Limits...
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 three pattern generator variants. The four graphs per panel (A,B,C) show the tip trajectory (top left), joint angle time courses (top middle; HS: red, SP: blue), the mean cross-correlogram (top right), and the sliding cross-correlogram (bottom). The latter plots the cross-correlation of the SP joint angle relative to the HS joint angle within a sliding window size of ±1 s. Each column of the image shows the cross-correlogram for a single time window (aligned on the center of the window), with the correlation coefficient coded in grayscale from white (r = 1) to black (r = −1). The mean cross-correlograms show the average correlation coefficient for each row of the sliding cross-correlogram below. For comparison, the dotted red curve shows the average values of mean cross-correlograms for the experimental (intact animals) data (n = 10).
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4543877&req=5

Figure 4: Comparison of three pattern generator variants. The four graphs per panel (A,B,C) show the tip trajectory (top left), joint angle time courses (top middle; HS: red, SP: blue), the mean cross-correlogram (top right), and the sliding cross-correlogram (bottom). The latter plots the cross-correlation of the SP joint angle relative to the HS joint angle within a sliding window size of ±1 s. Each column of the image shows the cross-correlogram for a single time window (aligned on the center of the window), with the correlation coefficient coded in grayscale from white (r = 1) to black (r = −1). The mean cross-correlograms show the average correlation coefficient for each row of the sliding cross-correlogram below. For comparison, the dotted red curve shows the average values of mean cross-correlograms for the experimental (intact animals) data (n = 10).

Mentions: The results in Figure 3 are a proof of principle, showing that a set of coupled CPGs can produce realistic, rhythmic but quasi-rhythmic antennal movements in the skeletal model. Next, we were interested to test whether the model could capture two important characteristics seen in the experimental data: First, experimental data reveal a stable phase difference between the SP and HS joint angle time courses that varies only a little (approximately 20°), with the SP joint leading the HS joint. Second, the experimental data show considerable trial-to-trial variability of the movement pattern, both within and among individual animals (see variability of frequency spectra in Figure 2). Thus, in a second set of experiments, three CPG model variants were compared and they differed with respect to the incorporation of frequency spectra of different trials. In the single-trial model, Mc, only the frequency spectrum of a single trial was incorporated into the pattern formation network. The mean frequency (mean of 10) model, Mm, considered the mean frequency spectrum of 10 trials from five animals. Finally, the variable frequency model, Mmsd, incorporated the mean frequency spectrum with added random variation in the range of the standard deviation observed in the experimental data. In order to test for the phase difference between the antennal joints, the same data analysis was used as done by Krause et al. (2013). Accordingly, each panel of Figure 4 shows the antennal tip trajectory, joint angle time courses, cross-correlograms, and mean cross-correlograms for a given model variant. For immediate comparison with the experimental data, the mean cross-correlogram of the experimental data is shown as well (red dotted curves in Figure 4). A characteristic of antennal movements in intact animals is the elliptical shape of the antennal tip trajectories. While both the Mc and Mm models could generate the characteristic shape of the trajectory, the pattern obtained from the Mmsd model strongly differed from the experimental data. The mean of 10 model (Mm) produced antennal tip trajectories in the form of filled ellipsoids (Figure 4B). In all three model variants, the phase lead of the SP joint ϕij was set to a constant of 20°, as can be seen in the experimental (real) data. Note, however, that the true, instantaneous phase difference depends on the corresponding coupling strength wij, and the spontaneous amplitude of the joint angle oscillations, which may vary from one period to another. Cross-correlation of the two joint angle time courses uncovered the pre-set inter-joint coupling in model variants Mc and Mm. As in the real stick insect, the SP joint was leading the HS joint, as can be seen by a negative time lag of the SP joint angle relative to the HS joint (in Figure 4, note the continuous or almost continuous horizontal white band at negative time lag in the sliding cross-correlograms). This persistent pattern of inter-joint coordination was lost in the case of variable frequency model Mmsd (see Figure 4C). Accordingly, the mean cross-correlogram for this model variant had much lower correlation coefficients than that of the experimental data. In comparison, the two other model variants had very similar mean cross-correlograms and their match with the experimental values was much better.


