A mathematical model-based approach to optimize loading schemes of isometric resistance training sessions

Individualized resistance training is necessary to optimize training results. A model-based optimization of loading schemes could provide valuable impulses for practitioners and complement the predominant manual program design by customizing the loading schemes to the trainee and the training goals. We compile a literature overview of model-based approaches used to simulate or optimize the response to single resistance training sessions or to long-term resistance training plans in terms of strength, power, muscle mass, or local muscular endurance by varying the loading scheme. To the best of our knowledge, contributions employing a predictive model to algorithmically optimize loading schemes for different training goals are nonexistent in the literature. Thus, we propose to set up optimal control problems as follows. For the underlying dynamics, we use a phenomenological model of the time course of maximum voluntary isometric contraction force. Then, we provide mathematical formulations of key performance indicators for loading schemes identified in sport science and use those as objective functionals or constraints. We then solve those optimal control problems using previously obtained parameter estimates for the elbow flexors. We discuss our choice of training goals, analyze the structure of the computed solutions, and give evidence of their real-life feasibility. The proposed optimization methodology is independent from the underlying model and can be transferred to more elaborate physiological models once suitable ones become available.