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Stable phase-shift despite quasi-rhythmic movements: a CPG-driven dynamic model of active tactile exploration in an insect.

Harischandra N, Krause AF, Dürr V - Front Comput Neurosci (2015)

Bottom Line: The effect of proprioceptor ablations could be simulated by changing the amplitude and offset parameters of the joint oscillators, only.We found that the phase-lead of the distal scape-pedicel (SP) joint relative to the proximal head-scape (HS) joint was essential for producing the natural tactile exploration behavior and, thus, for tactile efficiency.Based on our modeling results, we propose that a constant phase difference is coded into the CPG of the antennal motor system and that proprioceptors are acting locally to regulate the joint movement amplitude.

View Article: PubMed Central - PubMed

Affiliation: Department of Biological Cybernetics, Faculty of Biology, Bielefeld University Bielefeld, Germany ; Cognitive Interaction Technology Center of Excellence (CITEC), Bielefeld University Bielefeld, Germany.

ABSTRACT
An essential component of autonomous and flexible behavior in animals is active exploration of the environment, allowing for perception-guided planning and control of actions. An important sensory system involved is active touch. Here, we introduce a general modeling framework of Central Pattern Generators (CPGs) for movement generation in active tactile exploration behavior. The CPG consists of two network levels: (i) phase-coupled Hopf oscillators for rhythm generation, and (ii) pattern formation networks for capturing the frequency and phase characteristics of individual joint oscillations. The model captured the natural, quasi-rhythmic joint kinematics as observed in coordinated antennal movements of walking stick insects. Moreover, it successfully produced tactile exploration behavior on a three-dimensional skeletal model of the insect antennal system with physically realistic parameters. The effect of proprioceptor ablations could be simulated by changing the amplitude and offset parameters of the joint oscillators, only. As in the animal, the movement of both antennal joints was coupled with a stable phase difference, despite the quasi-rhythmicity of the joint angle time courses. We found that the phase-lead of the distal scape-pedicel (SP) joint relative to the proximal head-scape (HS) joint was essential for producing the natural tactile exploration behavior and, thus, for tactile efficiency. For realistic movement patterns, the phase-lead could vary within a limited range of 10-30° only. Tests with artificial movement patterns strongly suggest that this phase sensitivity is not a matter of the frequency composition of the natural movement pattern. Based on our modeling results, we propose that a constant phase difference is coded into the CPG of the antennal motor system and that proprioceptors are acting locally to regulate the joint movement amplitude.

No MeSH data available.


Comparison of left antennal tip trajectories obtained after varying the phase difference between HS and SP oscillators in Mc model. In each sub-figure, tip trajectory (left) and the mean cross-correlogram (right) are shown for a single simulated trial. See Figure 5 and text for more details. Phase lead of the SP joint with respect to the HS joint varied from −40 to 180°, as shown in (A–I). The natural situation is where the SP joint leads HS joint by 20° (E).
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Figure 6: Comparison of left antennal tip trajectories obtained after varying the phase difference between HS and SP oscillators in Mc model. In each sub-figure, tip trajectory (left) and the mean cross-correlogram (right) are shown for a single simulated trial. See Figure 5 and text for more details. Phase lead of the SP joint with respect to the HS joint varied from −40 to 180°, as shown in (A–I). The natural situation is where the SP joint leads HS joint by 20° (E).

Mentions: Like walking stick insects, our model showed persistent inter-joint coordination in antennal movement, with the SP joint leading HS joint by approximately 20°. Thus, we were interested in understanding how important this phase difference is for generating the typical antennal movement pattern. Owing to the complex shape of the patterns, their quasi-rhythmicity (variability), and the non-orthogonal slanted axes of antennal joints, it is not trivial to predict how the magnitude of the model parameter setting, the phase difference, i.e., ϕij in Equation (2), will affect the antennal tip trajectory or the joint angle time courses. In order to investigate the significance of this parameter, we systematically varied ϕij in the single-trial model variant Mc. Figure 6 shows separate simulations with the phase lead of the SP oscillator ranging from −40, −20, 0, 10, 20, 40, 60, 90, and 180°. Judging from the antennal tip trajectories and mean cross-correlograms for HS and SP joint angle time courses, the antennal movement pattern increasingly deviated from the natural reference condition () as the phase lead increased or decreased. If the phase difference had been irrelevant to the movement pattern, we would have expected an elliptical tip trajectory for all values of ϕij, with varying width and orientation. Instead, the elliptical shape of the movement pattern could be seen only within the limits of approximately 10° above or below the natural reference (i.e., from 10 to 30° lead). Moreover, when the two joint oscillators were in phase (), we would have expected the antennal tip to move along a slanted line. Instead, due to the variability introduced into the pattern generators, antennal tip trajectories ran along several lines (Figure 6C). In order to determine whether this is true for single-trial models simulating the data from other individuals, we repeated the same experiment with different Pattern Formation networks (Equation 5), i.e., after setting the frequency characteristics (Figure 2) according to the frequency spectra measured from four further animals. In all of these cases, we found the same result: the antennal movement pattern substantially deteriorated for phase differences beyond ±15° with regard to the natural reference.


