Editor's evaluation: A hierarchical model for external electrical control of an insect, accounting for inter-individual variation of muscle force properties
Year: 2023
Type: peer-review
Abstract: Full text Figures and data Side by side Abstract Editor's evaluation eLife digest Introduction Results Discussion Materials and methods Appendix 1 Data availability References Decision letter Author response Article and author information 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 Decision letter eLife's review process 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). Figure 1 Download asset Open asset 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. Figure 2 Download asset Open asset 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) τi∼N(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,j∼N(μ=βjTi,σ), (3) βj∼N(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) τi∼N(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,j∼N(μ=βj{Ti}γ,σ), (6) βj∼N(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,j∼N(μ=β{Ti}γj,σ), (8) γj∼N(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,j∼N(μ=βj{Ti}γj,σ), (10) βj∼N(μ=μβ,σβ), (11) γj∼N(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 and the WAIC and, therefore, the best predictive performance. the model with individual differences for both and exhibited the prediction performance, that inter-individual variation of the exponent not model estimates. Figure 3 Download asset Open asset Model of inter-individual variation of We compared the six models that were explained in the (A), (B), and (C) show plots of the WAIC (Watanabe, 2018) values for the protractor, retractor, and levator animals The parameters with and indicate that the parameters inter-individual PWM parameters were set as V, 2.0 V, V, and at 50 and 30% duty ratio. values were obtained for models and for all and all The WAIC indicates the best prediction model, as explained in the show Bayesian predictive for the protractor retractor and levator stimulation experiments with PWM parameters 2.0 V, 50 Hz, and 30% duty ratio. The differences in the indicate individual animals. In each the indicates the of the distribution The represent from the distribution in order of Source code and data are available on Dryad https://doi.org/10.5061/dryad.wpzgmsbsw). Bayesian of the generated torque for a given burst duration Figure shows the predictive distributions for data of a new animal using the Bayesian distribution for the six models. The results were obtained with PWM at 2.0 voltage, 50 frequency, and 30% duty ratio. The results show that the hierarchical models and model for the parameter can and the of experimental results on protractor, retractor, and levator torques for all animals. This compared with models, the hierarchical models can account for inter-individual variation of muscle properties for new unknown animals. Figure the distributions by the linear hierarchical model for each individual by the experimental data in Figure Figure Download asset Open asset distributions from the linear hierarchical model for each 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 indicates the order of the stimulations: blue (1) to yellow (n). In each the indicates the of the predictive distribution. The represent from the distribution in order of The results that the linear hierarchical model an predictive distribution in the up to 500ms. Source code and data are available on Dryad https://doi.org/10.5061/dryad.wpzgmsbsw). of an individual animal and applied voltage on muscle properties Figure presents the in the muscle characteristic parameters β and γ in response to changes in the applied In the experiments, we a order of voltage from 1 to V, for each Furthermore, we that between 1 and not 1 the number of electrical stimuli to each muscle in each We the changes in β and γ with to the applied voltage by the experimental results using the six Bayesian models. Figure Download asset Open asset of muscle parameters on the applied voltage and individual animals in the six The (A), (B), and (C) represent the for β for the applied voltage varied from to for the six models. (A) and (B) and and (C) and the protractor, retractor, and levator respectively. In (A) to the upper and lower show and hierarchical models for β, respectively. The right and represent the for γ in applied voltage In to the panel shows linear models the middle and right and hierarchical models for γ, respectively. For hierarchical models the from the distribution in order of inter-individual Source code and data are available on Dryad https://doi.org/10.5061/dryad.wpzgmsbsw). 1 of insects used in the stimulation experiments for each muscle. the number of the stick insects. We analyzed animal data from to for and to experimental and we could not stimulation data for all three muscles from the same animal on the same we experiments to data for animals for each muscle through experiments using animals. The results indicate the three (1) β varied with the applied voltage, and an voltage that (2) for nonlinear models and γ has a low on the applied and (3) β is strongly subject to inter-individual variation γ is Discussion In this we investigated 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 analysis of the joint torques generated by leg muscles, we used Bayesian statistical analysis and modeling to account for inter-individual A of the six models combinations of linear, nonlinear, and hierarchical that the two models that inter-individual variation of slope parameter β performed Models and the most of the predictive distribution. The exponent γ is a of the generated joint torque, that is the of of the stimulus-torque is linear when slope parameter β the of of the generated torque. In a of the prediction performance of models in Figure the index WAIC revealed that the models and β was a hierarchical performed the Since hierarchical parameters account for inter-individual variation, we that β is strongly by individual γ is invariant among we found that the properties of leg muscles are common to all individuals in the slope β, that is the by which the three of leg muscles to electrical stimulation. Furthermore, as in Figure
Source: eLife
Author: Gordon J Berman
Institution: Emory University
Language: English
Subfield: Biomedical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,500
OpenAlex ID: W4386710091