Neural models of reaching

Plamondon & Alimi (P&A) have unified much data on speed/accuracy trade-offs during reaching movements using a deltalognormal form factor that describes “the asymptotic behavior of a large number of dependent linear systems,” notably neuromuscular systems. Their approach raises questions about whether a large number of systems is needed, whether they are linear, and whether the results disclose the neural design principles that control reaching behaviors. The authors admit that “it is difficult . . . to provide a direct biological interpretation for the system parameters” (sect. 6, para. 4). The VITE model (Bullock & Grossberg 1988) of neural trajectory formation implies Fitts’ law, and various failures, as emergent properties of trajectory dynamics. VITE was derived to explain how motor synergies form, and how synergies contract synchronously at variable speeds. These three S’s (synergy, synchrony, speed) of reaching behavior imply Fitts’ law, as well as asymmetric velocity profiles and their invariances. They do so using a single, weakly nonlinear system rather than a large number of linear systems. VITE multiplies a difference vector (DV), which codes the difference between desired target position and an outflow representation of present position – and a volitional GO signal. Are there other neural systems that use DV-style computations and that are cascaded together to provide multiple VITE-like contributions to Fitts’ law, none of which involves neuromuscular computations? The VITEWRITE model (Bullock, Grossberg & Mannes 1993) embeds VITE into a movement-planning circuit for generating handwriting movements. The script letters are an emergent property of circuit interactions that enable writing to preserve its form as volitional acts flexibly change its size or speed. The script letters have an invariant representation as a spatial pattern of synergycontrolling DVs that are stored in a working memory. As in VITE, GO volitional signals can alter their speed of execution. GRO volitional signals alter their size by multiplying the DV that is read out of working memory; this product is then input to the VITE circuit. Feedback from VITE to working memory releases the next working-memory DV only when the VITE DV is maximal or zero. Complex data about stroke coordination, such as the “two-thirds power law” of Lacquaniti et al. (1983), arise as emergent properties of these feedback interactions. Nowhere does the circuit need the virtual targets or minimization principles that the authors mention. DVs also occur during visually guided control of motorequivalent reaching to targets in space. The direct model (Bullock, Grossberg & Guenther 1993) shows how accurate reaches can be made with novel tools of variable lengths, clamped joints, distortions of visual input by a prism, and unexpected perturbations. The coordinate transformations from retinal, to headcentered, and finally to the body-centered coordinates that control reaches also use DV computations. Why are DVs so ubiquitous in the spatial planning and motor execution of reaches? We propose that this is the correct computational format for autonomously learning the coordinate transformations and movement parameters that keep sensory-motor coordination accurate within a growing body (Grossberg et al. 1993; Guenther et al. 1994). P&A note that their approach “does not provide too many clues about the learning process itself.” P&A say that VITE does not describe “the mechanical properties of the muscles.” This is because VITE concerns itself with outflow positional control. The FLETE model (Bullock & Grossberg 1991) links outflow VITE commands to spinal and cerebellar circuits that maintain positional accuracy of contracting muscles under variable tension. FLETE models identified spinal and motor components, such as Renshaw cells and gamma motoneurons, and simulated the multiple velocity peaks during ballistic movements (Bullock & Grossberg 1992) which P&A consider “one of the most powerful characteristics of” their model. VITE has since been extended to a model circuit for controlling reaching movements of variable speed and force in the presence of obstacles (Bullock et al. 1997). This model simulates the neurophysiological firing patterns of six identified cell types in cortical areas 4 and 5 during a wide variety of behavioral tasks. P&A mention Weber law control of timed movements. A model of learning in the cerebellum describes how metabotropic glutamate receptors, acting at cerebellar Purkinje cell spines, may control adaptively timed learning that obeys a Weber law (Fiala et al. 1996). In summary, whereas Plamondon & Alimi provide a stimulating account of how speed/accuracy data may arise from deltalognormal processing, recent neural models of reaching behavior provide an alternative view of the design principles and nonlinear mechanisms whereby these data may arise as emergent properties. Where in the world is the speed/accuracy trade-off? P. A. Hancocka and Willem B. Verweyb aHuman Factors Research Laboratory, University of Minnesota, Minneapolis, MN 55455. bTNO Human Factors Research Institute, NL 3769 ZG, Soesterberg, The Netherlands. peter6reality.psych.umn.edu; www.hawk.psych.umn.edu verwey6arb-phys.uni-dortmund.de Abstract: Even though Plamondon’s kinematic model fits the data well, Even though Plamondon’s kinematic model fits the data well, we do not share the view that it explains movements other than ballistic ones. The model does not account for closed-loop control, which is the more common type of movement in everyday life, nor does it account for recent data indicating interference with ongoing processing. Plamondon & Alimi (P&A) state two specific goals. The first is to demonstrate the absence of a cohesive account for aimed movements; the second is to advance Plamondon’s kinematic theory as such an account. In general, P&A are successful with respect to these goals and are therefore to be congratulated. However, we have a number of questions, which principally concern real-world application of the findings, consistency with other data, and a potential weakness of the model itself. It is our contention that P&A’s work only relates to a very small and generally atypical segment of the full spectrum of movement capability. Only under highly constrained and artificial conditions, such as in the experimental laboratory or at sporting events, does any individual regularly engage in ballistic movements occurring at or near their maximum movement velocity. Very few daily skills require performance at the levels of velocity and accuracy typical in the cited research (although an obvious exception is keyboardHancock, P.A., & Verwey, W.B. (1997). Where in the world is the speed-accuracy trade-off? Behavioral and Brain Sciences, 20, 310-311.