INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

OXYGEN UPTAKE (O₂) rises monoexponentially to its new steady state with an amplitude of 9-10 ml O₂ · W¹ · min¹ for work rate increments below the lactic acid threshold (LAT). For work rate transitions above LAT, an additional component (referred to as the slow component) is superimposed on the initial monoexponential function, which raises the final O₂ cost above 10 ml O₂ · W¹ · min¹ (Fig. 1). Mathematical modeling has shown that the slow component begins 90-150 s after the onset of the transition (1, 11). However, not all researchers agree with the concept of a delayed onset (9); there is still debate over whether the two phases are physiologically best described with common or independent time delays. If the slow component is a delayed O₂ demand, then it has implications for calculation of the O₂ deficit.

View larger version (15K): [in this window] [in a new window]   Fig. 1.   Three-breath rolling average O2 uptake (O2) and exponential model 3 fit for a transition from unloaded cycling to above lactic acid threshold (LAT) during an 8-min bout of heavy exercise (H8). A1 and A2, amplitudes of fast and slow components, respectively; TD1 and TD2, time delays for onset of fast and slow components, respectively; 1 and 2, time constants for fast and slow components after their time delays, respectively.

For moderate work rates (i.e., below LAT), the O₂ deficit is equal to or less than the recovery O₂ consumption (ROC) (7, 11, 13). However, asymmetry between the on- and off-transition phases has led to the observation that the O₂ deficit overpredicts the ROC (11, 13) for heavy exercise (i.e., above LAT). Therefore, heavy exercise appears quantitatively and qualitatively more complex.

Accurate estimation of the O₂ deficit requires determination of baseline O₂ and of the O₂ demand for the exercise. Traditionally, the end-exercise steady-state O₂ was assumed to be the O₂ demand throughout the exercise. This is based on the belief that the energy demand for completing a task, including motor unit recruitment, does not vary during the transition to the new steady state. The determination of a second, slow component to the O₂ kinetics demands a reevaluation of these assumptions and raises questions about the relationship between the O₂ deficit and ROC.

The physiological bases of the O₂ deficit-ROC relationship are still unclear. The ROC is the excess O₂ consumed above baseline during the recovery period and is related to the O₂ deficit primarily by a restoration of tissue O₂ saturation (myoglobin and venous PO₂) and resynthesis of ATP and phosphocreatine (PCr). However, the ROC is not a direct reflection of the O₂ deficit, because it also includes factors such as lactate metabolism and the metabolic demand of elevated cardiac output, ventilation, catecholamines, and temperature (6).

The purpose of this study was twofold: 1) to test a new model for the calculation of the O₂ deficit above LAT that includes separate deficit phases corresponding to the biphasic O₂ kinetics and 2) to test an implication of the traditional O₂ deficit model, namely that the ROC for 3 min of heavy exercise should be equivalent to the deficit calculated using the steady-state O₂ for a long bout of the same intensity (final exercise steady state). This means that the ROC would be larger than the deficit calculated using the observed kinetics projection for the 3-min bout. Our model predicts that the O₂ demand for the fast phase of the transition is its projected asymptote and not the final steady-state O₂. We tested this discrepancy in model predictions using 3- and 8-min cycling bouts at the same intensity.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Subjects

Exercise Testing

The system was calibrated with known gases spanning the expected range of O₂ and CO₂ in the expirate immediately before every test. A 15-point flowmeter calibration took place before every pair of tests with use of a 3-liter syringe (Hans Rudolph). LAT was estimated from gas exchange with use of the ventilatory equivalent and modified V-slope methods (2, 14, 15). The threshold determined by these two methods was not significantly different. Peak O₂ (O_{2 peak}) was taken as the highest 15-s average achieved during the test.

