On the Shape of the Force-Velocity Relationship in Skeletal Muscles: The Linear, the Hyperbolic, and the Double-Hyperbolic

Abstract

The shape of the force-velocity (F-V) relationship has important implications for different aspects of muscle physiology, such as muscle efficiency and fatigue, the understanding of the pathophysiology of several myopathies or the mechanisms of muscle contraction per se , and may be of relevance for other fields, such as the development of robotics and prosthetic applications featuring natural muscle-like properties. However, different opinions regarding the shape of the F-V relationship and the underlying mechanisms exist in the literature. In this review, we summarize relevant evidence on the shape of the F-V relationship obtained over the last century. Studies performed at multiple scales ranging from the sarcomere to the organism level have described the concentric F-V relationship as linear, hyperbolic or double-hyperbolic. While the F-V relationship has most frequently been described as a rectangular hyperbola, a large number of studies have found deviations from the hyperbolic function at both ends of the F-V relation. Indeed, current evidence suggests that the F-V relation in skeletal muscles follows a double-hyperbolic pattern, with a breakpoint located at very high forces/low velocities, which may be a direct consequence of the kinetic properties of myofilament cross-bridge formation. Deviations at low forces/high velocities, by contrast, may be related to a recently discovered, calcium-independent regulatory mechanism of muscle contraction, which may also explain the low metabolic cost of very fast muscle shortening contractions. Controversial results have also been reported regarding the eccentric F-V relationship, with studies in prepared muscle specimens suggesting that maximum eccentric force is substantially greater than isometric force, whereas in vivo studies in humans show only a modest increase, no change, or even a decrease in force in lengthening contractions. This review discusses possible reasons reported in the literature for these discrepant findings, including the testing procedures (familiarization, pre-load condition, and temperature) and a potential neural inhibition at higher lengthening velocities. Finally, some unresolved questions and recommendations for F-V testing in humans are reported at the end of this document.

Human muscle activity and lower limb biomechanics of overground walking at varying levels of simulated reduced gravity and gait speeds

“…A possible explanation for the decrease in plantarflexor moment without an accompanying decrease in plantarflexion muscle activity may be that the plantarflexors were operating at a less effective point of the forcelength relationship at reduced gravity levels. Maximum muscle force is dependent on both the muscle length and velocity of the contraction [49,56,57]. If gravity level influenced the length and speed of muscle contraction, then electromyography values may not change even though the resultant muscle force may be different.…”

Force-velocity profiling in athletes: Reliability and agreement across methods

“…In multi-joint movements, the FV-relationship is commonly described as linear [ 8 ], in contrast to the hyperbolic relationship observed in isolated muscles or single-joint movements [ 7 ]. In practice, athletes can perform maximal efforts against different loads while force and velocity are measured during vertical jumping or similar multi-joint movements.…”

Comparison of linear, hyperbolic and double‐hyperbolic models to assess the force–velocity relationship in multi‐joint exercises

“…Hill's equation has been considered a reference equation in different muscle preparations and during in situ conditions in humans. However, several studies found deviations from Hill's hyperbolic function in the high-force/low-velocity region of the F-V relationship (6).…”