Skip Navigation LinksHome > July 2003 - Volume 35 - Issue 7 > Variable Dose-Response Relationship between Exercise Trainin...
Medicine & Science in Sports & Exercise:
APPLIED SCIENCES: Physical Fitness and Performance

Variable Dose-Response Relationship between Exercise Training and Performance


Collapse Box


BUSSO, T. Variable Dose-Response Relationship between Exercise Training and Performance. Med. Sci. Sports Exerc., Vol. 35, No. 7, pp. 1188–1195, 2003.

Introduction: The aim of this study was to propose a nonlinear model of the effects of training on performance. The new formulation introduced a variable to account for training-related changes in the magnitude and duration of exercise-induced fatigue.

Methods: Goodness-of-fit of the proposed model was compared with that of earlier models presented in the literature. Models were applied to six previously untrained subjects volunteers over a 15-wk endurance-training program composed of an 8-wk period with three sessions per week and a 4-wk period with five sessions, and the remaining weeks without training. Training sessions were composed of performance trial and intermittent exercise with 5-min work interspersed with 3-min recovery repeated four or five times. Performance was measured three times each week using average power during a 5-min all-out exercise.

Results: The training program resulted in 30 ± 7% improvement in performance. The proposed model exhibited significantly improved fit with actual performance obtained in each subject. Standard error was 6.47 ± 0.71 W for the proposed model and from 9.20 ± 2.27 W to 10.31 ± 1.56 W for earlier models. The model output using model parameters averaged over the six subjects was found to be similar to data published elsewhere obtained in athletes with more intense training.

Conclusion: The data obtained allowed us to demonstrate an inverted-U-shape relationship between daily amounts of training and performance. The fit between experimental data and model-derived predictions in similar situations showed the usefulness of the proposed model to predict responses to training with varied regimens.

The relationship between the amount of work performed and the improvement in physical performance achieved appears to be more complex than a simple dose-response effect. Too much training with insufficient recovery between sessions could provide a level of performance lower than expected. Little data are available to examine the quantitative relationship between training and performance. In 1975, Banister and coauthors (1) proposed systems modeling to quantify the relationship. In their model, variations in performance over time were related to training doses, quantified from exercise intensity and duration. The systems model was able to differentiate between the influence of fatigue and adaptation on performance. Model derivations yielded a better understanding of the particular features of tapering and overtraining (12,22,23,26). A study in elite swimmers demonstrated that the decrease in negative influence of training with its progressive reduction during 3 or 4 wk resulted in around 3% improvement in performance (26). Such a duration for the taper period did not compromise the positive influence of training. Nevertheless, model limitations arise from the observed differences among published results (6,7,24). The comparison of the published model parameters showed that they could be dependent on the severity of the training doses (8). With greater and more frequent training doses, the model parameters would contribute to a greater magnitude and duration of the fatigue induced by each training bout. To explore this possible modification of the training response to a single training bout according to the past training doses, a recursive least squares algorithm was proposed to allow the model parameters to vary over time (8). A recent study using this algorithm showed that the increase in training frequency yielded a progressive increase in the magnitude and duration of the fatigue induced by a same training bout (5). A decrease in the gain of performance for a single training bout was also observed. The model initially proposed by Banister and coworkers could provide an imperfect description of training-induced fatigue produced by various work regimens. Consequently, a new formulation of the systems model is needed to take into account the increase in the fatigue effect resulting from repeated training sessions.

More precisely, the performance ascribed to system output was mathematically related to the training doses ascribed to system input. The model generally used in the literature is defined by a transfer function composed of two first-order filters where the impulse response is k1 e-t/τ1 − k2 e-t/τ2. Response to training dose is characterized by the parameters of the two antagonistic first-order systems: i.e., two gain terms k1 and k2 and two time constants τ1 and τ2. To allow the dose-response relationship to vary between training dose and performance, the model development proposed in this study is that the gain term for the negative component varies with training doses according to a first order relationship. The gain term for the negative component would thus be a state variable varying with system input in which the impulse response is k3 e-t/τ3. The resulting impulse response of performance output to systems input would be k1 e-t/τ1 − k2(t)e-t/τ2 in which the gain term for the negative component would vary over time with the repetition of training doses. The proposed nonlinear expression of the model would yield a performance response to a single training bout that would be dependent on the intensity of past training. Such a model would be, however, fundamentally different from the model with time-varying parameters using the recursive least square method (5,8). The model proposed in this study assumes that the gain term for fatigue effect is mathematically related to training dose using a first-order filter. Conversely, the time-varying parameters in the earlier model did not assume their variations over time. Leaving model parameters free to vary over time enabled posterior analysis of response to training (5,8). The reliability of the model proposed in this study would provide further evidence of a dose-response relationship varying over time according to the cumulative amount of training. Furthermore, a systems model that would better describe response to training could be a useful tool to study the importance of training periodization for optimizing performance improvement.

The aim of this study was thus to develop the systems model with time-invariant parameters by introducing variations in the fatiguing effect of a single training bout. To evaluate its reliability, the goodness-of-fit of performance using this extended model was compared with existing models. The refinement of the model introducing new parameters needs to be evaluated by testing whether the increase in model complexity would yield a significant better fit of performance response to training. The data used in this study were taken from a previous experiment (5). Because the point of the new formulation of the model is to better describe response to various training regimens, the different models were compared using a step increase in training after a period of adaptation to lower training doses. Another goal of this study was to determine whether the present data extrapolated to more intensified training could be compared with athletes’ response to overtraining.

©2003The American College of Sports Medicine


Article Tools


Search for Similar Articles
You may search for similar articles that contain these same keywords or you may modify the keyword list to augment your search.

Connect With Us