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 three pattern generator variants. The four graphs per panel (A,B,C) show the tip trajectory (top left), joint angle time courses (top middle; HS: red, SP: blue), the mean cross-correlogram (top right), and the sliding cross-correlogram (bottom). The latter plots the cross-correlation of the SP joint angle relative to the HS joint angle within a sliding window size of ±1 s. Each column of the image shows the cross-correlogram for a single time window (aligned on the center of the window), with the correlation coefficient coded in grayscale from white (r = 1) to black (r = −1). The mean cross-correlograms show the average correlation coefficient for each row of the sliding cross-correlogram below. For comparison, the dotted red curve shows the average values of mean cross-correlograms for the experimental (intact animals) data (n = 10).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4543877&req=5

Figure 4: Comparison of three pattern generator variants. The four graphs per panel (A,B,C) show the tip trajectory (top left), joint angle time courses (top middle; HS: red, SP: blue), the mean cross-correlogram (top right), and the sliding cross-correlogram (bottom). The latter plots the cross-correlation of the SP joint angle relative to the HS joint angle within a sliding window size of ±1 s. Each column of the image shows the cross-correlogram for a single time window (aligned on the center of the window), with the correlation coefficient coded in grayscale from white (r = 1) to black (r = −1). The mean cross-correlograms show the average correlation coefficient for each row of the sliding cross-correlogram below. For comparison, the dotted red curve shows the average values of mean cross-correlograms for the experimental (intact animals) data (n = 10).
Mentions: The results in Figure 3 are a proof of principle, showing that a set of coupled CPGs can produce realistic, rhythmic but quasi-rhythmic antennal movements in the skeletal model. Next, we were interested to test whether the model could capture two important characteristics seen in the experimental data: First, experimental data reveal a stable phase difference between the SP and HS joint angle time courses that varies only a little (approximately 20°), with the SP joint leading the HS joint. Second, the experimental data show considerable trial-to-trial variability of the movement pattern, both within and among individual animals (see variability of frequency spectra in Figure 2). Thus, in a second set of experiments, three CPG model variants were compared and they differed with respect to the incorporation of frequency spectra of different trials. In the single-trial model, Mc, only the frequency spectrum of a single trial was incorporated into the pattern formation network. The mean frequency (mean of 10) model, Mm, considered the mean frequency spectrum of 10 trials from five animals. Finally, the variable frequency model, Mmsd, incorporated the mean frequency spectrum with added random variation in the range of the standard deviation observed in the experimental data. In order to test for the phase difference between the antennal joints, the same data analysis was used as done by Krause et al. (2013). Accordingly, each panel of Figure 4 shows the antennal tip trajectory, joint angle time courses, cross-correlograms, and mean cross-correlograms for a given model variant. For immediate comparison with the experimental data, the mean cross-correlogram of the experimental data is shown as well (red dotted curves in Figure 4). A characteristic of antennal movements in intact animals is the elliptical shape of the antennal tip trajectories. While both the Mc and Mm models could generate the characteristic shape of the trajectory, the pattern obtained from the Mmsd model strongly differed from the experimental data. The mean of 10 model (Mm) produced antennal tip trajectories in the form of filled ellipsoids (Figure 4B). In all three model variants, the phase lead of the SP joint ϕij was set to a constant of 20°, as can be seen in the experimental (real) data. Note, however, that the true, instantaneous phase difference depends on the corresponding coupling strength wij, and the spontaneous amplitude of the joint angle oscillations, which may vary from one period to another. Cross-correlation of the two joint angle time courses uncovered the pre-set inter-joint coupling in model variants Mc and Mm. As in the real stick insect, the SP joint was leading the HS joint, as can be seen by a negative time lag of the SP joint angle relative to the HS joint (in Figure 4, note the continuous or almost continuous horizontal white band at negative time lag in the sliding cross-correlograms). This persistent pattern of inter-joint coordination was lost in the case of variable frequency model Mmsd (see Figure 4C). Accordingly, the mean cross-correlogram for this model variant had much lower correlation coefficients than that of the experimental data. In comparison, the two other model variants had very similar mean cross-correlograms and their match with the experimental values was much better.

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.