Optimal trajectory formation of constrained human arm reaching movements

Opening a door, turning a steering wheel, and rotating a coffee mill are typical examples of human movements that are constrained by the physical environment. The constraints decrease the mobility of the human arm and lead to redundancy in the distribution of actuator forces (either joint torques or muscle forces). Due to this actuator redundancy, there is an infinite number of ways to form a specific arm trajectory. However, humans form trajectories in a unique way. How do humans resolve the redundancy of the constrained motions and specify the hand trajectory? To investigate this problem, we examine human arm movements in a crank-rotation task. To explain the trajectory formation in constrained point-to-point motions, we propose a combined criterion minimizing the hand contact force change and the actuating force change over the course of movement. Our experiments show a close matching between predicted and experimental data.     

Temperature-dependent viscoelastic properties of the human supraspinatus tendon

Temperature effects on the viscoelastic properties of the human supraspinatus tendon were investigated using static stress-relaxation experiments and the quasi-linear viscoelastic (QLV) theory. Twelve supraspinatus tendons were randomly assigned to one of two test groups for tensile testing using the following sequence of temperatures: (1) 37, 27, and 17 °C (Group I, n=6), or (2) 42, 32, and 22 °C (Group II, n=6). QLV parameter C was found to increase at elevated temperatures, suggesting greater viscous mechanical behavior at higher temperatures. Elastic parameters A and B showed no significant difference among the six temperatures studied, implying that the viscoelastic stress response of the supraspinatus tendon is not sensitive to temperature over shorter testing durations. Using regression analysis, an exponential relationship between parameter C and test temperature was implemented into QLV theory to model temperature-dependent viscoelastic behavior. This modified approach facilitates the theoretical determination of the viscoelastic behavior of tendons at arbitrary temperatures.     

Three-dimensional model to predict muscle forces and their relation to motor variances in reaching arm movements

A three-dimensional (3-D) arm movement model is presented to simulate kinematic properties and muscle forces in reaching arm movements. Healthy subjects performed reaching movements repetitively either with or without a load in the hand. Joint coordinates were measured. Muscle moment arms, 3-D angular acceleration, and moment of inertias of arm segments were calculated to determine 3-D joint torques. Variances of hand position, arm configuration, and muscle activities were calculated. Ratios of movement variances observed in the two conditions (load versus without load) showed no differences for hand position and arm configuration variances. Virtual muscle force variances for all muscles except deltoid posterior and EMG variances for four muscles increased significantly by moving with the load. The greatly increased variances in muscle activity did not imply equally high increments in kinematic variances. We conclude that enhanced muscle cooperation through synergies helps to stabilize movement at the kinematic level when a load is added.     

Measuring the viscoelastic properties of human platelets with the atomic force microscope.

We have measured force curves as a function of the lateral position on top of human platelets with the atomic force microscope. These force curves show the indentation of the cell as the tip loads the sample. By analyzing these force curves we were able to determine the elastic modulus of the platelet with a lateral resolution of approximately 100 nm. The elastic moduli were in a range of 1-50 kPa measured in the frequency range of 1-50 Hz. Loading forces could be controlled with a resolution of 80 pN and indentations of the platelet could be determined with a resolution of 20 nm.     

Some viscoelastic properties of human erythrocyte spectrin networks end-linked in vitro

