Strategies to Ensure Accurate Calculation of Parameters of the VO₂ Response Profile During Heavy Intensity Cycle Ergometer Exercise

1. Background

The pulmonary VO₂ response profile in exercise reflects the underlying metabolic activity in the muscles (1, 2). In moderate intensity exercise, work rates below the lactate threshold, the metabolic response is mirrored by the mono-exponential increase in VO₂ leading to rapid attainment of a steady state (1). For exercise in the heavy domain, which comprises work rates above the lactate threshold and up to critical power or critical speed, the asymptote of the relationship between time to exhaustion and work rate or speed (3-5), the rate of lactate production is said to be balanced by the rate of removal, so the blood lactate concentration will increase in the first few minutes and then decrease gradually or stay steady (6); this metabolic profile is reflected in the two-phase VO₂ response, which features (i) a primary phase or fast response followed by (ii) a slow phase or slow component, which emerges after ~2 min of exercise and leads to a steady-state VO₂ (7). In severe exercise, there is two-phase VO₂ response and, if exercise is continued long enough, the slow component will bring the VO₂ to VO_2max (7).

Characteristics of the VO₂ response profile -or parameters of the kinetics of the VO₂ response- are determined using a three-phase process: data collection, data processing, and data fitting (8). Since the advent of automated gas analysis systems that provide VO₂ data on a breath-by-breath (B×B) basis, these are the systems of choice for collecting data. The second phase, data processing, involves treating the data to ensure that parameters are estimated with the greatest precision and accuracy during the final phase. This data processing aims to improve the signal (the underlying responses) to noise (breath to breath variability) ratio (1, 9, 10). The final phase is data fitting, the mathematical process of fitting the breath-by-breath VO₂ data to an appropriate mathematical model using iterative nonlinear regression procedures on any number of readily available statistical or graphing packages to identify what the values of the parameters are the best describe how closely the actual data fit the model. Using these packages, parameter estimates are generated, each with an associated SEE, which describes the precision of the estimates.

The focus of the present study is on the second phase, data processing. We assume that data are collected carefully on a B×B basis, using calibrated equipment, under reasonable environmental conditions, from participants who are properly prepared and motivated. We assume that an appropriate statistical analysis package is available and that an acceptable model has been selected.

Two approaches have been taken in order to improve the precision, and ensure the accuracy, of parameter estimates. First, the breath-by-breath data have been ‘smoothed’ -for example, by using interpolation to generate second-by-second values or by generating three-breath (3-B), five-breath (5-B), or seven-breath (7-B) (etc.) rolling averages- prior to performing the iterative progression (9). Second, data have been collected from several identical exercise tests -the parameter estimates generated by mathematical modeling of the data from each test can been combined (averaged) or the data from the tests can been combined prior to mathematical modeling (8, 9). While it may be inherently obvious that smoothing data or replicating the exercise tests would improve the precision of parameter estimates, relatively little research has sought to determine the optimal treatment of exercise data to ensure the accuracy of the parameter values (9).

2. Objectives

The objective of this study was to evaluate the impact of these two strategies to improve the accuracy of the descriptors of the VO₂ response profile during heavy intensity cycle ergometer exercise. Twenty participants performed six identical exercise tests. B×B data from each test, as well as rolling 3-B, 5-B, and 7-B averages, were fitted to a two-component (primary + slow) model. Parameter estimates from the combinations of number of tests used (one to six) and the methods of smoothing (none, 3-B, 5-B, and 7-B rolling averages) were compared against a criterion value. The purpose of this study was to identify the optimal smoothing method and the minimum number of tests necessary to ensure accurate estimation of the parameters of the VO₂ response in heavy intensity exercise.

3. Methods

3.1. Participants

The study procedures were approved by the Institutional Review Board for the Protection of Human Subjects in Research at the university prior to any recruitment of participants. The study was conducted in accordance with the latest Declaration of Helsinki (11). Eight women (mean ± SD: age 22 ± 1 y, height 167 ± 9 cm, weight 66 ± 11 kg, VO_2max 39 ± 6 mL.kg^-1.min^-1) and twelve men (23 ± 2 y, 182 ± 8 cm, 79 ± 12 kg, 43 ± 5 mL.kg^-1.min^-1) volunteered to participate and provided informed consent. These 20 participants were involved in recreational sport or fitness activities, but not organized sport activities. They were all familiar with exercise testing procedures and with breathing through a mouthpiece. They verified that they did not change their exercise routines, diet, or sleep habits over the course of the study.

