The energetic basis for smooth human arm movements
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Curated by eLife
Evaluation Summary:
This paper will be of interest to researchers in the fields of biomechanics, movement control, and decision making. It presents a novel mechanistic model of metabolic cost that includes a cost for rate of muscle force production explains metabolic cost better than current models. They next demonstrate how this metabolic model can improve our understanding of movement control by revealing an energetic basis for smooth movements.
This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #2 agreed to share their name with the authors.
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Abstract
The central nervous system plans human reaching movements with stereotypically smooth kinematic trajectories and fairly consistent durations. Smoothness seems to be explained by accuracy as a primary movement objective, whereas duration seems to economize energy expenditure. But the current understanding of energy expenditure does not explain smoothness, so that two aspects of the same movement are governed by seemingly incompatible objectives. Here, we show that smoothness is actually economical, because humans expend more metabolic energy for jerkier motions. The proposed mechanism is an underappreciated cost proportional to the rate of muscle force production, for calcium transport to activate muscle. We experimentally tested that energy cost in humans (N = 10) performing bimanual reaches cyclically. The empirical cost was then demonstrated to predict smooth, discrete reaches, previously attributed to accuracy alone. A mechanistic, physiologically measurable, energy cost may therefore explain both smoothness and duration in terms of economy, and help resolve motor redundancy in reaching movements.
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Evaluation Summary:
This paper will be of interest to researchers in the fields of biomechanics, movement control, and decision making. It presents a novel mechanistic model of metabolic cost that includes a cost for rate of muscle force production explains metabolic cost better than current models. They next demonstrate how this metabolic model can improve our understanding of movement control by revealing an energetic basis for smooth movements.
This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #2 agreed to share their name with the authors.
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Reviewer #1 (Public Review):
The authors propose two main advances. First, they present a novel mechanistic model of metabolic cost that is proposed to account for phenomena not explained by current models. They demonstrate using a combination of elegant experiments and simple models that the limitation of current models is in their inability to account for the energetic cost associated with the rate of developing force. Second they demonstrate that this novel model of metabolic cost is capable of reproducing stereotypical arm reaching trajectories, and thus provides an energetic basis for smooth movements. The novelty of this second advance is that thus far reaching movements have been oft explained as the consequence of maximizing accuracy. This new metabolic model, suggests that energetics play a role in determining movement control.
Reviewer #1 (Public Review):
The authors propose two main advances. First, they present a novel mechanistic model of metabolic cost that is proposed to account for phenomena not explained by current models. They demonstrate using a combination of elegant experiments and simple models that the limitation of current models is in their inability to account for the energetic cost associated with the rate of developing force. Second they demonstrate that this novel model of metabolic cost is capable of reproducing stereotypical arm reaching trajectories, and thus provides an energetic basis for smooth movements. The novelty of this second advance is that thus far reaching movements have been oft explained as the consequence of maximizing accuracy. This new metabolic model, suggests that energetics play a role in determining movement control.
The first advance is compelling and will add significantly to our current understanding of the fundamental basis of metabolic cost. The experiments are thorough, the cross-validation is impressive, and the model is simple, yet elegant. The second advance, energetic cost as a basis for movement control, could be strengthened. Firstly, energetic cost is already generally assumed to play a role in movement control, it is the quantification that has been difficult. This paper thus provides such a quantification (with its first advance). Demonstrating that it can explain bell-shaped profiles, while nice, feels lacking given the number of cost functions that can generate those same profiles and the fact that other factors such as accuracy likely play a role. Further tests of the metabolic model's ability to explain features of movement control will help strengthen the work. Similarly, examples of where the model fails will also help determine its limits and identify future directions. Taken together, the authors hope to demonstrate the significance of this model of metabolic cost on movement control, yet support is lacking.
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Reviewer #2 (Public Review):
This paper shows that the rate of muscle force production as cost function term predicts the metabolic cost of reaching movements better than other more commonly used terms. This an important contribution to the field and will be of interest to the motor control and biomechanics field.
The work is an initial attempt to unify two theories in motor control: minimum-variance (focused on endpoint accuracy) and energy minimization as in optimal feedback control. This work shows that a new energy minimization term (the rate of muscle force production):
- more accurately metabolic cost on their experimental data;
- produces smooth movements; thereby offering an initial attempt to unify energy minimization with minimum-variance theory.
Their first contribution is clearly important and sufficient for this work to have …
Reviewer #2 (Public Review):
This paper shows that the rate of muscle force production as cost function term predicts the metabolic cost of reaching movements better than other more commonly used terms. This an important contribution to the field and will be of interest to the motor control and biomechanics field.
The work is an initial attempt to unify two theories in motor control: minimum-variance (focused on endpoint accuracy) and energy minimization as in optimal feedback control. This work shows that a new energy minimization term (the rate of muscle force production):
- more accurately metabolic cost on their experimental data;
- produces smooth movements; thereby offering an initial attempt to unify energy minimization with minimum-variance theory.
Their first contribution is clearly important and sufficient for this work to have broad impact. The second contribution, while interesting and potentially very important, is more speculative and not fully fleshed out. For instance, I believe that optimal feedback control (Todorov 2002) also predicts smooth motions, and, more importantly, minimum-variance theory predicts more than smooth motions (i.e., the speed-accuracy tradeoff). The new cost function term has no impact to the speed-accuracy tradeoff (energy impacts movement duration, but movement duration does not increase when accuracy requirements increase). Hence, the unification proposed in the abstract remains to be accomplished, which doesn't take anything out of this important contribution to the field.
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