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Exercise: Kinetic Considerations for Gas Exchange

Harry B. Rossiter

10.1002/cphy.c090010

Source: Volume 1, Issue 1, January 2011

Published online: November 2010

Full Article on Wiley Online Library



Abstract

The activities of daily living typically occur at metabolic rates below the maximum rate of aerobic energy production. Such activity is characteristic of the nonsteady state, where energy demands, and consequential physiological responses, are in constant flux. The dynamics of the integrated physiological processes during these activities determine the degree to which exercise can be supported through rates of O2 utilization and CO2 clearance appropriate for their demands and, as such, provide a physiological framework for the notion of exercise intensity. The rate at which O2 exchange responds to meet the changing energy demands of exercise—its kinetics—is dependent on the ability of the pulmonary, circulatory, and muscle bioenergetic systems to respond appropriately. Slow response kinetics in pulmonary O2 uptake predispose toward a greater necessity for substrate‐level energy supply, processes that are limited in their capacity, challenge system homeostasis and hence contribute to exercise intolerance. This review provides a physiological systems perspective of pulmonary gas exchange kinetics: from an integrative view on the control of muscle oxygen consumption kinetics to the dissociation of cellular respiration from its pulmonary expression by the circulatory dynamics and the gas capacitance of the lungs, blood, and tissues. The intensity dependence of gas exchange kinetics is discussed in relation to constant, intermittent, and ramped work rate changes. The influence of heterogeneity in the kinetic matching of O2 delivery to utilization is presented in reference to exercise tolerance in endurance‐trained athletes, the elderly, and patients with chronic heart or lung disease. © 2011 American Physiological Society. Compr Physiol 1:203‐244, 2011.

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Figure 1. Figure 1.

A schematic diagram of the physiological systems interactions that determine gas exchange kinetics during exercise. Reactants are shown in circles, and flows and processes are in rectangular boxes. Dashed boxes illustrate internal system structures. The center panel describes the mass balance relationships between the active muscle and pulmonary systems, which are separated by the circulation. The relationship between the O2 concentration of the inflow and the local oxygen exchange (O2) to blood flow () ratio determines the O2 concentration of the effluent from the muscle and lung compartments. These are heterogeneous tissues and therefore the local o2/ can vary widely depending on the local conditions (as indicated by the dashed lines in the center panel). The mass balances for gas exchange at the alveoli and the mouth are depicted in the upper panel, together with the process that has the potential to dissociate them (alveolar gas storage). The lower panel illustrates the processes determining muscle O2 consumption, where the key downstream dynamics of the putative determinants of the rate of oxidative phosphorylation are shown: oxygen; the redox status (from the fluxes if the TCA cycle and glycolysis); and phosphates (from the balance between the energy‐consuming processes and the phosphocreatine system capacitance). See text for a full explanation. Key. Subscripts: a, arterial; A, alveolar; b, body; E, expired; I, inspired; m, muscle; p, pulmonary; t, total; v, venous; bar (e.g. or ) represents mean, or “mixed” values. Capitals: C, content; F fraction; , blood flow; , gas flow; V, volume. Abbreviations: ATP, ADP, AMP, adenosine tri‐, di‐, or monophosphate; Bf, breath frequency; CHO, carbohydrates (glucose or glycogen); CO2 carbon dioxide; Cr, creatine; Δ, change; EELV, end‐expiratory lung volume; FFA, free fatty acid; H+, proton; HCO3−, bicarbonate; L−, lactate; Mb, myoglobin; MITO, mitochondrion; O2 oxygen; PCr, phosphocreatine; Pi, inorganic phosphate; Pyr, pyruvate; T, transporter; TCA, tricarboxylic acid cycle; REDOX, redox potential; Vd, dead space volume; Vt, tidal volume.
Figure 2. Figure 2.

Predicted profiles of muscle (O2m) and pulmonary (O2p) kinetic responses (the “output”) to deterministic work rate forcings (the “input”) for a dynamically linear first‐order system. The step and ramp‐incremental exercise patterns are the first and second integrals, respectively, of the pulse work rate input. Control systems theory for a dynamically linear system suggests that the O2 responses would be similarly related, with parameters (the time constant, τ, or mean response time, τ′; and gain G; ) that are invariant across all conditions. Adapted from Reference 456.
Figure 3. Figure 3.

