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After a short historical account, and a discussion of Hill and Meyerhof’s theory of the energetics of muscular exercise, we analyse steady-state rest and exercise as the condition wherein coupling of respiration to metabolism is most perfect. The quantitative relationships show that the homeostatic equilibrium, centred around arterial pH of 7.4 and arterial carbon dioxide partial pressure of 40 mmHg, is attained when the ratio of alveolar ventilation to carbon dioxide flow ($${\dot{V}}_{A}/{\dot{V}}_{R}{CO}_{2}$$ V ˙ A / V ˙ R CO 2 ) is − 21.6. Several combinations, exploited during exercise, of pertinent respiratory variables are compatible with this equilibrium, allowing adjustment of oxygen flow to oxygen demand without its alteration. During exercise transients, the balance is broken, but the coupling of respiration to metabolism is preserved when, as during moderate exercise, the respiratory system responds faster than the metabolic pathways. At higher exercise intensities, early blood lactate accumulation suggests that the coupling of respiration to metabolism is transiently broken, to be re-established when, at steady state, blood lactate stabilizes at higher levels than resting. In the severe exercise domain, coupling cannot be re-established, so that anaerobic lactic metabolism also contributes to sustain energy demand, lactate concentration goes up and arterial pH falls continuously. The $${\dot{V}}_{A}/{\dot{V}}_{R}{CO}_{2}$$ V ˙ A / V ˙ R CO 2 decreases below − 21.6, because of ensuing hyperventilation, while lactate keeps being accumulated, so that exercise is rapidly interrupted. The most extreme rupture of the homeostatic equilibrium occurs during breath-holding, because oxygen flow from ambient air to mitochondria is interrupted. No coupling at all is possible between respiration and metabolism in this case.

Purpose We tested the vagal withdrawal concept for heart rate (HR) and cardiac output (CO) kinetics upon moderate exercise onset, by analysing the effects of vagal blockade on cardiovascular kinetics in humans. We hypothesized that, under atropine, the φ1 amplitude (A1) for HR would reduce to nil, whereas the A1 for CO would still be positive, due to the sudden increase in stroke volume (SV) at exercise onset. Methods On nine young non-smoking men, during 0–80 W exercise transients of 5-min duration on the cycle ergometer, preceded by 5-min rest, we continuously recorded HR, CO, SV and oxygen uptake ($$ \dot{V} $$ V ˙ O2) upright and supine, in control condition and after full vagal blockade with atropine. Kinetics were analysed with the double exponential model, wherein we computed the amplitudes (A) and time constants (τ) of phase 1 (φ1) and phase 2 (φ2). Results In atropine versus control, A1 for HR was strongly reduced and fell to 0 bpm in seven out of nine subjects for HR was practically suppressed by atropine in them. The A1 for CO was lower in atropine, but not reduced to nil. Thus, SV only determined A1 for CO in atropine. A2 did not differ between control and atropine. No effect on τ1 and τ2 was found. These patterns were independent of posture. Conclusion The results are fully compatible with the tested hypothesis. They provide the first direct demonstration that vagal blockade, while suppressing HR φ1, did not affect φ1 of CO.

Introduction Measuring physiological parameters at depth is an emergent challenge for athletic training, diver's safety and biomedical research. Recent advances in wearable sensor technology made this challenge affordable; however, its impact on breath-hold diving has never been comprehensively discussed. Methods We performed a systematic review of the literature in order to assess what types of sensors are available or suitable for human breath-hold diving, within the two-fold perspective of safety and athletic performance. Results In the 52 studies identified, sensed physiological variables were: electrocardiogram, body temperature, blood pressure, peripheral oxygen saturation, interstitial glucose concentration, impedance cardiography, heart rate, body segment inertia and orientation. Conclusions Limits and potential of each technology are separately reviewed. Inertial sensor technology and transmission pulse oximetry could produce the greatest impact on breath-hold diving performances in the future.

The power–duration relationship has been variously modelled, although duration must be acknowledged as the dependent variable and is supposed to represent the only source of experimental error. However, there are certain situations, namely extremely high power outputs or outdoor field conditions, in which the error in power output measurement may not remain negligible. The geometric mean (GM) regression method deals with the assumption that also the independent variable is subject to a certain amount of experimental error, but has never been utilized in this context. We applied the GM regression method for the two- and three-parameter critical power models and tested it against the usual weighted least square (WLS) procedure with our previous published data. There were no significant differences between parameter estimates of WLS and GM. Bias and limit of agreements between the two methods were low, while correlation coefficients were high (0.85–1.00). GM provided equivalent results with respect to WLS in fitting the critical power model to experimental data and for its conceptual characteristics must be preferred wherever concerns on the precision of P measurement are present, such as for in-field power meters.

