΔE/ΔV˙CO2, ΔE/ΔHR, and ΔRR/ΔHR). No significant differences between methods were observed during C, FT, and ST for V˙O2@VCP, either as an absolute value or as a percentage of V˙O2peak predicted (Table 2).

In the analysis of between-method differences for VCP detection, once the independency between the variability and the magnitude of the measurement were assessed, a good agreement was found between the ΔE/ΔV˙CO2, ΔE/ΔHR, and ΔRR/ΔHR methods during C, FT, and ST protocols. The mean bias ± 95% confidence interval of the between-methods differences are shown in Figure 4 (Table, Supplemental Digital Content 3, Of notice, VCP differed by more than 100 mL·min−1 of V˙O2 in only 2 (14%) of 14 subjects during C and ST when comparing ΔE/ΔV˙CO2 versus ΔRR/ΔHR and during both FT and ST when comparing ΔE/ΔHR versus ΔRR/ΔHR. The mean coefficients of variation between methods, ΔV˙E/ΔV˙CO2 versus ΔE/ΔHR, ΔE/ΔV˙CO2 versus ΔRR/ΔHR, and ΔE/ΔHR versus ΔRR/ΔHR, were 1.7% ± 1.6%, 1.8% ± 2.2%, and 1.2% ± 1.4%, respectively, for C; 1.1% ± 0.7%, 0.9% ± 0.8%, and 1.4% ± 1.3%, respectively, for FT; and 0.7% ± 0.6%, 1.5% ± 1.3%, and 1.7% ± 1.3%, respectively, for ST.



More interestingly, absolute values of E/HR and RR/HR at VCP (E/HR@VCP and RR/HR@VCP) as well as S2 of ΔE/ΔHR and S1 and S2 of ΔRR/ΔHR were not different between C and T and between FT and ST, although the R2 values were lower for ΔRR/ΔHR (Table 2).

In the ΔE/ΔHR plot, another and earlier break point corresponding to the LAT was discernable in 12 (86%) of 14 subjects during C and in 11 (78%) of 14 during the FT and ST protocols; in this case, the ΔE/ΔHR relationship resulted in a trilinear response. In the ΔRR/ΔHR plot, a break point corresponding to the LAT was discernable in 13 (93%) of 14 subjects; the R2 of this relationship between LAT and VCP was significantly lower compared with ΔE/ΔHR (Table 2; Figs. 1, 2, and 3, panels A and C).

Of notice, a loss of linearity in the HR-versus-V˙O2 plot with a downward deflection of the relationship (also called the HRDP) was observed only in 2, none, and 7 of 14 subjects (14%, 0%, and 54%, respectively) during C, FT, and ST, respectively (Figure, Supplemental Digital Content 4,

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The main findings of this study are as follows: 1) VCP can be reliably detected by evaluating the change in either the ΔE/ΔHR or the ΔRR/ΔHR slopes during both C and T (at different speeds, i.e., FT and ST) incremental protocols, and 2) the limits of agreement and the coefficient of variation (in terms of V˙O2 value) observed between the ΔE/ΔV˙CO2, ΔE/ΔHR, and ΔRR/ΔHR methods for VCP estimation are quite narrow and, therefore, acceptable because they fall by far inside the between-day intrasubject V˙O2 variability (38,39). However, despite an excellent between-methods agreement, it is up to the practitioner to decide whether or not to accept it, according to the practical relevance.

The current study has demonstrated that these new methods (particularly the ΔE/ΔHR) of VCP estimation are simple to use and of special practical importance (considering the relevance of this threshold in exercise prescription) (9,23) because practitioners are able to individualize specific training programs without the need for gas exchange measurements.

The E-versus-HR (or more precisely the HR vs E) relationship during incremental exercise has been originally investigated because of its implication in algorithms of rate-adaptive pacemakers, which indirectly assess E by measuring changes in transthoracic impedance and, thus, can closely match paced HR with metabolic demand. However, in the first algorithms, the E and paced HR relationship was described by a parabolic profile (i.e., exponential regression), thereby showing some limitations such as a tendency of the pacing rate to reach the upper rate earlier during exercise compared with the normal sinus node’s response (19). Further studies revealed that the HR-to-E coupling could be approximated (considering also age- and sex-specific differences) by a bilinear response with a change of the relationship’s steepness (break point) at LAT only (32,34). The existence of a bilinear response in the ΔE/ΔHR relationship was confirmed by our previous study carried out in healthy untrained subjects undergoing C exercise. However, we found that change of steepness of this bilinear response corresponded to VCP and not to LAT (28).

