Endpoint Force Research Articles

Extraction of Individual Muscle Mechanical Action From Endpoint Force

Most motor tasks require the simultaneous coordination of multiple muscles. That coordination is poorly understood in part because there is no noninvasive means of isolating a single muscle's contribution to the resultant endpoint force. The contribution of a single motor unit to isometric tasks can, however, be characterized using the spike-triggered averaging (STA) technique, applied to a single motor unit's spike train. We propose that a technique analogous to STA, which we call electromyogram (EMG)-weighted averaging (EWA), can be applied to surface EMGs to extract muscle mechanical action from the natural endpoint force fluctuations generated during steady isometric contraction. We demonstrate this technique on simultaneous recordings of fingertip force and surface EMG from the first dorsal interosseous (FDI) and extensor indicis (EI) of humans. The EWA direction was approximately the same across a wide range of fingertip force directions, and the average EWA direction was consistent with mechanical action direction of these muscles estimated from cadaveric and imaging data: the EWA directions were 193 +/- 2 degrees for the FDI and 71 +/- 5 degrees for the EI (95% confidence). EWA transient behavior also appears to capture temporal characteristics of muscle force fluctuations with peak force time and general waveform shape similar to that of the associated spike-triggered averages from single motor units. The EWA may provide a means of empirically characterizing the complex transformation between muscle force and endpoint force without the need for invasive electrode recordings or complex anatomical measurements of musculoskeletal geometry.

The sensitivity of endpoint forces produced by the extrinsic muscles of the thumb to posture

This study utilizes a biomechanical model of the thumb to estimate the force produced at the thumb-tip by each of the four extrinsic muscles. We used the principle of virtual work to relate joint torques produced by a given muscle force to the resulting endpoint force and compared the results to two separate cadaveric studies. When we calculated thumb-tip forces using the muscle forces and thumb postures described in the experimental studies, we observed large errors. When relatively small deviations from experimentally reported thumb joint angles were allowed, errors in force direction decreased substantially. For example, when thumb posture was constrained to fall within ±15° of reported joint angles, simulated force directions fell within experimental variability in the proximal–palmar plane for all four muscles. Increasing the solution space from ±1° to an unbounded space produced a sigmoidal decrease in error in force direction. Changes in thumb posture remained consistent with a lateral pinch posture, and were generally consistent with each muscle’s function. Altering thumb posture alters both the components of the Jacobian and muscle moment arms in a nonlinear fashion, yielding a nonlinear change in thumb-tip force relative to muscle force. These results explain experimental data that suggest endpoint force is a nonlinear function of muscle force for the thumb, support the continued use of methods that implement linear transformations between muscle force and thumb-tip force for a specific posture, and suggest the feasibility of accurate prediction of lateral pinch force in situations where joint angles can be measured accurately.

722 表面筋電位を用いた手先力推定に基づく力覚提示装置の制御法(GS-15 システム制御)

722 表面筋電位を用いた手先力推定に基づく力覚提示装置の制御法(GS-15 システム制御)

2P1-E14 筋骨格モデルを基にした擾乱による手先力変化からの筋活動度の推定法

To analyze dexterous manipulation by a human hand, activation levels of finger muscles should be estimated. Surface EMG is a possible way to measure them in a noninvasive manner, but cross-talk problem must be solved by identifying a relationship between the EMGs and the actual activation levels. In order to identify this relationship, this paper proposes a method to estimate muscle activation levels based on the musculoskeletal model. Considering the muscle tension variation property, the activation levels are estimated from the observed end-point force in two different states, a static one and a dynamic one triggered by a disturbance. To verify the proposed method, an experiment is conducted and elbow joint is chosen as a target. The actual activation levels are directly measured by EMGs and compared to the estimated levels by the proposed method. The results show that the proposed method can estimate the activation levels without using EMGs.

Differences in End-Point Force Trajectories Elicited by Electrical Stimulation of Individual Human Calf Muscles

The purpose of this study was to investigate the end-point force trajectories of the fibularis longus (FIB), lateral gastrocnemius (LG), and medial gastrocnemius (MG) muscles. Most information about individual muscle function has come from studies that use models based on electromyographic (EMG) recordings. In this study (N = 20 subjects) we used electrical stimulation (20 Hz) to elicit activity in individual muscles, recorded the end-point forces at the foot, and verified the selectivity of stimulation by using magnetic resonance imaging. Unexpectedly, no significant differences were found between LG and MG force directions. Stimulation of LG and MG resulted in downward and medial or lateral forces depending on the subject. We found FIB end-point forces to be significantly different from those of LG and MG. In all subjects, stimulation of FIB resulted in downward and lateral forces. Based on our results, we suggest that there are multiple factors determining when and whether LG or MG will produce a medial or lateral force and FIB consistently plays a significant role in eversion/abduction and plantar flexion. We suggest that the intersubject variability we found is not simply an artifact of experimental or technical error but is functionally relevant and should be addressed in future studies and models.

