A spiking neural model of adaptive arm control

Abstract

We present a spiking neuron model of the motor cortices and cerebellum of the motor control system. The model consists of anatomically organized spiking neurons encompassing premotor, primary motor, and cerebellar cortices. The model proposes novel neural computations within these areas to control a nonlinear three-link arm model that can adapt to unknown changes in arm dynamics and kinematic structure. We demonstrate the mathematical stability of both forms of adaptation, suggesting that this is a robust approach for common biological problems of changing body size (e.g. during growth), and unexpected dynamic perturbations (e.g. when moving through different media, such as water or mud). To demonstrate the plausibility of the proposed neural mechanisms, we show that the model accounts for data across 19 studies of the motor control system. These data include a mix of behavioural and neural spiking activity, across subjects performing adaptive and static tasks. Given this proposed characterization of the biological processes involved in motor control of the arm, we provide several experimentally testable predictions that distinguish our model from previous work.

Keywords: cerebellum; computational neuroscience; large-scale spiking neuron models; motor control; motor cortices.

Figure 1.

An overview of the REACH model, shown controlling a three-link arm. Numbers identify major communication pathways. Dashed lines indicate closed-loop feedback signals generated from the senses. The premotor cortex (PMC) generates a trajectory for the system to follow with a sequence of (x, y) coordinates. The primary motor cortex (M1) receives these target positions (1) from the PMC and compares them with the current system state, received from the sensory cortices (SCx), through (2). M1 combines this signal with locally calculated Jacobians to transform the desired hand movement commands into a low-level signal that is sent to the arm and cerebellum (CB) along (3). The CB projects an adaptive signal to the body along (4) that compensates for velocity and movement errors. Visual and proprioceptive feedback projects from the body along (5) to the CB and SCx. (Online version in colour.)

Figure 2.

(a) Normal reaching from a centre point outward to eight equidistant targets, repeated five times. Human data, taken from [44], is on the left and model simulation results are presented on the right. (b) The mean (thin centre line) and variance (thick grey line) of the velocity profiles for each of the eight reaches in the above figure. Human data, adapted from [45], are displayed on the left, and model simulation results are presented on the right. To account for the damping effects of muscles (which are not included in the arm model), a skewed Gaussian response has been used to model muscle dynamics [46].

Figure 3.

(a) Reaching from a centre point outward to eight equidistant targets with an end-effector velocity-based force field applied. Human subjects required approximately 750 trials to reach an average of 0.9 correlation with the original reach trajectories. The model's adaptation was significantly faster, requiring less than two full trials to reach 0.9 correlation with the original reach trajectories. Human data, taken from [44], are shown on the left, and model results are shown in the middle. Top: movement with the force field applied, before adaptation. Bottom: movement with the force field applied, after adaptation. (b) The arm tracing a desired elliptical trajectory (dotted red line) starting with an incorrect internal model of the arm. Over time, the system learns to correct this model by adapting the Jacobian. We calculate the tracking error by integrating the Euclidean distance from the hand to the target at every time step. Initial average tracking error across two cycles: 0.273 m; final average tracking error across two cycles: 0.065 m. (Online version in colour.)

Figure 4.

(a) Plots of the neurons from the primary motor cortex (M1; left column) and cerebellum (CB; right column) correlating with various high-level movement parameters, reflecting the same correlations found in experimental research as detailed in electronic supplementary material, table S1. The dotted lines are fit with linear regression (all correlations above 0.85), and the black dots are samples of neural activity, collected during reaching trials. (b) Examining a neuron's activity profile in response to the arm reaching out to eight surround-centre targets over five trials. Top: original results from [48] on the left, and REACH model results on the right. Bottom: performing the same sinusoidal regression as in [48] allows a quantitative comparison. Here, the correlation coefficient between the two curves is 0.985. (c) jPCA analysis applied to data collected from monkeys and the model during reach trials. Results from the original analysis are on the left, and from model analysis on the right. Both analyses were performed on activity from 218 neurons, recorded across 108 reaching trials. The colour is determined by the starting position of the neural activity. Both analyses exhibit a similar rotating path through the low-dimensional state space over time. The grouping in the state space trajectories for the REACH model is likely owing to there being more noise in the neural data than in the model (see electronic supplementary material, figure S6). (Online version in colour.)