3.2. Overview

Participants performed an incremental test for determination of their VO_2max and the VO₂ at the ventilatory threshold. Then they performed a series of six 6-min tests at a work rate individually selected so that the oxygen demand would be midway between VO_2max and the VO₂ at the ventilatory threshold. The testing sessions were separated by at least 24 hours and were scheduled at the same time of day for each participant to avoid the confounding effects of time of day that we have reported on responses associated with the ventilatory threshold (12) and in severe intensity VO₂ kinetics (13); the work rates used in the present study lay between the ventilatory threshold and the lower boundary of the severe intensity domain. Tests were performed under similar conditions in a temperature-controlled laboratory (20ºC to 22ºC; ~50% relative humidity), with no distractions. Data collection was completed in a three-week period. Participants were instructed to sleep at least six hours the night before each test; not to exercise and not to ingest carbonated beverages, caffeine, or alcohol for 12 hours before each test; and not to eat a heavy meal in the three hours before each test. Actual dietary intake was at each participant’s discretion and was not recorded. They were tested only if they verified that they had adhered to all these instructions.

3.3. Incremental Tests to Determine VO₂max

The incremental tests were performed on an Monark Ergomedic 828E (Varberg, Sweden) cycle ergometer, with pedaling cadence of ~80 revolutions per min (rev/min). A digital readout of the cadence was visible during the tests. The tests began with three minutes of baseline data collection during seated rest. The initial work rates were 40 W for women and 80 W for men. Work rate was abruptly increased 20 W each minute.

Throughout each test, expired gases were analyzed using a MedGraphics (St. Paul, Minnesota, USA) Express metabolic cart. The cart was calibrated before each test according to the manufacturer’s instructions. Breath-by-breath VO₂ data were reduced to serial 15-s averages. Tests were terminated when the participant allowed the cadence to drop below 70 rev.min^-1 for five seconds, despite strong verbal encouragement. VO_2max was determined as the highest average of adjacent 15-s averages. The ventilatory threshold was identified as described by Wasserman and colleagues (14).

3.4. Constant Power Heavy Intensity Tests

Tests were performed using the same Monark ergometer as for the incremental tests, and during each test, expired gases were analyzed using the same MedGraphics metabolic cart. The tests began with three minutes of baseline data collection during seated rest. After the rest, the participant began pedaling and rapidly brought the pedaling cadence up to 80 (rev.min^-1) as the resistance was abruptly increased to provide the work rate that had been individually pre-determined by the primary investigator.

3.5. VO₂ Kinetics in the Constant Power Tests

For each individual, for each test, data from the first 20 s of exercise were removed (8) and the remaining B×B, 3-B, 5-B, or 7-B data points were fit to the following model (1) using iterative regression procedures in KaleidaGraph 4.5 software (Reading, PA USA) (Equation 1):

VO_2baseline is the steady state VO₂ at the end of the three minutes of seated rest prior to exercise, A_primary and A_slow are the projected increases in VO₂ due to the primary and slow component responses, TD_primary and TD_slow are the time delays preceding the two responses, and tau_primary and tau_slow are the time constants of the two responses.

The mean response time (MRT_primary) represents the time from the start of exercise until the VO₂ has increased 63% of the A_primary. It is calculated as the sum of TD_primary and tau_primary and tends to be more stable and reliable than either of the parameters which it comprises. MRT_primary was used as a supplementary variable to describe the primary phase of the VO₂ response.

The actual increase in VO₂ due to the slow component, A’_slow, was calculated as (Equation 2):

A’_slow and TD_slow were used to describe the characteristics of the slow component in all tests.

3.6. Statistical Analyses

Descriptive characteristics of participants were calculated separately for women and men. For all other analyses, data were collapsed across the sexes. Sample size was 20.

First, to identify which smoothing method would be selected to provide the criterion measure for each parameter, the SEE of each parameter that was directly generated using the iterative regression procedure in KaleidaGraph (TD_primary, tau_primary, A_primary, and TD_slow) were compared using a two-way (type of smoothing [B×B, 3-B, 5-B, 7-B] × test number [first, second, third, fourth, fifth, sixth]) repeated-measures analysis of variance (ANOVA) in SPSS V.22 (SPSS, Armonk, NY, USA). Two other descriptors of the VO₂ response profile, MRT_primary and A’_slow, were not included because they are calculated values, and not directly generated by KaleidaGraph. Data were tested for sphericity using Mauchly’s test of sphericity and, if assumptions were violated, results were interpreted using a Greenhouse-Geisser correction. Significance was set at P < 0.05. The post hoc comparisons of SEE were performed using paired-means t tests with a fixed level of significance (P < 0.05) rather than correcting the P-level because of multiple comparisons; given that these comparisons were a tool to identify the criterion measure and any difference was considered meaningful. Data are presented as mean ± SD.

