The performance of motor tasks requires the coordinated control and continuous adjustment of myriad individual muscles. The basic commands for the successful performance of a sensorimotor task originate in "higher" centers such as the motor cortex, but the actual muscle activation and resulting torques and motion are considerably shaped by the integrative function of the spinal interneurons. The relative contributions of brain and spinal cord are less clear for reaching movements than for automatic tasks such as locomotion. We have modeled a two-axis, four-muscle wrist joint with realistic musculoskeletal mechanics and proprioceptors and a network of regulatory circuitry based on the classical types of spinal interneurons (propriospinal, monosynaptic Ia-excitatory, reciprocal Ia-inhibitory, Renshaw inhibitory, and Ib-inhibitory pathways) and their supraspinal control (via biasing activity, presynaptic inhibition, and fusimotor gain). The modeled system has a very large number of control inputs, not unlike the real spinal cord that the brain must learn to control to produce desired behaviors. It was surprisingly easy to program this model to emulate actual performance in four very different but well described behaviors: (1) stabilizing responses to force perturbations; (2) rapid movement to position target; (3) isometric force to a target level; and (4) adaptation to viscous curl force fields. Our general hypothesis is that, despite its complexity, such regulatory circuitry substantially simplifies the tasks of learning and producing complex movements.

This is the first demonstration that a realistic model of the SC + MS is capable of generating the required dynamics of center-out reaching. The interpolability observed is important for the feasibility of storing motor programs in memory rather than computing them from internal models of the musculoskeletal plant. Successful interpolation of command programs required them to have similar muscle recruitment patterns, which are thought by many to arise from hard-wired muscle synergies rather than learned as in our model system. These properties of the SC + MS along with its tendency to generate energetically efficient solutions might usefully be employed by motor cortex to generate voluntary behaviors such as reaching to targets.

Muscles convert metabolic energy into mechanical work. A computational model of muscle would ideally compute both effects efficiently for the entire range of muscle activation and kinematic conditions (force and length). We have extended the original Virtual Muscle algorithm (Cheng , 2000) to predict energy consumption for both slow- and fast-twitch muscle fiber types, partitioned according to the activation process (E(a)), cross-bridge cycling (E(xb)) and ATP/PCr recovery (E(recovery)). Because the terms of these functions correspond to identifiable physiological processes, their coefficients can be estimated directly from the types of experiments that are usually performed and extrapolated to dynamic conditions of natural motor behaviors. We also implemented a new approach to lumped modeling of the gradually recruited and frequency modulated motor units comprising each fiber type, which greatly reduced computational time. The emergent behavior of the model has significant implications for studies of optimal motor control and development of rehabilitation strategies because its trends were quite different from traditional estimates of energy (e.g., activation, force, stress, work, etc.). The model system was scaled to represent three different human experimental paradigms in which muscle heat was measured during voluntary exercise; predicted and observed energy rate agreed well both qualitatively and quantitatively.

Experimental descriptions of the anatomy and physiology of individual components of sensorimotor systems have revealed substantial complexity, making it difficult to intuit how complete systems might work. This has led to increasing efforts to develop and employ mathematical models to study the emergent properties of such systems. Conversely, the development of such models tends to reveal shortcomings in the experimental database upon which models must be constructed and validated. In both cases models are most useful when they point up discrepancies between what we think we know and possibilities that we may have overlooked. This overview considers those components of complete sensorimotor systems that currently appear to be potentially important but poorly understood. These are generally omitted completely from modeled systems or buried in implicit assumptions that underlie the design of the model.

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