Abstract
The purpose of this study was to examine a new method for calculating the O_{2} deficit that considered the O_{2} uptake (V˙o _{2}) kinetics during exercise as two separate phases in light of previous research in which it was shown that the traditional O_{2} deficit calculation overestimated the recovery O_{2} consumption (ROC). Eight subjects completed exercise transitions between unloaded cycling and 25% (heavy, H) or 50% (very heavy, VH) of the difference between the lactic acid threshold (LAT) and peakV˙o _{2} for 8 min. The O_{2} deficit, calculated in the traditional manner, was significantly greater than the measured ROC for both aboveLAT exercises: 4.03 ± 1.01 vs. 2.63 ± 0.80 (SD) liters for VH and 2.36 ± 0.91 vs. 1.74 ± 0.63 liters for H for the O_{2}deficit vs. ROC (P < 0.05). When the kinetics were viewed as two separate components with independent onsets, the calculated O_{2} deficit (2.89 ± 0.79 and 1.71 ± 0.70 liters for VH and H, respectively) was not different from the measured ROC (P < 0.05). Subjects also performed the same work rate for only 3 min. These data, from bouts terminated before the slow component could contribute appreciably to the overallV˙o _{2} response, show that the O_{2} requirement during the transition is less than the final steady state for the work rate, as evidenced by symmetry between the O_{2} deficit and ROC. This new method of calculating the O_{2} deficit more closely reflects the expected O_{2} deficitROC relationship (i.e., ROC ≥ O_{2}deficit). Therefore, estimation of the O_{2} deficit during heavy exercise transitions should consider the slow component ofV˙o _{2} as an additional deficit component with delayed onset.
 recovery oxygen consumption
 lactic acid threshold
 square wave
 steady state
oxygen uptake(V˙o _{2}) rises monoexponentially to its new steady state with an amplitude of 9–10 ml O_{2} ⋅ W^{−} ^{1} ⋅ min^{−} ^{1}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 finalV˙o _{2} cost above 10 ml O_{2} ⋅ W^{−} ^{1} ⋅ min^{−} ^{1}(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 O_{2} demand, then it has implications for calculation of the O_{2} deficit.
For moderate work rates (i.e., below LAT), the O_{2}deficit is equal to or less than the recovery O_{2}consumption (ROC) (7, 11, 13). However, asymmetry between the on and offtransition phases has led to the observation that the O_{2} 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 O_{2} deficit requires determination of baseline V˙o _{2}and of the O_{2} demand for the exercise. Traditionally, the endexercise steadystateV˙o _{2} was assumed to be the O_{2} 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 O_{2} kinetics demands a reevaluation of these assumptions and raises questions about the relationship between the O_{2}deficit and ROC.
The physiological bases of the O_{2} deficitROC relationship are still unclear. The ROC is the excess O_{2} consumed above baseline during the recovery period and is related to the O_{2} deficit primarily by a restoration of tissue O_{2} saturation (myoglobin and venous
The purpose of this study was twofold: 1) to test a new model for the calculation of the O_{2} deficit above LAT that includes separate deficit phases corresponding to the biphasicV˙o _{2} kinetics and 2) to test an implication of the traditional O_{2} deficit model, namely that the ROC for 3 min of heavy exercise should be equivalent to the deficit calculated using the steadystateV˙o _{2} 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 3min bout. Our model predicts that the O_{2} demand for the fast phase of the transition is its projected asymptote and not the final steadystateV˙o _{2}. We tested this discrepancy in model predictions using 3 and 8min cycling bouts at the same intensity.
METHODS
Subjects
Eight active, nonsmoking volunteers [7 men and 1 woman (subject 2)] took part in the study after giving informed consent and completing a medical history questionnaire. The University Human Subjects Review Board approved the procedures. Subjects were tested on 3 separate days. On all testing days, subjects arrived at the laboratory 6 h after their last meal and had been instructed not to consume alcohol or caffeine for 12 h before arrival and not to engage in strenuous exercise for 24 h before arrival. Compliance with these guidelines was checked by questionnaire on arrival at the laboratory each day. There was 100% compliance.