Purpose We hypothesised that, during a light-to-moderate exercise transient, compared to an equivalent rest-to-exercise transient, (1) a further baroreflex sensitivity (BRS) decrease would be slower, (2) no rapid heart rate (HR) response would occur, and (3) the rapid cardiac output (CO) response would have a smaller amplitude (A1). Hence, we analysed the dynamics of arterial baroreflexes and the HR and CO kinetics during rest-to-50 W (0–50 W) and 50-to-100 W (50–100 W) exercise transients. Methods 10 subjects performed three 0–50 W and three 50–100 W on a cycle ergometer. We recorded arterial blood pressure profiles (photo-plethysmography) and R-to-R interval (RRi, electrocardiography). The former were analysed to obtain beat-by-beat mean arterial pressure (MAP) and stroke volume (SV). CO was calculated as SV times HR. BRS was measured by modified sequence method. Results During 0–50 W, MAP transiently fell (− 9.0 ± 5.7 mmHg, p −1 at 50 W (p −1, p −1 at 100 W (p −1, p = 0.07 vs. 50 W). A1 for HR was 9.2 ± 6.0 and 6.0 ± 4.5 min−1 in 0–50 W and 50–100 W, respectively (p = 0.19). The corresponding A1 for CO were 2.80 ± 1.54 and 0.91 ± 0.55 l∙min−1 (p Conclusion During 50–100 W, with respect to 0–50 W, BRS decreased more slowly, in absence of a prompt pressure decrease. BRS decrease and rapid HR response in 50–100 W were unexpected and ascribed to possible persistence of some vagal tone at 50 W.

Vinetti, G, Pollastri, L, Lanfranconi, F, Bruseghini, P, Taboni, A, and Ferretti, G. Modeling the power-duration relationship in professional cyclists during the Giro d'Italia. J Strength Cond Res XX(X): 000-000, 2022-Multistage road bicycle races allow the assessment of maximal mean power output (MMP) over a wide spectrum of durations. By modeling the resulting power-duration relationship, the critical power (CP) and the curvature constant (W') can be calculated and, in the 3-parameter (3-p) model, also the maximal instantaneous power (P0). Our aim is to test the 3-p model for the first time in this context and to compare it with the 2-parameter (2-p) model. A team of 9 male professional cyclists participated in the 2014 Giro d'Italia with a crank-based power meter. The maximal mean power output between 10 seconds and 10 minutes were fitted with 3-p, whereas those between 1 and 10 minutes with the 2- model. The level of significance was set at p0.05. 3-p yielded CP 357 ± 29 W, W' 13.3 ± 4.2 kJ, and P0 1,330 ± 251 W with a SEE of 10 ± 5 W, 3.0 ± 1.7 kJ, and 507 ± 528 W, respectively. 2-p yielded a CP and W' slightly higher (+4 ± 2 W) and lower (-2.3 ± 1.1 kJ), respectively (p0.001 for both). Model predictions were within ±10 W of the 20-minute MMP of time-trial stages. In conclusion, during a single multistage racing event, the 3-p model accurately described the power-duration relationship over a wider MMP range without physiologically relevant differences in CP with respect to 2-p, potentially offering a noninvasive tool to evaluate competitive cyclists at the peak of training.

Purpose: The three-parameter model of critical power (3-p) implies that in the severe exercise intensity domain time to exhaustion (Tlim) decreases hyperbolically with power output starting from the power asymptote (critical power, ẇcr) and reaching 0 s at a finite power limit (ẇ0) thanks to a negative time asymptote (k). We aimed to validate 3-p for short Tlim and to test the hypothesis that ẇ0 represents the maximal instantaneous muscular power.Methods: Ten subjects performed an incremental test and nine constant-power trials to exhaustion on an electronically braked cycle ergometer. All trials were fitted to 3-p by means of non-linear regression, and those with Tlim greater than 2 min also to the 2-parameter model (2-p), obtained constraining k to 0 s. Five vertical squat jumps on a force platform were also performed to determine the single-leg (i.e., halved) maximal instantaneous power.Results: Tlim ranged from 26 ± 4 s to 15.7 ± 4.9 min. In 3-p, with respect to 2-p, ẇcr was identical (177 ± 26 W), while curvature constant W' was higher (17.0 ± 4.3 vs 15.9 ± 4.2 kJ, p < 0.01). 3-p-derived ẇ0 was lower than single-leg maximal instantaneous power (1184 ± 265 vs 1554 ± 235 W, p < 0.01).Conclusions: 3-p is a good descriptor of the work capacity above ẇcr up to Tlim as short as 20 s. However, since there is a discrepancy between estimated ẇ0 and measured maximal instantaneous power, a modification of the model has been proposed.