Pulmonary oxygen uptake (O2p), heart rate (HR), and ventilation (E) responses for two subjects (A and B) during constant work rate cycle ergometry for 30‐min duration or to the limit of tolerance (whichever was the sooner). Note that subject A reaches the limit of tolerance at ∼10 min (at a O2p of 3.25 liteṛmin−1), whereas subject B was able to complete the 30‐min task (with a steady‐state O2p of 2.91 liteṛmin−1), despite both subjects exercising at the same work rate (215 W), which was estimated using “standard criteria” to be 85% O2max in each case.
Figure 4. Figure 4.

Schematic diagram of the dynamics of O2, arterial blood lactate ([L−]), and their relationship with the tolerable duration of constant work rate exercise. The characteristics of the O2 (A) and blood [L−] (C) responses are used to demark four different intensity domains, with the limit of tolerance above critical power (CP) being determined by the shape of the power‐duration relationship (B). Moderate intensity: Exercise below the lactate threshold (LT) where O2 quickly attains a steady state, and the initial small increase in blood [L−] is rapidly attenuated toward resting levels (or below). Heavy intensity: Exercise between LT and CP with evidence of a O2 “slow component,” where O2 takes longer to stabilize and increases above value extrapolated from the fundamental exponential (dashed line). The action of the O2 slow component in this domain is to reduce the work efficiency and occurs in association with a sustained but stabilized metabolic acidosis. Very heavy intensity: Exercise above CP where the O2 slow component and blood [L−] progressively increase throughout exercise until the limit of tolerance, predicted by the relationship between power output and tolerable duration. Severe intensity: Exercise where the metabolic rate exceeds the maximal aerobic capacity (O2max) from exercise onset (as depicted by the extrapolation of the fundamental O2 above O2max; dashed line) and intolerance ensues before a O2 slow component develops. Circles indicate intolerance.
Figure 5. Figure 5.

A model to illustrate the effect of the circulatory dynamics (muscle blood flow; m) on pulmonary oxygen uptake (O2p) kinetics at the onset of moderate‐intensity exercise. The model is based on the assumptions stated in Barstow et al. 27 and is presented here for a 100‐W exercise increment from a 0‐W baseline during cycle ergometry (0.5 liteṛmin−1 O2p). Model parameter values used are O2m time constant (τ) = 30 s; τm = 25 s; venous volume = 3 liters; Cao2 = 0.2 mḷml−1; G = 10 mḷmin−1̣W−1; steady‐state = 5̣(O2p + 1) liteṛmin−1; resting fractional O2m = 0.18%; resting fractional m = 0.15%. (A) Venous O2 content draining the muscle (Cvo2m; bottom panel) is summed with the body compartment in proportion to it is respective flow (Cvo2m+b; middle panel) and reaches the lung (O2; upper panel) after a transit delay dependent on the venous volume and the instantaneous blood flow. (B) The pulmonary and muscular O2 and kinetics at exercise onset. The monophasic O2m and m kinetics (bottom) give rise to a biphasic pattern in O2p (top) because of the conflation of pulmonary blood flow (t) and O2. O2p kinetics determine the O2 deficit (O2df), which is assumed to reflect the difference between steady‐state and instantaneous O2p. The O2df is reflected in changes in the concentration of high‐energy phosphates (∼P, but predominantly PCr), changes in [L−] and changes in stored O2. (C) Model predictions for the degree of dissociation between muscle and lung gas exchange. The color scale shows the extent to which differs from O2p at any combination of m and O2m kinetics. Refer to Figure 1 for a flow diagram illustrating the variables contributing to the O2p response at exercise onset.
Figure 6. Figure 6.

The intensity dependence of O2p kinetics during the transition to and from constant work rate exercise. The data illustrate the goodness of fit of on‐ and off‐transient kinetics when modeled with the appropriate combination of “fundamental” and “slow” components (phase I has been omitted from the model fits for simplicity). The influence of increasing exercise intensity is shown by following the panels counterclockwise, starting at the bottom left (moderate) and ending at the top left (severe). The text panels therefore indicate the presence or absence of the O2p slow component (O2sc) within each intensity domain at either exercise onset (above) or exercise cessation (left). For example, severe‐intensity exercise is associated with a O2sc at cessation but not at exercise onset. Redrawn from Özyener et al. 328.
Figure 7. Figure 7.