Second, the optimal smoothing method and the minimum number of tests necessary to ensure accurate estimation of the parameters of the VO₂ response in heavy intensity exercise, six values for each parameter (TD_primary, tau_primary, MRT_primary, A_primary, TD_slow, and A’_slow, and for the SEE associated with the four parameters that were directly generated by KaleidaGraph) obtained using each smoothing method were calculated. The first of the six values was simply the value from the first test, the second was the average of the values from the first and second tests, the third was the average of the values from the first three tests, etc. These values were compared using a two-way (type of smoothing [B×B, 3-B, 5-B, 7-B] × number of tests used to calculate the value [1, 2, 3, 4, 5, 6]) repeated-measures ANOVA. In addition, correlations between each value and the criterion measure were calculated.

Finally, a Bland-Altman plot (15) was created for each comparison. Arguably, use of a Bland-Altman analysis is preferred when the task is to identify methods that produce the same answer (in this case, to identify methods that produce an answer that is the same as the criterion), as opposed to identifying values or methods that are different. As proposed by Krouwer (16), criterion values were on the x-axis and differences between values and the criterion were on the y-axis. Aside from the fact that 23 Bland-Altman plots were needed to assess the agreement between the various means and the criterion measure for each variable, one challenge of using Bland-Altman plots was that levels of agreement (defined by the 95% confidence interval around the mean difference for each comparison) were different for each comparison, even for comparisons for the same variable. This meant, for example, that for any given parameter, some types of smoothing faced stricter limits of agreement than others. In addition, Bland and Altman (15) noted that the levels of agreement that they propose (95% confidence interval around the mean difference) may be unacceptably large in some situations, such as clinical testing, and this was the case in the present study: the 95% confidence interval in many cases was simply too broad, and allowed deviations from the criterion value that would be inappropriate in research or practical applications. In order to address the issue of inequity caused by using the 95% confidence intervals that were unique to each comparison, as well as to address the issue of appropriateness, we used stricter levels of agreement. We constructed the levels of agreement to be 0.0 ± 1.0 × SEE of the criterion measure. Thus, we used the same limits of agreement for all comparisons involving a given variable; the levels of agreement were similar to the 85% confidence interval. We also constructed levels of agreement that were 0.0 ± 1.5 × SEE of the criterion measure. We estimate that these ranges were similar to the 90% confidence interval. In each case, these plots then were intolerant of bias; they defined a range of ‘accepted’ individual values that were close enough to the criterion value to meet the requirements of research or practical applications.

4. Results

Results of the two-way ANOVA that was used to identify which smoothing method would be selected to provide the criterion measure for each parameter revealed a significant effect of type of smoothing (P < 0.05) for three of the SEE associated with the parameter estimates that were directly generated using KaleidaGraph (tau_primary, A_primary, and TD_slow, but not TD_primary). The mean values associated with the main effects are presented in the farthest right column of Tables 1-4 and the results of the post hoc t tests are provided below, with differences significant at the 0.05 level:

SEE TD_primary, B×B = 7-B = 3-B = 5-B

SEE tau_primary, B×B > 3-B = 7-B > 5-B

SEE A_primary, B×B > 3-B = 7-B = 5-B

SEE TD_slow, B×B > 3-B > 5-B = 7-B.

Based on the mathematically smaller SEE associated with parameters generated using 5-B smoothing, this method was chosen to identify the criterion values for all parameters. We note that the coefficient of variation among the values from the six tests tended to be smallest for 5-B averages, as well (these results not provided, but can be inferred from data in Tables 1-4). We assumed that the average value from all six tests would be most representative of the ‘true’ or criterion value.

Mean values for the parameter that were obtained using the 24 combinations of kind-of-smoothing (B×B, 3-B, 5-B, 7-B) and number-of-tests used to calculate the values (1 to 6) are presented in Tables 1-5. Results of the two-way ANOVAs that were used to investigate the effects of smoothing and number of tests revealed no significant main or interaction effects. Thus, we cannot argue that there were any differences among the reported values, regardless of the type of smoothing or the number of tests used to calculate the values. Similarly, the results of the correlational analyses, which are also presented in the tables, showed that values from almost all combinations of type of smoothing and number of tests used were strongly correlated with the criterion 5-B six test values. Because of space limitations, results for the MRT_primary, which was calculated as the sum of TD_primary and tau_primary, are not provided in tabular form. Variability in MRT_primary is much less than in either parameter individually; thus, the accuracy of MRT_primary generated with data from one test was acceptable, regardless of how the data were smoothed.