We hypothesized that during rapid uptilting at rest, due to vagal withdrawal, arterial baroreflex sensitivity (BRS) may decrease promptly and precede the operating point (OP) resetting, whereas different kinetics are expected during exercise steady state, due to lower vagal activity than at rest. To test this, eleven subjects were rapidly (−1 (SD = 17.1) in S and 16.7 ms·mmHg−1 (SD = 6.4) in U ( P < 0.01), RRi was 901 ms (SD = 118) in S and 749 ms (SD = 98) in U ( P < 0.01), and MAP was 76 mmHg (SD = 11) in S and 83 mmHg (SD = 8) in U ( P < 0.01). During uptilt, BRS decreased promptly [first BRS sequence was 19.7 ms·mmHg−1 (SD = 5.0)] and was followed by an OP resetting (MAP increase without changes in RRi). At exercise, BRS and OP did not differ between supine and upright positions [BRS was 7.7 ms·mmHg−1 (SD = 3.0) and 7.7 ms·mmHg−1 (SD = 3.5), MAP was 85 mmHg (SD = 13) and 88 mmHg (SD = 10), and RRi was 622 ms (SD = 61) and 600 ms (SD = 70), respectively]. The results support the tested hypothesis. The prompt BRS decrease during uptilt at rest may be ascribed to a vagal withdrawal, similarly to what occurs at exercise onset. The OP resetting may be due to a slower control mechanism, possibly an increase in sympathetic activity.

New findings What is the central question of this study? We modelled the alveolar pathway during breath holding on the hypothesis that it follows a hypoventilation loop on the O2 -CO2 diagram. What is the main finding and its importance? Validation of the model was possible within the range of alveolar gas compositions compatible with consciousness. Within this range, the experimental data were compatible with the proposed model. The model and its characteristics might allow predictions of alveolar gas composition whenever the alveolar ventilation goes to zero; for example, static and dynamic breath holding at the surface or during ventilation/intubation failure in anaesthesia. Abstract According to the hypothesis that alveolar partial pressures of O2 and CO2 during breath holding (BH) should vary following a hypoventilation loop, we modelled the alveolar gas pathways during BH on the O2 -CO2 diagram and tested it experimentally during ambient air and pure oxygen breathing. In air, the model was constructed using the inspired and alveolar partial pressures of O2 ( P I O 2 and P A O 2 , respectively) and CO2 ( P IC O 2 and P AC O 2 , respectively) and the steady-state values of the pre-BH respiratory exchange ratio (RER). In pure oxygen, the model respected the constraint of P AC O 2 = - P A O 2 + P I O 2 . To test this, 12 subjects performed several BHs of increasing duration and one maximal BH at rest and during exercise (30 W cycling supine), while breathing air or pure oxygen. We measured gas flows, P A O 2 and P AC O 2 before and at the end of all BHs. Measured data were fitted through the model. In air, P I O 2 = 150 ± 1 mmHg and P IC O 2 = 0.3 ± 0.0 mmHg, both at rest and at 30 W. Before BH, steady-state RER was 0.83 ± 0.16 at rest and 0.77 ± 0.14 at 30 W; P A O 2 = 107 ± 7 mmHg at rest and 102 ± 8 mmHg at 30 W; and P AC O 2 = 36 ± 4 mmHg at rest and 38 ± 3 mmHg at 30 W. By model fitting, we computed the RER during the early phase of BH: 0.10 [95% confidence interval (95% CI) = 0.08-0.12] at rest and 0.13 (95% CI = 0.11-0.15) at 30 W. In oxygen, model fitting provided P I O 2 : 692 (95% CI = 688-696) mmHg at rest and 693 (95% CI = 689-698) mmHg at 30 W. The experimental data are compatible with the proposed model, within its physiological range.