The kinetic responses of O2p and blood lactate ([L−]) during intermittent exercise at 120% O2max over a range of duty cycles (each at a 1:2 work:rest cycle for an example subject). Duty cycle is inset to each panel (top right), and [L−] values are inset at the times measured along the time axis. The solitary solid and open circles (along the ordinate axis) in each figure are the values of the lactate threshold and O2max for this subject. The figure is organized in a fashion similar to that of Figure 6 (with the moderate response shown at the bottom left, and circulating anticlockwise to the severe‐intensity response at the top left) in order to highlight the similarity between the general kinetic features of intermittent and constant work rate exercise. In the former, relative intensity is modulated by duty cycle duration at a constant work rate, and in the latter, the relative intensity is modulated by work rate with the target duration remaining constant. Redrawn from Reference 414.
Figure 8. Figure 8.

The breath‐by‐breath gas exchange and ventilatory responses of a healthy subject during ramp‐incremental cycle ergometry (20 Ẉmin−1) to the limit of tolerance. (A) The “V‐slope” graph (CO2p as a function of O2p). The breakpoint in the V‐slope corresponds well to the threshold of lactate accumulation measured in arterial blood (LT). Noninvasive validation of this estimate benefits from the consideration of the kinetics of additional features of gas exchange and ventilatory dynamics, especially (B) the fractional concentration of end‐tidal O2 and CO2; (C) The ventilatory equivalents for O2 and CO2 (e/O2p and e/CO2p); and (D) The respiratory exchange ratio (RER; ). The vertical alignment of these six profiles during ramp‐incremental exercise facilitates the verification of noninvasive estimation of LT by visual inspection. The point at which the slope of the CO2p‐O2p relationship increases (the breakpoint in the V‐slope) is the primary index of LT attainment. The end‐tidal and ventilatory equivalent relationships are used to determine that the hyperpnea accompanying the CO2p increase is not a “true” hyperventilation (i.e., the increase in Feto2 and e/O2p occurs at a metabolic rate where FETCO2 and e/CO2p are stable). A subsequent fall in Fetco2 and rise in e/CO2p later in the response profiles signify the onset of respiratory compensation for the metabolic acidosis. The RER is used to corroborate that the LT estimation does not coincide with an RER “inflection point,” which can result from changes in CO2 storage dynamics (i.e., unrelated to blood [L−]). Note that because the S1 slope of the V‐slope graph does not intercept at the origin, the RER slope can be constant, or even decreasing whereas that between CO2p and O2p is increasing. Also note that the response profiles early in the ramp‐incremental exercise (i.e., at O2p values of ∼0.8‐1.2 liteṛmin−1 in this example) are dependent on gas exchange and ventilation kinetics following exercise onset. Therefore, the dynamics during the very early stages of the ramp‐incremental exercise (∼3‐4 min in healthy subjects) do not correspond to events related to blood [L−]. The responses at rest and baseline cycling (20 W) are not displayed on this figure for clarity.
Figure 9. Figure 9.

A schematic diagram of the kinetic responses of O2p to ramp‐incremental exercise (incremented as a smooth function of time with a slope of 20 Ẉmin−1) for responses with different effective time constants (τ′) and/or gains (G; ). The model is for cycle ergometry of 20 W, assuming a baseline O2p of 800 mḷmin−1

. (A) The monoexponential response to ramp‐incremental exercise with constant G (10 mḷmin−1.W−1) but varying τ′ (45 and 120 s). (B) The monoexponential response to ramp‐incremental exercise with constant τ′ (45 s) but varying G (8 and 10 mḷmin−1̣W−1). (C) A putative linear relationship between τ′ and G. (D) The outcome of varying τ′ and G together (using the slope illustrated in panel C) throughout ramp‐incremental exercise to the limit of tolerance. The values shown are the outcome of the fitted estimates using Eq. 17. Note the similarity between the modeled responses for O2p in panels A and D but which derive from kinetics that manifest either fixed (A) or varying (D) values for their underlying parameters.
Figure 10. Figure 10.