Exercise Testing
On the 1st day, subjects completed an incremental exercise test (20 W/min, 80 rpm) on a cycle ergometer (Monark 868) until they could no longer maintain the pedal cadence for 15 s, despite verbal encouragement. Gas exchange variables were measured every breath with a Parvomedics MMS2400 system. Total dead space of the system (mouthpiece, valve, collection tube, pneumotach, mixing chamber, and sampling tube) was 4.98 liters. Because mixing chamber systems do not allow examination of the fine details of gas exchange kinetics during the rapid early adjustment phase, the venous return component was not modeled in this study.
The system was calibrated with known gases spanning the expected range of O_{2} and CO_{2} in the expirate immediately before every test. A 15point flowmeter calibration took place before every pair of tests with use of a 3liter syringe (Hans Rudolph). LAT was estimated from gas exchange with use of the ventilatory equivalent and modified Vslope methods (2, 14, 15). The threshold determined by these two methods was not significantly different. PeakV˙o _{2}(V˙o _{2 peak}) was taken as the highest 15s 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 basketloaded ergometer (Monark 824E), which allows instantaneous application of the resistance. The 8min bout length was chosen, because previous reports of squarewave transitions to these intensities have suggested that 6 min may not be long enough to attain a steady state. The 3min 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 3min bout length would allow use of the subsequent ROC as a marker of the O_{2} demand during the early phase of the transition.
The short bouts (3min: 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 (8min: 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 baselineV˙o _{2}. 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 andV˙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
Data were modeled for each work rate transition for each subject by nonlinear regression with minimization of the sum of squared residuals as the primary goal (SPSS 8.0 Professional Statistics package). The first 25 s were always removed from the analysis to ensure that the early venous return component (3, 17) did not influence the results. Iterations continued until successive repetitions reduced the sum of squared residuals by <10^{−} ^{8}.
On transition.
The long bouts (H8 and VH8) were fit with three models: model 1, a single monoexponential function with time delay
The short bouts (H3 and VH3) were fit with a single monoexponential function (Eq. 1 ).
Off transition.
Two models were applied to the off transitions: model 1
_{off}, a single monoexponential function with time delay
O_{2} 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 (TD_{2}), 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, O_{2}deficit calculations were based on model 3.
The O_{2} deficit is traditionally calculated (O_{2}def_{Trad}) as the difference between the O_{2} that would have been consumed if a steady state had been attained immediately at the onset of exercise (Fig.2
D) and that consumed during the exercise period (definite integral of Eq. 3
)
ROC.
For the 8min bouts, no significant difference was observed betweenmodels 1
_{off} and2
_{off} (P = 0.96). For the 3min bouts, A_{1} and A_{2} 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
Eight subjects are included in the data for the VH bouts, and seven are included for the H bouts because of complications in gas collection during the H8 bout for subject 4.
Statistical Analysis
Withinsubjects ANOVA was used for all group comparisons, with a randomized block design, on commercially available computer software (SPSS version 8.0). Tukey's honestly significant difference test was used whenever overall significance was found to determine the location of those differences. Models were compared by F test by using the sum of squared residuals as the criterion measure. The α was set equal to 0.05 for all analyses before data collection.
RESULTS
Subjects' age, height, mass,V˙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 ⋅ kg^{−} ^{1} ⋅ min^{−} ^{1}, and 47.8 ± 6.2%V˙o _{2 peak}, respectively. Model parameters for the on and off transitions can be found in Tables1 and 2, respectively. Asymptotic V˙o _{2}projections for each work rate were 23.4 ± 3.6 and 53.6 ± 17.0 (SD) %Δ for the H8 and VH8 bouts, respectively. The O_{2}deficit calculated by the traditional method for the 8min bouts (H8 and VH8) resulted in a significant overestimation of the subsequent ROC (P = 0.006 for H8 and P < 0.001 for VH8; Table3). Consideration of the O_{2}kinetics as two separate components, each with an independent starting time, asymptotic projection, and intrinsic O_{2} deficit, eliminated this overestimation; i.e., the O_{2} deficit and ROC were not different when the kinetics were considered as two separate components with separate time delays (Table 3, Fig.2 B).