In the present study, we were also able to detect in all instances a clear break point in the ΔE/ΔHR relationship that corresponded to the VCP identified by the ventilatory equivalent for CO2 method. In approximately 80% of the subjects, the ΔE/ΔHR relationship showed a trilinear response due to an earlier and less pronounced slope’s break point, compared with the VCP, which corresponded to the LAT. Possible explanations for this observation may include a) a lesser degree of accuracy for the LAT estimation (compared with VCP) by the analysis of the isolated ventilatory responses (i.e., E vs time or V˙O2) (Figure, Supplemental Digital Content 4,, which can be affected by different factors such as volitional hyperventilation and/or the incremental protocol design (i.e., slow incremental tests); b) the inaccuracy of the isolated HR response measurement (i.e., Conconi test) (7) for LAT estimation (i.e., the HRDP) that has been clearly demonstrated (5,20,35) especially during C exercise with an incremental workload and a fixed cadence (29); c) a more evident increase in the slope steepness of the isolated E response during incremental exercises, which is expected at VCP compared with LAT (Figure, Supplemental Digital Content 4, (36,41); and d) a more significant coincidence of the HRDP with the VCP (Figure, Supplemental Digital Content 4, as reported by different authors (5,31), although it is also recognized that threshold estimation (LAT vs VCP) with such atype of analysis is highly dependent upon the type of exerciseperformed (i.e., running, cycling) and protocol used (i.e., fixed vs incremental performance cadence) (15,29,35). For the aforementioned reasons, we suggest to use the ΔE/ΔHR method only for VCP determination.

The VCP was detected in most of the subjects by also applying the ΔRR/ΔHR method. However, this method showed a lower degree of precision than the Δ E/ΔHR analysis, as demonstrated by the significant lower values of the R2 obtained, particularly before the VCP (Table 2; Figs. 1, 2, and 3, panels A and C). Previous authors have examined the reliability of exercise threshold estimation by the analysis of isolated RR response (i.e., RR vs time and/or workload) during incremental exercises, but conclusions have been discordant. Some investigators found a significant correlation between the point of the disproportioned increase in RR (RR break point) and the ventilatory threshold at LAT but not at VCP (16), whereas in another study, the ventilatory threshold corresponded to 70% and 88% (cycling and T, respectively) of the RR break point (26), thus indicating that the latter probably coincided with the VCP. In a recent study on amateur competitive cyclists, the authors used an iterative least squares regression technique for evaluation of the exercise RR response (6); at odds with previous and our observations, this type of analysis resulted unsatisfactorily, compared with gas exchange criteria, in determining exercise thresholds (LAT and VCP) (6). Although the use of exercise thresholds corresponding to workloads (W) instead of V˙′O2 (as in the present study) for interanalysis comparison could partially account for the apparent discrepancy between our results and those of other investigations, we do not have a clear physiological explanation for these observations.

The finding of lack of significant differences observed between C and T and between FT and ST in the absolute values of E/HR@VCP and RR/HR@VCP as well as in the S2 value of ΔE/ΔHR and in the S1 and S2 values of ΔRR/ΔHR is of particular interest, although the regressions of the latter relationship were less discriminatory compared with ΔE/ΔHR (Table 2; Figs. 1, 2, and 3, panels A and C). In our opinion, whether these variables are unaffected by the type of exercise and/or by the test protocol design still remains to be confirmed.

The comparison of principal exercise indexes between C and T and between the FT and ST protocols yielded to results that are mostly in accordance with previous observations (11,12,24,25). As expected, significant lower values were observed during C, compared with T, for V˙O2peak, LAT-V˙O2, Epeak, HRpeak, and V˙O2@VCP (for each method of detection), whereas similar values were obtained during both FT and ST. Finally, the lack of difference in V˙O2@VCP either as an absolute value, when comparing FT versus ST, or as a percentage of V˙O2peak, when comparing C versus T, is supported by some evidences in the literature showing the independence of VCP from either protocol design, as demonstrated during C incremental exercise in trained cyclists (40), or exercise modes, when expressed as a percentage of V˙O2peak (33); nevertheless, these observations need to be confirmed especially in untrained subjects of different sex and age while performing different C and T protocols.

In conclusion, the present study has demonstrated that both the ΔE/ΔHR and the ΔRR/ΔHR methods may represent new precise and practical methods for VCP estimation during C and T exercise (independently of speed) without the need for gas exchange measurement. These methods seem to open a new perspective for exercise prescription (i.e., during field tests) and for the development of an individualized exercise training program in healthy individuals.

Limitations to the current study are represented by the small sample size and the characteristics of our study population, which prevented the evaluation of possible factors such as age, sex, and/or level of fitness, which influence the variables of interest. Therefore, our investigation should be considered as a pilot study, and the conclusions should be applied only to healthy untrained young males. Further investigations with larger study populations with different characteristics and health conditions are needed to evaluate and to confirm the reliability and reproducibility of both the ΔE/ΔHR and the ΔRR/ΔHR methods for VCP estimation during different exercise modes and protocols.

The present study was not supported by grants, and the authors did not receive any funding.

For each author, there were no conflicts of interest.

The results of the present study do not constitute endorsement by the American College of Sports Medicine.

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