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

  1. Dai Owaki  Is a corresponding author
  2. Volker Dürr
  3. Josef Schmitz
  1. Department of Robotics, Graduate School of Engineering, Tohoku University, Japan
  2. Department of Biological Cybernetics, Faculty of Biology, Bielefeld University, Germany
  3. Centre for Cognitive Interaction Technology, Bielefeld University, Germany

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.

Editor's evaluation

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 compelling in supporting the outcomes.

https://doi.org/10.7554/eLife.85275.sa0

eLife digest

Hybrid insect-computer robots – an exciting fusion of biology and technology – herald a future of small, highly mobile and efficient devices. However, these robots require a way to control the movements of the insects, a task made complex due to the differences between different insects’ nervous and muscle systems.

To bridge this gap, Owaki, Dürr and Schmitz studied the relationship between electrical stimulation of three leg muscles in the legs of stick insects and the resultant torque. To do these experiments, the scientists kept the body of the stick insects fixed and electrically stimulated one out of three leg muscles to produce walking-like movements.

The results of these electrical stimulations allowed Owaki, Dürr and Schmitz to propose a model that predicts the torque created in the insect's joints when different patterns of electrical stimulation are applied to a leg muscle. The researchers identified a near-linear relationship between the duration of the electrical stimulus and the resultant torque. Moreover, the slope of this linear relationship can be estimated for individual animals with a few measurements only. This finding refines the precision of the motor control required to build individually tuned biohybrid robots.

Investigating the precise control of insect biohybrid robots, particularly using stick insects, can lead to advancements in biohybrid robotics and enrich our understanding of insect locomotion.

Owaki, Dürr and Schmitz’s insights could lead to the creation of adaptable and highly mobile devices with many applications, but key challenges need to be addressed. First, model testing must be implemented in free-walking insects, and the electrical stimuli must be refined to mimic natural neuromuscular signals more closely.

Introduction

Hybrid insect–computer robots (Krause et al., 2011; Li and Sato, 2018) represent cutting-edge approaches to develop robots with locomotor performances comparable to those of insects. With the advancement and diversity in micro-flexible and micro-printable electronics (Rogers et al., 2010; Rich et al., 2021), micro-mechanical fabrication, and micro-actuator technologies (Kim et al., 2020), such biohybrid, that is cyborg robots have been engineered to manipulate their gait and flight through electrical stimulation of target muscles in various insects, includings beetles (Sato, 2009; Sato and Maharbiz, 2010; Sato et al., 2015; Cao et al., 2016; Vo Doan et al., 2018; Nguyen et al., 2020; Kosaka et al., 2021), moths (Sane et al., 2007; Bozkurt et al., 2009; Hinterwirth et al., 2012; Ando and Kanzaki, 2017), and cockroaches (Sanchez et al., 2015). The advantage of biohybrid (cyborg) robots is that they do not require individual ‘design’, ‘fabrication’, and ‘assembly’ processes for each component because they use the body tissues of living insects (Cao et al., 2014). Moreover, cyborg robots have low power consumption, that is, a few milliwatts (Sato and Maharbiz, 2010). Although studies on insect cyborgs have demonstrated simple manufacturing and promising energy efficiency, they are still in the initial phase of development from the perspective of evaluating both feasibility and reliability of their control.

Perhaps, the greatest challenge in cyborg control comes with the inter-individual variability of animals. Past neurophysiological studies related to animal neural activity have discussed the failure of averaging-based approaches, in which a model formulated using the average data for a group cannot explain the characteristics of any individual in the group (Golowasch et al., 2002; Schulz et al., 2006). For example, variable and non-periodic patterns in feeding behavior of Aplysia have been reported to be subject to strong inter-individual variation (Horn et al., 2004; Brezina et al., 2005; Zhurov et al., 2005). In insect motor physiology, the prediction error of muscle models which are based on sample averages is very high (Blümel et al., 2012a) and may be halved using individual-specific model (Blümel et al., 2012b). At the level of leg movements, variability has been investigated in lobsters (Thuma et al., 2003) and stick insects (Hooper et al., 2006). The variability of whole-body locomotion arises from step parameter variation of single legs (Theunissen and Dürr, 2013) but also from variation of coupling strength among legs (Dürr, 2005). One possible approach for accounting for inter-individual variability in cyborg control of single-leg movement is to construct a feedback control system (Cao et al., 2014). Although the kinematics-control of joint angles (Cao et al., 2014) has exhibited remarkable performance, its applicability to the control of dynamic gaits, such as that for walking, is still controversial. Furthermore, insects have abundant control variables, that is, degrees of freedom in their actuators and sensors. At present, the number of control variables of current insect cyborgs has to be reduced owing to system implementation difficulties.

A promising approach to overcome the ‘pitfalls’ associated with averaging across individuals is to understand the underlying principles that govern inter-individual variability in insect motor control. Especially, the output characteristics of muscle are key for controlling the dynamics of movement: muscles convert neural activity into movement and then generate behavior from interactions with the environment. In conjunction with current models of muscle activation (Harischandra et al., 2019) and contraction dynamics (Blümel et al., 2012c), we can exploit experimental data to tell parameters that are strongly influenced by inter-individual variation as opposed to others that are common characteristics. To this end, we employed a hierarchical modeling framework based on the Bayesian statistical analysis (Watanabe, 2018; Gelman et al., 2013) that explicitly accounts for inter-individual variation in experimental data. In particular, we applied a set of hierarchical Bayesian models with different combinations of common and individually varying parameters and mathematically evaluated their prediction performance.

The main objective of this study was to systematically evaluate how muscle force and corresponding joint torques depend on external electrical stimulation, as a fundamental pre-requisite for precise insect cyborg control. To this end, we measured joint torques induced by stimulating one out of three leg muscles in the middle leg of the stick insect species Carausius morosus (Sinéty, 1901): these were the protractor coxae, retractor coxae, and levator trochanteris. We focused on these three proximal muscles because the retractor coxae is the primary muscle for propulsion (Rosenbaum et al., 2010), the pro/retractor coxae contributes to weight-dependent postural adjustment by regulating joint stiffness (Dallmann et al., 2019; Günzel et al., 2022), and the levator trochanteris is important for postural termination and swing initiation (Dallmann et al., 2017). Using a custom-built electrical stimulator to generate parameter-tunable pulse-width-modulated (PWM) signals, we simulated burst-like activity of motor neurons in insects and measured the corresponding joint torques generated in response to our electrical stimuli. Using Bayesian statistical modeling and the ‘widely applied information criterion’ (WAIC) index (Watanabe, 2018) for model prediction, we evaluated six model variants, namely a simple linear, hierarchical linear, simple nonlinear, and three hierarchical nonlinear models, to identify the model that best explained the experimental data. In particular, we evaluated the predictive performances of model variants with and without inter-individual variation of experimental parameter estimates. A piecewise linear relationship was observed between the burst duration and the joint torque generated for a given parameter set of the PWM burst. Linearity was found to hold for burst durations of up to 500ms, which corresponds to the stance phase (300–500ms) and swing phase (to 250ms) of a stick insect walking at medium to fast speeds (Dürr et al., 2018). Furthermore, the hierarchical Bayesian modeling revealed both invariant and individually varying characteristics of joint torque generation in stick insects. This allows for individual tuning of electrical stimulation parameters for highly precise insect cyborg control.

With regard to our general understanding of insect motor control, our study demonstrates that the dependency of joint torque on electrical stimulus duration is linear, despite nonlinear activation and contraction dynamics of insect muscle. Furthermore, the proposed hierarchical Bayesian model allows for a quick, simple and reliable measurement of the individual characteristics and, therefore, quantification of inter-individual differences. Whereas several studies have reported on inter-individual differences in neural (Golowasch et al., 2002; Schulz et al., 2006) and muscle activity (Horn et al., 2004; Brezina et al., 2005; Zhurov et al., 2005; Blümel et al., 2012b; Blümel et al., 2012a; Thuma et al., 2003; Hooper et al., 2006), we propose how hierarchical Bayesian models may be used to harness inter-individual differences in insect locomotion research.

Results

Joint torque measurements

Since movement at a given leg joint is effected by joint torque, the goal of our experimental measurements was measure jont torque as a function of electrical stimulation. This was done for the two proximal joints of the stick insect middle leg. The insect was fixed dorsal side up on a wooden support, with its right middle leg coxa reaching beyond the edge (Figure 1A right). We selected three leg muscles (protractor, retractor, and levator) for electrical stimulation (Figure 1B). When stick insects walk, they use the protractor to swing the leg forward during the swing phase, the retractor to move the leg backward during the stance phase, and levator to initiate the stance-to-swing transition (Rosenbaum et al., 2010; Dallmann et al., 2019; Günzel et al., 2022; Bässler and Wegner, 1983). Moreover, co-contraction of the protractor and retractor are known to vary based on the overall load distribution, thus being important for postural control by regulating joint stiffness (Dallmann et al., 2019; Günzel et al., 2022). Accordingly, electrical stimulation of the protractor and retractor muscles generated forward and backward movements at the thorax–coxa (ThC) joint, as measured by a calibrated custom-made force transducer with a strain gauge held against the femur with known distance from the joint. Stimulation of the levator muscle generated an upward movement at the coxa–trochanter (CTr) joint (Dallmann et al., 2016).

Experimental setup and joint torque calculation (A) The insect was fixed dorsal side up on a balsa wood platform.

Two small insect pins attached to the tip of the force transducer held the middle part of the femur segment of the middle leg. (B) Electrodes (arrows) implanted into the three leg muscles protractor, retractor, and levator, in the right middle leg. (C) We systematically analyzed how joint torques depended on the three PWM burst parameters amplitude [V], frequency [Hz], and duty ratio [%], and identified the combinations that most effectively and repeatedly produced torque. The upper graph shows the profile of an electrical stimulation signal for each muscle. The lower graph shows the profile of the sensor value measured with the force transducer. (D). The panel shows the calculated ThC-joint torque profile versus the burst duration Ti during the protractor stimulations (animal05, n=74). In this experiment, the burst duration Ti was varied at random, and the torque was calculated from force measurements with calibrated conversion factor and moment arm (see (C)). The voltage, frequency, and duty ratio of the PWM signals were 2.0 V, 50 Hz, and 30%, respectively. The color of the dots represents the number of stimulations (blue–yellow: 1–74). The orange dotted vertical line indicates Ti at 500ms.

