Development and validation of dynamic bioenergetic model for intermittent ergometer cycling

Abstract

Purpose: The aim of this study was to develop and validate a bioenergetic model describing the dynamic behavior of the alactic, lactic, and aerobic metabolic energy supply systems as well as different sources of the total metabolic energy demand.

Methods: The bioenergetic supply model consisted of terms for the alactic, lactic, and aerobic system metabolic rates while the demand model consisted of terms for the corresponding metabolic rates of principal cycling work, pulmonary ventilation, and accumulated metabolites. The bioenergetic model was formulated as a system of differential equations and model parameters were estimated by a non-linear grey-box approach, utilizing power output and aerobic metabolic rate (MR_ae) data from fourteen cyclists performing an experimental trial (P2) on a cycle ergometer. Validity was assessed by comparing model simulation and measurements on a similar follow-up experimental trial (P3).

Results: The root mean square error between modelled and measured MR_ae was 61.9 ± 7.9 W and 79.2 ± 30.5 W for P2 and P3, respectively. The corresponding mean absolute percentage error was 8.6 ± 1.5% and 10.6 ± 3.3% for P2 and P3, respectively.

Conclusion: The validation of the model showed excellent overall agreement between measured and modeled MR_ae during intermittent cycling by well-trained male cyclist. However, the standard deviation was 38.5% of the average root mean square error for P3, indicating not as good reliability.

Keywords: Anaerobic work capacity; Cycle ergometer; Oxygen deficit; Oxygen kinetics; Parameter estimation.

Fig. 1

Intermittent test protocols used during test day 2 (P2) and test day 3 (P3) where the numbers reflect the duration in minutes of each period of constant power. The constant power levels are shown to the left where PR is passive rest (no pedaling), AR is active rest, and L1, L2, etc., are individual ergometer power levels (see Table 1) intentionally designed to activate the subjects’ different metabolic energy supply systems to varying degrees

Fig. 2

Sampled and smoothed ergometer power output for one representative subject for P2. The data was smoothed by setting the power output equal to the mean power output for each section. Additionally, the 100 first seconds and final 60 s were deleted to avoid smoothing error and reduce calculation times

Fig. 3

Sampled and smoothed breath-by-breath oxygen uptake (Panel A) and expiratory minute ventilation as STPD (Panel B) for one representative subject for P2. Data was smoothed using locally weighted linear regression with a 40-s time window and resampled to 0.5 Hz using linear interpolation

Fig. 4

Bland–Altman plot showing the mean of and difference between measured and modeled MR_ae for all data samples from all subjects during P2 (Panel A) and P3 (Panel B) including the model-to-measurement mean difference and 95% confidence intervals. 94.6% of the data points reside inside the confidence interval for P2 and 94.0% for P3

Fig. 5

Time resolved mean and SD (Panel A) and statistical parametric mapping from the two-tailed paired t-test (Panel B) of measured and modeled individual MR_ae normalized with MR_ae,max for P2 (n = 11). Results from three subjects are omitted due to deviations in duration during one or more periods (same subjects as in Fig. 6). Data for the period leading to volitional exhaustion has been stretched/squeezed to allow comparison across the subjects. The dashed lines show the critical t-value, indicating the limit for significant differences (p < 0.05) between measured and modeled data

Fig. 6

Time resolved mean and SD (Panel A) and statistical parametric mapping from the two-tailed paired t-test (Panel B) of measured and modeled individual MR_ae normalized with MR_ae,max for P3 (n = 11). Results from three subjects are omitted due to deviations in duration during one or more periods (same subjects as in Fig. 5). Data for the period leading to volitional exhaustion has been stretched/squeezed to allow comparison across the subjects. The dashed lines show the critical t-value, indicating the limit for significant differences (p < 0.05) between measured and modeled data

Fig. 7

Metabolic supply rates (Panel A) and metabolic demand rates (Panel B) for P2 in a representative subject (S8). MR_al is alactic metabolic rate, MR_la lactic metabolic rate, MR_ae modeled aerobic metabolic rate, MR_dem total metabolic demand rate and Measured MR_ae is the smoothed measured aerobic metabolic rate. MR_acc is metabolic demand rate due to accumulated metabolites, MR_ve metabolic demand rate due to ventilation, MR_f metabolic demand rate due to the fundamental work and MR_rest the metabolic demand rate at rest. In Panel A MR_rest is included in MR_ae

Fig. 8

Metabolic supply rates (Panel A) and metabolic demand rates (Panel B) for P3 in a representative subject (S8). MR_al is alactic metabolic rate, MR_la lactic metabolic rate, MR_ae modeled aerobic metabolic rate, MR_dem total metabolic demand rate and Measured MR_ae is the smoothed measured aerobic metabolic rate. MR_acc is metabolic demand rate due to accumulated metabolites, MR_ve metabolic demand rate due to ventilation, MR_f metabolic demand rate due to the fundamental work and MR_rest the metabolic demand rate at rest. In Panel A MR_rest is included in MR_ae