We have succeeded in making macroscopic networks of end-linked human erythrocyte spectrin. The network junctions were made using erythrocyte protein 4.1 irreversibly attached to 5 nm (diameter) colloidal gold particles. Rotary shadowing electron microscopy verifies that the protein 4.1-labelled colloidal gold particles bind only to the tail end of the spectrin molecules. Electron micrographs of protein 4.1-labelled colloidal gold particles incubated at 4 degrees C with spectrin dimers reveal that 1-5 spectrin dimers attach to each protein 4.1-labelled colloidal gold particle yielding a spider-like appearance of these complexes. Incubation with a low concentration of spectrin tetramers instead of dimers leads to extensive formation of spectrin microaggregates whereas use of spectrin concentrations higher than 3 mg/ml and a molar ratio between spectrin tetramers and protein 4.1/Au of 4 leads to formation of macroscopic spectrin networks. We have quantitated the viscoelastic properties of such end-linked macroscopic spectrin networks using a gravitational pendulum viscoelastometer. We find that in vitro end-linked spectrin networks can be described by linear viscoelastic theory. The dynamic storage modulus increases almost linearly with the spectrin-protein 4.1/gold particle concentration when the spectrin concentration exceeds about 3 mg/ml and the molar ratio between spectrin tetramers and protein 4.1/Au is 4. At a spectrin concentration of 6 mg/ml and the same ratio between spectrin and protein 4.1/Au, we find a dynamic storage modulus at low frequency of about 80 dyn/cm2. This is in adequate agreement with what is predicted by simple elastomer theory.     

Relation between object properties and EMG during reaching to grasp

In order to stably grasp an object with an artificial hand, a priori knowledge of the object’s properties is a major advantage, especially to ensure subsequent manipulation of the object held by the hand. This is also true for hand prostheses: pre-shaping of the hand while approaching the object, similar to able-bodied, allows the wearer for a much faster and more intuitive way of handling and grasping an object. For hand prostheses, it would be advantageous to obtain this information about object properties from a surface electromyography (sEMG) signal, which is already present and used to control the active prosthetic hand.We describe experiments in which human subjects grasp different objects at different positions while their muscular activity is recorded through eight sEMG electrodes placed on the forearm. Results show that sEMG data, gathered before the hand is in contact with the object, can be used to obtain relevant information on object properties such as size and weight.     

A comparison of contractile properties in human arm and leg muscles

Isometric twitch properties have been compared in two pairs of opposing human limb muscles; these were the brachial biceps and triceps, and the anterior tibial and plantarflexor muscles. All four muscles were examined in each of 24 healthy subjects (16 men and 8 women). The brachial triceps had the shortest contraction and half-relaxation times and the greatest twitch potentiation, while the plantarflexors had the most prolonged twitches and least potentiation; the anterior tibial and brachial biceps muscles had similar characteristics. Susceptibility to fatigue was less in the plantarflexors than in the other three muscles. When muscles were assessed without reference to their anatomical sites, a significant relationship was noted between contraction time and potentiation, but not between either of these features and fatiguability. There was no evidence that muscles were uniformly 'faster' or 'slower' in some subjects than in others.     

Learning the dynamics of reaching movements results in the modification of arm impedance and long-latency perturbation responses

 Some characteristics of arm movements that humans exhibit during learning the dynamics of reaching are consistent with a theoretical framework where training results in motor commands that are gradually modified to predict and compensate for novel forces that may act on the hand. As a first approximation, the motor control system behaves as an adapting controller that learns an internal model of the dynamics of the task. It approximates inverse dynamics and predicts motor commands that are appropriate for a desired limb trajectory. However, we had previously noted that subtle motion characteristics observed during changes in task dynamics challenged this simple model and raised the possibility that adaptation also involved sensory–motor feedback pathways. These pathways reacted to sensory feedback during the course of the movement. Here we hypothesize that adaptation to dynamics might also involve a modification of how the CNS responds to sensory feedback. We tested this through experiments that quantified how the motor system's response to errors during voluntary movements changed as it adapted to dynamics of a force field. We describe a nonlinear approach that approximates the impedance of the arm, i.e., force response as a function of arm displacement trajectory. We observe that after adaptation, the impedance function changes in a way that closely matches and counters the effect of the force field. This is particularly prominent in the long-latency (>100 ms) component of response to perturbations. Therefore, it appears that practice not only modifies the internal model with which the brain generates motor commands that initiate a movement, but also the internal model with which sensory feedback is integrated with the ongoing descending commands in order to respond to error during the movement. Received: 10 January 2001 / Accepted in revised form: 30 May 2001     

Effect of muscle fatigue on internal model formation and retention during reaching with the arm.