Figure 2 illustrates the obtained relation between the PWM burst duration and the generated joint torques for the protractor (A), retractor (B), and levator (C) muscles from 10 animals (N=10). The parameters of the PWM signals were set to 2.0 V, 50 Hz, and 30% duty ratio. During one trial, we stimulated one muscle n times with fixed PWM parameters and measured the generated torque at the corresponding joint.

Joint torques as a function of burst duration.

Data from 10 animals with three muscles, each: (A) protractor, (B) retractor, and (C) levator muscle stimulation. The PWM burst parameters were 2.0 V. 50 Hz, and 30% duty ratio. n gives the number of stimulations for each animal. Electrical stimulations were performed manually and randomly; therefore, the total number of stimuli was different for each animal. The color of the symbols indicates the order of the stimulations: blue (1) to yellow (n). The positive values of joint torque represent intended (A) forward, (B) backward and (C) upward rotation of the coxa relative to the thorax. Source code and data are available on Dryad (Figure2.zip, https://doi.org/10.5061/dryad.wpzgmsbsw).

The results indicate the input–output relation (burst duration and generated torque) corresponded to a linear function or a power function with an exponent of less than 1.0. Furthermore, the relationship holds for burst durations up to 500ms for all animals, corresponding to the duration of swing and stance phases in medium to fast walking stick insects (Dürr et al., 2018). Maximum torques for ThC and CTr joints were 60 µNm, 120 µNm, and 40 µNm (Dallmann et al., 2019). For a given set of PWM parameters, the generated torque characteristics remained almost constant during all stimulations under the same condition, suggesting that muscle fatigue or warm-up effects were negligible for at least n=50 stimulations. Furthermore, we verified that no significant changes occurred in muscle characteristics owing to the pre- and post-experimental relationship.

Bayesian statistical modeling

To investigate joint-torque properties generated by muscle stimulation while explicitly considering inter-individual variation of muscle physiology, we used a Bayesian statistical analysis and modeling framework. The probabilistic nature of Bayesian models makes them appropriate for modeling ‘uncertainty’, as introduced by inter-individual variation (Gelman et al., 2013). Bayesian analysis can be used to estimate a probabilistic distribution (model) that encodes an unknown observation target by using observed data and updating the distribution in the model. Furthermore, hierarchical model variants allow the inclusion of a hyperparameter, thus allowing for a parameter of choice to be drawn from yet another probabilistic distribution. In our case, hierarchical-model variants were used to account for inter-individual differences (Watanabe, 2018).

Here, we modeled the relationship between the burst duration of the electrical stimulation and the joint torque generated using a single model (a power function) with six variants (for details, see subsection ‘Models’). All model variants were specified in a probabilistic programming language developed by Stan (Stan Development Team, 2023). Here, we used non-informative uniform priors for the parameters β, γ, and σ, unless stated otherwise. For estimation, we used the numerical Markov Chain Monte Carlo (MCMC) method, and scripted the models in R (v.4.1.3; R Development Core Team, 2023), in which the Stan code was compiled and executed using the R package ‘rstan’ (Stan Development Team, 2023). The software performed sampling from prior distributions using No-U-Turn Sampler (NUTS; Hoffman and Gelman, 2014). Sampling convergence was detected through trace plots and the quantitative Gelman–Rubin convergence statistic Rhat (Gelman and Rubin, 1992), where Rhat<1.10.

Models

τi and Ti represent the calculated joint torque based on the force-transducer value and the burst duration of a PWM signal for electrical stimulation, respectively. We assumed that τi follows a normal distribution, described by the N(μ,σ) function, where µ and σ represent the mean and standard deviation (S.D.) of the distribution. Indexes i and j represent the numbers of stimulations and animals, respectively.

Model 1-1: Linear model representing the linear relationship between burst duration and joint torque

(1) τiN(μ=βTi,σ),

where β represents the inclination of the estimated linear function.

Model 1-2: Hierarchical model representing the linear relation between burst duration and joint torque

(2) τi,jN(μ=βjTi,σ),
(3) βjN(μ=μβ,σβ),

where βj represents the inclination of the estimated linear function on the (j)th animal. Furthermore, in this hierarchical model, βj is drawn out of a normal distribution that captures inter-individual variation, where μβ and σβ represent the mean and S.D. of the distribution, respectively.

Model 2-1: Non-linear model representing the nonlinear relationship between burst duration and joint torque

(4) τiN(μ=β{Ti}γ,σ),

where, β and γ represent the magnitude of the base and exponent of the estimated non-linear power function, respectively.

Model 2-2: Hierarchical model representing the nonlinear relationship between burst duration and joint torque

(5) τi,jN(μ=βj{Ti}γ,σ),
(6) βjN(μ=μβ,σβ),

where βj and γ represent the magnitude of the base on the (j)th animal and the exponent of the estimated nonlinear power function, respectively. In this model, βj follows a normal distribution as described above, where, μβ and σβ represent the mean and S.D. of the distribution.

Model 2-3: Hierarchical model representing the nonlinear relation between burst duration and joint torque

(7) τi,jN(μ=β{Ti}γj,σ),
(8) γjN(μ=μγ,σγ),

where β and γj represent the magnitude of the base and the exponent on the (j)th animal for the estimated nonlinear, power function, respectively. In this model, γj follows a normal distribution as described above, where μγ and σγ represent the mean and S.D. of the distribution.

Model 2-4: Hierarchical model representing the nonlinear relationship between burst duration and joint torque

(9) τi,jN(μ=βj{Ti}γj,σ),
(10) βjN(μ=μβ,σβ),
(11) γjN(μ=μγ,σγ),

where βj and γj represent the magnitude of the base and the exponent of the estimated nonlinear power function, respectively, on the (j)th animal. In this model, βj and γj follow normal distributions as described above, where μβ and μβ are the means, and σγ and σβ are the S.D.s of the distribution.

Comparison of model predictability

Using the WAIC described in the ‘Materials and methods’ section, we compared the prediction performance of the six models. Figure 3 (A)–(C) shows the WAIC values for each voltage applied (1.0–4.0 V) and models 1–1 to 2–4. Figure 3 (A)–(C) show the results for the protractor, retractor, and levator muscles, respectively. For stimulation experiments on each of the three muscles, the models with a hierarchical parameter for expressing individual differences for β~ (models 1–2 and 2–2) had the lowest WAIC and, therefore, the best predictive performance. Conversely, the model with individual differences for both β~ and γ~ (model 2–4) exhibited the lowest prediction performance, indicating that inter-individual variation of the exponent does not improve model estimates.

Model comparison underscores significance of inter-individual variation of slope.

We compared the six models that were explained in the ‘Model’ subsection. (A), (B), and (C) show plots of the WAIC (Watanabe, 2018) values for the protractor, retractor, and levator stimulations, respectively (N=10 animals per muscle). The parameters with tilde, β~ and γ~, indicate that the parameters include inter-individual variation. PWM parameters were set as follows: (1.0 V, 2.0 V, 3.0 V, and 4.0 V), at 50 Hz and 30% duty ratio. Negative values were obtained for models 1–2 and 2–2 for all voltages and all muscles. The lowest WAIC indicates the best prediction model, as explained in the "WAIC" subsection. Right panels show Bayesian predictive estimation for the protractor (D), retractor (E), and levator (F) stimulation experiments with PWM parameters 2.0 V, 50 Hz, and 30% duty ratio. The differences in the point styles indicate individual animals. In each panel, the violet shading indicates the probability density of the distribution predictive. The green lines represent twenty samples from the posterior distribution in decreasing order of probability density. Source code and data are available on Dryad (Figure3-5.zip, https://doi.org/10.5061/dryad.wpzgmsbsw).

Bayesian estimation of the generated torque for a given burst duration

Figure 3(D)-(F) shows the predictive distributions for data of a new animal using the Bayesian posterior distribution for the six models. The results were obtained with PWM bursts at 2.0 V voltage, 50 Hz frequency, and 30% duty ratio. The results show that the hierarchical models (model 1–2 and model 2–2) for the β~ parameter can successfully and adequately capture the range of experimental results on (D) protractor, (E) retractor, and (F) levator torques for all animals. This suggests that, compared with other models, the hierarchical models can appropriately account for inter-individual variation of muscle properties for new unknown animals. Figure 4 depicts the distributions predicted by the linear hierarchical model (model 1–2) for each individual by overlapping the experimental data shown in Figure 2.

Predictive distributions from the linear hierarchical model (1-2) for each individual: The protractor (A), retractor (B), and levator (C) stimulation experiments with PWM parameters, 2.0 V, 50 Hz, and 30% duty ratio.

n gives the number of stimulations for each animal. The color legend indicates the order of the stimulations: blue (1) to yellow (n). In each panel, the violet shading indicates the probability density of the predictive distribution. The green lines represent twenty samples from the posterior distribution in decreasing order of probability density. The results demonstrate that the linear hierarchical model had an accurate predictive distribution in the range up to 500ms. Source code and data are available on Dryad (Figure3-5.zip, https://doi.org/10.5061/dryad.wpzgmsbsw).

Effect of an individual animal and applied voltage on muscle properties

Figure 5 presents the variations in the muscle characteristic parameters β and γ in response to changes in the applied voltage. In the voltage-change experiments, we followed a specific order of voltage application, gradually increasing from 1 V to 4 V, for each individual. Furthermore, we confirmed that applying voltages ranging between 1 and 4 V did not induce fatigue. Table 1 summarizes the number of electrical stimuli administered to each muscle in each individual. We determined the changes in β and γ with respect to the applied voltage by analyzing the experimental results using the six Bayesian models.

Dependence of muscle property parameters on the applied voltage and individual animals in the six models: The left graphs (A), (B), and (C) represent the estimation for β for the applied voltage varied from 1.0 to 4.0 V for the six models.

(A) and (D), (B) and (E), and (C) and (F) illustrate the protractor, retractor, and levator stimulations, respectively. In (A) to (C), the upper and lower panels show non-hierarchical (1-1, 2-1, 2-3) and hierarchical (1-2, 2-2, 2-4) models for β, respectively. The right graphs (D), (E), and (F) represent the estimation for γ in applied voltage changes. In (D) to (F), the left panel shows linear models (γ=1, 1–1, 1–2); the middle and right panels illustrate non-hierarchical (2-1, 2-2), and hierarchical (2-3, 2-4) models for γ, respectively. For hierarchical models (1-2, 2-2, 2-3, 2-4), the plot includes thirty samples from the posterior distribution in decreasing order of probability density, showing inter-individual variation. Source code and data are available on Dryad (Figure3-5.zip, https://doi.org/10.5061/dryad.wpzgmsbsw).

Table 1
List of Stick insects used in the stimulation experiments for each muscle.

