Dinant A. Kistemaker

The central nervous system does not minimize energy cost in arm movements

It has been widely suggested that the many degrees of freedom of the musculoskeletal system may be exploited by the CNS to minimize energy cost. We tested this idea by having subjects making point-to-point movements while grasping a robotic manipulandum. The robot created a force field chosen such that the minimal energy hand path for reaching movements differed substantially from those observed in a null field. The results show that after extended exposure to the force field, subjects continued to move exactly as they did in the null field and thus used substantially more energy than needed. Even after practicing to move along the minimal energy path, subjects did not adapt their freely chosen hand paths to reduce energy expenditure. The results of this study indicate that for point-to-point arm movements minimization of energy cost is not a dominant factor that influences how the CNS arrives at kinematics and associated muscle activation patterns.

Can proprioceptive training improve motor learning

Recent work has investigated the link between motor learning and sensory function in arm movement control. A number of findings are consistent with the idea that motor learning is associated with systematic changes to proprioception (Haith A, Jackson C, Mial R, Vijayakumar S. Adv Neural Inf Process Syst 21: 593-600, 2008; Ostry DJ, Darainy M, Mattar AA, Wong J, Gribble PL. J Neurosci 30: 5384-5393, 2010; Vahdat S, Darainy M, Milner TE, Ostry DJ. J Neurosci 31: 16907-16915, 2011). Here, we tested whether motor learning could be improved by providing subjects with proprioceptive training on a desired hand trajectory. Subjects were instructed to reproduce both the time-varying position and velocity of novel, complex hand trajectories. Subjects underwent 3 days of training with 90 movement trials per day. Active movement trials were interleaved with demonstration trials. For control subjects, these interleaved demonstration trials consisted of visual demonstration alone. A second group of subjects received visual and proprioceptive demonstration simultaneously; this group was presented with the same visual stimulus, but, in addition, their limb was moved through the target trajectory by a robot using servo control. Subjects who experienced the additional proprioceptive demonstration of the desired trajectory showed greater improvements during training movements than control subjects who only received visual information. This benefit of adding proprioceptive training was seen in both movement speed and position error. Interestingly, additional control subjects who received proprioceptive guidance while actively moving their arm during demonstration trials did not show the same improvement in positional accuracy. These findings support the idea that the addition of proprioceptive training can augment motor learning, and that this benefit is greatest when the subject passively experiences the goal movement.

Control of position and movement is simplified by combined muscle spindle and Golgi tendon organ feedback

Whereas muscle spindles play a prominent role in current theories of human motor control, Golgi tendon organs (GTO) and their associated tendons are often neglected. This is surprising since there is ample evidence that both tendons and GTOs contribute importantly to neuromusculoskeletal dynamics. Using detailed musculoskeletal models, we provide evidence that simple feedback using muscle spindles alone results in very poor control of joint position and movement since muscle spindles cannot sense changes in tendon length that occur with changes in muscle force. We propose that a combination of spindle and GTO afferents can provide an estimate of muscle-tendon complex length, which can be effectively used for low-level feedback during both postural and movement tasks. The feasibility of the proposed scheme was tested using detailed musculoskeletal models of the human arm. Responses to transient and static perturbations were simulated using a 1-degree-of-freedom (DOF) model of the arm and showed that the combined feedback enabled the system to respond faster, reach steady state faster, and achieve smaller static position errors. Finally, we incorporated the proposed scheme in an optimally controlled 2-DOF model of the arm for fast point-to-point shoulder and elbow movements. Simulations showed that the proposed feedback could be easily incorporated in the optimal control framework without complicating the computation of the optimal control solution, yet greatly enhancing the systems response to perturbations. The theoretical analyses in this study might furthermore provide insight about the strong physiological couplings found between muscle spindle and GTO afferents in the human nervous system.