The dynamic relationships between intramuscular PCr and O2p kinetics from simultaneous determination of quadriceps PCr (○) and O2p (•) during moderate‐intensity knee‐extension exercise lying prone inside the bore of a superconducting magnet. The PCr scale is inverted and time‐aligned to account for the limb‐to‐lung transit delay (indicated by *) and to illustrate the kinetics identity between the variables. Sub‐LT (A) and supra‐LT (B) responses are redrawn from Reference 365, with permission. (C) The time constant (τ) of the fundamental phase of intramuscular PCr and O2p responses during sub‐LT (•) and supra‐LT (○) exercise in healthy young subjects. The tightness of the scatter around the line of identity suggests that the kinetics of O2p in health are closely related to intramuscular feedback processes within the phosphate system. Data are from 34 healthy subjects, using the methods described in Rossiter et al. 368, during sub‐LT (n = 34) and supra‐LT (n = 27) knee‐extension exercise. Values are taken from References 368,369,371,373 and unpublished measurements.
Figure 11. Figure 11.

A schematic diagram to illustrate the changes in key reactants in the control of muscle oxygen consumption on transition from rest to exercise. Panels A‐D illustrate the relationships between reaction velocity (O2m as a percentage of the maximum rate; Vmax) and reactant concentration for: (A) ADP; (B) Pi; (C) Po2; and (D) NADH/NAD+. The open circle shows the relative position in the resting state. The dashed arrow shows the proposed trajectory of each metabolite at exercise onset. O2m is highly dependent on [ADP] in a fashion consistent with classical Michaelis‐Menten enzyme kinetics for conditions where the other Pi, Po2, and NADH/NAD+ are in excess. Therefore, for Pi, Po2, and NADH/NAD+, there effectively exists a family of curves (not shown) between the resting state and the maximum flux. At high flux rates, the relative position of ADP on its curve means that it becomes increasing less influential in determining O2m, but any fall in Po2 and/or NADH/NAD+ pushes these reactants closer to the steep portion of their curves. Typically [Pi] increases during exercise, moving away from its Km. Panels E‐H illustrate the effect of increased maximal enzyme activity on O2m, PCr, and ADP kinetics on transition to exercise. (E) An increase in aerobic enzyme activity (dashed curves) increases the Vmax of ADP‐stimulated O2m in comparison to the control condition (solid curves). Open circles show resting values and closed circles the steady‐state position. Kinetic responses over time are shown for (F) O2m, (G) PCr, and (H) ADP. Dotted arrows indicate the initial rates of change in each case and closed circles show the time constant under increased aerobic enzyme activity (dashed curves) or control (solid curves) conditions. Overall the figure illustrates that the relative significance of each key reactant or enzyme activity in driving O2m may shift during the exercise transient, a shortfall in one variable potentially being overcome by an increase in another. See text for full description.
Figure 12. Figure 12.

A simple model to illustrate the influence of kinetic coupling between O2m and m. The model is based on the assumptions described in Barstow et al. 27 for a moderate‐intensity exercise increment between 0 and 100 W. The model shows the effect of varying the time constant (τ) of O2m (15‐45 s) with a fixed of 25 s 132. With sufficient substrate availability, the is determined by the rate of [ADP] accumulation, reflected in the [PCr] decrement (Δ[PCr]) (B). The instantaneous therefore determines the Cvo2m profile on transition to exercise, illustrated here for slow (A) and fast (D) values. Under conditions where O2m lags m (C, upper curves) Cvo2m is well maintained in the transient. Conditions where m lags O2m (C, lower curves) causes Cvo2m to overshoot the steady state in the transient. The model allows Cvo2m to fall to zero (*), although this is unrealistic under physiological conditions. A transiently low Cvo2m (i.e., < 1.0; C) could result in a limitation of O2m kinetics and/or precipitate compensatory effects in Δ[PCr], [NADH], and lactate production. (This figure has been amended since first publication: The order of magnitude of “Time” in panels A, B, and D has been corrected to minutes.)
Figure 13. Figure 13.