The motor system adapts to novel dynamic environments by forming internal models that predict the muscle forces needed to move skillfully. The goal of this study was to determine how muscle fatigue affects internal model formation during arm movement and whether an internal model acquired while fatigued could be recalled accurately after rest. Twelve subjects adapted to a viscous force field applied by a lightweight robot as they reached to a target. They then reached while being resisted by elastic bands until they could no longer touch the target. This protocol reduced the strength of the muscles used to resist the force field by approximately 20%. The bands were removed, and subjects adapted again to the viscous force field. Their adaptive ability, quantified by the amount and time constant of adaptation, was not significantly impaired following fatigue. The subjects then rested, recovering approximately 70% of their lost force-generation ability. When they reached in the force field again, their prediction of the force field strength was different than in a nonfatigued state. This alteration was consistent with the use of a higher level of effort than normally used to counteract the force field. These results suggest that recovery from fatigue can affect recall of an internal model, even when the fatigue did not substantially affect the motor system's ability to form the model. Recovery from fatigue apparently affects recall because the motor system represents internal models as a mapping between effort and movement and relies on practice to recalibrate this mapping.     

Effect of stretching training on the viscoelastic properties of human tendon structures in vivo.

The purpose of this study was to examine whether stretching training altered the viscoelastic properties of human tendon structures in vivo. Eight men performed the stretching training for 3 wk. Before and after the stretching training, the elongation of the tendon and aponeurosis of medial gastrocnemius muscle was directly measured by ultrasonography while the subjects performed ramp isometric plantar flexion up to the voluntary maximum, followed by a ramp relaxation. The relationship between the estimated muscle force (Fm) and tendon elongation (L) during the ascending phase was fitted to a linear regression, the slope of which was defined as stiffness of tendon structures. The percentage of the area within the Fm-L loop to the area beneath the curve during ascending phase was calculated as an index representing hysteresis. To assess the flexibility, the passive torque of the plantar flexor muscles was measured during the passive stretch from 0 degrees (anatomic position) to 25 degrees of dorsiflexion with a constant velocity of 5 degrees/s. The slope of the linear portion of the passive torque-angle curve during stretching was defined as flexibility index. Flexibility index decreased significantly after stretching training (-13.4 +/- 4.6%). On the other hand, the stretching training produced no significant change in stiffness but significantly decreased hysteresis from 19.9 +/- 11.7 to 12.5 +/- 9.5%. The present results suggested that stretching training affected the viscosity of tendon structures but not the elasticity.     

Experimental study and constitutive modeling of the viscoelastic mechanical properties of the human prolapsed vaginal tissue

In this paper, the viscoelastic mechanical properties of vaginal tissue are investigated. Using previous results of the authors on the mechanical properties of biological soft tissues and newly experimental data from uniaxial tension tests, a new model for the viscoelastic mechanical properties of the human vaginal tissue is proposed. The structural model seems to be sufficiently accurate to guarantee its application to prediction of reliable stress distributions, and is suitable for finite element computations. The obtained results may be helpful in the design of surgical procedures with autologous tissue or prostheses.     

Changes to the viscoelastic properties of brain tissue after traumatic axonal injury

While it has been shown that repetitive mild brain injuries can cause cumulative damage to the brain, changes to the mechanical properties of brain tissue at large deformations were also noted in the literature. The goal of this study was to show that the viscoelastic properties of brain tissue significantly change after traumatic axonal injury (TAI). An impact acceleration model was used to create TAI in the rat brainstem which was quantified with an immunohistochemistry technique at the ponto-medullary junction (PmJ) and pyramidal decussation (PDx). The viscoelastic properties at these two points with and without preconditioning were characterized using an indentation technique combined with finite element analysis and a comparison was made between injured and uninjured specimens, which revealed statistically significant reduction in the instantaneous elastic force at PDx where the brain tissue sustained a significantly higher level of injury. The result of this study can be used to characterize a damage function for the brain tissue undergoing large deformation.     

