Cardinal features of involuntary force variability can arise from the closed-loop control of viscoelastic afferented muscles

Involuntary force variability below 15 Hz arises from, and is influenced by, many factors including descending neural drive, proprioceptive feedback, and mechanical properties of muscles and tendons. However, their potential interactions that give rise to the well-structured spectrum of involuntary force variability are not well understood due to a lack of experimental techniques. Here, we investigated the generation, modulation, and interactions among different sources of force variability using a physiologically-grounded closed-loop simulation of an afferented muscle model. The closed-loop simulation included a musculotendon model, muscle spindle, Golgi tendon organ (GTO), and a tracking controller which enabled target-guided force tracking. We demonstrate that closed-loop control of an afferented musculotendon suffices to replicate and explain surprisingly many cardinal features of involuntary force variability. Specifically, we present 1) a potential origin of low-frequency force variability associated with co-modulation of motor unit firing rates (i.e.,‘common drive’), 2) an in-depth characterization of how proprioceptive feedback pathways suffice to generate 5-12 Hz physiological tremor, and 3) evidence that modulation of those feedback pathways (i.e., presynaptic inhibition of Ia and Ib afferents, and spindle sensitivity via fusimotor drive) influence the full spectrum of force variability. These results highlight the previously underestimated importance of closed-loop neuromechanical interactions in explaining involuntary force variability during voluntary ‘isometric’ force control. Furthermore, these results provide the basis for a unifying theory that relates spinal circuitry to various manifestations of altered involuntary force variability in fatigue, aging and neurological disease.Author summary: Involuntary fluctuations in muscle force are an unavoidable consequence of human motor control and underlie movement execution errors. Amplification and distortion of involuntary force variability are common phenomena found in various neurological conditions and in fatigue. However, the underlying mechanisms for this are often unclear. We investigated the generation and modulation of involuntary force variability arising from different sources, as well as their interactions. We used a closed-loop simulation which included a physiologically-grounded model of an afferented musculotendon and an error-controller. We show that interactions among neural noise, musculotendon mechanics, proprioceptive feedback, and error correction are critical components of force control, and by taking these into account, our model was able to both replicate and explain many cardinal features of involuntary force variability previously reported experimentally. Also, our results suggest previously unrecognized pathways through which force variability may be altered in fatigue and in certain neurological diseases. Finally, we emphasize the potential for important clinical and scientific information to be extracted from relatively simple, non-invasive measurements of force.