Animal ** denotes the identification number of the stick insects. We analyzed 20 animal data from ‘Animal 01’ to ‘Animal 22’ except for ‘12’ and ‘16’. Due to experimental failures and time limitations, we could not obtain stimulation data for all three muscles from the same animal on the same day. Therefore, we conducted experiments to collect data for ten animals (N=10) for each muscle through experiments using 20 animals.

DateProtractor1,2,3,4 VRetractor1,2,3,4 VLevator1,2,3,4 V
2018.8.21.Animal 0150,49,60,50Animal 0160,65,55,72
2018.8.22.Animal 0249,55,51,40Animal 0255,68,58,65Animal 0237,68,67,70
2018.8.27.Animal 0360,77,91,72Animal 0394,81,63,75
2018.8.28.Animal 0474,69,80,77
2018.8.30.Animal 0567,74,79,79
2018.8.31.Animal 0675,86,76,76
2018.9.03.Animal 0781,79,74,78Animal 0782,77,81,75Animal 0775,75,75,75
2018.9.04.Animal 0875,75,79,75Animal 0875,71,77,84
2018.9.05.Animal 1074,74,74,75Animal 0975,95,75,75
2018.9.19.Animal 1362,60,70,69Animal 1150,50,50,50
2018.9.20.Animal 1459,59,60,59Animal 1460,60,60,60
2018.9.21.Animal 1559,59,59,59Animal 1561,60,60,51
2018.9.23.Animal 1759,59,60,69Animal 1759,61,60,61
2018.9.24.Animal 1961,61,61,60Animal 1860,60,59,66
2018.9.25.Animal 2062,60,70,60
2018.9.26.Animal 2159,59,60,59Animal 2260,60,60,60
TotalN=10N=10N=10

The results indicate the following three points: (1) β varied with the applied voltage, and there exists an optimal voltage that maximizes β; (2) except for non-hierarchical nonlinear models (models 2–1 and 2–3), γ has a low dependence on the applied voltage; and (3) β is strongly subject to inter-individual variation (large variability), whereas γ is affected much less.

Discussion

In this study, we investigated externally controlled joint torques induced by external electrical stimulation of one out of three leg muscles (protractor, retractor, and levator) in the stick insect Carausius morosus. For a given parameter set for PWM burst stimulation, we found a piecewise linear relationship between the burst duration and generated joint torque. Linearity holds for a burst duration up to 500ms. For a more detailed analysis of the joint torques generated by leg muscles, we used Bayesian statistical analysis and modeling to account for inter-individual variation. A comparison of the six models (with combinations of linear, nonlinear, non-hierarchical, and hierarchical models) showed that the two models that include inter-individual variation of slope parameter β performed best. Models 1–2 and 2–2 provide the most accurate predictions of the posterior predictive distribution.

The exponent γ is a macroscopic property of the generated joint torque, that is the degree of non-linearity of the stimulus-torque characteristic; it is linear when γ=1. Conversely, slope parameter β defines the rate of increase of the generated torque. In a comparison of the prediction performance of models in Figure 3, the mathematical index WAIC revealed that the models 1–2 and 2–2, wherein only β was a hierarchical parameter, performed the best. Since only hierarchical parameters account for inter-individual variation, we conclude that β is strongly affected by individual differences, whereas γ is invariant among specimens. Thus, we found that the macroscopic properties of leg muscles are common to all individuals, whereas individuals differ in the slope β, that is the rate by which the three types of leg muscles respond to electrical stimulation. Furthermore, as shown in Figure 5, we found that β was highly affected by the applied voltage, whereas the exponent γ was close to unity, largely independent of the applied voltage, indicating that the macroscopic properties of leg muscles were invariant to the applied voltage. We conclude that linearity was an invariant feature of the stimulus-torque characteristic, whereas the slope of this characteristic varies among individual stick insects and with the applied voltage. These results are in line with those of existing studies on the properties of myogenic forces in other insect species (Cao et al., 2014; Blümel et al., 2012a; Harischandra et al., 2019): The generated torque depends considerably less on the PWM voltage and frequency (Blümel et al., 2012a; Harischandra et al., 2019) than on the burst duration, suggesting that the total number of subsequent input pulses is important. This is indeed expected for a slow insect muscle (Blümel et al., 2012a) that essentially ‘counts’ incoming spikes within a given time window. Compared to the nonlinear properties of muscle, we demonstrated that our monitoring of torques in an intact animal resulted in a linear characteristic (for intervals up to 500ms) that would not be expected from isometric force measurements of isolated muscles. Furthermore, changing the PWM frequency was found to be comparable to changing the number of spikes over a given period, whereas changing the duty ratio was found to be comparable to varying the average voltage over a given period (see Appendix 1—figures 1 and 2). Therefore, from both technical and cyborg control viewpoints, the control of burst duration provides beneficial insights into feasibility.

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. Models with lower WAIC can generate predictive distributions closer to the true distribution while using fewer parameters (Watanabe, 2018), suggesting that the experimental results obtained in this study can be adequately explained using a linear hierarchical Bayesian model (1-2). This model renders it useful for predicting the generated torque for each new animal in real-time during an experiment. Specifically, by assuming the linear hierarchical Bayesian model, we can measure responses to very few PWM stimulus bursts and estimate β for the current individual’s stimulus-torque characteristic. This allows an experimenter to acquire an appropriate muscle model of an unknown animal in a short time without having to use potentially time-consuming machine learning methods, such as deep learning algorithms. Moreover, the properties were linear for stimulus burst durations up to 500ms. This linearity region corresponds to the stance and swing phase durations of medium-speed to fastwalking stick insects of the species Carausius morosus (Dürr et al., 2018). The magnitudes of the joint torques generated by the protractor, retractor, and levator were comparable to those for resisted movement during stick-insect walking, for example coxa-trochanter joint depression during stance (Dallmann et al., 2016). This suggests that the estimated stimulus-torque characteristic captures the natural dynamic properties of leg muscles during walking in terms of both the duration of excitation and maximum torque. However, the hierarchical nonlinear model (model 2–2) would be more appropriate for estimating properties related to longer time scales, such as those associated with the complete range of muscle excitation. Nevertheless, we emphasize once again that a key contribution of this study lies in demonstrating, based on experimental data, that the muscle property γ across the complete excitation range exhibits inter-individual variations and is independent of linear or nonlinear properties; hence, the weight β^ assigned to these properties represents individual differences.

This study takes a first but important step towards highly precise insect cyborg control. In previous studies, we defined Motion Hacking (Owaki et al., 2019; Owaki and Dürr, 2022) as a technique for controlling insect leg movements through external electrical stimulation, while retaining the insect’s own nervous system and sensorimotor loops. This approach requires a collaborative effort of engineering and biology in order to elucidate how adaptive walking ability of insects may be exploited for biohybrid control of motor flexibility. The Motion Hacking (Owaki et al., 2019; Owaki and Dürr, 2022) method strives to observe the adaptation process in the insect’s own sensorimotor system as leg movements are intentionally controlled by a human operator, so as to reveal hidden mechanisms underlying natural locomotion. Thus far, research on insect cyborg control has addressed aspects of flight control (Sato, 2009; Sato and Maharbiz, 2010; Sato et al., 2015; Kosaka et al., 2021; Sane et al., 2007; Bozkurt et al., 2009; Hinterwirth et al., 2012), gait control (Cao et al., 2016; Vo Doan et al., 2018; Nguyen et al., 2020; Ando and Kanzaki, 2017; Sanchez et al., 2015), and controlling jellyfish propulsion (Xu and Dabiri, 2020a; Xu et al., 2020b; Xu et al., 2020c). In contrast to our present study, the main objective of the mentioned studies was to convert target animals into cyborgs, with little examination of the control mechanisms and/or muscle properties involved. Here, we used PWM pulse bursts to mimic motor neuron commands during insect locomotion, and selected key muscles to estimate stimulus-torque characteristics reliably and in very short time. Then, we used Bayesian statistical modeling to tell which parameters were subject to inter-individual variation and which were not. Our finding of linear characteristics with inter-individual variation of slope show compellingly how a systematic engineering intervention to an otherwise intact animal motor system can yield a simple, technically exploitable description of motor system properties. We argue that this description could not have been obtained by methods addressing isolated neural circuits or partial anatomical structures, but required the physical intactness of the natural system.

The contributions of this research are as follows: (1) this study demonstrates that compared to the nonlinear activation and contraction dynamics of insect muscles, the joint torque generated through electrical stimulation increases linearly with the duration of the stimulus, particularly during the stance and swing phases that characterize stick insect locomotion; (2) it introduces a hierarchical Bayesian model that allows for a reliable and simple description of the individual differences observed in neuromuscular system parameters. These contributions not only advance the field of insect cyborg control but also enhance our understanding of insect locomotion mechanisms. Animal locomotion is not solely governed by the brain and nervous system but also relies on the physical properties of the body and its interactions with the environment (Chiel et al., 2009; Nishikawa et al., 2007). Arthropods, in particular, effectively utilize mechanical properties and environmental interactions in their locomotion. Studies have revealed various related strategies, including the joint stiffness nonlinearity and hysteresis in spiders (Blickhan, 1986), generation of large motor outputs during escape maneuvers (Card, 2012) and posture stabilization (Blickhan, 1986) by adjusting the joint stiffness, mechanical sensing based on frequency characteristics that vary with the joint stiffness and posture in web-making spiders (Blickhan and Barth, 1985; Mhatre et al., 2018), transitions in movement patterns in response to mechanical interactions with the environment (Othayoth et al., 2020), and transitions in the coordinated movements of the body and legs (Wang et al., 2022) in cockroaches. Similarly, to elucidate the animal locomotion mechanisms emerging from such complex interactions, Sponberg et al., 2011a; Sponberg et al., 2011b conducted experiments similar to those in our study by perturbing neural feedback through artificial interventions on muscle action potentials (MAPs) in cockroaches Blaberus discoidalis (L.). In follow-up studies, we further estimated the passive joint stiffness and analyzed the phase responses of stick insects during walking by accurately controlling the joint torque based on the linear stimulus duration-joint torque model derived in this study. We believe that these approaches will contribute to a deeper understanding of stick insect walking mechanisms, such as their use of two different stride lengths in response to their environment (Theunissen and Dürr, 2013).