Testing sessions 2 and 3 began 48 h after the incremental exercise test. Each session consisted of two randomized cycling bouts, one short (3 min) and one long (8 min), on a basket-loaded ergometer (Monark 824E), which allows instantaneous application of the resistance. The 8-min bout length was chosen, because previous reports of square-wave transitions to these intensities have suggested that 6 min may not be long enough to attain a steady state. The 3-min bout length was chosen, because 3 min should be sufficient to develop the fast component without considerable contribution of the slow component if the slow component is of delayed onset. Furthermore, the 3-min bout length would allow use of the subsequent ROC as a marker of the O₂ demand during the early phase of the transition.

The short bouts (3-min: heavy, H3 and very heavy, VH3) began with 4 min of unloaded cycling (80 rpm) followed by an immediate transition to the work rate for 3 min and return to unloaded cycling for another 8 min. The long bouts (8-min: H8 and VH8) also began with 4 min of unloaded cycling (80 rpm) but were followed by 8 min at the work rate and return to unloaded cycling for 15 min. The recovery periods were sufficient for all subjects to return to baseline O₂. Subjects were unaware of which bout they would be completing and did not know when the work rate transitions were coming.

The work rates were chosen to elicit 25% (H) and 50% (VH) of the difference between LAT and O_{2 peak}. Work rates were assigned randomly each day, but on a given day, both tests were at the same work rate. Bouts were separated by 1 h.

Data Modeling

8

On transition. The long bouts (H8 and VH8) were fit with three models: model 1, a single monoexponential function with time delay

(1)

model 2, a double monoexponential function with common time delay

(2)

where TD₁ = TD₂, and model 3, a double monoexponential function with independent time delays

(3)

where O₂(t) is the O₂ at any time t, BO₂ is baseline O₂ (the average O₂ for the last 30 s of the 4-min unloaded warm-up), A₁ and A₂ are O₂ amplitudes for the fast and slow components, respectively, TD₁ and TD₂ are time delays for the fast and slow components, respectively, and ₁ and ₂ are time constants for the fast and slow components after their time delays, respectively. For Eq. 3, the statistical model was constrained with a conditional term that forced the slow component {A₂[1  e^{(t  TD₂)/₂}]} to be included only when t  TD₂. This conditional statement is important, because without it the model allows the slow component to exert influence on the predicted O₂ at earlier time points, i.e., before the component actually begins for this model.

Off transition. Two models were applied to the off transitions: model 1_off, a single monoexponential function with time delay

(4)

and model 2_off, a double monoexponential function with common time delay

(5)

where TD₁ = TD₂ and EEO₂ is exercise O₂ and is equal to the model O₂ at the end of exercise minus BO₂. Different time delays were not explored in the recovery response, because the slow and fast components are present at the end of exercise and there is no reason to think that their recoveries would not begin immediately.

O₂ deficit. Model 2 fit the data significantly better than model 1 (P < 0.001). Additionally, model 3 fit the data significantly better than model 2 (P = 0.017), which is in agreement with previous research (1, 11). Model 2 constrains the second time delay (TD₂), whereas model 3 is free to fit the data without this constraint. This means that model 3 could result in equal time delays if this was the optimal solution as defined by the nonlinear regression goal of minimizing the sum of the squared residuals. Model 3, even when the starting values in the iterative estimation algorithm for the time delays were the same, did not, for any subject on any test, return a solution where the time delays were <66 s apart. Therefore, the constraints of equal time delays forced model 2 to find a locally optimal solution that was not the globally optimal solution. Accordingly, O₂ deficit calculations were based on model 3.

(6)

(7)

(t  TD₂)/₂

View larger version (16K): [in this window] [in a new window]   Fig. 2.   A: 2-compartment model with delayed-onset slow component and respective O2 deficits for transitions to work rates above LAT. B: superimposition of A and new model for O2 deficit; gray area, hypothesized overpredicted amount from traditional calculation. C: 2-component model with common time delay. D: superimposition of C and traditional concept of O2 deficit, which led to overestimation of recovery O2 consumption.