The upper limit for steady‐state exercise (critical power; CP) as a function of phase II pulmonary O2 kinetics (O2p) during cycle ergometry. The figure is derived from values reported in the literature of 35 papers between 1982 and 2008. The values used were limited to supra‐LT exercise where analysis of the phase II O2p kinetics was made and the groups were approximately matched for age, O2max, and health status. Groups presented are as follows: Endurance trained, 18‐30 years, n = 52, 1185,209,392, 229,44,91,242,243; active healthy young subjects, 18‐29 years, n = 14, 3126,314; healthy elderly, 66‐71 years, n = 38, 4317,318,325, 5107; and patients with chronic obstructive pulmonary disease (COPD) 56‐73 years, n = 78, 6287,317,350, 7320,351,394.


Figure 1.

A schematic diagram of the physiological systems interactions that determine gas exchange kinetics during exercise. Reactants are shown in circles, and flows and processes are in rectangular boxes. Dashed boxes illustrate internal system structures. The center panel describes the mass balance relationships between the active muscle and pulmonary systems, which are separated by the circulation. The relationship between the O2 concentration of the inflow and the local oxygen exchange (O2) to blood flow () ratio determines the O2 concentration of the effluent from the muscle and lung compartments. These are heterogeneous tissues and therefore the local o2/ can vary widely depending on the local conditions (as indicated by the dashed lines in the center panel). The mass balances for gas exchange at the alveoli and the mouth are depicted in the upper panel, together with the process that has the potential to dissociate them (alveolar gas storage). The lower panel illustrates the processes determining muscle O2 consumption, where the key downstream dynamics of the putative determinants of the rate of oxidative phosphorylation are shown: oxygen; the redox status (from the fluxes if the TCA cycle and glycolysis); and phosphates (from the balance between the energy‐consuming processes and the phosphocreatine system capacitance). See text for a full explanation. Key. Subscripts: a, arterial; A, alveolar; b, body; E, expired; I, inspired; m, muscle; p, pulmonary; t, total; v, venous; bar (e.g. or ) represents mean, or “mixed” values. Capitals: C, content; F fraction; , blood flow; , gas flow; V, volume. Abbreviations: ATP, ADP, AMP, adenosine tri‐, di‐, or monophosphate; Bf, breath frequency; CHO, carbohydrates (glucose or glycogen); CO2 carbon dioxide; Cr, creatine; Δ, change; EELV, end‐expiratory lung volume; FFA, free fatty acid; H+, proton; HCO3−, bicarbonate; L−, lactate; Mb, myoglobin; MITO, mitochondrion; O2 oxygen; PCr, phosphocreatine; Pi, inorganic phosphate; Pyr, pyruvate; T, transporter; TCA, tricarboxylic acid cycle; REDOX, redox potential; Vd, dead space volume; Vt, tidal volume.



Figure 2.

Predicted profiles of muscle (O2m) and pulmonary (O2p) kinetic responses (the “output”) to deterministic work rate forcings (the “input”) for a dynamically linear first‐order system. The step and ramp‐incremental exercise patterns are the first and second integrals, respectively, of the pulse work rate input. Control systems theory for a dynamically linear system suggests that the O2 responses would be similarly related, with parameters (the time constant, τ, or mean response time, τ′; and gain G; ) that are invariant across all conditions. Adapted from Reference 456.



Figure 3.

Pulmonary oxygen uptake (O2p), heart rate (HR), and ventilation (E) responses for two subjects (A and B) during constant work rate cycle ergometry for 30‐min duration or to the limit of tolerance (whichever was the sooner). Note that subject A reaches the limit of tolerance at ∼10 min (at a O2p of 3.25 liteṛmin−1), whereas subject B was able to complete the 30‐min task (with a steady‐state O2p of 2.91 liteṛmin−1), despite both subjects exercising at the same work rate (215 W), which was estimated using “standard criteria” to be 85% O2max in each case.



Figure 4.