Dynamic measurement of the viscoelastic properties of skin

A wave propagation technique was used to measure the dynamic viscoelastic properties of excised skin when subjected to a low incremental strain. The propagation velocity, attenuation, and storage and loss moduli were determined from measured characteristics of a pulse propagating along a strip of skin. Experiments were conducted with the skin subjected to static stresses of 1500 Pa and 20,000 Pa. At low static stresses the skin response was viscoelastic with a loss tangent of approximately 0.6. In the frequency range of 0-1000 Hz, the wave velocity was relatively constant while the attenuation increased roughly linearly with frequency. However, results depended on the static stress. At the higher stress level the velocity was greater and the attenuation less than at the lower stress. At low stresses both the storage and loss moduli were relatively constant over the frequency range tested. The strong viscoelastic behavior of the tissue at higher frequencies is not predicted from models of the tissue determined from quasi-static test methods. In selecting a model to describe the behavior of skin, the test methods used for establishing the model must be consistent with its intended application.     

Invertebrate neurobiology: visual direction of arm movements in an octopus

An operant task in which octopuses learn to locate food by a visual cue in a three-choice maze shows that they are capable of integrating visual and mechanosensory information to direct their arm movements to a goal.     

Effect of arm swing direction on forward and backward jump performance

This study quantified and compared how the directional differences in arm swing affected mechanical and physiological parameters during forward and backward jumping. Seven subjects maximally performed three types of forward and backward squat jumps-no arm swing (FJ, BJ), forward arm swing (FJF, BJF), and backward arm swing (FJB, BJB) from a force platform. All performances were captured with a 3-D motion capture system. Electromyograms (EMGs) of the lower extremity muscles were obtained. Variables were calculated by combining kinematic and kinetic data. The jump displacement and center of mass velocity at take-off were significantly larger in FJF than in FJ or FJB and larger in BJB than in BJ or BJF, suggesting that the best performance was obtained by employing the same arm swing direction as a given jump direction. The total work by three lower and two upper extremity joints was significantly larger in FJF than in FJ or FJB and larger in BJB than in BJ or BJF. For the lower extremity joints, hip work was the greatest in FJF and BJB. The integrated EMG of the biceps femoris when the hip power was produced was significantly larger in FJF and BJB than under other conditions. These results suggest that if the arm swing direction is the same as a given jump direction, the activation level of the hip extensor is greater to counter large loads which make the hip joint flex during the push-off phase, which result in increased hip extension torque, power, and work.     

A method for measuring linearly viscoelastic properties of human tympanic membrane using nanoindentation

A viscoelastic nanoindentation technique was developed to measure both in-plane and through-thickness viscoelastic properties of human tympanic membrane (TM). For measurement of in-plane Young's relaxation modulus, the TM sample was clamped on a circular hole and a nanoindenter tip was used to apply a concentrated force at the center of the TM sample. In this setup, the resistance to nanoindentation displacement can be considered due primarily to the in-plane stiffness. The load-displacement curve obtained was used along with finite element analysis to determine the in-plane viscoelastic properties of TM. For measurements of Young's relaxation modulus in the through-thickness (out-of-plane) direction, the TM sample was placed on a relatively rigid solid substrate and nanoindentation was made on the sample surface. In this latter setup, the resistance to nanoindentation displacement arises primarily due to out-of-plane stiffness. The load-displacement curve obtained in this manner was used to determine the out-of-plane relaxation modulus using the method appropriate for viscoelastic materials. From our sample tests, we obtained the steady-state values for in-plane moduli as approximately 17.4 MPa and approximately 19.0 MPa for posterior and anterior portions of TM samples, respectively, and the value for through-thickness modulus as approximately 6.0 MPa for both posterior and anterior TM samples. Using this technique, the local out-of-plane viscoelastic modulus can be determined for different locations over the entire TM, and the in-plane properties can be determined for different quadrants of the TM.