ROC. For the 8-min bouts, no significant difference was observed between models 1_off and 2_off (P = 0.96). For the 3-min bouts, A₁ and A₂ became interchangeable, so that the regression solution would become any suggested value for either amplitude so long as the sum was equal to the overall amplitude. The result was a sum of squared residuals identical to that for the monoexponential fit. This means that the off transition for these data was monoexponential. Therefore, the simpler model was used, and the ROC was calculated by integration of Eq. 4 with considerations for the time delay and time constant similar to those for calculation of the deficit

(8)

where t is time, EE is end exercise, ER is end recovery, EEO₂ is end-exercise O₂, and A₁ is the amplitude of recovery O₂ with time constant (₁) after a time delay (TD₁).

Statistical Analysis

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Subjects' age, height, mass, O_{2 peak}, and LAT (means ± SD) were 27.1 ± 5.3 yr, 177.7 ± 7.0 cm, 79.4 ± 12.7 kg, 49.2 ± 6.5 ml · kg¹ · min¹, and 47.8 ± 6.2% O_{2 peak}, respectively. Model parameters for the on and off transitions can be found in Tables 1 and 2, respectively. Asymptotic O₂ projections for each work rate were 23.4 ± 3.6 and 53.6 ± 17.0 (SD) % for the H8 and VH8 bouts, respectively. The O₂ deficit calculated by the traditional method for the 8-min bouts (H8 and VH8) resulted in a significant overestimation of the subsequent ROC (P = 0.006 for H8 and P < 0.001 for VH8; Table 3). Consideration of the O₂ kinetics as two separate components, each with an independent starting time, asymptotic projection, and intrinsic O₂ deficit, eliminated this overestimation; i.e., the O₂ deficit and ROC were not different when the kinetics were considered as two separate components with separate time delays (Table 3, Fig. 2B).

The O₂ deficit and ROC were not different in the H3 work rate, as our new model predicts. In contrast, the ROC was significantly larger than the O₂ deficit for the VH3 work rate when the 3-min projected asymptote was used as the O₂ demand. However, using the higher steady-state O₂ requirement from the VH8 bout as the initial O₂ requirement for this short bout resulted in overprediction of the observed ROC. Taking into account the small amount of slow component that had developed by the 3rd min (as determined from modeling the 8-min bout of the same intensity) restored the relationship predicted by our model (Fig. 3, Table 3).

View larger version (14K): [in this window] [in a new window]   Fig. 3.   Response for 8-min bout of very-heavy-intensity exercise (VH8,) and 3-min bout of very-heavy-intensity exercise (VH3, ) in same subject. Calculating O2 deficit for 3-min bout from its projection (solid area) underpredicted recovery O2 consumption in VH3 bouts. New, 2-compartment model (hatched area) accounted for this difference and resulted in an O2 deficit equivalent to recovery O2 consumption. All subjects recovered to baseline O2 within test time on all tests. See Table 3 and DISCUSSION for more details.

A steady state was reached for all subjects in the lower of the two intensities. Steady state was defined as reaching a O₂ 1 ml O₂ · kg body mass¹ · min¹ of the model asymptote, because this value is within the error of the measurement system. Thus we have confidence that the model was a good estimation of the final O₂ demand. Only subjects 1, 7, and 8 reached a steady state by 8 min at the higher intensity. However, the asymptotic projection for all subjects was below O_{2 peak}. During the recovery phase, all subjects returned to baseline O₂ within the test time.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Our data suggest that calculation of the O₂ deficit in the traditional manner (i.e., the difference between O₂ consumed and that consumed if the final projected steady-state O₂ had been reached immediately) is not valid for above-LAT exercise. This finding is accurate under the assumption that the O₂ deficit should not be larger than the ROC. If this assumption is true, then the more accurate calculation of the O₂ deficit above the LAT should consider two distinct components of O₂, each with its own deficit (Fig. 2B). These data also support the contention that O₂ above LAT is composed of two phases, including one that does not begin until ~2-3 min after the onset of the work rate transition. The slow component amplitude (A₂) contributed 15% on average to the overall O₂ for a given work rate (~10% at small % and 20% at the higher %).