Purpose We analysed the characteristics of arterial baroreflexes during the first phase of apnoea (φ1). Methods 12 divers performed rest and exercise (30 W) apnoeas (air and oxygen). We measured beat-by-beat R-to-R interval (RRi) and mean arterial pressure (MAP). Mean RRi and MAP values defined the operating point (OP) before (PRE-ss) and in the second phase (φ2) of apnoea. Baroreflex sensitivity (BRS, ms·mmHg−1) was calculated with the sequence method. Results In PRE-ss, BRS was (median [IQR]): at rest, 20.3 [10.0–28.6] in air and 18.8 [13.8–25.2] in O2; at exercise 9.2[8.4–13.2] in air and 10.1[8.4–13.6] in O2. In φ1, during MAP decrease, BRS was lower than in PRE-ss at rest (6.6 [5.3–11.4] in air and 7.7 [4.9–14.3] in O2, p 2. After attainment of minimum MAP (MAPmin), baroreflex resetting started. After attainment of minimum RRi, baroreflex sequences reappeared. In φ2, BRS at rest was 12.1 [9.6–16.2] in air, 12.9 [9.2–15.8] in O2. At exercise (no φ2 in air), it was 7.9 [5.4–10.7] in O2. In φ2, OP acts at higher MAP values. Conclusion In apnoea φ1, there is a sudden correction of MAP fall via baroreflex. The lower BRS in the earliest φ1 suggests a possible parasympathetic mechanism underpinning this reduction. After MAPmin, baroreflex resets, displacing its OP at higher MAP level; thus, resetting may not be due to central command. After resetting, restoration of BRS suggests re-establishment of vagal drive.

Objective. Total lung capacity (TLC) assessment outside of a research laboratory is challenging. We describe a novel method for measuring TLC that is both simple and based only on portable equipment, and report preliminary data in healthy subjects.Approach. We developed an open circuit system to administer a known amount of oxygen to a subject in a single maximal inspiratory maneuver. Oxygen fraction, expired and inspired flows were continuously monitored to allow a precise computation of the mass balance. Values of TLC and functional residual capacity (FRC) were compared with standard methods (body plethysmography and multiple-breath helium dilution). Twenty healthy subjects participated to the study, eleven of which performed the maneuver twice to assess test-retest reliability.Main results.There was high agreement in TLC between the proposed method and the two standard methods (R2 > 0.98, bias not different from 0, and 95% limits of agreements 0.99 and no bias). Results were similar for FRC, with a slightly higher variability due its sensitivity to changes in posture or breathing pattern.Significance.Single-breath oxygen dilution is accurate and reliable in assessing TLC and FRC in healthy subjects. The technique is appealing for time- or resource-limited settings, such as field physiological research expeditions or mass screenings.

To check whether the evolution of alveolar pressures of O2 (PAO2) and CO2 (PACO2) explains the cardiovascular responses to apnoea, eight divers performed resting apnoeas of increasing duration in air and in O2. We measured heart rate (fH), arterial pressure (AP), and peripheral resistances (TPR) beat-by-beat, PAO2 and PACO2 at the end of each apnoea. The three phases of the cardiovascular response to apnoea were observed. In O2, TPR increase (9 ± 4 mmHg min l−1) and fH decrease (-11 ± 8 bpm) were lower than in air (15 ± 5 mmHg min l−1 and -28 ± 13 bpm, respectively). At end of maximal apnoeas in air, PAO2 and PACO2 were 50 ± 9 and 48 ± 5 mmHg, respectively; corresponding values in O2 were 653 ± 8 mmHg and 55 ± 5 mmHg. At end of phase II, PAO2 and PACO2 in air were 90 ± 13 mmHg and 42 ± 4 mmHg respectively; corresponding values in O2 were 669 ± 7 mmHg and 47 ± 6 mmHg. The PACO2 increase may trigger the AP rise in phase III.

The baroreflex system is a complex mechanism for short-term regulation of arterial blood pressure, involving the heart rate (HR), the heart contractility and the vascular tone in its efferent branches. The study of arterial baroreflexes relies on two different experimental approaches. On one hand, the closed-loop approach analyses the mutual relationship between HR and arterial blood pressure, both in steady state and in dynamic conditions. This article is protected by copyright. All rights reserved.