A model of open-loop control of equilibrium position and stiffness of the human elbow joint

According to the equilibrium point theory, the control of posture and movement involves the setting of equilibrium joint positions (EP) and the independent modulation of stiffness. One model of EP control, the α-model, posits that stable EPs and stiffness are set open-loop, i.e. without the aid of feedback. The purpose of the present study was to explore for the elbow joint the range over which stable EPs can be set open-loop and to investigate the effect of co-contraction on intrinsic low-frequency elbow joint stiffness (Kilf). For this purpose, a model of the upper and lower arm was constructed, equipped with Hill-type muscles. At a constant neural input, the isometric force of the contractile element of the muscles depended on both the myofilamentary overlap and the effect of sarcomere length on the sensitivity of myofilaments to [Ca2+] (LDCS). The musculoskeletal model, for which the parameters were chosen carefully on the basis of physiological literature, captured the salient isometric properties of the muscles spanning the elbow joint. It was found that stable open-loop EPs could be achieved over the whole range of motion of the elbow joint and that Kilf, which ranged from 18 to 42 N m·rad−1, could be independently controlled. In the model, LDCS contributed substantially to Kilf (up to 25 N m·rad−1) and caused Kilf to peak at a sub-maximal level of co-contraction.

Bimanual proprioception: are two hands better than one?

Information about the position of an object that is held in both hands, such as a golf club or a tennis racquet, is transmitted to the human central nervous system from peripheral sensors in both left and right arms. How does the brain combine these two sources of information? Using a robot to move participants passive limbs, we performed psychophysical estimates of proprioceptive function for each limb independently and again when subjects grasped the robot handle with both arms. We compared empirical estimates of bimanual proprioception to several models from the sensory integration literature: some that propose a combination of signals from the left and right arms (such as a Bayesian maximum-likelihood estimate), and some that propose using unimanual signals alone. Our results are consistent with the hypothesis that the nervous system both has knowledge of and uses the limb with the best proprioceptive acuity for bimanual proprioception. Surprisingly, a Bayesian model that postulates optimal combination of sensory signals could not predict empirically observed bimanual acuity. These findings suggest that while the central nervous system seems to have information about the relative sensory acuity of each limb, it uses this information in a rather rudimentary fashion, essentially ignoring information from the less reliable limb.

The cost of moving optimally: kinematic path selection

It is currently unclear whether the brain plans movement kinematics explicitly or whether movement paths arise implicitly through optimization of a cost function that takes into account control and/or dynamic variables. Several cost functions are proposed in the literature that are very different in nature (e.g., control effort, torque change, and jerk), yet each can predict common movement characteristics. We set out to disentangle predictions of the different variables using a combination of modeling and empirical studies. Subjects performed goal-directed arm movements in a force field (FF) in combination with visual perturbations of seen hand position. This FF was designed to have distinct optimal movements for muscle-input and dynamic costs while leaving kinematic cost unchanged. Visual perturbations in turn changed the kinematic cost but left the dynamic and muscle-input costs unchanged. An optimally controlled, physiologically realistic arm model was used to predict movements under the various cost variables. Experimental results were not consistent with a cost function containing any of the control and dynamic costs investigated. Movement patterns of all experimental conditions were adequately predicted by a kinematic cost function comprising both visually and somatosensory perceived jerk. The present study provides clear behavioral evidence that the brain solves kinematic and mechanical redundancy in separate steps: in a first step, movement kinematics are planned; and in a second, separate step, muscle activation patterns are generated.

In Vivo Dynamics of the Musculoskeletal System Cannot Be Adequately Described Using a Stiffness-Damping-Inertia Model

Background Visco-elastic properties of the (neuro-)musculoskeletal system play a fundamental role in the control of posture and movement. Often, these properties are described and identified using stiffness-damping-inertia (KBI) models. In such an approach, perturbations are applied to the (neuro-)musculoskeletal system and subsequently KBI-model parameters are optimized to obtain a best fit between simulated and experimentally observed responses. Problems with this approach may arise because a KBI-model neglects critical aspects of the real musculoskeletal system. Methodology/Principal Findings The purpose of this study was to analyze the relation between the musculoskeletal properties and the stiffness and damping estimated using a KBI-model, to analyze how this relation is affected by the nature of the perturbation and to assess the sensitivity of the estimated stiffness and damping to measurement errors. Our analyses show that the estimated stiffness and damping using KBI-models do not resemble any of the dynamical parameters of the underlying system, not even when the responses are very accurately fitted by the KBI-model. Furthermore, the stiffness and damping depend non-linearly on all the dynamical parameters of the underlying system, influenced by the nature of the perturbation and the time interval over which the KBI-model is optimized. Moreover, our analyses predict a very high sensitivity of estimated parameters to measurement errors. Conclusions/Significance The results of this study suggest that the usage of stiffness-damping-inertia models to investigate the dynamical properties of the musculoskeletal system under control by the CNS should be reconsidered.

