Mathematical models may provide a method of describing and predicting the effect of training on performance. The current models attempt to describe the effects of single or multiple bouts of exercise on the performance of a specific task on a given day. These models suggest that any training session increases fitness and provokes a fatigue response. Various methods of quantifying the training stimulus (training impulse, absolute work, psychophysiological rating) and physical performance (criterion scale, arbitrary units) are employed in these models. The models are empirical descriptions and do not use current knowledge regarding the specificity of training adaptations. Tests of these models with published data indicate discrepancies between the predicted and measured time course of physiological adaptations, and between the predicted and measured performance responses to training. The relationship between these models and the underlying physiology requires clarification. New functional models that incorporate specificity of training and known physiology are required to enhance our ability to guide athletic training, rehabilitation and research.
Coaches and health professionals typically approach the relationship between training and performance empirically. Predictions of the effect of training on an individual's performance are guided by on-going monitoring, and art and experience. Experimental studies to investigate the physiological adaptations underlying training responses have produced an extensive body of knowledge[1]that is seldom systematically related to performance.[2]
Researchers use models to develop and test hypotheses, and to identify important parameters and variables for measurement. For those interested in applications, mathematical models might provide a method of describing and predicting the effect of training on physical capability. While mathematical models are frequently used to describe the response to acute exercise,[3]relatively few investigators have attempted to quantitatively relate chronic training stimuli to change in performance. The few proposed models have not achieved widespread use by researchers, coaches or health professionals. A review of current models may suggest approaches to improving their utility.
Dose-response models have been used to evaluate the relationship between regular exercise and health.[4]However, those analyses assume that a constant 'dose' of exercise is maintained over the duration of the study period. They regard deviations from the prescribed training as imperfect compliance. The dose-response models do not examine how rapidly a desired response is achieved but at least obliquely address the relationship of the effect to underlying physiological responses.[5]Compared with pharmacological studies that employ the dose response concept, the exercise studies only crudely quantify the input dose and make infrequent measures of the responses.
At the extremes, models may be purely empirical (models of data) or precisely based on underlying structure.[6]However, most modelling is based on simplified abstractions of the underlying complex structures. The question arises of how much underlying structure should be incorporated into models of the relationship of training and performance.
The tension between structural and empirical approaches was evident in the first mathematical model of training and performance that started with cardiovascular, strength, skill and psychological components as possible determinants of performance.[7]However, the skill, psychology and strength components were soon dropped due to difficulties in identifying useful measures and in relating the components. In subsequent studies, some authors have explored the relationship between their model terms and physiological measures,[8]while others treat the models as purely empirical descriptions. Existing models do not use current knowledge regarding physiological adaptations to training. In sections 1, 2 and 3 of this review, the components of the present models are examined. In section 4, the common features are reviewed and the strengths and shortcomings of the models are discussed.