The 3-min bouts gave us an opportunity to use the ROC as an upper-limit indicator of the expected deficit. If the O₂ demand during the first few minutes of the transition is the final steady-state O₂, then the sum of the areas in Fig. 3 should be equal to or less than the ROC. For both intensities, this deficit was significantly greater than the ROC (P = 0.0005 for H3 and P = 0.001 for VH3; Table 3). If it is assumed that the deficit is always equal to or less than the ROC, this suggests that the O₂ demand during the first minutes of the transition is actually less than the final steady-state O₂. With only the monoexponential projection of the 3-min data (solid area in Fig. 3), there was no difference between the deficit and ROC at 25%; however, the deficit at 50% was significantly less than the following ROC (P = 0.005; Table 3 and Fig. 3). With use of our new model, which included the small portion of the deficit that had developed during the end of the 3-min bouts (solid and hatched areas of Fig. 3), the O₂ deficit and ROC measurements were not different at either intensity.

Symmetry was observed between the O₂ deficit and ROC for the H3 bout without correction for any partially developed slow component. This is most likely due to a combination of a slightly larger TD₂ (i.e., later onset of the slow component) and a significantly smaller A₂ during these bouts. This would not have contributed enough to the O₂ demand before the end of exercise to enlarge the ROC, as it did at the heavier work rate.

Calculation of the O₂ deficit requires accurate determination of resting (or baseline) O₂ and a reliable measurement or estimation of the O₂ demand for the exercise. Traditionally, the final steady-state O₂ has been interpreted as the O₂ requirement for the exercise, and it was assumed that this demand was constant throughout the exercise. The latter assumption is based on the idea that the energy demand for completing a task does not vary during the transition to the new steady state. Our data, in concert with others (11, 13), question the validity of this assumption for work rate transitions above the LAT.

Two possibilities exist for the delayed onset of the slow component: 1) it is an O₂ requirement at the onset of the transition and is late to develop, or 2) it is an O₂ demand that does not begin until later in the exercise transition. Our data suggest that the slow component is a delayed-onset O₂ requirement. This means that one might consider the transition to heavy exercise as two separate transitions: one immediate and one delayed (Fig. 2A). Although this is almost certainly an oversimplified view of the complex kinetics, it should provide a basis for understanding the cause of the slow component and its implications for exercise testing and the O₂ deficit-ROC relationship.

The mechanism(s) involved in developing the slow component is not well understood. However, Poole et al. (12) demonstrated that the exercising skeletal muscle is its likely origin, with 86% of the slow component attributed to the cycling legs in their study. In light of this discovery, the present findings are supported by recent ³¹P-NMR research, which points to a delayed high-energy phosphate demand that correlates with a drop in intracellular pH ~2-3 min after the heavy work rate transition (10, 16). Whipp et al. (16) recently described a method of simultaneous quadriceps ³¹P-NMR and pulmonary O₂ measurements during heavy knee extension exercise. Examination of Fig. 5 presented in their study suggests that PCr concentration may have slow component characteristics that coincide temporally with the O₂ kinetics (16). In support of this, one intriguing finding reported in the literature is the time course of intracellular pH and PCr concentration changes during forearm exercise in humans (10). At ~150 s there appeared to be an additional drop in PCr concentration to a new, lower steady-state level during heavy exercise. Calculations of intracellular H⁺ concentration during the same exercise showed no change from resting values until the same time point, ~150 s. Using ³¹P-NMR, Hogan et al. (8) recently reported a tight coupling between H⁺ concentration and fatigue in human ankle plantar flexors. It is likely that, for work rates above LAT, a drop in intracellular and/or local extracellular pH causes a reduction in power output, demanding the recruitment of an additional pool of less economical motor units (4, 5). The recruitment of an additional motor unit pool would raise the O₂ demand for the work rate, resulting in the biphasic O₂ demand and two-compartment O₂ deficit supported by the present study.

Conclusion