Schematic diagram of the dynamics of O2, arterial blood lactate ([L−]), and their relationship with the tolerable duration of constant work rate exercise. The characteristics of the O2 (A) and blood [L−] (C) responses are used to demark four different intensity domains, with the limit of tolerance above critical power (CP) being determined by the shape of the power‐duration relationship (B). Moderate intensity: Exercise below the lactate threshold (LT) where O2 quickly attains a steady state, and the initial small increase in blood [L−] is rapidly attenuated toward resting levels (or below). Heavy intensity: Exercise between LT and CP with evidence of a O2 “slow component,” where O2 takes longer to stabilize and increases above value extrapolated from the fundamental exponential (dashed line). The action of the O2 slow component in this domain is to reduce the work efficiency and occurs in association with a sustained but stabilized metabolic acidosis. Very heavy intensity: Exercise above CP where the O2 slow component and blood [L−] progressively increase throughout exercise until the limit of tolerance, predicted by the relationship between power output and tolerable duration. Severe intensity: Exercise where the metabolic rate exceeds the maximal aerobic capacity (O2max) from exercise onset (as depicted by the extrapolation of the fundamental O2 above O2max; dashed line) and intolerance ensues before a O2 slow component develops. Circles indicate intolerance.



Figure 5.

A model to illustrate the effect of the circulatory dynamics (muscle blood flow; m) on pulmonary oxygen uptake (O2p) kinetics at the onset of moderate‐intensity exercise. The model is based on the assumptions stated in Barstow et al. 27 and is presented here for a 100‐W exercise increment from a 0‐W baseline during cycle ergometry (0.5 liteṛmin−1 O2p). Model parameter values used are O2m time constant (τ) = 30 s; τm = 25 s; venous volume = 3 liters; Cao2 = 0.2 mḷml−1; G = 10 mḷmin−1̣W−1; steady‐state = 5̣(O2p + 1) liteṛmin−1; resting fractional O2m = 0.18%; resting fractional m = 0.15%. (A) Venous O2 content draining the muscle (Cvo2m; bottom panel) is summed with the body compartment in proportion to it is respective flow (Cvo2m+b; middle panel) and reaches the lung (O2; upper panel) after a transit delay dependent on the venous volume and the instantaneous blood flow. (B) The pulmonary and muscular O2 and kinetics at exercise onset. The monophasic O2m and m kinetics (bottom) give rise to a biphasic pattern in O2p (top) because of the conflation of pulmonary blood flow (t) and O2. O2p kinetics determine the O2 deficit (O2df), which is assumed to reflect the difference between steady‐state and instantaneous O2p. The O2df is reflected in changes in the concentration of high‐energy phosphates (∼P, but predominantly PCr), changes in [L−] and changes in stored O2. (C) Model predictions for the degree of dissociation between muscle and lung gas exchange. The color scale shows the extent to which differs from O2p at any combination of m and O2m kinetics. Refer to Figure 1 for a flow diagram illustrating the variables contributing to the O2p response at exercise onset.



Figure 6.

The intensity dependence of O2p kinetics during the transition to and from constant work rate exercise. The data illustrate the goodness of fit of on‐ and off‐transient kinetics when modeled with the appropriate combination of “fundamental” and “slow” components (phase I has been omitted from the model fits for simplicity). The influence of increasing exercise intensity is shown by following the panels counterclockwise, starting at the bottom left (moderate) and ending at the top left (severe). The text panels therefore indicate the presence or absence of the O2p slow component (O2sc) within each intensity domain at either exercise onset (above) or exercise cessation (left). For example, severe‐intensity exercise is associated with a O2sc at cessation but not at exercise onset. Redrawn from Özyener et al. 328.



Figure 7.

The kinetic responses of O2p and blood lactate ([L−]) during intermittent exercise at 120% O2max over a range of duty cycles (each at a 1:2 work:rest cycle for an example subject). Duty cycle is inset to each panel (top right), and [L−] values are inset at the times measured along the time axis. The solitary solid and open circles (along the ordinate axis) in each figure are the values of the lactate threshold and O2max for this subject. The figure is organized in a fashion similar to that of Figure 6 (with the moderate response shown at the bottom left, and circulating anticlockwise to the severe‐intensity response at the top left) in order to highlight the similarity between the general kinetic features of intermittent and constant work rate exercise. In the former, relative intensity is modulated by duty cycle duration at a constant work rate, and in the latter, the relative intensity is modulated by work rate with the target duration remaining constant. Redrawn from Reference 414.



