The origins of intolerance during exercise have perplexed scientists for well over a century. A better understanding of the processes that contribute to limiting high-intensity exercise have far-reaching implications, not only for elite exercise performance, but also for the wide spectrum of health, quality of life and mortality. It is intriguing, therefore, that there has existed for about 50 years a mathematical model that has the capacity to predict intolerance during high-intensity constant-work rate exercise. This hyperbolic power–duration (P–d) relationship was first described by Monod and Scherrer for a single muscle group in 1965, and has since been extended to whole-body exercise (e.g. Poole et al. 1988). This model characterises a ‘critical’ power output (CP) or speed (CS) that, once exceeded, will lead to exhaustion in a duration predicted by the completion of a constant amount of work (W′) (Morton, 2006). CP, which lies between the lactate threshold and maximum oxygen uptake (), reflects an intrinsic threshold of aerobic energy provision – defining the highest constant-work rate for which steady states in ventilation, gas exchange (e.g. ) and metabolic (e.g. muscle and blood acid–base status) variables can be achieved (Poole et al. 1988). That CP reflects a parameter of aerobic function is supported by the fact that it is sensitive to interventions affecting oxygen transport and utilisation, such as breathing hypoxic gas mixtures or endurance exercise training. While W′ has been likened to a (predominantly) anaerobic energy source (Monod & Scherrer, 1965; potentially comprising stores of intramuscular glycogen, high-energy phosphates and oxygen), relatively less is known about the physiological underpinnings of this parameter. Importantly, the robust nature of the P–d relationship is demonstrated in its ability to characterise exercise tolerance for a wide range of exercise modalities (including cycling, running, swimming, kayaking, rowing and knee-extension over durations of ∼2–30 min; Morton, 2006), for different subject populations (ranging from adolescents to the elderly, and from elite athletes to patients with chronic heart or lung diseases), and for different species (humans, lungless salamanders, ghost crabs, mice, horses and now also rats; Copp et al. 2010). It is our belief, therefore, that a better understanding of the basis of the P–d relationship will elucidate the factor (or factors) that contribute to limiting exercise performance – the secrets of which are defined within the parameters that shape its curve. Surprisingly, however, there is relatively little evidence supporting the physiological origins of the P–d relationship. As such, the underlying physiological equivalents of the defining mathematical P–d parameters, CP and W′, remain conjectural. The recent characterisation of the P–d curve in the running rat published in The Journal of Physiology by Copp et al. (2010) has opened a new avenue for invasive investigations of the physiological determinants of the P–d relationship. Copp et al. (2010) examined the distribution of blood flow during running above and below the critical speed (CS) in rats. The authors circumvented the usual technical and ethical limitations inherent in human investigation, by using a well validated rat model that provided reliable signs of exercise intolerance and allowed access to measurements of inter- and intra-muscular blood flows. Following familiarisation with testing procedures seven male Sprague–Dawley rats (aged 8–10 weeks) were investigated in the study. Each rat performed (in a randomised order) five constant-speed exercise tests to intolerance on a custom-built treadmill to estimate CS, D′ (the finite distance capacity; later converted to W′) and . Exercise tolerance was taken as the duration for which rats could maintain pace with the treadmill belt. The provision of maximal effort (rather than, for example, reluctance for exercise) was an important aspect of the study, and a complex issue to resolve in an animal model. The careful identification by the authors of adjustments in running speed, gait and attenuation of the righting reflex following exhaustion provided signs of the attainment of physiological limits that were central to the interpretation of the responses. Rats subsequently performed tests at speeds corresponding to ∼15% above and below CS (performed ≥45 min apart) for estimation of exercise tolerance, during which (using a flow-through chamber) and hindlimb muscle blood flow distribution (using microsphere injection via an indwelling carotid artery catheter advanced to the aortic arch) were both measured. After this the animals were killed by an overdose of pentobarbital, the hindlimb muscles removed and the relationship between blood flow and muscle fibre-type composition assessed via radioactive counting and histochemistry. Copp et al. (2010) found that the relationship between running speed and the tolerable duration of exercise conformed to a hyperbolic relationship (r2= 0.93 ± 0.02; mean ± SEM) with a CS of 48.6 ± 1.0 m min−1. Sub-CS exercise tolerance was ∼5× greater compared to above CS (∼45 vs. 10 min). at the limit of tolerance during exercise above CS (81.7 ± 2.5 ml kg−1 min−1) was not different from the determined during preceding tests (87.2 ± 2.6 and 84.0 ± 1.8 ml kg−1 min−1) but was higher than the during sub-CS exercise (P < 0.05; 58.5 ± 2.5 ml kg−1 min−1). During exercise above CS blood flow was significantly greater to 15 of the 28 