A hierarchical model for external electrical control of an insect, accounting for inter-individual variation of muscle force properties

  1. Dai Owaki
  2. Volker Dürr
  3. Josef Schmitz

  • Curated by eLife

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    eLife assessment

    This valuable work presents new results to characterize the relationship between electrical excitation and torque generation in stick insect joints. The evidence supporting this work is a series of torque-voltage measurements across individuals. The strength of evidence is solid in supporting the outcomes, but some details of the methodology, which could potentially shed light on the sources of this variation, are missing.

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Abstract

Cyborg control of insect movement is promising for developing miniature, high-mobility, and efficient biohybrid robots. However, considering the inter-individual variation of the insect neuromuscular apparatus and its neural control is challenging. We propose a hierarchical model including inter-individual variation of muscle properties of three leg muscles involved in propulsion (retractor coxae), joint stiffness (pro- and retractor coxae), and stance-swing transition (protractor coxae and levator trochanteris) in the stick insect Carausius morosus . To estimate mechanical effects induced by external muscle stimulation, the model is based on the systematic evaluation of joint torques as functions of electrical stimulation parameters. A nearly linear relationship between the stimulus burst duration and generated torque was observed. This stimulus-torque characteristic holds for burst durations of up to 500ms, corresponding to the stance and swing phase durations of medium to fast walking stick insects. Hierarchical Bayesian modeling revealed that linearity of the stimulus-torque characteristic was invariant, with individually varying slopes. Individual prediction of joint torques provides significant benefits for precise cyborg control.

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  1. Version published to 10.7554/elife.85275 on eLife
  2. eLife

    eLife assessment

    This valuable work presents new results to characterize the relationship between electrical excitation and torque generation in stick insect joints. The evidence supporting this work is a series of torque-voltage measurements across individuals. The strength of evidence is solid in supporting the outcomes, but some details of the methodology, which could potentially shed light on the sources of this variation, are missing.

  3. eLife

    Reviewer #1 (Public Review):

    This work serves to fill an important gap in our understanding of the control of insect walking: characterization of the structure of inter-individual variability. The authors use an extensive novel dataset to exhaustively test across models. Such integration of mechanistic theory and experimental analyses is both crucial and not seen enough in the literature.

    In this study, the authors perform experiments using external electrical muscle stimulation in intact, immobilised animals and measure joint torques in three muscles: the retractor coax (which is involved in propulsion and joint stiffness), the protractor coxae (which is involved in joint stiffness and in the swing-stance transition), and the levator trochanteris (which is involved in the swing stance transition). These experiments quantify the relationship between electrical stimulus and torque generated in each joint. Because these experiments are performed on many animals, the authors are able to investigate how this relationship varies between (and within) each individual. The results of these experiments are then interpreted in the context of a hierarchical Bayesian model.

    The results of this work are helpful towards our understanding of the role of inter-individual variation in the control of insect walking. Proper links between such variation observed in biomechanical studies in freely walking animals will require an understanding of how the variability characterized in this study interplays with other behavioural factors. The authors make note of this: their work takes place in immobilised animals, and thus cannot explicitly test the predictions of their model parameters on performance in freely-behaving insects. They outline a possible path forward to this end, which involves using their previously presented Motion Hacking method in unrestrained locomotion. This is an exciting future direction that is set up by the results here, but is outside the scope of the current work; the authors are upfront and reasonable about the limitations of their study.

    The clarity of this work suffers from its structure: the models (and the parameters within) are central to the results of this study. The integration of data-driven modelling and experiment is a main reason this work is exciting! Yet, these are introduced far after the results are presented. While this is partially due to the section structure set forward, some basic aspects of the models and experimental system should be introduced prior to delineating the Results.

  4. eLife

    Reviewer #2 (Public Review):

    In this manuscript, the authors study the generation of joint torques in stick insects under external electrical excitation. The goal of this paper is to develop a model for the relationship between torque and excitation period, with a specific focus on accounting for inter-individual variances in the model. The long-term motivation for this work is to be able to generate controlled external excitation of insect muscle to create "cyborg" systems where computer-controlled electronics generate movement of living systems.