Still, there are several limitations to the present study. First, as in many neurophysiological experiments (Berg et al., 2012; Lepreux et al., 2019), stick insects were fixed and not walking in the experimental setup (Figure 1A). Although there are only few studies on the natural dispersal behavior of stick insects, it is clear that they spend a lot of their lifetime at rest, for example in camouflage. Their tendency to attain camouflage postures can be exploited in experiments, as it is relatively easy to restrain active, spontaneous leg movements in an experimental setup. Nevertheless, the possibility to conduct combined motion capture and EMG recordings in freely walking stick insects (Dallmann et al., 2019; Günzel et al., 2022; Dallmann et al., 2017; Bidaye et al., 2018) suggests that Motion Hacking during unrestrained, voluntary locomotion will be feasible in the future. Whereas the range of PWM burst duration and the joint torques generated are well within the physiological range, there is still considerable discrepancy between the PWM signals generated by our Raspberry Pi microcontroller and the natural firing patterns of motor neuron pools (Günzel et al., 2022). Future research will need to examine how much the simplification of the driving burst input affects the time course of the torque generated. So far, it is re-assuring that the simplified PWM signal used here could be applied more than 50 times in a sequence without causing muscle fatigue, that is with a sustained level of generated torque.

Finally, so far we have not fully investigated the effects of the electrical muscle stimulation on sensory feedback. The maximum voltage of 4 V used here did not cause abnormal motion that could be attributed to cross-talk stimulation of sensory afferents. Therefore, we conclude that unintended electrical stimulation of sensory afferents was negligible. Moreover, control measurements confirmed that muscles other than those stimulated by the electrodes were not active and did not generate force, as it would be expected from unintended stimulation via cross-talk. More generally, the activation of sensory organs during cyborg control is an interesting topic, with strong potential for expanding the concept of Motion Hacking. In the future, we will examine the performance of external leg movement control in an experimental setup, both without load (i.e. on a tether, without substrate contact) and with natural load distribution (i.e. by intervention during free walking). We are confident that these experiments, will provide further support of the Motion Hacking method and will reveal findings that could not be obtained by more conventional experiments without external stimulation of the neuro-muscular system. This will also contribute to potential applications in highly precise insect cyborg control.

Materials and methods

Animals

We tested 20 adult female Carausius morosus from our laboratory colony at Bielefeld University in 2018. The animals were raised under a 12 hr:12 hr light:dark cycle at a temperature of 23.9 ±1.3 °C (mean ± S.D). All experiments were conducted at room temperature (20–24 °C). Table 1 lists the stick insects used in the electrical stimulation experiments. Owing to a combination of experimental failures and time constraints, we could not obtain stimulation data for all three muscles from the same animal on a single day. Therefore, we collected data from 10 animals (N=10) for each muscle through experiments with 20 animals. Joint torques were measured with custom-built force sensors with strain gauges. Prior to the experiments, the measured force [mN] was calibrated from the force-sensor value [V] with weights of known mass (0.2–5 g). Two small insect pins attached to the tip of the force transducer held the middle part of the femur of the middle leg (Figure 1A right). The length between the ThC or CTr joints and the attachment point at the femur was measured and used as the moment arm for the calculation of torque.

Electrical stimulation

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We developed a custom-built electrical stimulator for stimulating muscles (Figure 1A left). An extension circuit board was designed for Raspberry Pi 3 B+ (Raspberry Pi Foundation), including isolated 8-channel PWM signal outputs. The parameters of the PWM signals, for example, frequency (1–120 Hz) and duty ratio (0 to 100%), were changed using a Raspberry Pi microprocessor. The amplitude of the output voltage (0–9 V) was changed using variable resistors on the circuit board, which enabled the investigation of the effects of these parameters on torque generation due to muscle stimulation. In this study, we systematically analyzed the joint torques generated by muscle contraction as induced by bursts of PWM pulses. To do so, we varied the amplitude [V], frequency [Hz] and duty ratio [%] of the PWM-signal, and identified the combinations that most effectively and repeatedly produced torque.

For one trial of the stimulation experiments, the frequency, duty ratio, and amplitude (voltage) of the PWM signals were not changed, but the burst duration Ti of the signals was changed (Figure 1C top). Owing to the slow activation dynamics of an insect muscle, burst duration is one of two key parameters for controlling isometric muscle-contraction force because the muscle essentially acts as a second-order low-pass filter (Harischandra et al., 2019). The pulse frequency is the other key parameter, which can be held constant because burst duration alone is sufficient to effectively control joint torques in the range of 0–1.0 [s].

Electrode implementation

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A pair of stimulation electrodes was implanted into each muscle through two small holes in the cuticle. Holes were pierced using an insect pin, and wires were fixed with dental glue (Figure 1B). The stimulation electrodes were thin silver wires (A-M Systems, diameter = 127 µm, without insulation; 178 µm with Teflon insulation). The insulation at the end of the silver wire was removed, and the wires were implanted. The other end of the stimulation electrode was connected to the output of the electrical stimulator. The correctness of the electrode implantation was verified through triggered resistance reflexes, which are responses to imposed movements of the ThC and CTr joints for the corresponding muscles.

Data collection

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We determined the parameter set with a frequency of 50 Hz and a duty ratio of 30%, which would allow continuous and effective torque generation in a pre-experiment. We performed electrical stimulation experiments in the following order: (i) first, we selected one of the three muscles (protractor, retractor, levator) to be stimulated in each stick insect and (ii) performed electrical stimulation of the selected muscle more than 50 times at 1 V (50 Hz, 30%). The duration of the electrical stimulation, Ti, was set manually and randomly; this was followed by a (iii) 3-min-resting-period to reduce the effect of muscle fatigue (the resting period was determined in the pre-experiment). (iv) We then performed electrical stimulations at 2 V, 3 V, and 4 V for more than 50 times each; note that each stimulation was preceded by a 3-min-resting-period. (v) A voltage from 1 to 4 V that effectively generated the torque for the corresponding muscle was selected. (vi) Following this selection, we conducted electrical stimulation experiments for each combination of frequency (30 Hz, 50 Hz, 70 Hz, 90 Hz, and 110 Hz) and duty ratio (10%, 30%, 50%) for more than 50 times, with a resting time of 3 min between each condition. (vii) The next muscles were selected depending on the condition of the stick insect and within the time constraints, and we repeated steps (ii)–(vi) and recorded the data. (viii) The individuals were changed (on another day), and steps (i)–(vii) were repeated. We collected 10 individuals (N=10 in Table 1) for each muscle using this procedure. Notably, even after such a large number of electrical stimulations of the muscles, we did not observe any significant biological damage to the stick insect nor any fatigue or warm-up effects.

Data analysis

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To investigate the dependence of externally induced joint torques by electrostimulating one out of the three leg muscles, we measured the force generated at the attachment point and multiplied it with the known moment arm as follows: (1) For different burst duration Ti we estimated peak-to-peak sensor values Sp2p(i) [V] (Figure 1C left). (2) Applying the conversion factor obtained from the previous calibration, we obtained peak-to-peak force change [mN] in response to stimulation. (3) The force was then multiplied with the measured moment arm [mm] to obtain the joint torque τi [µNm] (Figure 1C right).

Widely applied information criterion (WAIC)

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We compared the predictive performances of the formulated models using the mathematical index WAIC (Watanabe, 2018Watanabe, 2005; Watanabe, 2010a; Watanabe, 2010b). The WAIC is a measure of the degree to which an estimate of the predictive distribution is accurate relative to the true distribution (Watanabe, 2018). Essentially, it is based on the difference between the information conveyed by the mean and that conveyed by the variance. This difference is negative if the term corresponding to the mean exceeds that corresponding to the variance. The smaller (or more negative) the WAIC index, the higher the predictive value of the model variant.

When calculating the WAIC index for a hierarchical model, several calculation methods can be used, depending on the definition of the predictive distribution, that is, the type of unknown data distribution being predicted (Watanabe, 2018). We were interested in predicting muscle properties with electrostimulation for a new, additional animal, not including experimental date, to enable individualized leg ‘control’. From this perspective, we constructed a new distribution of the predictive parameters of a new animal by marginalizing intermediate parameters assigned to each hierarchical model (models 1–2, 2–2, 2–3, 2–4; Watanabe, 2018; Wakita et al., 2020; Harada et al., 2020). This allows for a fair comparison of the prediction performance of hierarchical and non-hierarchical models. Referring to the method from the previous studies (Wakita et al., 2020; Harada et al., 2020), the WAIC was computed by numerical integration with MCMC (Markov Chain Monte Carlo) samples by using Simpson’s law and the ‘log_sum_exp’ function provided by Stan (Stan Development Team, 2023).

From the models described above, the model with the smallest WAIC value was considered the most appropriate predictive model in terms of predictivity for a new animal.

Appendix 1

Effect of frequency and duty ratio of PWM

Appendix 1 figure (Appendix 1—figure 1) 1 presents the variation of parameters and of the muscle characteristics with the PWM frequency for the six Bayesian models. The results indicate the following: (1) increases with frequency, but there exists an optimal frequency for each muscle; (2) is independent of the frequency; and (3) is affected by individual differences, whereas exhibits cross-individual consistency. In this study, we employed a frequency of 50 Hz, which had minimal effect on the individual differences in .

Furthermore, Appendix 1—figure 2 presents the variation in the parameters and for the six Bayesian models as a function of the PWM duty ratio. The results reveal the following: (1) linearly increases with the duty ratio; (2) is independent of the duty ratio; and (3) is affected by individual differences, whereas is consistent across individuals. We employed an intermediate duty ratio of 30%, which yielded consistent data.

Appendix 1—figure 1
Dependence of muscle property parameters on the applied frequency of the PWM signals (2.0 V and 30% duty ratio) for the six models.

The left graphs (A), (B), and (C) present the value of β estimated for an applied frequency ranging from 50 to 110 Hz for the six models. (A) and (D), (B) and (E), and (C) and (F) illustrate the protractor, retractor, and levator stimulations, respectively. In (A) to (C), the upper and lower panels refer to the non-hierarchical (1-1, 2-1, 2-3) and hierarchical (1-2, 2-2, 2-4) models for,β respectively. The right graphs (D), (E), and (F) present the value of γ estimated for the applied voltage changes. In (D) to (F), the left panel refers to the linear models (γ=1, 1–1, 1–2), and the middle and right panels refer to the non-hierarchical models (2-1, 2-2) and hierarchical (2-3, 2-4) models for,γ respectively. Source code and data are available on Dryad (Figure6-7.zip, https://doi.org/10.5061/dryad.wpzgmsbsw).

Appendix 1—figure 2
Dependence of muscle property parameters on the applied duty ratio of the PWM signals (2.0 V and 50 Hz) in the six models.

