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The three-dimensional impulse-response model: Modeling the training process in accordance with energy system-specific
Hilkka Kontro1, Armando Mastracci2, Stephen S Cheung3
1Faculty of Kinesiology, University of Calgary, Alberta, Canada.
Plos One
|February 6, 2026
Summary
This study introduces a new 3D model for athletic training, moving beyond single metrics to better quantify exercise stress and performance adaptation across energy systems. It offers a more accurate way to understand training responses.
Area of Science:
- Exercise Physiology
- Sports Science
- Biomechanical Modeling
Background:
- Athletic training involves physiological adaptation to exercise stress, leading to performance improvements.
- Existing models simplify training load into a single metric, ignoring diverse responses to different exercise types.
- This simplification limits the accuracy of predicting training-induced performance changes.
Purpose of the Study:
- To propose a novel three-dimensional impulse-response model for athletic training.
- To address the limitations of current single-metric models in quantifying training stress.
- To provide a framework for accurately predicting performance adaptations based on energy system stress.
Main Methods:
- Developed a three-dimensional impulse-response model using three training load inputs.
- Utilized a three-parameter critical power model to represent stress on alactic, lactic, and aerobic energy systems.
- Defined three performance metrics as outputs corresponding to the energy system stresses.
Main Results:
- The proposed model quantifies training load across three distinct energy systems.
- It allows for a more nuanced understanding of the relationship between training stress and performance adaptation.
- The model moves beyond single-metric limitations of previous impulse-response approaches.
Conclusions:
- The three-dimensional model offers a more comprehensive approach to understanding athletic training responses.
- It provides a scientifically grounded and practically implementable method for quantifying training stress.
- This framework enhances the prediction of performance improvements by considering the distinct demands on the body's energy systems.
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