## Abstract

**The V′_{E}–V′_{CO2} relationship during incremental exercise has a major impact on peak exercise capacity across the range of COPD severity.** https://bit.ly/2RU1fCy

*To the Editor*:

Exercise intolerance constitutes a key patient-oriented outcome in COPD [1]. There is mounting evidence that the so-called “ventilatory inefficiency” (as established by the linear minute ventilation (*V*′_{E}) to carbon dioxide output (*V*′_{CO2}) relationship during incremental cardiopulmonary exercise testing (CPET)) [2] has an important role in setting the limits of exercise tolerance in this disease [3]. The rationale is straightforward: the faster *V*′_{E} increases (*i.e.* the steeper the *V*′_{E}–*V*′_{CO2} slope), and the higher its resting value (∼y-intercept) [2], the sooner *V*′_{E} is expected to reach a lower compared to a higher maximum breathing capacity (MBC) [4]. Recognising that *V*′_{E} close to MBC cannot be sustained for a prolonged period of time without intolerable dyspnoea [5], it can be hypothesised that peak work rate (WR) would change inversely with *V*′_{E}–*V*′_{CO2} slope and intercept, but directly with MBC. Since the first two parameters are influenced by the fraction of *V*′_{E} “wasted” in the physiological dead space and the “set-point” for the arterial partial pressure for carbon dioxide [2], whereas MBC is linked to the resting ventilatory capacity [6], it is not surprising that the exertional ventilatory demand–capacity relationship varies markedly among patients with COPD [7].

However, understanding the complex interplay between exertional demand (*V*′_{E}) and capacity (MBC) *in vivo* is not a trivial task, as several confounders are likely to obscure (or distort) the underlying relationship. For instance, the “qualitative” features of the *V*′_{E} response (breathing pattern, operating lung volumes, inspiratory constraints) are also key to exercise limitation, being highly variable at a given *V*′_{E} and MBC [7]. In addition, the *V*′_{E} response may be curtailed by precocious exercise termination due to symptoms other than dyspnoea, such as heightened leg discomfort [8]. Additional sources of *V*′_{E} stimuli (*e.g.* early lactic acidosis, hypoxaemia, increased cortical discharge secondary to anxiety) [2] are also common. Considering that an animal study is unlikely to have external validity in this scenario, we reasoned that an *in silico* approach would be helpful to shed new light on this conundrum without multiple concomitant confounders.

In order to develop a modelling strategy with biological plausibility, we reviewed our CPET database with 612 patients with mild to end-stage COPD (forced expiratory volume in 1 s (FEV_{1}) ranging from 104% predicted to 18% predicted; transfer factor of the lung for carbon monoxide (*T*_{LCO}) ranging from 88% pred to 31% pred). We identified the most frequent *V*′_{E}–*V*′_{CO2} slopes, which were rounded to multiples of five: 25 L·L^{−1} (n=73), 30 L·L^{−1} (n=253), 35 L·L^{−1} (n=144), 40 L·L^{−1} (n=62), 45 L·L^{−1} (n=49) and 50 L·L^{−1} (n=31). The estimated (FEV_{1}×40) MBC was rounded to 40 L·min^{−1} in those with FEV_{1} up to 1 L (typically Global Initiative for Chronic Obstructive Lung Disease (GOLD) [1] category III–IV; n=216), 60 L·min^{−1} in those with FEV_{1} >1–1.5 L (typically GOLD II; n=273) and 80 L·min^{−1} in those with FEV_{1} >1.5 L (GOLD I; n=123). We considered 10 L·min^{−1} as a representative value of those showing a “high” y-intercept (>5 L·min^{−1}; n=381) and 5 L·min^{−1} in those showing a “low” y-intercept (<5 L·min^{−1}; n=231). We then calculated the expected *V*′_{CO2} at V′_{E}/MBC=1, *i.e.* the point of ventilatory limitation from a “quantitative” perspective [6]. The work rate (W) at that specific point was calculated based on a *V*′_{CO2}–WR slope of 9 mL·min^{−1}·W^{−1} starting from unloaded *V*′_{CO2} of 0.4 L·min^{−1}.