Force Transmission Through a Structurally Flexible Beam: Dynamic Modeling and Feedback Control

This paper studies the control of end-point force in a constrained flexible beam actuated at the hub. To this end, transfer functions are obtained from the torque input at the hub to shear-force outputs along the link in a pinned-pinned configuration. The force output is selected to vary continuously on the beam from hub to tip. It is shown that these outputs exhibit strictly nonminimum-phase behavior. Formulas are derived for dominant zeros which yield upper limits on achievable closed-loop control bandwidths for force control at the end point of the link. A parameterized force output which exhibits marginally minimum phase behavior is obtained, and its control bandwidth is investigated. The performance of a redefined output force controller is further studied using numerical simulations and experiments.

Should the neural–mechanical behaviour of a muscle be coupled or co‐vary?

muscle (FDI) of the hand. By using this particular muscle, the authors were able to circumvent many of the limitations traditionally associated with making the neural‐mechanical comparisons at joints controlled by many muscles. The results from that study led the authors to conclude that the neural drive to the FDI muscle and the mechanical advantage of the muscle are coupled when the thumb changes position. The remainder of this note will focus on the impact of the study and the interpretation of the results, specifically with regard to whether the neural drive to the muscle and the muscle mechanics should co-vary or be coupled when performing motor tasks. The study by Hudson et al. (2009) recorded end-point forces produced (i) by ulnar nerve stimulation and (ii) during static index finger flexion efforts, with the thumb positioned in a number of ‘thumb up’ and ‘thumb down’ postures. Although a seemingly minor postural adjustment, ulnar nerve stimulation resulted in a 60% larger end-point twitch force in the thumb down position compared to thumb up. Furthermore, ultrasound results indicated that, relative to thumb up, the thumb down posture caused a 65% increase in the distance between the FDI tendon and the lateral tubercle of the second metacarpal, which was used to estimate FDI moment arm magnitude. Thus, the mechanical advantage for FDI force transmission across the metacarpophalangeal (MCP) joint was significantly increased with the thumb down, regardless of muscle force. Based on the mechanics, end-point force is directly proportional to the MCP joint torque, via the geometric configuration of the system. In other words, sincetheindexfingerwassplintedandMCP jointangleremainedconstant,momentarm magnitude was the main geometric factor determining how effectively FDI muscle force was transformed into end-point force. The end-point forces generated by supramaximal ulnar nerve stimulation (i.e. constant neural input) illustrate the proportionality between MCP joint torque and end-point force (a 65% increase in moment arm → 60% increase in end-point force). However, the mechanics are only one aspect of generating joint torques. Can, or does, the central nervous system

Hindlimb Endpoint Forces Predict Movement Direction Evoked by Intraspinal Microstimulation in Cats

We measured the forces produced at the cat's hindpaw by microstimulation of the lumbar spinal cord and the movements resulting from those forces. We also measured the forces and movements produced by co- and sequential activation of two intraspinal sites. Isometric force responses were measured at nine limb configurations with the paw attached to a force transducer. The active forces elicited at different limb configurations were summarized as patterns representing the sagittal plane component of the forces produced at the paw throughout the workspace. The force patterns divided into the same distinct types found with the femur fixed. The responses during simultaneous activation of two spinal sites always resembled the response for activation of one of the two sites, i.e., winner-take-all, and we did not observe vectorial summation of the forces produced by activation of each site individually as reported in chronic spinal animals. The movements produced by activation of each of the sites were consistent with the force orientations, and different movements could be created by varying the sequence of activation of individual sites. Our results highlight the absence of a vectorial summation phenomenon during intraspinal microstimulation in decerebrate animals, and the preservation during movement of the orientation of isometric forces.