Figure 8.

The breath‐by‐breath gas exchange and ventilatory responses of a healthy subject during ramp‐incremental cycle ergometry (20 Ẉmin−1) to the limit of tolerance. (A) The “V‐slope” graph (CO2p as a function of O2p). The breakpoint in the V‐slope corresponds well to the threshold of lactate accumulation measured in arterial blood (LT). Noninvasive validation of this estimate benefits from the consideration of the kinetics of additional features of gas exchange and ventilatory dynamics, especially (B) the fractional concentration of end‐tidal O2 and CO2; (C) The ventilatory equivalents for O2 and CO2 (e/O2p and e/CO2p); and (D) The respiratory exchange ratio (RER; ). The vertical alignment of these six profiles during ramp‐incremental exercise facilitates the verification of noninvasive estimation of LT by visual inspection. The point at which the slope of the CO2p‐O2p relationship increases (the breakpoint in the V‐slope) is the primary index of LT attainment. The end‐tidal and ventilatory equivalent relationships are used to determine that the hyperpnea accompanying the CO2p increase is not a “true” hyperventilation (i.e., the increase in Feto2 and e/O2p occurs at a metabolic rate where FETCO2 and e/CO2p are stable). A subsequent fall in Fetco2 and rise in e/CO2p later in the response profiles signify the onset of respiratory compensation for the metabolic acidosis. The RER is used to corroborate that the LT estimation does not coincide with an RER “inflection point,” which can result from changes in CO2 storage dynamics (i.e., unrelated to blood [L−]). Note that because the S1 slope of the V‐slope graph does not intercept at the origin, the RER slope can be constant, or even decreasing whereas that between CO2p and O2p is increasing. Also note that the response profiles early in the ramp‐incremental exercise (i.e., at O2p values of ∼0.8‐1.2 liteṛmin−1 in this example) are dependent on gas exchange and ventilation kinetics following exercise onset. Therefore, the dynamics during the very early stages of the ramp‐incremental exercise (∼3‐4 min in healthy subjects) do not correspond to events related to blood [L−]. The responses at rest and baseline cycling (20 W) are not displayed on this figure for clarity.



Figure 9.

A schematic diagram of the kinetic responses of O2p to ramp‐incremental exercise (incremented as a smooth function of time with a slope of 20 Ẉmin−1) for responses with different effective time constants (τ′) and/or gains (G; ). The model is for cycle ergometry of 20 W, assuming a baseline O2p of 800 mḷmin−1

. (A) The monoexponential response to ramp‐incremental exercise with constant G (10 mḷmin−1.W−1) but varying τ′ (45 and 120 s). (B) The monoexponential response to ramp‐incremental exercise with constant τ′ (45 s) but varying G (8 and 10 mḷmin−1̣W−1). (C) A putative linear relationship between τ′ and G. (D) The outcome of varying τ′ and G together (using the slope illustrated in panel C) throughout ramp‐incremental exercise to the limit of tolerance. The values shown are the outcome of the fitted estimates using Eq. 17. Note the similarity between the modeled responses for O2p in panels A and D but which derive from kinetics that manifest either fixed (A) or varying (D) values for their underlying parameters.



Figure 10.

The dynamic relationships between intramuscular PCr and O2p kinetics from simultaneous determination of quadriceps PCr (○) and O2p (•) during moderate‐intensity knee‐extension exercise lying prone inside the bore of a superconducting magnet. The PCr scale is inverted and time‐aligned to account for the limb‐to‐lung transit delay (indicated by *) and to illustrate the kinetics identity between the variables. Sub‐LT (A) and supra‐LT (B) responses are redrawn from Reference 365, with permission. (C) The time constant (τ) of the fundamental phase of intramuscular PCr and O2p responses during sub‐LT (•) and supra‐LT (○) exercise in healthy young subjects. The tightness of the scatter around the line of identity suggests that the kinetics of O2p in health are closely related to intramuscular feedback processes within the phosphate system. Data are from 34 healthy subjects, using the methods described in Rossiter et al. 368, during sub‐LT (n = 34) and supra‐LT (n = 27) knee‐extension exercise. Values are taken from References 368,369,371,373 and unpublished measurements.



