A computational neuroanatomy for motor control

Abstract

The study of patients to infer normal brain function has a long tradition in neurology and psychology. More recently, the motor system has been subject to quantitative and computational characterization. The purpose of this review is to argue that the lesion approach and theoretical motor control can mutually inform each other. Specifically, one may identify distinct motor control processes from computational models and map them onto specific deficits in patients. Here we review some of the impairments in motor control, motor learning and higher-order motor control in patients with lesions of the corticospinal tract, the cerebellum, parietal cortex, the basal ganglia, and the medial temporal lobe. We attempt to explain some of these impairments in terms of computational ideas such as state estimation, optimization, prediction, cost, and reward. We suggest that a function of the cerebellum is system identification: to build internal models that predict sensory outcome of motor commands and correct motor commands through internal feedback. A function of the parietal cortex is state estimation: to integrate the predicted proprioceptive and visual outcomes with sensory feedback to form a belief about how the commands affected the states of the body and the environment. A function of basal ganglia is related to optimal control: learning costs and rewards associated with sensory states and estimating the "cost-to-go" during execution of a motor task. Finally, functions of the primary and the premotor cortices are related to implementing the optimal control policy by transforming beliefs about proprioceptive and visual states, respectively, into motor commands.

Fig. 1

Accuracy constraints affect control of reaching. Volunteers were instructed to tap the two goal regions with a pen as many times as possible during a 15 sec period. Movement time increased as the accuracy requirements increased (width of target region decreased), and as weight of the hand-held pen increased. (figure constructed from data in Fitts 1954).

Fig. 2

Reward affects control of movements. A. The task is to make a rapid pointing movement so to maximize reward. Endpoints in the blue region are rewarded while those in the red region are penalized. Because movements are variable, subjects should plan their movements so that with increased error costs mean of the endpoint distributions shifts away from the penalty region (pink region). If the tool that they are holding increases their endpoint noise, the shift should increase. The left two columns are predicted performances with small and large noise. The right column is data from a typical subject (from Trommershauser et al. 2005). B. The task for the monkey is to saccade to a visual target that can appear in one of four locations (LU: left upper, RD: right down, etc.). However, only one target location in a given set is rewarded. Each set is identified by a column. The top row shows indicates the rewarded target location in each set (filled circle). The bottom four rows show saccade speed to each target location under each reward condition. When the target is rewarded, saccades to that location have a higher speed, smaller duration, and less variability (from Takikawa et al. 2002).

Fig. 3

A schematic model for generating goal directed movements. Please see the text for explanation of variables and box labels.

Fig. 4

Task dynamics affect reach trajectories. A. The task is to reach from point T1 to T2. In one condition, the reach takes place in free space (straight line). In another condition, a spring is attached to the hand. In this case, the subject chooses to move the hand along an arc (redrawn from Uno et al. 1989). B. A velocity dependent force field pushes the hand perpendicular to its direction of motion. For example, for an upward movement the forces push the hand to the left. The motion that minimizes cost of Eq. (1) is not a straight line, but one that has a curvature to the right. The data shows hand paths for a typical subject at start of training on day 1, and then end of training each day. Except for the 1^st and 3^rd trials, all other trajectories are average of 50 trials. C. A rationale for why a curved movement is of lower cost. The curves show simulation results on forces that the controller produces, and speed of movement, in the optimal control scenario of Eq. (1) and in a scenario where the objective is to minimize jerk. (Data in parts B and C from Izawa et al. 2006)

Fig. 5

Task constraints affect feedback response to perturbations. In this bi-manual task, there are either two cursors visible on a screen or a single cursor. In the two cursor condition, each hand controls one cursor. In the one cursor condition, the average position of each hand is reflected in cursor position. In the top row of this figure, the blue and red arrows show that a perturbation is applied to the left hand. The middle row shows the hand paths in each condition (black trace is the condition without a perturbation). The bottom row shows the hand velocities. In the two cursor condition, perturbation to the left hand is compensated by the left hand only. In the one cursor condition, the same perturbation is compensated by motion of both hands. (from Diedrichsen 2007)

Fig. 6

Predicting and compensating for consequences of motor commands depends on the cerebellum. Subject holds a ball with their left hand and releases it into a basket held by the right hand. Healthy individuals increase their grip force in anticipation of the ball’s impact. Patient HK, who suffered from cerebellar agenesis, has a grip force that rises in response to the impact but not before it. The bottom trace refers to the acceleration of the right hand (holding the basket). The impact of the ball is marked by the first vertical line. (from Nowak et al. 2007)

Fig. 7

Examples of motor skill learning in health and disease. A. Learning to control a tool that has novel force characteristics. Subjects reached to visual targets while the robot perturbed the hand with either no forces (null field), or fields A or B. In 1/6^th of the trials, the field was removed, resulting in catch trials. Learning was measured by the size of errors in catch trials. Data shown is for amnesic subject HM, other amnesic subjects (AMN), and normal control subjects (NCS). HM learned the task more slowly, but had excellent retention. Data from Shadmehr et al. (1998). B & C. Performance of cerebellar and Huntington’s disease patients on the same task. While cerebellar patients are profoundly impaired in learning, HD patients are normal. Data from Smith and Shadmehr (2005). D. Effect of stimulation of the cerebellar thalamus of patients with essential tremor on the same task. Stimulation of the cerebellar thalamus reduces tremor (data not shown), but impairs learning. Data from Chen et al. (2006). E. Learning to control a tool with novel kinematic characteristics: the mirror drawing paradigm. Data is form amnesic subject HM, redrawn from Milner et al. (1998). Each trial requires the subject to trace the star while keeping within the two lines. An error occurs when the pencil goes outside the two lines. F. Performance of two groups of cerebellar patients on the same task. Data from Sanes et al. (1990). G. Performance of patients with Parkinson’s disease on the same task. Filled symbols represent the patient group. Data from Agostino et al. (1996). H. Performance of patients with Huntington’s disease on the same task. NC is normal controls. Data from Gabrieli et al. (1997).

Fig. 8

Writing ability of patient FF, who suffered a lesion in the right caudate nucleus. Four- and eight-letter string copying (models on the upper lines) by the right (middle lines) and the left hand (lower lines). Micrographia was evident only with the right hand. (Barbarulo, Grossi, Merola, Conson, and Trojano, 2007).

Fig. 9

Reaching around an obstacle affects the subsequent trial when there is no obstacle. On any given trial, the target of the movement and the obstacle, if any, are present before the reach starts. Left column shows data from two control groups in which either all (A) or none of the movements (N) had an obstacle. The data displayed in the middle and right columns are for a group where the probability of an obstacle on any given trial was 50%. The marking ++ indicates that two consecutive movements had an obstacle, and the data shown is for the second of these two trials. The marking +- indicates that the last trial had an obstacle but the current trial does not. No two consecutive trials were to the same direction. The movement directions have been rotated for ease of comparison. (From Jax and Rosenbaum 2007)