If, as postulated, the end of the steady state phase (φ2) of cardiovascular responses to apnoea corresponds to the physiological breaking point, then we may hypothesize that φ2 should become visible if exercise apnoeas are performed in pure oxygen. We tested this hypothesis on 9 professional divers by means of continuous recording of blood pressure (BP), heart rate (fH), stroke volume (QS), and arterial oxygen saturation (SpO2) during dry maximal exercising apnoeas in ambient air and in oxygen. Apnoeas lasted 45.0 ± 16.9 s in air and 77.0 ± 28.9 s in oxygen (p

Introduction We tested the hypothesis that the alveolar gas composition at the transition between the steady phase II (φ2) and the dynamic phase III (φ3) of the cardiovascular response to apnoea may lay on the physiological breaking point curve (Lin et al., 1974). Methods Twelve elite divers performed maximal and φ2-interrupted apnoeas, in air and pure oxygen. We recorded beat-by-beat arterial blood pressure and heart rate; we measured alveolar oxygen and carbon dioxide pressures (P A O 2 and P A CO 2 , respectively) before and after apnoeas; we calculated the P A CO 2 difference between the end and the beginning of apnoeas (ΔP A CO 2 ). Results Cardiovascular responses to apnoea were similar compared to previous studies. P A O 2 and P A CO 2 at the end of φ2-interrupted apnoeas, corresponded to those reported at the physiological breaking point . For maximal apnoeas, P A CO 2 was less than reported by Lin et al. (1974). ΔP A CO 2 was higher in oxygen than in air. Conclusions The transition between φ2 and φ3 corresponds indeed to the physiological breaking point . We attribute this transition to ΔP A CO 2 , rather than the absolute P A CO 2 values, both in air and oxygen apnoeas.

We tested the linear critical power ( $$\dot{w}_{\text{cr}}$$ ) model for discrete incremental ramp exercise implying recovery intervals at the end of each step. Seven subjects performed incremental (power increment 25 W) stepwise ramps to subject’s exhaustion, with recovery intervals at the end of each step. Ramps’ slopes (S) were 0.83, 0.42, 0.28, 0.21, and 0.08 W s−1; recovery durations (t r) were 0 (continuous stepwise ramps), 60, and 180 s (discontinuous stepwise ramps). We determined the energy store component (W′), the peak power ( $$\dot{w}_{\text{peak}}$$ ), and $$\dot{w}_{\text{cr}}$$ . When t r = 0 s, $$\dot{w}_{\text{cr}}$$ and W′ were 187 ± 26 W and 14.5 ± 5.8 kJ, respectively. When t r = 60 or 180 s, the model for ramp exercise provided inconsistent $$\dot{w}_{\text{cr}}$$ values. A more general model, implying a quadratic $$\dot{w}_{\text{peak}}$$ versus $$\sqrt S$$ relationship, was developed. This model yielded, for t r = 60 s, $$\dot{w}_{\text{cr}}$$ = 189 ± 48 W and W′ = 18.6 ± 17.8 kJ, and for t r = 180 s, $$\dot{w}_{\text{cr}}$$ = 190 ± 34 W, and W′ = 16.4 ± 16.7 kJ. These $$\dot{w}_{\text{cr}}$$ and W′ did not differ from the corresponding values for t r = 0 s. Nevertheless, the overall amount of energy sustaining work above $$\dot{w}_{\text{cr}}$$ , due to energy store reconstitution during recovery intervals, was higher the longer t r, whence higher $$\dot{w}_{\text{peak}}$$ values. The linear $$\dot{w}_{\text{cr}}$$ model for ramp exercise represents a particular case (for t r = 0 s) of a more general model, accounting for energy resynthesis following oxygen deficit payment during recovery.

We hypothesized that the third dynamic phase (ϕ3) of the cardiovascular response to apnoea requires attainment of the physiological breaking point, so that the duration of the second steady phase (ϕ2) of the classical cardiovascular response to apnoea, though appearing in both air and oxygen, is longer in oxygen.Nineteen divers performed maximal apnoeas in air and oxygen. We measured beat-by-beat arterial pressure, heart rate (fH), stroke volume (SV), cardiac output (Q˙).The fH, SV and Q˙ changes during apnoea followed the same patterns in oxygen as in air. Duration of steady ϕ2 was 105 ± 37 and 185 ± 36 s, in air and oxygen (p0.05), respectively. At end of apnoea, arterial oxygen saturation was 1.00 ± 0.00 in oxygen and 0.75 ± 0.10 in air.The results support the tested hypothesis. Lack of hypoxaemia during oxygen apnoeas suggests that, if chemoreflexes determine ϕ3, the increase in CO2 stores might play a central role in eliciting their activation.