Stable phase-shift despite quasi-rhythmic movements: a CPG-driven dynamic model of active tactile exploration in an insect.

Harischandra N, Krause AF, Dürr V - Front Comput Neurosci (2015)

Comparison of left antennal tip trajectories obtained after varying the phase difference between HS and SP oscillators in Mc model. In each sub-figure, tip trajectory (left) and the mean cross-correlogram (right) are shown for a single simulated trial. See Figure 5 and text for more details. Phase lead of the SP joint with respect to the HS joint varied from −40 to 180°, as shown in (A–I). The natural situation is where the SP joint leads HS joint by 20° (E).
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Related In: Results  -  Collection

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Figure 6: Comparison of left antennal tip trajectories obtained after varying the phase difference between HS and SP oscillators in Mc model. In each sub-figure, tip trajectory (left) and the mean cross-correlogram (right) are shown for a single simulated trial. See Figure 5 and text for more details. Phase lead of the SP joint with respect to the HS joint varied from −40 to 180°, as shown in (A–I). The natural situation is where the SP joint leads HS joint by 20° (E).
Mentions: Like walking stick insects, our model showed persistent inter-joint coordination in antennal movement, with the SP joint leading HS joint by approximately 20°. Thus, we were interested in understanding how important this phase difference is for generating the typical antennal movement pattern. Owing to the complex shape of the patterns, their quasi-rhythmicity (variability), and the non-orthogonal slanted axes of antennal joints, it is not trivial to predict how the magnitude of the model parameter setting, the phase difference, i.e., ϕij in Equation (2), will affect the antennal tip trajectory or the joint angle time courses. In order to investigate the significance of this parameter, we systematically varied ϕij in the single-trial model variant Mc. Figure 6 shows separate simulations with the phase lead of the SP oscillator ranging from −40, −20, 0, 10, 20, 40, 60, 90, and 180°. Judging from the antennal tip trajectories and mean cross-correlograms for HS and SP joint angle time courses, the antennal movement pattern increasingly deviated from the natural reference condition () as the phase lead increased or decreased. If the phase difference had been irrelevant to the movement pattern, we would have expected an elliptical tip trajectory for all values of ϕij, with varying width and orientation. Instead, the elliptical shape of the movement pattern could be seen only within the limits of approximately 10° above or below the natural reference (i.e., from 10 to 30° lead). Moreover, when the two joint oscillators were in phase (), we would have expected the antennal tip to move along a slanted line. Instead, due to the variability introduced into the pattern generators, antennal tip trajectories ran along several lines (Figure 6C). In order to determine whether this is true for single-trial models simulating the data from other individuals, we repeated the same experiment with different Pattern Formation networks (Equation 5), i.e., after setting the frequency characteristics (Figure 2) according to the frequency spectra measured from four further animals. In all of these cases, we found the same result: the antennal movement pattern substantially deteriorated for phase differences beyond ±15° with regard to the natural reference.

Bottom Line: The effect of proprioceptor ablations could be simulated by changing the amplitude and offset parameters of the joint oscillators, only.We found that the phase-lead of the distal scape-pedicel (SP) joint relative to the proximal head-scape (HS) joint was essential for producing the natural tactile exploration behavior and, thus, for tactile efficiency.Based on our modeling results, we propose that a constant phase difference is coded into the CPG of the antennal motor system and that proprioceptors are acting locally to regulate the joint movement amplitude.

View Article: PubMed Central - PubMed

Affiliation: Department of Biological Cybernetics, Faculty of Biology, Bielefeld University Bielefeld, Germany ; Cognitive Interaction Technology Center of Excellence (CITEC), Bielefeld University Bielefeld, Germany.

ABSTRACT
An essential component of autonomous and flexible behavior in animals is active exploration of the environment, allowing for perception-guided planning and control of actions. An important sensory system involved is active touch. Here, we introduce a general modeling framework of Central Pattern Generators (CPGs) for movement generation in active tactile exploration behavior. The CPG consists of two network levels: (i) phase-coupled Hopf oscillators for rhythm generation, and (ii) pattern formation networks for capturing the frequency and phase characteristics of individual joint oscillations. The model captured the natural, quasi-rhythmic joint kinematics as observed in coordinated antennal movements of walking stick insects. Moreover, it successfully produced tactile exploration behavior on a three-dimensional skeletal model of the insect antennal system with physically realistic parameters. The effect of proprioceptor ablations could be simulated by changing the amplitude and offset parameters of the joint oscillators, only. As in the animal, the movement of both antennal joints was coupled with a stable phase difference, despite the quasi-rhythmicity of the joint angle time courses. We found that the phase-lead of the distal scape-pedicel (SP) joint relative to the proximal head-scape (HS) joint was essential for producing the natural tactile exploration behavior and, thus, for tactile efficiency. For realistic movement patterns, the phase-lead could vary within a limited range of 10-30° only. Tests with artificial movement patterns strongly suggest that this phase sensitivity is not a matter of the frequency composition of the natural movement pattern. Based on our modeling results, we propose that a constant phase difference is coded into the CPG of the antennal motor system and that proprioceptors are acting locally to regulate the joint movement amplitude.

No MeSH data available.