individual muscles (or muscle regions) of the hindlimb, with 11 of these being composed predominantly of type-IIb/d/x muscle fibres. This was such that a significant positive correlation (r= 0.42) was established between the relative increase in muscle blood flow above versus below CS and the percentage type-IIb/d/x fibres of each muscle. The study by Copp et al. (2010) validates the P–d relationship in the running rat. Such invasive and innovative approaches are key to further unlocking the complex physiological make-up of the P–d curve and the parameters that shape it. Copp et al. (2010) are the first to show a disproportionate increase in skeletal muscle blood flow during exercise above, relative to below, CS. That these increases were, largely, directed towards muscles expressing predominantly glycolytic fibres is consistent with the notion that type-II fibre recruitment profiles may be key in determining the upper limit for steady state exercise (Poole et al. 1988). That is, the high rates of oxidative metabolism that are characteristic of type-I fibres, may help to protect against a progressive reduction in efficiency at high power outputs thereby contributing to setting the limits for CS (or CP). The disproportionately increased blood flow to type-II fibres during supra-CS exercise may therefore reflect an increased reliance on energy provision from these poorly efficient muscle fibres. This notion is consistent with the increasing heterogeneity of muscle fibre recruitment seen when transitioning between sub- and supra-CP exercise intensities in humans. It is also consistent with the observation that endurance athletes (with high % type-I fibres) have a higher CP compared to sprint-trained athletes (who have high % type-II fibres). Furthermore, the hypothesis coheres with the suggestion that the ability to adapt oxidative metabolism (reflected in the time-constant of kinetics) is related to CP – a relationship that remains evident even when extrapolated across groups ranging from elite athletes to patients with chronic heart and/or lung disease (Murgatroyd et al. 2011). By comparison, W′ is less well understood, which is perhaps surprising considering that W′ alone defines the tolerable duration of supra-CP exercise. Interestingly the ‘energy store’ that W′ notionally represents (Morton, 2006) is far greater in rats (∼800 J kg−1; Copp et al. 2010) than in humans (∼150–300 J kg−1; Poole et al. 1988; Murgatroyd et al. 2011). Whether this difference is related to a higher proportion of type-II fibre expression in rats (with greater [glycogen], [phosphocreatine] and glycolytic enzyme activity) remains to be determined, however. An alternative view to this ‘store’ is that W′ represents an ‘accumulation’ of fatigue-related metabolites to some critical limit. Fittingly, a ‘fatigue cascade’ has been proposed by Murgatroyd et al. (2011) linking the depletion of stored substrates, muscle fatigue and a progressive reduction in exercise efficiency (Fig. 1). The increased muscle blood flow observed in rats (Copp et al. 2010) suggests that increased muscle recruitment is part of this cascade. However, whether this recruitment is causal in linking W′ to reduced efficiency/economy during supra-CP (or supra-CS) exercise (Murgatroyd et al. 2011) remains to be determined. A schematic representation of the putative physiological events represented by W′ during high-intensity exercise above CP This ‘fatigue cascade’ continues to develop throughout supra-CP exercise to induce intolerance shortly after the attainment of . Specifically, depletion of finite energy stores (1) (originally proposed as physiological equivalents of W′) leads to the accumulation of metabolites implicated in skeletal muscle fatigue (2) via challenges to cellular homeostasis (3). Consequently, to maintain constant-work rate exercise, recruitment of additional muscle fibres is necessary (4). Whether this leads directly to the increased energy and oxygen costs of the exercise (5) (reflected in the slow component, ), or whether the fatigue itself reduces efficiency directly, or both occur, remains equivocal. This cycle continues until the attainment of at which point (or soon thereafter) intolerance ensues. Whether exercise intolerance is a direct consequence of attaining itself, the accelerated depletion of the residual energy stores or the perception of these events, also remains to be resolved. Continuous and dotted arrows denote demonstrated and hypothesised links, respectively. Like CP, therefore, the distribution and recruitment of oxidative and glycolytic muscle fibres appears to be at the heart of the physiological underpinnings of W′. It is important to consider inherent difficulties of investigating the P–d relationship, however, such as the inter-dependence of CP and W′ (i.e. interventions typically affect both parameters) and the intricate features that they describe, in that CP and W′ may be better reflected in multiple equivalents in view of the convoluted processes that underpin the performance of high-intensity exercise. As such, the invasive approaches, like that developed by Copp et al. (2010), will be invaluable in de-convoluting the physiological bases of the mathematical parameters CP and W′ that predict so well, high-intensity exercise tolerance. Limits imposed by The Journal precluded citation of additional evidence in support of key issues in this topic. We thank Dr Harry B. Rossiter for his suggestions and assistance in the preparation of this article.