Evaluation of linear and non-linear activation dynamics models for insect muscle

Abstract

In computational modelling of sensory-motor control, the dynamics of muscle contraction is an important determinant of movement timing and joint stiffness. This is particularly so in animals with many slow muscles, as is the case in insects—many of which are important models for sensory-motor control. A muscle model is generally used to transform motoneuronal input into muscle force. Although standard models exist for vertebrate muscle innervated by many motoneurons, there is no agreement on a parametric model for single motoneuron stimulation of invertebrate muscle. Although several different models have been proposed, they have never been evaluated using a common experimental data set. We evaluate five models for isometric force production of a well-studied model system: the locust hind leg tibial extensor muscle. The response of this muscle to motoneuron spikes is best modelled as a non-linear low-pass system. Linear first-order models can approximate isometric force time courses well at high spike rates, but they cannot account for appropriate force time courses at low spike rates. A linear third-order model performs better, but only non-linear models can account for frequency-dependent change of decay time and force potentiation at intermediate stimulus frequencies. Some of the differences among published models are due to differences among experimental data sets. We developed a comprehensive toolbox for modelling muscle activation dynamics, and optimised model parameters using one data set. The “Hatze-Zakotnik model” that emphasizes an accurate single-twitch time course and uses frequency-dependent modulation of the twitch for force potentiation performs best for the slow motoneuron. Frequency-dependent modulation of a single twitch works less well for the fast motoneuron. The non-linear “Wilson” model that optimises parameters to all data set parts simultaneously performs better here. Our open-access toolbox provides powerful tools for researchers to fit appropriate models to a range of insect muscles.

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

“…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, 2012c ; Harischandra et al, 2019 ): 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.…”

“…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, 2012b ), 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.…”

Fully 3D‐Printed Cuff Electrode for Small Nerve Interfacing

“…This phenomenon can be attributed to the stronger depolarization caused by tetanic contraction, making the contraction last longer. [ 27 ] While both stimulation protocols (using 2 or 4 electrodes) delivered the same charge, movement could not be elicited for some combinations, suggesting that the electrode configuration influences the stimulation pattern.…”

The self-oscillation paradox in the flight motor ofDrosophila melanogaster

“…There is broad consistency between estimates of r across sinusoidal testing and impulse response datasets, with no estimate exceeding r ≈ 0.74 [42]. We note, however, that these estimates are coarse: in particular, TIIR estimates are likely to represent overestimates of the peak r for their respective datasets; but also, do not account for nonlinearities that may make muscular oscillation differ from step response behaviour [53]. The value of the TIIR process is that it allows conservative estimates of maximum r —a crucial parameter for our analysis over §§4 and 5—to be made using only low-precision graphs of strain rate impulse response, which are unsuitable for detailed fitting to viscoelastic models such as equation (3.5).…”