Development and validation of dynamic bioenergetic model for intermittent ergometer cycling.

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 (MRae) 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 MRae 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 MRae 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.

Validity and Reliability of Hydraulic-Analogy Bioenergetic Models in Sprint Roller Skiing.

Purpose: To develop a method for individual parameter estimation of four hydraulic-analogy bioenergetic models and to assess the validity and reliability of these models' prediction of aerobic and anaerobic metabolic utilization during sprint roller-skiing. Methods: Eleven elite cross-country skiers performed two treadmill roller-skiing time trials on a course consisting of three flat sections interspersed by two uphill sections. Aerobic and anaerobic metabolic rate contributions, external power output, and gross efficiency were determined. Two versions each (fixed or free maximal aerobic metabolic rate) of a two-tank hydraulic-analogy bioenergetic model (2TM-fixed and 2TM-free) and a more complex three-tank model (3TM-fixed and 3TM-free) were programmed into MATLAB. The aerobic metabolic rate (MR ae ) and the accumulated anaerobic energy expenditure (E an,acc ) from the first time trial (STT1) together with a gray-box model in MATLAB, were used to estimate the bioenergetic model parameters. Validity was assessed by simulation of each bioenergetic model using the estimated parameters from STT1 and the total metabolic rate (MR tot ) in the second time trial (STT2). Results: The validity and reliability of the parameter estimation method based on STT1 revealed valid and reliable overall results for all the four models vs. measurement data with the 2TM-free model being the most valid. Mean differences in model-vs.-measured MR ae ranged between -0.005 and 0.016 kW with typical errors between 0.002 and 0.009 kW. Mean differences in E an,acc at STT termination ranged between -4.3 and 0.5 kJ and typical errors were between 0.6 and 2.1 kJ. The root mean square error (RMSE) for 2TM-free on the instantaneous STT1 data was 0.05 kW for MR ae and 0.61 kJ for E an,acc , which was lower than the other three models (all P < 0.05). Compared to the results in STT1, the validity and reliability of each individually adapted bioenergetic model was worse during STT2 with models underpredicting MR ae and overpredicting E an,acc vs. measurement data (all P < 0.05). Moreover, the 2TM-free had the lowest RMSEs during STT2. Conclusion: The 2TM-free provided the highest validity and reliability in MR ae and E an,acc for both the parameter estimation in STT1 and the model validity and reliability evaluation in the succeeding STT2.