Figure 11.

A schematic diagram to illustrate the changes in key reactants in the control of muscle oxygen consumption on transition from rest to exercise. Panels A‐D illustrate the relationships between reaction velocity (O2m as a percentage of the maximum rate; Vmax) and reactant concentration for: (A) ADP; (B) Pi; (C) Po2; and (D) NADH/NAD+. The open circle shows the relative position in the resting state. The dashed arrow shows the proposed trajectory of each metabolite at exercise onset. O2m is highly dependent on [ADP] in a fashion consistent with classical Michaelis‐Menten enzyme kinetics for conditions where the other Pi, Po2, and NADH/NAD+ are in excess. Therefore, for Pi, Po2, and NADH/NAD+, there effectively exists a family of curves (not shown) between the resting state and the maximum flux. At high flux rates, the relative position of ADP on its curve means that it becomes increasing less influential in determining O2m, but any fall in Po2 and/or NADH/NAD+ pushes these reactants closer to the steep portion of their curves. Typically [Pi] increases during exercise, moving away from its Km. Panels E‐H illustrate the effect of increased maximal enzyme activity on O2m, PCr, and ADP kinetics on transition to exercise. (E) An increase in aerobic enzyme activity (dashed curves) increases the Vmax of ADP‐stimulated O2m in comparison to the control condition (solid curves). Open circles show resting values and closed circles the steady‐state position. Kinetic responses over time are shown for (F) O2m, (G) PCr, and (H) ADP. Dotted arrows indicate the initial rates of change in each case and closed circles show the time constant under increased aerobic enzyme activity (dashed curves) or control (solid curves) conditions. Overall the figure illustrates that the relative significance of each key reactant or enzyme activity in driving O2m may shift during the exercise transient, a shortfall in one variable potentially being overcome by an increase in another. See text for full description.



Figure 12.

A simple model to illustrate the influence of kinetic coupling between O2m and m. The model is based on the assumptions described in Barstow et al. 27 for a moderate‐intensity exercise increment between 0 and 100 W. The model shows the effect of varying the time constant (τ) of O2m (15‐45 s) with a fixed of 25 s 132. With sufficient substrate availability, the is determined by the rate of [ADP] accumulation, reflected in the [PCr] decrement (Δ[PCr]) (B). The instantaneous therefore determines the Cvo2m profile on transition to exercise, illustrated here for slow (A) and fast (D) values. Under conditions where O2m lags m (C, upper curves) Cvo2m is well maintained in the transient. Conditions where m lags O2m (C, lower curves) causes Cvo2m to overshoot the steady state in the transient. The model allows Cvo2m to fall to zero (*), although this is unrealistic under physiological conditions. A transiently low Cvo2m (i.e., < 1.0; C) could result in a limitation of O2m kinetics and/or precipitate compensatory effects in Δ[PCr], [NADH], and lactate production. (This figure has been amended since first publication: The order of magnitude of “Time” in panels A, B, and D has been corrected to minutes.)



Figure 13.

The upper limit for steady‐state exercise (critical power; CP) as a function of phase II pulmonary O2 kinetics (O2p) during cycle ergometry. The figure is derived from values reported in the literature of 35 papers between 1982 and 2008. The values used were limited to supra‐LT exercise where analysis of the phase II O2p kinetics was made and the groups were approximately matched for age, O2max, and health status. Groups presented are as follows: Endurance trained, 18‐30 years, n = 52, 1185,209,392, 229,44,91,242,243; active healthy young subjects, 18‐29 years, n = 14, 3126,314; healthy elderly, 66‐71 years, n = 38, 4317,318,325, 5107; and patients with chronic obstructive pulmonary disease (COPD) 56‐73 years, n = 78, 6287,317,350, 7320,351,394.

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Article Title: Exercise: Kinetic Considerations for Gas Exchange
 

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Harry B. Rossiter. Exercise: Kinetic Considerations for Gas Exchange. Compr Physiol 2010, 1: 203-244. doi: 10.1002/cphy.c090010