In keeping with our hypothesis, the steeper the slope, the higher the intercept and the lower the MBC, the faster *V*′_{E} reached MBC; accordingly, estimated peak WR varied negatively with the *V*′_{E}–*V*′_{CO2} parameters, but positively with MBC (figure 1a and 1c). The effect of *V*′_{E}–*V*′_{CO2} was large: for instance, a “patient” with only mild disease (MBC_{1}), but a particularly steep slope (50 L·L^{−1}), showed a peak WR similar to that observed in moderate (MBC_{2}) and severe (MBC_{3}) “patients”, provided their slopes were 40 L·L^{−1} and 25 L·L^{−1}, respectively (figure 1a and 1c for 5 L·min^{−1} and 10 L·min^{−1} intercepts, respectively). At a given MBC (figure 1b and 1d), we observed that, regardless of the intercept, peak WR decreased nonlinearly as the slope increased. All curves were well fitted by a two-parameter quadratic hyperbola (r^{2} ∼1, p<0.0001; regression equations shown in figure 1b and 1d). Of note, the curvature constant increased significantly from MBC_{3} to MBC_{1}, *i.e.* less severe “patients” showed a larger variability on peak WR as the slope increased (p<0.05 by two-way ANOVA). In keeping with what it would be expected from parallel hyperbolas with progressively higher asymptotes (*i.e.* MBC_{1}>MBC_{2}>MBC_{3}) (p<0.05), relative (%) decrease in peak WR from MBC_{1} to MBC_{2} and MBC_{2} to MBC_{3} at a given slope remained unaltered (being, of course, larger in the latter scenario due to the lower absolute WRs in more severe “patients”) (figure 1b and 1d).

How to apply our findings to the real world? Firstly, we provided objective evidence that, in the absence of confounders, ventilatory inefficiency has a major effect on the rate at which *V*′_{E} reaches its theoretical “ceiling” during incremental exercise. It should be emphasised that a high *V*′_{E}–*V*′_{CO2} is translated into worsening exertional dyspnoea, being frequently associated with a low *T*_{LCO}, higher “wasted” ventilation in the dead space and more extensive emphysema [3, 9–11] Therefore, there is a sound physiological rationale to explain the clinical importance of ventilatory inefficiency in COPD. Secondly, major intersubject differences in absolute peak WR (W) can be expected from relatively modest variations in the *V*′_{E}–*V*′_{CO2} slope and, secondarily, in the intercept. This is even truer the milder the disease, *i.e.* the higher the MBC (figure 1a and c). These results might help explain our previous findings that the ventilatory inefficiency explains a larger fraction of peak WR in mild–moderate than in severe–very severe COPD [10]. These assertions should be tempered with our previous findings that whereas the slope increases from age-matched controls to mild–moderate COPD, it decreases in more-severe patients as the mechanical constraint progresses [11]. Even considering this important caveat, we previously found that speeding the rate of increase *V*′_{E} by accelerating *V*′_{CO2} (induced by progressively higher constant WRs) led to a hyperbolic decrease in the time to ventilatory limitation in severe COPD [5]. Similar considerations were made (on a theoretical basis) by Whipp and Ward [12] as pertaining to the effects of interventions. The corollary is that a lower slope may reflect different phenomena depending on the relative contribution of a low drive (beneficial) *versus* critical mechanical constraints (deleterious) [7]. Thirdly, the major impact of steeper slopes in peak WR is a refreshing call for the key importance of addressing COPD comorbidities known to heighten exertional *V*′_{E}, *e.g.* pulmonary hypertension [13], lung fibrosis [14] and heart failure [15]. Finally, despite the fact that no intervention (apart from oxygen supplementation in hypoxaemic patients) [3] has so far consistently decreased the *V*′_{E}–*V*′_{CO2} slope (or the intercept) in COPD, our results show that this remains an important unmet need to improve patients’ exercise tolerance.

As expected from a modelling study with limited degrees of freedom, our study has some limitations. Would the combination of different slopes and intercepts [10] provide a different picture? Firstly, we looked at the pattern of responses in a large population; thus, model parameters do hold external validity. As mentioned, we did not take into consideration a plethora of other factors affecting the time course of *V*′_{E} during incremental exercise [4]. However, we contend that this is exactly the key advantage of an *in silico* study, since the fundamental relationship of interest (*V*′_{E}–*V*′_{CO2} to MBC) can be relatively “isolated” from its confounders. The estimated MBC is a crude index of the ventilatory ceiling, overestimating and underestimating the expected peak *V*′_{E} in milder and severe patients, respectively [4].

Under the inherent limitations of an *in silico* study, we herein provide novel evidence that the *V*′_{E}–*V*′_{CO2} relationship during incremental exercise may have a major impact on peak WR across the range of potential MBCs (COPD “severity”). Considering our limited potential to effectively improve patients’ ventilatory capacity (↑ MBC), fighting the determinants of a heightened ventilatory demand (↓ *V*′_{E}–*V*′_{CO2}) assumes foremost relevance to mitigate the devastating effects of exercise intolerance in this patient population.

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### Supplementary Material

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## Acknowledgements

This work is dedicated to the memory of Brian J. Whipp (1937–2011), a pioneer and enthusiast of the concept of ventilatory (in)efficiency as applied to cardiopulmonary diseases.

## Footnotes

Conflict of interest: J.A. Neder has nothing to disclose.

- Received February 29, 2020.
- Accepted April 14, 2020.

- Copyright ©ERS 2020