The left graphs (A), (B), and (C) present the estimation for β with the applied duty ratio varied from 10 to 30% for the six models. (A) and (D), (B) and (E), and (C) and (F) illustrate the protractor, retractor, and levator stimulations, respectively. In (A) to (C), the upper and lower panels present the non-hierarchical (1-1, 2-1, 2-3) and hierarchical (1-2, 2-2, 2-4) models for β, respectively. The right graphs (D), (E), and (F) present the estimation for γ under the applied voltage changes. In (D) to (F), the left panel shows linear models (γ=1, 1–1, 1–2), and the middle and right panels illustrate the non-hierarchical (2-1, 2-2) and hierarchical (2-3, 2-4) models for γ, respectively. Source code and data are available on Dryad (Figure6-7.zip, https://doi.org/10.5061/dryad.wpzgmsbsw).

Relationship between generated joint torque and body morphology

We also examined the relationship between the joint torque generated by electrical muscle stimulation and body morphology, though in a separate sample of N=9 individuals (Appendix 1—figure 3) that was different from the sample used for Figures 25, Appendix 1—figures 1 and 2. This is because experiments for Figures 25, Appendix 1—figures 1 and 2 did not log size data, and experiments with suitable data on animal did not cover all three leg muscles (retractor, retractor, and levator). We considered the femur segment length (i.e., the length between the ThC and FTi joints) of the stimulated middle leg and the body length (i.e., the length from head to tail) as body morphology features. Both lengths were measured from top-view videos of stick insects. As the characteristic parameters of joint torque, we considered the maximum joint torque Tmax [µNm] during electrical stimulation of the protractor and retractor muscles, and the average value of β [µNm/s] in the linear models (model 1–2) for each individual. Note that there were no differences in joint torque characteristics between the figures (Figures 25, Appendix 1—figures 1 and 2) and Appendix 1—figure 3.

Appendix 1—figure 3A shows the correlation coefficients (color: purple = 1 to orange = –1) and p-values (numbers in the panel) between femur length, body length, Tmax, and average β for the protractor and retractor muscles. Statistically significant correlations (p<0.05) were found only between either length measured (Appendix 1—figure 3B, r=0.669,p=0.0487) and Tmax and β for the protractor (r=0.869,p=0.00233) and retractor (r=0.866,p=0.00251), respectively. Between femur length and joint torque features, we found a negative correlation for protractor Tmax and β (upper left of Appendix 1—figure 3C), and a positive correlation for retractor Tmax and β (upper right of App.Figure 3C). We likewise observed weak positive correlations between the body length and torque features for both the protractor (bottom left of App.Figure 3C) and retractor (bottom right of App.Appendix 1—figure 3C). Thus, no consistent pattern of correlation was found between individual differences in generated joint torque and bodily characteristics in this experimental data (N=9 in App.Figure 3). Nonetheless, because weak correlations were observed, bodily characteristics may be considered as the input of a more precise prediction model that accounts for individual differences.

Appendix 1—figure 3
Relationship between generated joint torque and body morphology.

(A) Correlation coefficients (color: purple = 1 to orange=-1) and p-values (numbers in the panel) between middle femur length, body length, Tmax, and the averaged β for protractor and retractor muscles. (B) Linear regression between middle femur length and body length. The purple line represents the linear regression line. (C) Linear regression between middle femur length (upper)/body length (lower) and Tmax and β for protractor (left) and retractor (right) muscles, respectively. For (B) and (C), color differences in plot points indicate individual differences (N=9), and the gray area represents the 95% confidence interval. The correlation coefficient r and p-value are indicated in each panel. These data are for future follow-up studies and cannot be disclosed.

Data availability

We have now made our data and code (Figures 2–5, Appendix 1—Figures 1 and 2) accessible to the following link, ensuring that they are available for scrutiny and that our approach can be replicated by others. https://doi.org/10.5061/dryad.wpzgmsbsw.

The following data sets were generated
    1. Owaki D
    (2023) Dryad Digital Repository
    Data from: A hierarchical model for external electrical control of an insect, accounting for inter-individual variation of muscle force properties.
    https://doi.org/10.5061/dryad.wpzgmsbsw

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    3. Schmitz J
    (2019) Motion hacking -toward control of insect walking
    Proc. of 9th International Symposium on Adaptive Motion of Animals and Machines (AMAM 2019.
    https://doi.org/10.5075/epfl-BIOROB-AMAM2019-33
  2. Software
    1. R Development Core Team
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    The Journal of Machine Learning Research 11:3571–3594.

Decision letter

  1. Gordon J Berman
    Reviewing Editor; Emory University, United States
  2. Anna Akhmanova
    Senior Editor; Utrecht University, Netherlands
  3. Nick Gravish
    Reviewer; University of California, San Diego, United States

Our editorial process produces two outputs: (i) public reviews designed to be posted alongside the preprint for the benefit of readers; (ii) feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.

Decision letter after peer review:

Thank you for submitting your article "A hierarchical model for external electrical control of an insect, accounting for inter-individual variation of muscle force properties" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Anna Akhmanova as the Senior Editor. The following individual involved in the review of your submission has agreed to reveal their identity: Nick Gravish (Reviewer #2).

The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.

Essential revisions:

1) 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 modeling and experiment is the 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 in order to provide clarity.

2) The referees were concerned that it was not clear from the presentation of the results how substantial the contributions in this paper are to the field as a whole. The authors should better articulate the importance of their contributions, or, missing that, they should better explain what the challenges have been and what would need to be done to overcome them.

3) Along these lines, authors are missing an opportunity to make their work more impactful, by limiting the motivation and discussion to the domain of cyborgs, which is in itself important but quite a small field of research. There are many important animal locomotions, and even mechanical sensing, problems where this understanding is extremely relevant and useful. For example, stiffening the legs can help animals generate larger forces during locomotion in rough terrain, in behaviors that can benefit from higher forces (e.g., escape from predators, fighting between males during courtship), even in mechanical sensing (e.g., web-making spiders may modulate leg stiffness as part of its strategies to modulate how prey vibration is sensed by vibration sensors in its legs). A few studies that may help the authors appreciate and think about the broad implications:

a. Sponberg et al. (2011), A single muscle's multifunctional control potential of body dynamics for postural control and running, Phil. Trans. Royal Soc. B. 366(1570): 1592-1605.

b. Blickhan (1986), Stiffness of an arthropod leg joint, J. Biomechanics, 19(5), 375-384.

c. Wang et al. (2022), Cockroaches adjust body and appendages to traverse cluttered large obstacles, J. Exp. Biol., 225(10), jeb243605.

d. Mhatre et al. (2018), Posture controls mechanical tuning in the black widow spider mechanosensory system, bioRxiv, 484238.

Please comment on the relationship of the results in this study to the above line of research.

4) While it is interesting that inter-individual differences are important in the torque output from the joint, are these inter-individual differences related to any distinct differences among the insects studied (e.g., body mass, limb length, cross-sectional muscle area, and age all would likely influence torque)? While the referees are not advocating that all of the above parameters (age, size, etc) be added into a more complex model, they think it is important to provide any known information about the variance in individual size/age/etc, perhaps as a supplementary table.

5) Line 145 states that "Models 1-2 and 2-1 most accurately predicted the posterior predictive distribution.", is this a typo? The referees were under the impression that Models 1-2 and 2-2 are the best, as they are 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 the question is: might there be reasons from muscle physiology on stick insects to expect a non-linear model? While the linear model had the marginally lowest WAIC 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 the referees got the impression the goal was to best model the torque-voltage relationship, which would include the full excitation range and incorporates known information from muscle physiology. Please comment on these concerns and edit the manuscript as needed.

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

7) 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.

8) 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 is between 49-79 stimulations. So, were another ~50 stimulations performed at the three other voltages? And if so, was fatigue a possible issue?

9) Also, were there "warm-up" effects too where the muscle force increased with subsequent stimulations? It would be important to provide some characterization of this.

10) 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.

11) 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.

12) The authors also seem to be only addressing certain parameters rather than the potential adjustable parameters. PWM, voltage, and frequency are adjustable, but the paper only varied voltage and burst duration. It is unclear whether factors such as frequency (which has been shown to affect muscle force values) were investigated or not. If they were investigated in preliminary experiments, it would help if they were described; if not, it would also help to explain why, to help the readers understand why only burst duration and voltage were varied.

13) The data and code were not yet made available. The referees request access to both the data set and the code, as both are necessary to assess the reproducibility of this study.

14) Given the potential ethical considerations of 'cyborg control of insects,' the authors should discuss the potential ethical implications of extensions of their work with respect to animal welfare and other societal implications.

Reviewer #1 (Recommendations for the authors):

Overall, I think this is an interesting and useful study and that it will nicely move the field forward. The primary suggestion I have is a slight reorganisation as noted in the Public Review: while I understand that journal section structure puts some limitations on this (and while I agree that overly technical information should be placed so as not to disrupt the flow of the narrative), introducing some basic features of the experiments and models upfront (perhaps in a Table form) would be very helpful in understanding what the results mean. I also recommend moving Figure 5 before the results Figures.

The data and code were not yet made available (as far as I can tell), which is a bit disappointing. From the text, I understand they will be made available upon publication; but it is difficult to assess the reproducibility of this study without access to these as a referee.

Reviewer #3 (Recommendations for the authors):

1. The work itself seems not very substantial. It seems that the authors did relatively simple experiments, and just tried many different simple models to fit the data. It is not clear whether there is a substantial contribution. The authors should think harder about this and better articulate the contribution to the field with such a relatively simple study (as it appears). Or explain better what the challenges have been to better show why this initial first step is not as straightforward as it appears to be.

2. I think the author is missing an opportunity to make their work more impactful, by limiting the motivation and discussion to the domain of cyborgs, which is in itself important but quite a small field of research. There are many important animal locomotions and even mechanical sensing problems where this understanding is extremely relevant and useful. For example, stiffening the legs can help animals generate larger forces during locomotion in rough terrain, in behaviors that can benefit from higher forces (e.g., escape from predators, fighting between males during courtship), even in mechanical sensing (e.g., web-making spiders may modulate leg stiffness as part of its strategies to modulate how prey vibration is sensed by vibration sensors in its legs). A few studies that may help the authors appreciate and think about the broad implications:

a. Sponberg et al. (2011), A single muscle's multifunctional control potential of body dynamics for postural control and running, Phil. Trans. Royal Soc. B. 366(1570): 1592-1605.

b. Blickhan (1986), Stiffness of an arthropod leg joint, J. Biomechanics, 19(5), 375-384.

c. Wang et al. (2022), Cockroaches adjust body and appendages to traverse cluttered large obstacles, J. Exp. Biol., 225(10), jeb243605.

d. Mhatre et al. (2018), Posture controls mechanical tuning in the black widow spider mechanosensory system, bioRxiv, 484238.

