Ian E. Brown

A hierarchical foundation for models of sensorimotor control.

Abstract Successful performance of a sensorimotor task arises from the interaction of descending commands from the brain with the intrinsic properties of the lower levels of the sensorimotor system, including the dynamic mechanical properties of muscle, the natural coordinates of somatosensory receptors, the interneuronal circuitry of the spinal cord, and computational noise in these elements. Engineering models of biological motor control often oversimplify or even ignore these lower levels because they appear to complicate an already difficult problem. We modeled three highly simplified control systems that reflect the essential attributes of the lower levels in three tasks: acquiring a target in the face of random torque-pulse perturbations, optimizing fusimotor gain for the same perturbations, and minimizing postural error versus energy consumption during low- versus high-frequency perturbations. The emergent properties of the lower levels maintained stability in the face of feedback delays, resolved redundancy in over-complete systems, and helped to estimate loads and respond to perturbations. We suggest a general hierarchical approach to modeling sensorimotor systems, which better reflects the real control problem faced by the brain, as a first step toward identifying the actual neurocomputational steps and their anatomical partitioning in the brain.

Virtual muscle: a computational approach to understanding the effects of muscle properties on motor control

This paper describes a computational approach to modeling the complex mechanical properties of muscles and tendons under physiological conditions of recruitment and kinematics. It is embodied as a software package for use with Matlab and Simulink that allows the creation of realistic musculotendon elements for use in motor control simulations. The software employs graphic user interfaces (GUI) and dynamic data exchange (DDE) to facilitate building custom muscle model blocks and linking them to kinetic analyses of complete musculoskeletal systems. It is scalable in complexity and accuracy. The model is based on recently published data on muscle and tendon properties measured in feline slow- and fast-twitch muscle, and incorporates a novel approach to simulating recruitment and frequency modulation of different fiber-types in mixed muscles. This software is distributed freely over the Internet at http://ami.usc.edu/mddf/virtualmuscle.

A Reductionist Approach to Creating and Using Neuromusculoskeletal Models

There are many possible approaches for developing models of physical systems. At one extreme exists the black-box model in which only the inputs and outputs of the system are considered important aspects of the model (see Chapter 9). Alternatively one can divide a system into separate components and model each component separately (see Chapter 8). The most obvious difference between these approaches is that there is more information in the latter model than just the inputs and outputs of the system. This latter approach is loosely termed reductionism—the form of the model for the system is ‘reduced’ into smaller components, each of which should have some testable relationship to a corresponding physical structure.

Measured and modeled properties of mammalian skeletal muscle. II. The effects of stimulus frequency on force-length and force-velocity relationships.

Interactions between physiological stimulus frequencies, fascicle lengths and velocities were analyzed in feline caudofemoralis (CF), a hindlimb skeletal muscle composed exclusively of fast-twitch fibers. Split ventral roots were stimulated asynchronously to produce smooth contractions at sub-tetanic stimulus frequencies. As described previously, the peak of the sub-tetanic force-length relationship was found to shift to longer lengths with decreases in stimulus frequency, indicating a length dependence for activation that is independent of filament overlap. The sub-tetanic force-velocity (FV) relationship was affected strongly both by stimulus frequency and by length; decreases in either decreased the slope of the FV relationship around isometric. The shapes of the force transients following stretch or shortening revealed that these effects were not due to a change in the instantaneous FV relationship; the relative shape of the force transients following stretch or shortening was independent of stimulus frequency and hardly affected by length. The effects of stimulus frequency and length on the sub-tetanic FV relationship instead appear to be caused by a time delay in the length-dependent changes of activation. In contrast to feline soleus muscle, which is composed exclusively of slow-twitch fibers, CF did not yield at sub-tetanic stimulus frequencies for the range of stretch velocities tested (up to 2 L0/s). The data presented here were used to build a model of muscle that accounted well for all of the effects described. We extended our model to account for slow-twitch muscle by comparing our fast-twitch model with previously published data and then changing the necessary parameters to fit the data. Our slow-twitch model accounts well for all previous findings including that of yielding.