The O_{2} 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 O_{2} deficit for the VH3 work rate when the 3min projected asymptote was used as the O_{2} demand. However, using the higher steadystate O_{2} requirement from the VH8 bout as the initial O_{2} 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 8min bout of the same intensity) restored the relationship predicted by our model (Fig.3, Table 3).
A steady state was reached for all subjects in the lower of the two intensities. Steady state was defined as reaching aV˙o _{2} ≤1 ml O_{2} ⋅ kg body mass^{−} ^{1} ⋅ min^{−} ^{1}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 O_{2} 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 V˙o _{2 peak}. During the recovery phase, all subjects returned to baselineV˙o _{2} within the test time.
DISCUSSION
Our data suggest that calculation of the O_{2} deficit in the traditional manner (i.e., the difference between O_{2}consumed and that consumed if the final projected steadystateV˙o _{2} had been reached immediately) is not valid for aboveLAT exercise. This finding is accurate under the assumption that the O_{2} deficit should not be larger than the ROC. If this assumption is true, then the more accurate calculation of the O_{2} deficit above the LAT should consider two distinct components ofV˙o _{2}, each with its own deficit (Fig. 2 B). These data also support the contention thatV˙o _{2} 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 (A_{2}) contributed 15% on average to the overallV˙o _{2} for a given work rate (∼10% at small %Δ and 20% at the higher %Δ).
The 3min bouts gave us an opportunity to use the ROC as an upperlimit indicator of the expected deficit. If the O_{2} demand during the first few minutes of the transition is the final steadystateV˙o _{2}, 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 O_{2} demand during the first minutes of the transition is actually less than the final steadystateV˙o _{2}. With only the monoexponential projection of the 3min data (solid area in Fig. 3), there was no difference between the deficit and ROC at 25%Δ; however, the deficit at 50%Δ 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 3min bouts (solid and hatched areas of Fig. 3), the O_{2} deficit and ROC measurements were not different at either intensity.
Symmetry was observed between the O_{2} 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 TD_{2} (i.e., later onset of the slow component) and a significantly smaller A_{2} during these bouts. This would not have contributed enough to the O_{2} demand before the end of exercise to enlarge the ROC, as it did at the heavier work rate.
Calculation of the O_{2} deficit requires accurate determination of resting (or baseline)V˙o _{2} and a reliable measurement or estimation of the O_{2} demand for the exercise. Traditionally, the final steadystateV˙o _{2} has been interpreted as the O_{2} 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 O_{2} requirement at the onset of the transition and is late to develop, or 2) it is an O_{2} demand that does not begin until later in the exercise transition. Our data suggest that the slow component is a delayedonset O_{2} requirement. This means that one might consider the transition to heavy exercise as two separate transitions: one immediate and one delayed (Fig. 2 A). 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 O_{2} deficitROC 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^{31}PNMR research, which points to a delayed highenergy 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^{31}PNMR and pulmonaryV˙o _{2} 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 theV˙o _{2} 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 steadystate 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 ^{31}PNMR, 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 O_{2} demand for the work rate, resulting in the biphasic O_{2} demand and twocompartment O_{2} deficit supported by the present study.
Conclusion
Our data support the hypothesis that an additional O_{2}demand begins some time after the onset of the work rate transition for work rates above LAT. Thus the O_{2} demand for the exercise transition does not appear to be constant over the transition period but seems to be biphasic in nature. The previously described disparity in the O_{2} deficitROC relationship during exercise above LAT may be rectified by using a model that considersV˙o _{2} kinetics above LAT as two separate components with corresponding O_{2} deficits.
Acknowledgments
We thank Dr. Tom Barstow (Kansas State University) and Dr. L. Bruce Gladden (Auburn University) for critical reviews during preparation of the manuscript.
Footnotes

Address for reprint requests and other correspondence: R. J. Moffatt, 436 Sandels Bldg., The Florida State University, Tallahassee FL 32306 (Email: rmoffatt{at}mailer.fsu.edu).

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 Copyright © 2000 the American Physiological Society