3. The authors seem to be only addressing certain parameters rather than the potential adjustable parameters. PWM, voltage, and frequency are adjustable, but the paper only varied voltage and burst duration. It is unclear whether factors such as frequency (which has been shown to affect muscle force values) were investigated or not. If they were investigated in preliminary experiments, it would help if they were described; if not, it would also help to explain why, to help the readers understand why only burst duration and voltage were varied.

4. It is difficult to understand the Results and Discussion without reading the Method and Materials first. I know that eLife has Methods later, but the meaning of certain acronyms was not at least briefly explained until later in the paper, making it hard to understand when one reads it.

5. What are the resulting modelling equations generated for each? Is it possible to output the resulting modeling equations created from the Makrov Chain Monte Carlo method? It is difficult to see how they compare and are different from the simple linear and power equations that are used for 1-1 and 2-1.

a. What is the power function constant used for 2-1? It seems to be that \γ is 1, but doesn't that make it a linear function?

6. It is unclear how the author settled at the default parameters of the PWM signals to 2 V, 50 Hz, and 30% duty ratio.

7. For Figure 3, why is the prediction only compared with models 1-2? From what I gather, models 1-2 and 2-2 were the most accurate in predicting the posterior predictive distribution, why is specifically 1-2 addressed?

8. The intro addresses how inter-species variability can cause issues with the precise control of different animals. Is this issue addressed in this paper? It is not clear to me how this modelling can account for individual species variability considering the models only include variables for the burst duration and joint torque. Is the assumption that generating an appropriate model can lead to creating a robust feedback control system to control for interspecies variability?

9. The pictures of the experimental setup are confusing, it would be helpful if there was a schematic of the setup and some labels were given on where the muscles that were tested are located.

10. Not sure what the difference between hierarchical models and non-hierarchical models is, and where it is addressed.

11. Overall there are too many plots to understand, reducing the number of plots and increasing the font size on the plots will help increase the clarity and understanding of each figure.

Specific Comments:

1. Can you explain why there is a different number of simulations (n) for each animal? (Referring to Figure 3)

2. Unknown o? on line 349, not sure if hierarchical model o is a thing.

3. The labels for each of the y values and x values are very hard to see and are very blurry, it is hard to get a good sense of what these numbers mean for Figure 4, or what the y-axis and x-axis mean. Increasing the number font would be helpful for reading any of these graphs.

https://doi.org/10.7554/eLife.85275.sa1

Author response

Essential revisions:

1) 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 modeling and experiment is the 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 in order to provide clarity.

Thank you for your valuable comment and suggestion. As correctly pointed out, Bayesian statistical modeling, the parameters of the models, and the experimental setup used to obtain the data are central to the results of this study. In light of this, we have restructured the manuscript by moving the "Experimental setup” (this is combined with “Burst duration and generated joint torque” and changed to "Joint torque measurements”), "Bayesian statistical modeling,” and "Model" subsections from the “Methods and Materials” section to the “Results” section. Additionally, we have adjusted the order of figures to align with this revised structure. We believe that these changes will significantly facilitate readers’ understanding of the study. The differences between the structure of the original version and that of the revised manuscript are summarized below:

[original paper]

Results

Burst duration and generated joint torque (Figure 1)

Comparison of model predictability (Figure 2)

Bayesian estimation of generated torque for a given burst duration (Figure 3)

Effect of an individual animal and applied voltage on muscle properties (Figure 4)

Methods and Materials

Animals

Experimental setup (Figure 5)

Electrical stimulation

Electrode implementation

Data analysis

Bayesian statistical modeling

Models

Widely Applied Information Criterion (WAIC)

[revised paper]

Results

Joint torque measurements (Figures 1 and 2)

Bayesian statistical modeling

Models

Comparison of model predictability (Figure 3)

Bayesian estimation of the generated torque for a given burst duration (Figure 4)

Effect of an individual animal and applied voltage on muscle properties (Figure 5)

Methods and Materials

Animals

Electrical stimulation

Electrode implementation

Data collection (new)

Data analysis

Widely applied information criterion (WAIC)

This comment significantly contributes to the reader's understanding of the paper. We greatly appreciate your kind suggestion.

2) The referees were concerned that it was not clear from the presentation of the results how substantial the contributions in this paper are to the field as a whole. The authors should better articulate the importance of their contributions, or, missing that, they should better explain what the challenges have been and what would need to be done to overcome them.

Thank you for your valuable feedback. As discussed in the second paragraph of the “Introduction” section in the first version of the manuscript, the inter-individual variability of animals is a central challenge that must be overcome, not only for cyborg control but also to understand animal locomotion. To emphasize the significance of our contribution more clearly, we have included the following sentences in the last paragraph of the “Introduction” section.

Introduction, last paragraph, L96-L104

“With regard to our general understanding of insect motor control, our study demonstrates that the dependency of joint torque on electrical stimulus duration is linear, despite nonlinear activation and contraction dynamics of insect muscle. Furthermore, the proposed hierarchical Bayesian model allows for a quick, simple and reliable measurement of the individual characteristics and, therefore, quantification of inter-individual differences. Whereas several studies have reported on inter-individual differences in neural (Golowasch et al., 2002; Schulz et al., 2006;) and muscle activity (Horn et al., 2004; Brezina et al., 2005; Zhurov et al., 2005; Blümel et al., 2012c,a; Thuma et al., 2003; Hooper et al., 2006), we propose how hierarchical Bayesian models may be used to harness inter-individual differences in insect locomotion research.”

3) Along these lines, authors are missing an opportunity to make their work more impactful, by limiting the motivation and discussion to the domain of cyborgs, which is in itself important but quite a small field of research. There are many important animal locomotions, and even mechanical sensing, problems where this understanding is extremely relevant and useful. For example, stiffening the legs can help animals generate larger forces during locomotion in rough terrain, in behaviors that can benefit from higher forces (e.g., escape from predators, fighting between males during courtship), even in mechanical sensing (e.g., web-making spiders may modulate leg stiffness as part of its strategies to modulate how prey vibration is sensed by vibration sensors in its legs). A few studies that may help the authors appreciate and think about the broad implications:

a. Sponberg et al. (2011), A single muscle's multifunctional control potential of body dynamics for postural control and running, Phil. Trans. Royal Soc. B. 366(1570): 1592-1605.

b. Blickhan (1986), Stiffness of an arthropod leg joint, J. Biomechanics, 19(5), 375-384.

c. Wang et al. (2022), Cockroaches adjust body and appendages to traverse cluttered large obstacles, J. Exp. Biol., 225(10), jeb243605.

d. Mhatre et al. (2018), Posture controls mechanical tuning in the black widow spider mechanosensory system, bioRxiv, 484238.

Please comment on the relationship of the results in this study to the above line of research.

Thank you for your valuable comments. To highlight the importance and practical implications of our approach and findings, we have incorporated the following paragraph into the “Discussion” section, which introduces relevant studies related to animal locomotion, particularly in arthropods, and discusses their relevance to our study.

Discussion, sixth paragraph (new), L307-L332

“The contributions of this research are as follows: (1) this study demonstrates that compared to the nonlinear activation and contraction dynamics of insect muscles, the joint torque generated through electrical stimulation increases linearly with the duration of the stimulus, particularly during the stance and swing phases that characterize stick insect locomotion; (2) it introduces a hierarchical Bayesian model that allows for a reliable and simple description of the individual differences observed in neuromuscular system parameters. These contributions not only advance the field of insect cyborg control but also enhance our understanding of insect locomotion mechanisms. Animal locomotion is not solely governed by the brain and nervous system but also relies on the physical properties of the body and its interactions with the environment (Chiel et al., 2009; Nishikawa et al., 2007). Arthropods, in particular, effectively utilize mechanical properties and environmental interactions in their locomotion. Studies have revealed various related strategies, including the joint stiffness nonlinearity and hysteresis in spiders (Blickhan, 1986), generation of large motor outputs during escape maneuvers (Card, 2012) and posture stabilization (Blickhan, 1986) by adjusting the joint stiffness, mechanical sensing based on frequency characteristics that vary with the joint stiffness and posture in web-making spiders (Blickhan and Barth, 2004; Mhatre et al., 2018), transitions in movement patterns in response to mechanical interactions with the environment (Othayoth et al., 2020), and transitions in the coordinated movements of the body and legs (Wang et al., 2022) in cockroaches. Similarly, to elucidate the animal locomotion mechanisms emerging from such complex interactions, Sponberg et al. (Sponberg et al., 2011b,a) conducted experiments similar to those in our study by perturbing neural feedback through artificial interventions on muscle action potentials (MAPs) in cockroaches (Blaberus discoidalis (L.)). In follow-up studies, we further estimated the passive joint stiffness and analyzed the phase responses of stick insects during walking by accurately controlling the joint torque based on the linear stimulus duration-joint torque model derived in this study. We believe that these approaches will contribute to a deeper understanding of stick insect walking mechanisms, such as their use of two different stride lengths in response to their environment (Theunissen and Dürr, 2013).”

4) While it is interesting that inter-individual differences are important in the torque output from the joint, are these inter-individual differences related to any distinct differences among the insects studied (e.g., body mass, limb length, cross-sectional muscle area, and age all would likely influence torque)? While the referees are not advocating that all of the above parameters (age, size, etc) be added into a more complex model, they think it is important to provide any known information about the variance in individual size/age/etc, perhaps as a supplementary table.

We sincerely appreciate the valuable comments. The questions, where the observed inter-individual differences come from or what they are related to is an interesting question – though not at the heart of our study. To address your point, we examined the relationship between the joint torque generated by electrical muscle stimulation and body morphology as a supplementary topic. The data were collected from a different sample than that presented in the paper (N = 9 in a follow-up study in 2019), simply because the video material for the 2018 sample used for Figures 2–5, Appendix 1 figures 1 and 2 were not suitable for measuring body size (unfortunately, we did not log body size in the lab book). In the 2019 sample we did not measure characteristics for all three muscles per animal, but the joint torque features of each muscle type were identical to those obtained in 2018. Owing to the fact that the data come from separate sets of experiments, we would like to emphasize this by making the additional figure (Appendix 1 figure 3), rather than a genuine part of the main paper (Figure 2-5, Appendix 1 figure 1 and 2). The results in Appendix 1 figure 3 show no consistent and little significant correlation between individual differences in generated joint torque and body size. However, because weak correlations were present, we now state that bodily characteristics may potentially be used as model input for further improvement of the prediction models. Further research is required to facilitate a more detailed analysis so as to reveal the factors contributing to the observed individual differences in torque generation.

