A mathematical model of neuromuscular adaptation to resistance training and its application in a computer simulation of accommodating loads

Abstract

A large corpus of data obtained by means of empirical study of neuromuscular adaptation is currently of limited use to athletes and their coaches. One of the reasons lies in the unclear direct practical utility of many individual trials. This paper introduces a mathematical model of adaptation to resistance training, which derives its elements from physiological fundamentals on the one side, and empirical findings on the other. The key element of the proposed model is what is here termed the athlete's capability profile. This is a generalization of length and velocity dependent force production characteristics of individual muscles, to an exercise with arbitrary biomechanics. The capability profile, a two-dimensional function over the capability plane, plays the central role in the proposed model of the training-adaptation feedback loop. Together with a dynamic model of resistance the capability profile is used in the model's predictive stage when exercise performance is simulated using a numerical approximation of differential equations of motion. Simulation results are used to infer the adaptational stimulus, which manifests itself through a fed back modification of the capability profile. It is shown how empirical evidence of exercise specificity can be formulated mathematically and integrated in this framework. A detailed description of the proposed model is followed by examples of its application-new insights into the effects of accommodating loading for powerlifting are demonstrated. This is followed by a discussion of the limitations of the proposed model and an overview of avenues for future work.

Computer-Aided Parameter Selection for Resistance Exercise Using Machine Vision-Based Capability Profile Estimation

“…The universal characteristics of force production for individual muscles are modulated by the plurality of involved musculature, attachment structure of individual muscles and the change in the biomechanics throughout the lift. It is an important observation that in the model proposed in [12] these are not modelled separately-all performance prediction and adaptation experienced over time is based on the corresponding capability profile which captures the total effective force exerted against the load. The model is employed by predicting exercise performance first.…”

“…1. For further in-depth technical detail on the model, the reader is referred to the original publication [12].…”

“…ConceptuallyFðd; vÞ can be thought of as a generalization of the force-length [13][14][15] and force-velocity characteristics [16,17] of an isolated skeletal muscle to an arbitrary and in practice usually biomechanically complex exercise [12]. Force-length and force-velocity characteristics, while trainable [18] and variable between different people as well as across different muscles of the same person, Table 1 A summary of the key mathematical notation used in this paper…”

“…This is a crucial element in the pipeline described in subsequent sections. Specifically, the reconstruction of an athlete's capability profile [12], which is based on the elevation-velocity characteristics, and the corresponding force exerted against the load in the performed lifts, are both inferred from the motion extracted here.…”

“…The central concept in the computational model introduced in [12] is the capability profile of an athlete in a given exercise. It is instrumental in predicting performance as well as in capturing the nature and magnitude of training adaptations.…”