Mechanics of feline soleus: I. Effect of fascicle length and velocity on force output

SummaryThe aim of the present study was to quantify how fascicle length and velocity modify force production in cat soleus. A computerized muscle puller controlled the length and velocity of the whole-muscle. We recorded the force output at the tendon and the length of muscle fascicles using sonomicrometry during whole-muscle isometric and isokinetic contractions. Peak muscle stress was estimated as 31.8±4.1 N cm-2 (mean and sd) and optimal fascicle length, L0, was estimated as 3.8±0.6 cm which corresponds to an optimal sarcomere length of 2.49±0.08 μm. The isometric force-length data followed closely the expected force-length relationship for cat sarcomeres. The force-velocity relationship was found to be similar in shape between cats, but the per cent increment of force over isometric levels for lengthening contractions was highly variable. Estimates of the kinematics of the fascicles based on whole-muscle length were systematically incorrect; whole-muscle velocity was 21% greater than fascicle velocity. The force-velocity data demonstrated consistent dependencies on fascicle length. At lengths below 0.7 L0 (1.74 μm), the shape of the force-velocity relationship was altered by the inclusion of a passive, repulsive force in the estimate of active isometric force. The shape of the force-velocity relationship changed at lengths greater than 0.7 L0, but was restricted to lengthening velocities where the increment of force with respect to isometric levels was found to increase with fascicle length. This change in shape in the force-velocity relationship for lengthening contractions reveals a systematic, but previously unknown interdependence between fascicle length and velocity on muscle force production.

MEDARM: a rehabilitation robot with 5DOF at the shoulder complex

A key approach for reducing motor impairment and regaining independence after stroke is frequent and repetitive functional training. A number of robotic devices have been developed to assist therapists with the labourious task of providing treatment. Although robotic technology is showing significant potential, its effectiveness for upper limb rehabilitation is limited in part by the inability to make functional reaching movements. A major contributor to this problem is that current robots do not replicate motion of the shoulder girdle despite the fact that the shoulder girdle plays a critical role in stabilizing and orienting the upper limb during activities of daily living. To address this issue, a new adjustable robotic exoskeleton called MEDARM is proposed for motor rehabilitation of the shoulder complex. MEDARM provides independent control of six degrees of freedom (DOF) of the upper limb: two at the sternoclavicular joint, three at the glenohumeral joint and one at the elbow. Its joint axes are optimally arranged to mimic the natural upper- limb workspace while avoiding singular configurations and while maximizing manipulability. This mechanism also permits reduction to planar shoulder/elbow motion in any plane by locking all but the last two joints. Electric motors actuate the joint using a combination of cable and belt transmissions designed to maximize the power-to-weight ratio of the robot while maintaining backdriveability and minimizing inertia. Thus, the robot can provide any level of movement assistance and gravity compensation. This paper describes the proposed technical design for MEDARM.

MECHANICS OF FELINE SOLEUS : II. DESIGN AND VALIDATION OF A MATHEMATICAL MODEL

SummaryWe have developed a mathematical model to describe force production in cat soleus during steady-state activation over a range of fascicle lengths and velocities. The model was based primarily upon a three element design by Zajac but also considered the many different features present in other previously described models. We compared quantitatively the usefulness of these features and putative relationships to account for a set of force and length data from cat soleus whole-muscle described in a companion paper. Among the novel features that proved useful were the inclusion of a short-length passive force resisting compression, a new normalisation constant for connective-tissue lengths to replace the potentially troublesome slack length, and a new length dependent term for lengthening velocities in the force-velocity relationship. Each feature of this model was chosen to provide the most accurate description of the data possible without adding unneeded complexity. Previously described functions were compared with novel functions to determine the best description of the experimental data for each of the elements in the model.

Measured and modeled properties of mammalian skeletal muscle: IV. dynamics of activation and deactivation.

