A model-based estimation of critical torques reduces the experimental effort compared to conventional testing.

PURPOSE: Critical torque (CT) is an important fatigue threshold in exercise physiology and can be used to analyze, predict, or optimize performance. The objective of this work is to reduce the experimental effort when estimating CTs for sustained and intermittent isometric contractions using a model-based approach. MATERIALS AND METHODS: We employ a phenomenological model of the time course of maximum voluntary isometric contraction (MVIC) torque and compute the highest sustainable torque output by solving an optimization problem. We then show that our results are consistent with the steady states obtained when simulating periodic maximum loading schemes. These simulations correspond to all-out tests, which are used to estimate CTs in practice. Based on these observations, the estimation of CTs can be formulated mathematically as a parameter estimation problem. To minimize the statistical uncertainty of the parameter estimates and consequently of the estimated CTs, we compute optimized testing sessions. This reduces the experimental effort even further. RESULTS: We estimate CTs of the elbow flexors for sustained isometric contractions to be 28% of baseline MVIC torque and for intermittent isometric contractions consisting of a 3 s contraction followed by 2 s rest to be 41% of baseline MVIC torque. We show that a single optimized testing session is sufficient when using our approach. CONCLUSIONS: Our approach reduces the experimental effort considerably when estimating CTs for sustained and intermittent isometric contractions.

A phenomenological model of the time course of maximal voluntary isometric contraction force for optimization of complex loading schemes.

PURPOSE: The time course of maximal voluntary isometric contraction (MVIC) force is of particular interest whenever force capacities are a limiting factor, e.g., during heavy manual work or resistance training (RT) sessions. The objective of this work was to develop a mathematical model of this time course that is suitable for optimization of complex loading schemes. MATERIALS AND METHODS: We compiled a literature overview of existing models and justified the need for a new model. We then constructed a phenomenological ordinary differential equation model to describe the time course of MVIC force during voluntary isometric contractions and at rest. We validated the model with a comprehensive set of published data from the elbow flexors. For this, we estimated parameters from a subset of the available data and used those estimates to predict the remaining data. Afterwards, we illustrated the benefits of our model using the calibrated model to (1) analyze fatigue and recovery patterns observed in the literature (2) compute a work-rest schedule that minimizes fatigue (3) determine an isometric RT session that maximizes training volume. RESULTS: We demonstrated that our model (1) is able to describe MVIC force under complex loading schemes (2) can be used to analyze fatigue and recovery patterns observed in the literature (3) can be used to optimize complex loading schemes. CONCLUSIONS: We developed a mathematical model of the time course of MVIC force that can be efficiently employed to optimize complex loading schemes. This enables an optimal use of MVIC force capacities.