    The authors performed measurements of joint torque generated from three different muscles across two excitation parameters (voltage and excitation time). The authors study the relationship between excitation parameters and muscle torque comparing a linear relationship, and a non-linear (power-law) relationship between torque and voltage. In addition, the authors also compare a hierarchical version of the model which includes inter-individual differences, with a pooled model that ignores individual differences. The authors use an information criteria metric to then identify the best model.

    I believe that the methods of this paper and the findings are all sound; however, I have the following comments and questions.

    Main questions:
    1. It is interesting to find that inter-individual differences are important in the torque output from the joint. However, in some sense, this is what I would have expected. I am curious if these inter-individual differences can be related to any distinct differences among the insects studied: for example body mass, limb length, cross-sectional muscle area, and age all would likely influence torque. Now I am not advocating that all of the above parameters (age, size, etc) be added into a more complex model because I don't think that is necessarily the right path. However, I do think it would be beneficial to present the known information about the variance in individual size/age/etc, some of which may be unknown.

    2. Line 145 states that "Models 1-2 and 2-1 most accurately predicted the posterior predictive distribution.", but is this not a typo? I thought Models 1-2 and 2-2 are the best as they are the linear and nonlinear models with hierarchical slopes.

    In the paragraph starting at line 147 and the subsequent paragraph it is argued that while the nonlinear model 2-2 worked well, the linear model is still better. "The comparison of the linear model (model 1-2) with the nonlinear model (model 2-2) using the WAIC for all conditions (muscle type and applied voltage) resulted in lower values for the linear model." But certainly, both are quite close in WAIC, and my question is, might there be reasons from muscle physiology on stick insects to expect a non-linear model? While the linear model had the lowest WAIC (marginally from looking at Fig 2) without any prior assumptions about the torque-duration curve, certainly much is known about the effect of stimulation on force production, and might including that information validate the non-linear model over linear?

    Alternatively, if the goal is to just model the data under 500ms stimulation because this is the relevant timescale for walking behavior (line 181) then the linear model is fine. But reading the manuscript I got the impression the goal was to best model the torque-voltage relationship, which I would think includes the full excitation range and incorporates known information from muscle physiology.

    3. Fig 3 is a bit confusing as this is meant to compare the experimental data with the hierarchical model distribution. However, all the model distributions across the 10 insects look identical. I thought the point of the hierarchical model is that the slope parameter varies across individuals (isn't this what Fig 4 demonstrates?). So shouldn't the distributions and green fit lines all be different for the individuals?

    I have some questions that should be clarified about the methods:
    4. It is stated that 20 insects were tested, but all the plots show only 10. Is this just because the other 10 were not presented? Or were observations discarded from the other 10 insects for some reason? This is important to describe so that readers can assess the results.

    5. More information should be provided about the ordering of the different excitation experiments. The methods do not describe what the time duration between excitations was, how many were performed over what time period, etc. Additionally, it looks like four different voltage amplitudes were performed which I could only observe from figures 2 and 4. It would be beneficial to describe in detail the full sequence of data collection on an insect.

    6. What is the order of presentation of different voltages? It is stated that muscle fatigue should be negligible for under 50 stimulations, but the range of the 2V experiments alone was between 49-79 stimulations. So were another ~50 stimulations performed at the three other voltages? And if so was fatigue a possible issue?
    Also, were there "warm up" effects too where the muscle force increased with subsequent stimulations? It would be useful to provide some characterization of this.

  5. eLife

    Reviewer #3 (Public Review):

    This paper combines experiments and simple modeling to try to identify the relationship between external muscle torque vs. a stimulus burst duration on several leg muscles of a stick insect. The authors created a setup to input PWM and voltage values and measured the output torque through load cells. They found an appropriate model for estimating muscle torque through different PWM burst durations and voltage values by comparing WAIC values for each modeling equation. They found that the linear hierarchical model relating burst duration and joint torque and a nonlinear hierarchical model relating burst duration and joint torque to a power function represent the muscle torque activation the best.

    The problem that the study tries to address is of great importance to the field of cyborg, biomechanics, neuromechanics, mechano-sensing, and animal locomotion (see below). There have been very few studies that tried to quantify how muscle activation in invertebrates affects force/torque output, which is important for understanding the dynamics of their movement, and this is one of the first to investigate this. The approach is technically sound, and the experimental data and modeling analyses are solid and support the conclusions drawn.

  6. Version published to 10.1101/2022.12.19.521014v1 on bioRxiv