The interactive effects of length and stimulus frequency on rise and fall times and on sag were investigated in fast-twitch feline caudofemoralis at normal body temperature. The length and stimulus frequency ranges studied were 0.8–1.2 L0 and 15–60 pps. Isometric rise times were shortest under two sets of conditions: short lengths + low stimulus frequencies and long lengths + high stimulus frequencies. In contrast the isometric fall time relationship showed a single minimum at short lengths + low stimulus frequencies. Velocity was shown to have an additional effect on fall time, but only at higher stimulus frequencies (40–60 pps): fall times were shorter during movement in either direction as compared to isometric. The effects of sag were greatest at shorter lengths and lower stimulus frequencies during isometric stimulus trains. Potential mechanisms underlying this last effect were investigated by comparing isometric twitches elicited prior to and immediately following a sag-inducing stimulus train. Post-sag twitches produced less force, reached peak force earlier and initially decayed more quickly compared to pre-sag twitches. However, the final rate of force decay and the initial rate of force rise (during the first 15 ms) were unaffected by sag. We construct a logical argument based on these findings to hypothesize that the predominant mechanism underlying sag is an increase in the rate of sarcoplasmic calcium ion removal. All of the above findings were used to construct a model of activation dynamics for fast-twitch muscle, which was then extrapolated to slow-twitch muscle. When coupled with a previous model of kinematic dynamics, the complete model produced accurate predictions of the forces actually recorded during experiments in which we applied concurrent dynamic changes in length, velocity and stimulus frequency.

Congruence of mossy fiber and climbing fiber tactile projections in the lateral hemispheres of the rat cerebellum

We have examined the spatial relationship between the mossy fiber and climbing fiber projections to crus IIa in the lateral hemispheres of the rat cerebellum. Experiments were performed in ketamine/xylazine anesthetized rats using extracellular recordings and high‐density micromapping techniques. Responses were elicited using small, tactile stimuli applied to the perioral and forelimb regions at a rate of 0.5 Hz. In our first series of experiments we demonstrate that the primary (i.e., strongest) receptive field for a single Purkinje cells complex spike is similar to the primary receptive field of the granule cells immediately subjacent to that Purkinje cell. In our second series of experiments we demonstrate that the granule cell region most strongly activated by a particular peripheral stimulus is immediately subjacent to the Purkinje cells whose complex spikes are also activated most strongly by the same stimulus. The region of climbing fibers activated by a localized peripheral stimulus is “patchy”; it clearly does not conform to the notion of a continuous microzone. These results support original observations first reported in the 1960s using evoked potential recording techniques that the mossy fiber and climbing fiber pathways converge in cerebellar cortex. However, we extend this earlier work to show that the two pathways converge at the level of single Purkinje cells. Many cerebellar theories assume that mossy fiber and climbing fiber pathways carry information from different peripheral locations or different modalities to cerebellar Purkinje cells. Our results appear to contradict this basic assumption for at least the tactile regions of the lateral hemispheres. J. Comp. Neurol. 429:59–70, 2001.

Measured and modeled properties of mammalian skeletal muscle. I. The effects of post-activation potentiation on the time course and velocity dependencies of force production

Activation of mammalian fast-twitch skeletal muscle induces a persistent effect known as post-activation potentiation (PAP), classically defined as an increase in force production at sub-maximal levels of activation. The underlying mechanism is thought to be phosphorylation of the myosin regulatory light chain (MRLC), which leads to an increase in the rate constant for cross-bridge attachment (Sweeney et al., 1993). If true, this suggests the hypothesis that other contractile properties should be affected during PAP. Using a feline fast-twitch whole-muscle preparation (caudofemoralis) at 37∘C, we observed that PAP greatly increased tetanic forces during active lengthening, decreased isometric tetanic rise times and delayed isometric tetanic force relaxation. The first two of these effects were length dependent with a greater effect occurring at shorter lengths. These findings confirmed that PAP has other functionally important effects beyond a simple increase in sub-maximal isometric forces. Furthermore, length was found to have an effect independent of PAP on the shortening half of the FV relationship (less force was produced at longer lengths) and on the rate of force relaxation during the later stages of isometric tetanic force decay (slower relaxation at longer lengths). All of these findings can be explained with a simplified, two-state model of cross-bridge dynamics that accounts for the interaction of both interfilament spacing and MRLC phosphorylation on the apparent rate constants for cross-bridge attachment and detachment. These findings are largely consistent with data collected previously from reduced preparations such as skinned fibers at cold, unphysiological temperatures (e.g. 5∘C). One finding that could not be explained by our model was that twitch fall times in the dispotentiated state were parabolically correlated with length, whereas in the potentiated state the relationship was linear. The time course of decay of this effect did not follow the time course of force dispotentiation, suggesting that there are other activation-dependent processes occurring in parallel with MRLC phosphorylation.