Non-linear dynamics in muscle fatigue and strength model during maximal self-perceived elbow extensors training

Our aim was to determine the dynamics in muscle strength increase and fatigue development during repetitive maximal contraction in specific maximal self-perceived elbow extensors training program. We will derive our functional model for m. triceps brachii in spirit of traditional Hill’s two-component muscular model and after fitting our data, develop a prediction tool for this specific training system. Thirty-six healthy young men (21±1.0 y, BMI 25.4±7.2 kg/m²), who did not take part in any formal resistance exercise regime, volunteered for this study. The training protocol was performed on the isoacceleration dynamometer, lasted for 12 weeks, with a frequency of five sessions per week. Each training session included five sets of 10 maximal contractions (elbow extensions) with a 1 min resting period between each set. The non-linear dynamic system model was used for fitting our data in conjunction with the Levenberg–Marquardt regression algorithm. As a proper dynamical system, our functional model of m. triceps brachii can be used for prediction and control. The model can be used for the predictions of muscular fatigue in a single series, the cumulative daily muscular fatigue and the muscular growth throughout the training process. In conclusion, the application of non-linear dynamics in this particular training model allows us to mathematically explain some functional changes in the skeletal muscle as a result of its adaptation to programmed physical activity—training.