Catching fly balls: a simulation study of the Chapman strategy.

Chapman [Chapman, S. (1968). Catching a baseball. American Journal of Physics, 36, 868-870] showed that a catcher may be guided to the landing spot of a fly ball by zeroing out its optical acceleration. Subsequently, various studies have provided evidence for what is now known as the Chapman strategy. However, in those studies the catchers own acceleration and the visuo-motor delay were ignored. This raises the question whether the Chapman strategy still provides an accurate description if those factors are taken into account. To address this question, we implemented the Chapman strategy in a forward dynamical model of the catchers locomotion in relation to the balls actual trajectory. Numerical simulations of the model revealed that catching performance was still successful under a broad range of ball trajectories. Furthermore, the model simulations largely reproduced the real running paths reported by McLeod and Dienes [McLeod, P., & Dienes, Z. (1996). Do fielders know where to go to catch the ball or only how to get there? Journal of Experimental Psychology: Human Perception and performance, 22, 531-543]. However, the simulations also revealed that real running paths exhibit some detailed characteristics that appear to be irreconcilable with the Chapman strategy.

Optimizing the Distribution of Leg Muscles for Vertical Jumping.

A goal of biomechanics and motor control is to understand the design of the human musculoskeletal system. Here we investigated human functional morphology by making predictions about the muscle volume distribution that is optimal for a specific motor task. We examined a well-studied and relatively simple human movement, vertical jumping. We investigated how high a human could jump if muscle volume were optimized for jumping, and determined how the optimal parameters improve performance. We used a four-link inverted pendulum model of human vertical jumping actuated by Hill-type muscles, that well-approximates skilled human performance. We optimized muscle volume by allowing the cross-sectional area and muscle fiber optimum length to be changed for each muscle, while maintaining constant total muscle volume. We observed, perhaps surprisingly, that the reference model, based on human anthropometric data, is relatively good for vertical jumping; it achieves 90% of the jump height predicted by a model with muscles designed specifically for jumping. Alteration of cross-sectional areas—which determine the maximum force deliverable by the muscles—constitutes the majority of improvement to jump height. The optimal distribution results in large vastus, gastrocnemius and hamstrings muscles that deliver more work, while producing a kinematic pattern essentially identical to the reference model. Work output is increased by removing muscle from rectus femoris, which cannot do work on the skeleton given its moment arm at the hip and the joint excursions during push-off. The gluteus composes a disproportionate amount of muscle volume and jump height is improved by moving it to other muscles. This approach represents a way to test hypotheses about optimal human functional morphology. Future studies may extend this approach to address other morphological questions in ethological tasks such as locomotion, and feature other sets of parameters such as properties of the skeletal segments.

Inverse dynamics of mechanical multibody systems: An improved algorithm that ensures consistency between kinematics and external forces

Inverse dynamics is a technique in which measured kinematics and, possibly, external forces are used to calculate net joint torques in a rigid body linked segment model. However, kinematics and forces are usually not consistent due to incorrect modelling assumptions and measurement errors. This is commonly resolved by introducing ‘residual forces and torques’ which compensate for this problem, but do not exist in reality. In this study a constrained optimization algorithm is proposed that finds the kinematics that are mechanically consistent with measured external forces and mimic the measured kinematics as closely as possible. The algorithm was tested on datasets containing planar kinematics and ground reaction forces obtained during human walking at three velocities (0.8 m/s, 1.25 and 1.8 m/s). Before optimization, the residual force and torque were calculated for a typical example. Both showed substantial values, indicating the necessity of developing a mechanically consistent algorithm. The proposed optimization algorithm converged to a solution in which the residual forces and torques were zero, without changing the ground reaction forces and with only minor changes to the measured kinematics. When using a rigid body approach, our algorithm ensures a consistent description of forces and kinematics, thereby improving the validity of calculated net joint torque and power values.