The shape of the force–elbow angle relationship for maximal voluntary contractions and sub-maximal electrically induced contractions in human elbow flexors

Abstract

The force–length relationship is a basic property of skeletal muscle. Knowledge of this relationship is necessary for most analyses of human movement, and in simulation models predicting movement control strategies. Studies on animal muscles have shown that force–length relationships for sub-maximal contractions are not related through a simple scaling procedure to the relationship for maximal contractions. Furthermore, potentiation might produce a shift of sub-maximal relative to maximal force–length relationships. In this study, we tested the hypothesis that human force–elbow angle relationships for sub-maximal unpotentiated contractions are shifted to larger elbow angles (i.e. larger muscle lengths) compared to the relationship for maximal voluntary contractions (MVC), and that this shift is reduced, or even abolished, for sub-maximal potentiated contractions. Force–elbow angle relationships (48–160°) were obtained from healthy subjects (n=13). At each of nine tested elbow angles, the test set consisted of a single twitch (ST_pre) and a doublet twitch (DT_pre) stimulation of m. biceps brachii, followed by an MVC, followed by another single twitch (ST_post) and a doublet twitch (DT_post) stimulation. The single and doublet twitches induced sub-maximal contractions. The force–elbow angle relationships for the pre-MVC (unpotentiated) twitch contractions were shifted to larger angles compared to those obtained for MVC. The force–elbow angle relationships for the post-MVC (potentiated) twitch contractions were shifted to smaller angles compared to those obtained for the unpotentiated twitch contractions. These results support the idea that the shift to larger muscle lengths for the sub-maximal, unpotentiated force–length relationships relative to the relationship for maximal contractions may be caused by a length-dependent Ca²⁺ sensitivity that may be offset, at least in part, by potentiation.

Introduction

The force–length relationship is arguably the most basic property of skeletal muscle. It relates the maximal isometric force to the length of the muscle or its contractile elements (fibres, sarcomeres). The force–length relationship has been recognised and described for well over a century (Blix (1891), Blix (1893), Blix (1894)), and many of the basic features have been well explained by myofilament geometry (Herzog et al., 1992; Gordon et al., 1966), the sliding filament theory (Huxley and Hanson, 1954; Huxley and Niedergerke, 1954), and the cross-bridge theory (Huxley, 1957; Huxley and Simmons, 1971). Most models of skeletal muscle force production contain the force–length relationship.

When analysing human movement, or using simulation models to predict movement control strategies, knowledge of the force–length relationship of the modelled muscles is essential. However, force–length relationships for sub-maximal contractions, which occur during everyday movements, may not be related through a simple scaling procedure to the relationship for maximal contractions. For example, Rack and Westbury (1969) showed for cat m. soleus that sub-maximal force–length relationships not only differed in force magnitude, but also exhibited a distinctly different shape than the corresponding maximal force–length relationship. It appears that sub-maximal force–length relationships of skeletal muscle are shifted to the right (i.e. larger muscle lengths) of the maximal force–length relationship, reaching absolute peak forces at larger muscle lengths than those of the maximal force–length relationship. Although the detailed mechanisms of this rightward shift of the sub-maximal relative to the maximal force–length relationship are not known, it is well accepted that it is associated with a length-dependent Ca²⁺ sensitivity (Balnave and Allen, 1996). For sub-maximal contractions, Ca²⁺ sensitivity increases with muscle length, thereby contributing to the shift of sub-maximal force–length relationships to larger muscle lengths relative to the maximal force–length relationship.

Potentiation is known to increase Ca²⁺ sensitivity at short muscle lengths (Levine et al., 1996; Sweeney et al., 1993), therefore potentiation might abolish, at least to a certain degree, the rightward shift of the sub-maximal force–length relationship relative to the maximal force–length relationship. Potentiation can easily be elicited by low-frequency stimulation or tetanic contractions (Close, 1972), and therefore may play a role in human voluntary muscle contraction. However, whether potentiation occurs during everyday movements, such as walking, and what effects such potentiation might have on the shape of human moment/force–angle relationships are unclear. The purpose of this study was to address the second point by investigating the (possible) shifts of sub-maximal force–elbow angle relationships in the unpotentiated and potentiated case relative to the corresponding force–elbow angle relationships obtained during maximal voluntary contractions (MVC). We hypothesised that the sub-maximal unpotentiated force–elbow angle relationships are shifted to larger angles (i.e. larger muscle lengths) relative to the maximal force–elbow angle relationship, and that this shift is reduced or abolished in the sub-maximal potentiated relationships.