Two hundred and seventy-six Bland-Altman plots were constructed (6 variables × 2 levels of agreement × 23 comparisons). Because of space restrictions, the plots are not reproduced here. The important results from these plots are summarized in the tables and can be explained as fallows: mean values from type-of-smoothing × number-of-tests combinations for which all individual values fell within very strict limits of agreement (± 1.0 × SEE) are identified by superscript ‘B’ and mean values for which all individual values fell within 50% broader limits of agreement are identified by superscript ‘C’. So, for example, for the 5-B tau_primary parameter value obtained using only data from the first test, all individual values fell within 5 s (1.5 × SEE) of their associated criterion value; when parameter values from the first two tests were averaged, all fell within 3 s (1.0 × SEE). This can be interpreted that a single test provides enough 5-B data to closely identify (within 5 s) the value of the tau_primary parameter and that, with data from two tests, individual values will be within 3 s of the ‘true’ value. Requiring more tests produces rapidly diminishing returns; we cannot even argue that accuracy and precision of these values improves when data from more than two or three tests were included in their calculation.

5. Discussion

The important finding in the present study is that curve fitting of 5-B data from only one exercise test can generate accurate values for parameters of the two-component VO₂ response profile in heavy intensity exercise. 3-B and 7-B smoothing methods were also very good to improve the signal-to-noise ratio and reduce the number of tests that must be performed. The use of two or three tests may be indicated if acceptable tolerance of deviation from the ‘true’ value of each parameter is very small, for example, less than 3 s for tau_primary, < 1 mL/kg/min for A_primary, < 6 s for TD_primary, and < 1 mL/kg/min for A_primary. Slightly better accuracy may be obtained if more tests are performed, but any improvements may not justify the extra demands on personnel, participants, and other resources.

Subsequent to the work of Lamarra and colleagues (10), it has often been assumed that multiple trials are required to minimize the signal-to-noise ratio, and often this is accomplished by combining data from the trials before smoothing the data, that is, before fitting them to a mathematical model (8). Benson and colleagues (8) applied a variety of smoothing interventions to one to ten sets of simulated moderate intensity. Like Francescato and colleagues (17), who also used simulated data, they found little difference between the effects of smoothing. They did report that four trials were optimal. They also found that combining data before modeling was superior to modeling and then combining the results (i.e., averaging the parameter estimates from different tests, as we did in the present study.) However, they noted that modeling results from tests individually and then averaging the results has been proposed and used (18) and may be statistically more appropriate (19). We note, that this method also allows the investigator to evaluate whether there is a trend in the results. i.e., to determine if responses are changing over time (they were not, in the present study).

In a study similar to the present study, Keir and colleagues (9) evaluated the effects of several smoothing techniques applied to data from four identical moderate intensity exercise tests (i.e., assuming that combining data from four tests was requisite for obtaining data with good precision). They concluded that modeling had no effect on the mean values for the parameter estimates but that it did affect the precision of the estimates, as judged by the 95% confidence intervals. Differences between their study and ours include that we used stricter confidence intervals, we tested the effect of performing multiple trials (rather than limiting analyses to data combined from all the trials that were performed), and we used data from heavy intensity exercise, rather than sub-threshold moderate intensity exercise. We fitted data to a two-component model, so that the effect of smoothing and the effect of number of trials was determined for primary phase and slow component parameters. Given the greater complexity of the response and greater number of parameters, compared to studies which used only a mono-exponential response, less precision might be expected around the parameter estimates generated in the present study. The good precision and accuracy that we report may reflect that our participants were familiar with exercise testing while breathing through a mouthpiece.

5.1. Conclusions

The accuracy and precision of estimates of the parameters of the primary and slow phases of the VO₂ response during heavy intensity exercise can be improved by using data from more than one test and by smoothing the data prior to fitting them to an appropriate mathematical model. Depending upon the accuracy required, that is depending upon how close each and every participant’s value must be to his or her ‘true’ value, smoothed data from one or two tests is sufficient to calculate the values that describe the two-parameter VO₂ response profile in heavy intensity cycling exercise.