Abstract
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. 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. 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. 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.
Highlights
Muscle fatigue is defined as an exercise-induced reduction in the ability to generate force or power [24]
First attempts to quantify the development of muscle fatigue were made around 1960 by Monod and Scherrer [51, 52] and Rohmert [58], who mathematically described the nonlinear relationship between contraction intensity and endurance time with algebraic equations
Since brain effort is only known for maximal efforts, the model was later extended by Xia and Law [75] by including a controller to account for the recruitment hierarchy of three different fiber types when matching the target force
Summary
Muscle fatigue is defined as an exercise-induced reduction in the ability to generate force or power [24]. MVIC force is considered one of the gold standards for determining muscle fatigue [73], as its measurements are easy to standardize and to conduct. It is used extensively by physiologists and sports scientists, who could benefit from a predictive model when designing experiments. Most everyday movements are of a dynamic nature, isometric contractions contribute to stabilization during those movements [2] For this reason, isometric strength capacities and especially their connection to possible injuries are of high interest, e.g. in ergonomics [36, 28] or sports [41]. Isometric resistance training can be used as part of a rehabilitation program, e.g. when joint movements are restricted or not advisable [38]
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