In our revision, we have added the following section. We have also added Appendix 1 figure 3 to “Appendix 1” as supplementary material.

Appendix 1, Relationship between generated joint torque and body morphology, L695-L722

“We also examined the relationship between the joint torque generated by electrical muscle stimulation and body morphology, though in a separate sample of N = 9 individuals (App. Figure 3) that was different from the sample used for Figures 2–5, App.Figures1 and 2. This is because experiments for Figures2–5, App.Figures1 and 2 did not log size data, and experiments with suitable data on animal did not cover all three leg muscles (retractor, retractor, and levator). We considered the femur segment length (i.e., the length between the ThC and FTi joints) of the stimulated middle leg and the body length (i.e., the length from head to tail) as body morphology features. Both lengths were measured from top-view videos of stick insects. As the characteristic parameters of joint torque, we considered the maximum joint torque Tmax [Nmm] during electrical stimulation of the protractor and retractor muscles, and the average value of β [Nmm/s] in the linear models (model 1-2) for each individual. Note that there were no differences in joint torque characteristics between the figures (Figures 2–5, App.Figures1 and 2) and App. Figure 3.

App. Figure 3 A shows the correlation coefficients (color: purple = 1 to orange = -1) and p-values (numbers in the panel) between femur length, body length, Tmax, and average β for the protractor and retractor muscles. Statistically significant correlations (p < 0.05) were found only between either length measured (App. Figure 3 B, r = 0.669, p = 0.0487) and Tmax and β for the protractor (r = 0.869, p = 0.00233) and retractor (r = 0.866, p = 0.00251), respectively. Between femur length and joint torque features, we found a negative correlation for protractor Tmax and β (upper left of App. Figure 3 C), and a positive correlation for retractor Tmax and β (upper right of App. Figure 3 C). We likewise observed weak positive correlations between the body length and torque features for both the protractor (bottom left of App. Figure 3 C) and retractor (bottom right of App. Figure 3 C). Thus, no consistent pattern of correlation was found between individual differences in generated joint torque and bodily characteristics in this experimental data (N = 9 in App. Figure 3). Nonetheless, because weak correlations were observed, bodily characteristics may be considered as the input of a more precise prediction model that accounts for individual differences.”

5) Line 145 states that "Models 1-2 and 2-1 most accurately predicted the posterior predictive distribution.", is this a typo? The referees were under the impression that Models 1-2 and 2-2 are the best, as they are 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 the question is: might there be reasons from muscle physiology on stick insects to expect a non-linear model? While the linear model had the marginally lowest WAIC 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 the referees got the impression the goal was to best model the torque-voltage relationship, which would include the full excitation range and incorporates known information from muscle physiology. Please comment on these concerns and edit the manuscript as needed.

First, as the reviewer correctly pointed out, the statements in L145 and L151 (in the original manuscript) should refer to model 2-2, rather than model 2-1. We have addressed this error in the revised version of the manuscript.

Discussion, first paragraph, L230

“Models 1-2 and 2-2 provide the most accurate predictions of the posterior predictive distribution.”

Discussion, second paragraph, L236

“models 1-2 and 2-2, wherein only β was a hierarchical parameter, performed the best.”

Second, we would like to thank you for the critical and valid remarks. As correctly pointed out, the accuracy and selection of a model depend on the phenomenon to be explained or the target value/parameter to be estimated. Therefore, to determine the most appropriate model, we should clarify the target of our explanation. In the present study, one goal was to understand leg movement control in stick insects during walking. Considering that the time scale corresponding to the walking behaviors (stance and swing phases: ~500 ms) was the most relevant to our analysis, we concluded that a simple hierarchical linear model (model 1-2) was appropriate owing to its simplicity and low error, as discussed in the third paragraph of the “Discussion” section in the original paper. By contrast, the hierarchical nonlinear model (model 2-2) is more appropriate for longer time scales, such as the complete excitation range of muscles (~500 ms). Therefore, we have added the following sentences to the “Discussion” section:

Discussion, third paragraph, L276-L282

“[…] This suggests that the estimated stimulus-torque characteristic captures the natural dynamic properties of leg muscles during walking in terms of both the duration of excitation and maximum torque. However, the hierarchical nonlinear model (model 2-2) would be more appropriate for estimating properties related to longer time scales, such as those associated with the complete range of muscle excitation. Nevertheless, we emphasize once again that a key contribution of this study lies in demonstrating, based on experimental data, that the muscle property γ across the complete excitation range exhibits inter-individual variations and is independent of linear or nonlinear properties; hence, the weight β assigned to these properties represents individual differences.”

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

Thank you for bringing this to our attention. We apologize for the confusion. In the previous version of the paper, Figures 2 and 3 (revised Figures 3 and 4) displayed the same distribution for all individuals because they represented the predicted distribution of unknown animal characteristics based on the experimental data. However, we acknowledge your suggestion for depicting the predicted distribution for each individual based on the data. Therefore, in the revised version, we have modified Figure 4 to present the predicted distribution for each individual and revised the explanation in the "Bayesian estimation of generated torque for a given burst duration" section as follows:

Results, Bayesian estimation of the generated torque for a given burst duration, L206-L208

“[…] Figure 4 depicts the distributions predicted by the linear hierarchical model (model 1-2) for each individual by overlapping the experimental data shown in Figure 2.”

7) 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.

Thank you for bringing this to our attention; we have clarified this point by revising the relevant content in the "Animals" subsection, as well as in Table 1, as follows:

Methods and Materials, Animals, L367-L371

“[…] The animals were raised under a 12h:12h light:dark cycle at a temperature of 23.9 ± 1.3 °C (mean ± S.D). All experiments were conducted at room temperature (20–24 °C). Table 1 lists the stick insects used in the electrical stimulation experiments. Owing to a combination of experimental failures and time constraints, we could not obtain stimulation data for all three muscles from the same animal on a single day. Therefore, we collected data from 10 animals (N=10) for each muscle through experiments with 20 animals.”

8) 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 is between 49-79 stimulations. So, were another ~50 stimulations performed at the three other voltages? And if so, was fatigue a possible issue?

Thank you for your thoughtful comments. In the voltage-change experiments, we followed a specific order of voltage application, starting from 1 V and gradually increasing to 4 V, for each individual. This sequence was determined based on a prior experiment, where we applied voltages as high as ~9 V to assess the endurance voltage, confirming that applying voltages of 5 V or lower would be sufficient to tolerate a large number of stimulus experiments, even when conducted for several hours a day. Therefore, we ensured that we could continue experiments at 4 V or lower without causing significant damage to the stick insect muscles, even when several stimuli were applied. Additionally, we verified the absence of fatigue induced by the magnitude of the applied voltage in the 1–4 V range. Table 1 summarizes the number of electrical stimuli administered to each muscle in each individual.

Accordingly, we have included the above explanation in the “Results” section and added relevant data to Table 1.

Results, Effect of an individual animal and applied voltage on muscle properties, L211-L214

“Figure 5 presents the variations in the muscle characteristic parameters β and γ in response to changes in the applied voltage. In the voltage-change experiments, we followed a specific order of voltage application, gradually increasing from 1 V to 4 V, for each individual. Furthermore, we confirmed that applying voltages ranging between 1 and 4 V did not induce fatigue. Table 1 summarizes the number of electrical stimuli administered to each muscle in each individual. We determined the changes in β and γ with respect to the applied voltage by analyzing the experimental results using the six Bayesian models.”

9) Also, were there "warm-up" effects too where the muscle force increased with subsequent stimulations? It would be important to provide some characterization of this.

As presented in the revised Figure 2 (Figure 1 in the original paper), in this study, we did not observe any significant changes in the generation force, including “fatigue” or “warm-up,” during the electrical stimulation of the muscles. This observation was consistent across experiments where the voltage and frequency (see below) were varied under the same conditions, as well as in the before-and-after experiments. As mentioned in our response to comment 8), we defined the experimental conditions after confirming that no significant changes occurred in torque generation over time in our prior experiments. To clarify this matter, we have modified the following sentence in the revised manuscript:

Revised paper, Results, Joint torque measurements, L132-L135

“For a given set of PWM parameters, the generated torque characteristics remained almost constant during all stimulations under the same condition, suggesting that muscle fatigue or warm-up effects were negligible for at least n = 50 stimulations. Furthermore, we verified that no significant changes occurred in muscle characteristics owing to the pre- and post-experimental relationship.”

10) 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.

Thank you for your comments. To provide more detailed information on the experimental procedures for data collection, we have added a subsection "Data collection" to "Methods and Materials,” along with corresponding descriptions.

Methods and Materials, Data collection, L404-L422

"We determined the parameter set with a frequency of 50 Hz and a duty ratio of 30%, which would allow continuous and effective torque generation in a pre-experiment. We performed electrical stimulation experiments in the following order: (i) first, we selected one of the three muscles (protractor, retractor, levator) to be stimulated in each stick insect and (ii) performed electrical stimulation of the selected muscle more than 50 times at 1 V. The duration of the electrical stimulation, Ti, was set manually and randomly; this was followed by a (iii) 3-min-resting-period to reduce the effect of muscle fatigue (the resting period was determined in the pre-experiment). (iv) We then performed electrical stimulations at 2 V, 3 V, and 4V for more than 50 times each; note that each stimulation was preceded by a 3-min-resting-period. (v) A voltage from 1 to 4 V that effectively generated the torque for the corresponding muscle was selected. (vi) Following this selection, we conducted electrical stimulation experiments for each combination of frequency (30 Hz, 70 Hz, 90 Hz, and 110 Hz) and duty ratio (10%, 30%, 50%) for more than 50 times, with a resting time of 3 min between each condition. (vii) The next muscles were selected depending on the condition of the stick insect and within the time constraints, and we repeated steps (ii)–(vi) and recorded the data. (viii) The individuals were changed (on another day), and steps (i)–(vii) were repeated. We collected 10 individuals (N=10 in Tab. 1) for each muscle using this procedure. Notably, even after such a large number of electrical stimulations of the muscles, we did not observe any significant biological damage to the stick insect nor any fatigue or warm-up effects."

11) 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.

These remarks are the same as those in comments 8) and 9), which are already addressed. Please refer to our previous responses.

