The three-dimensional impulse-response model: Modeling the training process in accordance with energy system-specific adaptation (2503.14841v2)

Abstract: Athletic training is characterized by physiological systems responding to repeated exercise-induced stress, resulting in gradual alterations in the functional properties of these systems. The adaptive response leading to improved performance follows a remarkably predictable pattern that may be described by a systems model provided that training load can be accurately quantified and that the constants defining the training-performance relationship are known. While various impulse-response models have been proposed, they are inherently limited in reducing training stress (the impulse) into a single metric, assuming that the adaptive responses are independent of the type of training performed. This is despite ample evidence of markedly diverse acute and chronic responses to exercise of different intensities and durations. Herein, we propose an alternative, three-dimensional impulse-response model that uses three training load metrics as inputs and three performance metrics as outputs. These metrics, represented by a three-parameter critical power model, reflect the stress imposed on each of the three energy systems: the alactic (phosphocreatine/immediate) system; the lactic (glycolytic) system; and the aerobic (oxidative) system. The purpose of this article is to outline the scientific rationale and the practical implementation of the three-dimensional impulse-response model.

The Three-Dimensional Impulse-Response Model: A Novel Approach to Energy System-Specific Adaptation in Athletic Training

This paper introduces an advanced modeling strategy for quantifying the training and adaptation process in athletes by employing a three-dimensional impulse-response model. Traditional models, such as the Banister model, conceptualize training adaptations as the outcome of balancing fitness and fatigue through a single performance metric. However, these models do not account for the diverse responses elicited by exercises of varying intensities and durations across different energy systems. This paper addresses this limitation by developing a multi-dimensional framework that accounts for the physiological complexities involved in energy system-specific adaptations.

Methodology

The proposed model utilizes a three-parameter critical power (CP) model to incorporate the distinct energy systems: the alactic (PCr), lactic (glycolytic), and aerobic (oxidative) systems. Each system is treated separately, allowing the simultaneous employment of three training load metrics as inputs and three performance metrics as outputs. This model advances existing power-based training metrics by assessing the metabolic strain through a novel "strain score" (SS) which considers both the intensity and duration of effort. The SS is calculated based on deviations from maximal sustainable power outputs (MPA) rather than steady-state levels alone.

Key Numerical Results and Claims

The strain score effectively quantifies the exertion on each energy system beyond what traditional metrics such as Training Stress Score (TSS) or TRIMP account for. These metrics typically condense vastly varied training efforts into one dimension, obfuscating the differential impacts on the distinct energy systems. The three-dimensional model plots training loads against the strain experienced by each energy system, offering a nuanced analysis that can potentially guide more precise training interventions.

Implications and Future Directions

The three-dimensional impulse-response model provides a refined tool for athletic training that harmonizes the principles of specificity and systemic modeling. By tailoring training to reflect stressors specific to each energy system, coaches and athletes can engage in more targeted interventions. This approach could optimize adaptations, performance peaks, and recovery strategies more effectively than current one-dimensional models.

The theoretical underpinnings of the model suggest potential for expansive applications across sports where multi-cost models of energy exertion and recovery are crucial, such as cycling, team sports, and track events with diverse power demands. However, practical implementation requires individualized time constants reflecting how distinct systems physiologically adapt to varying training loads.

Future research should further validate the model through empirical testing, focusing on real-world applications and varying sports contexts. Employing extensive datasets from power meters could facilitate this validation, offering insights into nuanced performance adaptations previously unaccounted for in sports training science. This would not only validate the model's utility against a broader spectrum of athletic events but may also refine the weighting factors (k) and time constants (τ) used to compute fitness and fatigue.

The introduction of such a model underscores the ongoing evolution of training sciences, moving toward systems that respect and accurately model the intricate physiological mechanics of human performance.