INTRODUCTION

All adaptive behaviors have some kind of goal, even when that goal is abstract and/or far off in space and time, e.g., saving up money to put the kids through university. Here, we consider goal-directed behaviors in the simplest, most literal sense: movements aimed toward some goal in three-dimensional (3-D) space, immediately or after a short delay. In particular, we will focus on the early spatial transformations associated with goal-directed gaze and hand movements.

As neuroscientists our ultimate goal is to describe how the brain implements these behaviors, but here we adopt the viewpoint that this topic cannot be approached without first having a firm understanding of the behavior itself. This extends beyond consideration of 3D location the end-point effecter – such as the location of the finger-tip— to the underlying multi-dimensional geometry of the systems that house the senses and control the effectors. Sometimes one would like to ignore these details, but the brain has no such luxury. As we shall see, the devil is in the details, in the sense that these details place important constraints on brain function.

Further, we also focus this review on the primate system, where possible the human species. Animal models have laid the modern foundations for this field and remain necessary to push the detailed boundaries of our knowledge, but in the past 10 years animal neurophysiology has been paralleled by equally important human experiments using technologies such as fMRI, TMS, and MEG. These technologies allow one to confirm the known animal physiology in humans, sometimes reveal interspecies differences, occasionally push our knowledge of basic function forward, and often bridge the gap from basic function to clinically observed deficits.

Finally, although no equations will appear in this review, we will take a computational perspective, approaching the subject of sensorimotor transformations as a series of computational problems, organized roughly in terms of the order that one would encounter these problems in a feed-forward transformation. From this perspective –although gaze and hand movements obviously have their differences both in terms of biomechanics and neural control- we might hope to reveal certain universal elements of goal-directed movement. For example, as we shall see, certain aspects of visuospatial memory that were once assumed to be the province of vision and eye movements have been shown to apply equally well to the reach system.

Before reviewing the details of how the brain might perform spatial transformations for hand and gaze control, we need to establish some background vocabulary: first in the general language of spatial representation and transformation, next in the basic spatial properties of our model systems, and finally in the language of cortical and sub-cortical physiology.