From spontaneous motor activity to coordinated behaviour: a developmental model

Abstract

In mammals, the developmental path that links the primary behaviours observed during foetal stages to the full fledged behaviours observed in adults is still beyond our understanding. Often theories of motor control try to deal with the process of incremental learning in an abstract and modular way without establishing any correspondence with the mammalian developmental stages. In this paper, we propose a computational model that links three distinct behaviours which appear at three different stages of development. In order of appearance, these behaviours are: spontaneous motor activity (SMA), reflexes, and coordinated behaviours, such as locomotion. The goal of our model is to address in silico four hypotheses that are currently hard to verify in vivo: First, the hypothesis that spinal reflex circuits can be self-organized from the sensor and motor activity induced by SMA. Second, the hypothesis that supraspinal systems can modulate reflex circuits to achieve coordinated behaviour. Third, the hypothesis that, since SMA is observed in an organism throughout its entire lifetime, it provides a mechanism suitable to maintain the reflex circuits aligned with the musculoskeletal system, and thus adapt to changes in body morphology. And fourth, the hypothesis that by changing the modulation of the reflex circuits over time, one can switch between different coordinated behaviours. Our model is tested in a simulated musculoskeletal leg actuated by six muscles arranged in a number of different ways. Hopping is used as a case study of coordinated behaviour. Our results show that reflex circuits can be self-organized from SMA, and that, once these circuits are in place, they can be modulated to achieve coordinated behaviour. In addition, our results show that our model can naturally adapt to different morphological changes and perform behavioural transitions.

Figure 1. The conceptual model used in this paper.

On the left are the biological mechanisms that support the model: (1) SMA is illustrated by the muscle contraction (large arrows), (2) the spinal reflex circuits, which mediate afferent (green) and efferent (red) connections, and (3) the descending signals from supraspinal circuits (blue), which modulate the activity of reflex circuits. Unfilled and filled circles illustrate the presence of excitatory and inhibitory reflex circuits, respectively. On the right, is the general model with the abstracted biological mechanisms as well as the processes that link them together, i.e. self-organization and modulation.

Figure 2. The learning framework.

1) Spontaneous motor activity stimulates the motor system and 2) causes the muscles to contract. 3) The generated forces are propagated through the musculoskeletal system (and the environment) and induce sensor stimulation in the primary () and secondary () spindle afferent fibers. 4) The correlation between the sensor and motor signals is used to self-organize the reflex networks, and which mediate the connectivity of afferents and respectively. 5) The reflex circuits are modulated from supraspinal systems using gains and which independently scale the reflex networks and respectively.

Figure 3. The default musculoskeletal model used in our experiments.

a) The leg model comprises six muscles, the iliacus (), the rectus femoris (), the vastus intermedius (), the gluteus maximus (), the long biceps (), and the short biceps (); and represent the height of the end-effector and the ground respectively, and represents the height of the hip. and show the centers of mass of the pelvis, femur and tibia, respectively. and are the lengths of the femur and the tibia, respectively; the centers of mass of these bodies are located in the geometrical center of the body. b) The 3-element muscle model used; it consists of a spring () and a damper () in parallel to the contractile element ().

Figure 4. Hinton diagrams of the reflex circuits obtained with the default leg model.

a) Circuits obtained for the Ia-type afferents, and b) those obtained for the II-type afferents. Unfilled circles represent excitatory connections, and filled circles represent inhibitory connections.

Figure 5. Convergence of all the reflex weights involving the Rectus Femoris motor element, .

a) Reflex weights relative to the Ia -type afferents, and b) relative to the II-type afferents. For clarity, the raw data has been smoothed using a moving average filter with a window of

Figure 6. The hip trajectory and the mean and standard deviation of the kinematic and dynamic variables obtained for the default leg model.

Kinematic and dynamic variables obtained for the system with a) an appropriate set of gains, and b) an inappropriate set of gains. S refers to the stance phase (when the end effector is in touch with the ground) and F refers to the flight phase (when the end effector is in the air). In b, because each hop has a different duration, the data relative to each hop has been linearly interpolated to match the durations across different hops. Note that in this plot the time indicated for the stance-to-flight transition is only relative to the first hop. In subsequent hops, and because they progressively decrease in duration, this transition occurs earlier than illustrated by the marker. The hip trajectory recorded for the system with c) an appropriate set of gains, and d) an inappropriate set of gains.

Figure 7. The hopping height progression achieved for different a) and b) .

The large magnitude of the gains is justified by the fact that we use SI units in the afferents – for type-Ia afferents and for type-II afferents.

Figure 8. The hopping height achieved when modifying the height of the ground.

The hopping height is shown in blue and the ground height is shown in orange.

Figure 9. The hip trajectory and the mean and standard deviation of the kinematic and dynamic variables obtained for the modified leg models.

Kinematic and dynamic variables obtained for the system with a) four muscles, b) modified and c) misplaced S refers to the stance phase (when the end effector is in touch with the ground) and F refers to the flight phase (when the end effector is in the air). The hip trajectory recorded for the system with d) four muscles, e) modified and f) misplaced

Figure 10. Hinton diagrams of the reflex circuits obtained for the system with the modified .

a) Connections involving Ia-type afferents and b) II-type afferents. Unfilled circles represent excitatory connections, and filled circles represent inhibitory connections. The red squares highlight the modified connections with respect to the default system.

Figure 11. Changes in the reflex weights of the motor element () when passing from the default system to the system with the misplaced and back to the default system.

Connections involving a) the Ia-type and b) the II-type afferents. For clarity, the data has been smoothed using a moving average filter with a window of

Figure 12. The hip trajectory and the mean and standard deviation of the kinematic and dynamic variables obtained for the default modified models using dynamic gain modulation.

Kinematic and dynamic variables obtained for the system with a) misplaced and b) misplaced S refers to the stance phase (when the end effector is in touch with the ground) and F refers to the flight phase (when the end effector is in the air). The hip trajectory recorded for the system with c) misplaced and d) misplaced

Figure 13. Hopping transitions.

a) The hopping height achieved after the behavioural transition and b) detail of a showing the behavioural transition.

Figure 14. Leg trajectories during point-to-point tasks.

The black lines display the initial leg position set for the point-to-point tasks, and the gray lines indicate the leg position achieved at the end of three different trajectories T1, T2, and T3.

Figure 15. The reflex circuitry involving spindle afferents from primary () and secondary () fibres.

Filled circles represent inhibitory connections and unfilled circles represent excitatory connections. From a qualitative point of view, the connectivity between both types of afferents (from different muscles) and the α-motoneuron of a given muscle is similar (see text). This figure has been adapted from .