12) The authors also seem to be only addressing certain parameters rather than the potential adjustable parameters. PWM, voltage, and frequency are adjustable, but the paper only varied voltage and burst duration. It is unclear whether factors such as frequency (which has been shown to affect muscle force values) were investigated or not. If they were investigated in preliminary experiments, it would help if they were described; if not, it would also help to explain why, to help the readers understand why only burst duration and voltage were varied.

Thank you for your constructive comments. We have thoroughly investigated the effects of the frequency and duty ratio in previous experiments, as described in the "Data collection" section. Based on your comment, we have included additional results in Appendix1 figures 1 and 2 of the revised manuscript. From a biological perspective, our findings suggest that the burst duration is a key variable, as discussed in the second paragraph of the “Discussion” section (L162–L166 in the original paper): "the generated torque depends much less on PWM voltage and frequency (Blümel et al., 2012c; Harischandra et al., 2019) than it depends on burst duration, suggesting the total number of subsequent input pules are important. This is indeed what would be expected for a slow insect muscle (Blümel et al., 2012c) that essentially "counts" incoming spikes within a given time window."

Changing the PWM frequency is comparable to varying the number of spikes within a given period, whereas changing the duty ratio is comparable to varying the average voltage during a given period. Therefore, from both the technical and cyborg control perspectives, the regulation of burst duration provides valuable insights into feasibility.

Consequently, we have incorporated the “Effect of frequency and duty ratio of PWM” in the “Appendix 1” section and in Appendix 1 figures 1 and 2, as well as the cyborg control technical perspective in the "Discussion" section of the revised paper.

Appendix 1, Effect of frequency and duty ratio of PWM, L653-L664

“Appendix 1 figure (App. Figure) 1 presents the variation of parameters β and γ of the muscle characteristics with the PWM frequency for the six Bayesian models. The results indicate the following: (1) β increases with frequency, but there exists an optimal frequency for each muscle; (2) γ is independent of the frequency; and (3) β is affected by individual differences, whereas γ exhibits cross-individual consistency. In this study, we employed a frequency of 50 Hz, which had minimal effect on the individual differences in β.

Furthermore, App. Figure 2 presents the variation in the parameters β and γ for the six Bayesian models as a function of the PWM duty ratio. The results reveal the following: (1) β linearly increases with the duty ratio; (2) γ is independent of the duty ratio; and (3) β is affected by individual differences, whereas γ is consistent across individuals. We employed an intermediate duty ratio of 30%, which yielded consistent data.”

Discussion, second paragraph, L254-L258

“[…]: The generated torque depends considerably less on the PWM voltage and frequency (Blümel et al., 2012c; Harischandra et al., 2019) than on the burst duration, suggesting that the total number of subsequent input pulses is important. This is indeed expected for a slow insect muscle (Blümel et al., 2012c) that essentially "counts" incoming spikes within a given time window. Compared to the nonlinear properties of muscle, we demonstrated that our monitoring of torques in an intact animal resulted in a linear characteristic (for intervals up to 500 ms) that would not be expected from isometric force measurements of isolated muscles. Furthermore, changing the PWM frequency was found to be comparable to changing the number of spikes over a given period, whereas changing the duty ratio was found to be comparable to varying the average voltage over a given period (see Appendix 1 figures 1 and 2). Therefore, from both technical and cyborg control viewpoints, the control of burst duration provides beneficial insights into feasibility.”

13) The data and code were not yet made available. The referees request access to both the data set and the code, as both are necessary to assess the reproducibility of this study.

We have now made our data and codes accessible to the following link, ensuring that they are available for scrutiny and that our approach can be replicated by others.

https://datadryad.org/stash/share/WXXJcMLl00KrfyEeZHi7rqfwoKmJd5GSVPQO7aKcQzk

14) Given the potential ethical considerations of 'cyborg control of insects,' the authors should discuss the potential ethical implications of extensions of their work with respect to animal welfare and other societal implications.

Thank you for your comments on this critical issue. We strongly agree with the responsibility and added a new ethics statement in which we discuss the following paper regarding animal experiments, whether on invertebrate animals that do not require specific approval or on vertebrate animals that do.

N. Xu et al., "Ethics of Biohybrid Robotic Jellyfish Modification and Invertebrate Research," preprint.org, doi: 10.20944/preprints202010.0008.v1, 2020.

Ethics statement, L462-L489

“At present, animal care regulations do not need to be considered for insect research at Bielefeld University and Tohoku University. We strongly agree with the responsibility and ethical issues discussed by (Xu et al., 2020a) regarding animal experiments, both for invertebrates that do not require specific approval or for vertebrates that do. We conducted experiments on stick insects (Carausius morosus) following the principles of harm minimization, precaution, and the 4Rs (reduction, replacement, refinement, and reproduction) at the individual level:

(1) Reduction: We set N=10 as the maximum number of insects in each muscle in the experiment, which was considered the minimum number necessary to obtain statistically significant results.

(2) Replacement: Although we previously surveyed various findings on the force characteristics generated in the muscles of stick insects based on nerve and muscle electrical stimulation (Blüme et al., 2012c,a,b; Harischandra et al., 2019), we still needed to conduct electrical stimulation experiments on animals.

(3) Refinement: Preliminary experiments were conducted on a few stick insects to determine parameters that would not affect their behaviors or lives. Because stick insects do not actively walk in daily life, we did not use anesthesia to insert the electrodes. Measurements were performed in a manner that minimized potential pain, suffering, and distress. Even after a large number of electrical stimulations, we found no effect on insect behaviors; they resumed their normal activities once they returned to their breeding boxes in the colony.

(4) Reproductivity: In subsequent studies, we conducted two experiments in which only the insect body was mounted: (i) an electric stimulation experiment for one leg in which all legs were in the air (no contact with the ground) and (ii) an electric stimulation experiment for one leg in which all legs were on the ground and generated gait patterns. The experiments yielded similar results under different conditions, reporting further findings using similar experimental protocols (paper in preparation).

Furthermore, the authors completely agree that future research on cyborg insects, which may push the boundaries that are yet to be entirely considered by ethicists and legislators, will require careful ethical considerations of both animal welfare and social consequences.”

https://doi.org/10.7554/eLife.85275.sa2

Article and author information

Author details

  1. Dai Owaki

    Department of Robotics, Graduate School of Engineering, Tohoku University, Sendai, Japan
    Contribution
    Conceptualization, Resources, Data curation, Software, Formal analysis, Funding acquisition, Validation, Investigation, Visualization, Methodology, Writing - original draft, Project administration, Writing - review and editing
    For correspondence
    owaki@tohoku.ac.jp
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-1217-3892
  2. Volker Dürr

    1. Department of Biological Cybernetics, Faculty of Biology, Bielefeld University, Bielefeld, Germany
    2. Centre for Cognitive Interaction Technology, Bielefeld University, Bielefeld, Germany
    Contribution
    Conceptualization, Resources, Supervision, Validation, Investigation, Writing - review and editing
    Competing interests
    No competing interests declared
  3. Josef Schmitz

    1. Department of Biological Cybernetics, Faculty of Biology, Bielefeld University, Bielefeld, Germany
    2. Centre for Cognitive Interaction Technology, Bielefeld University, Bielefeld, Germany
    Contribution
    Resources, Data curation, Supervision, Validation, Investigation, Methodology, Project administration, Writing - review and editing
    Competing interests
    No competing interests declared

Funding

Japan Society for the Promotion of Science (JP21H00317)

  • Dai Owaki

Japan Society for the Promotion of Science (JP17KK0109)

  • Dai Owaki

Tateishi Science and Technology Foundation (Research Grant A,2231006)

  • Dai Owaki

Japan Society for the Promotion of Science (JP23H00481)

  • Dai Owaki

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

This work was supported by JSPS KAKENHI Grant-in-Aid for Scientific Research on Innovative Areas "Science of Soft Robot" project (JP21H00317), a Grant-in-Aid for the Promotion of Joint International Research (Fostering Joint International Research) (JP17KK0109), a Grant-in-Aid for Scientific Research (A) (JP23H00481), and the Tateishi Science and Technology Foundation (2023, Reserch Grant A, 2231006).

Ethics

At present, animal care regulations do not need to be considered for insect research at Bielefeld University and Tohoku University. We strongly agree with the responsibility and ethical issues discussed by Xu et al., 2020c regarding animal experiments, both for invertebrates that do not require specific approval or for vertebrates that do. We conducted experiments on stick insects (Carausius morosus) following the principles of harm minimization, precaution, and the 4Rs (reduction, replacement, refinement, and reproduction) at the individual level: (1) Reduction: We set N=10 as the maximum number of insects in each muscle in the experiment, which was considered the minimum number necessary to obtain statistically significant results. (2) Replacement: Although we previously surveyed various findings on the force characteristics generated in the muscles of stick insects based on nerve and muscle electrical stimulation (Blüme et al., 2012c,a,b; Harischandra et al., 2019), we still needed to conduct electrical stimulation experiments on animals. (3) Refinement: Preliminary experiments were conducted on a few stick insects to determine parameters that would not affect their behaviors or lives. Because stick insects do not actively walk in daily life, we did not use anesthesia to insert the electrodes. Measurements were performed in a manner that minimized potential pain, suffering, and distress. Even after a large number of electrical stimulations, we found no effect on insect behaviors; they resumed their normal activities once they returned to their breeding boxes in the colony. (4) Reproductivity: In subsequent studies, we conducted two experiments in which only the insect body was mounted: (i) an electric stimulation experiment for one leg in which all legs were in the air (no contact with the ground) and (ii) an electric stimulation experiment for one leg in which all legs were on the ground and generated gait patterns. The experiments yielded similar results under different conditions, reporting further findings using similar experimental protocols (paper in preparation). Furthermore, the authors completely agree that future research on cyborg insects, which may push the boundaries that are yet to be entirely considered by ethicists and legislators, will require careful ethical considerations of both animal welfare and social consequences.

Senior Editor

  1. Anna Akhmanova, Utrecht University, Netherlands

Reviewing Editor

  1. Gordon J Berman, Emory University, United States

Reviewer

  1. Nick Gravish, University of California, San Diego, United States

Version history

  1. Received: November 30, 2022
  2. Preprint posted: December 21, 2022 (view preprint)
  3. Accepted: August 29, 2023
  4. Version of Record published: September 13, 2023 (version 1)

Copyright

© 2023, Owaki et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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  1. Dai Owaki
  2. Volker Dürr
  3. Josef Schmitz
(2023)
A hierarchical model for external electrical control of an insect, accounting for inter-individual variation of muscle force properties
eLife 12:e85275.
https://doi.org/10.7554/eLife.85275

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https://doi.org/10.7554/eLife.85275

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