Offline Decoding of End-Point Forces Using Neural Ensembles: Application to a Brain–Machine Interface

Brain-machine interfaces (BMIs) hold a lot of promise for restoring some level of motor function to patients with neuronal disease or injury. Current BMI approaches fall into two broad categories--those that decode discrete properties of limb movement (such as movement direction and movement intent) and those that decode continuous variables (such as position and velocity). However, to enable the prosthetic devices to be useful for common everyday tasks, precise control of the forces applied by the end-point of the prosthesis (e.g., the hand) is also essential. Here, we used linear regression and Kalman filter methods to show that neural activity recorded from the motor cortex of the monkey during movements in a force field can be used to decode the end-point forces applied by the subject successfully and with high fidelity. Furthermore, the models exhibit some generalization to novel task conditions. We also demonstrate how the simultaneous prediction of kinematics and kinetics can be easily achieved using the same framework, without any degradation in decoding quality. Our results represent a useful extension of the current BMI technology, making dynamic control of a prosthetic device a distinct possibility in the near future.

Robot-amplified manual exploration improves load identification.

We tested how manual exploration with anisotropic loading (Viscosity-Only (negative), Inertia-Only, or Combined-Load) influenced skill transfer to the isolated inertial load. Intact subjects (N=39) performed manual exploration with an anisotropic load before evaluation with prescribed circular movements. Combined-Load resulted in lower error (6.89±3.25%) compared to Inertia-Only (8.40±4.32%) and Viscosity-Only (8.17±4.13%) according to radial deviation analysis (% of trial mean radius). An analysis of sensitivity to load variation in normal and catch trials reveals performance differences were likely due to changes in feedforward mass compensation. Analysis of exploration movement revealed higher average speeds (12.0%) and endpoint forces (22.9%) with Combined-Load exploration compared to Inertia-Only. Our findings suggest that free movements amplified by negative viscosity can enhance the ability to identify changes in inertial loading.

Task-Space Iterative Learning for Redundant Robots: Simultaneous Acquirements of Desired Motion and Force Trajectories under Constraints

Abstract This paper focuses on iterative learning control (ILC) for multi-joint robots with redundancy in degrees of freedom (DOFs) when task descriptions are given only in task-space. The specified task is of precise tracking of both endpoint position and force trajectories given on the plane by a five-DOF robot arm whose endpoint contacts with a plane during motion. Even in the case of twice continuously differentiable desired motion and force trajectories given only in task-space, it is possible to construct a learning update law in task-space by using the desired trajectories together with measured data correspond to them. The convergence of trajectory tracking under constraints by the proposed task space ILC is proved theoretically on the basis of nonlinear robot dynamics with DOF-redundancy.

Torque Interaction among Adjacent Joints due to the Action of Biarticular Muscles

In our musculoskeletal system, multiple muscles are involved in the generation of torque about a joint. Hence, an infinite number of combinations of muscle activities may exist in producing a certain amount of joint torque. Many studies have assumed that the level of muscle activity level depends on torque about the joint it spans. However, this assumption does not hold true in the presence of biarticular muscles. Here we show that the muscle activity level is modulated according to a scheme called "cosine tuning" based on our experiment on the isometric force exerted by the lower limb, that is, the muscle activity about the knee and the hip joints can be represented by a linear summation of the knee and hip joint torques. This way of modulation is very simple, but it is unintuitive on the point that the activation level of the monoarticular muscles explicitly depends on the torque of the adjacent joint that they do not span. It is demonstrated that such nontrivial cosine tuning can be mathematically explained by assuming that the muscle activity pattern is determined so as to minimize the variability of the end point force. Finally, the implications of the cosine tuning for muscle strength training and motor control are discussed.

Modularity of Endpoint Force Patterns Evoked Using Intraspinal Microstimulation in Treadmill Trained and/or Neurotrophin-Treated Chronic Spinal Cats

Chronic spinal cats with neurotrophin-secreting fibroblasts (NTF) transplants recover locomotor function. To ascertain possible mechanisms, intraspinal microstimulation was used to examine the lumbar spinal cord motor output of four groups of chronic spinal cats: untrained cats with unmodified-fibroblasts graft (Op-control) or NTF graft and locomotor-trained cats with unmodified-fibroblasts graft (Trained) or NTF graft (Combination). Forces generated via intraspinal microstimulation at different hindlimb positions were recorded and interpolated, generating representations of force patterns at the paw. Electromyographs (EMGs) of hindlimb muscles, medial gastrocnemius, tibialis anterior, vastus lateralis, and biceps femoris posterior, were also collected to examine relationships between activated muscles and force pattern types. The same four force pattern types obtained in spinal-intact cats were found in chronic spinal cats. Proportions of force patterns in spinal cats differed significantly from those in intact cats, but no significant differences in proportions were observed among individual spinal groups (Op-control, NTF, Trained, and Combination). However, the proportions of force patterns differed significantly between trained (Trained and Combination) and untrained groups (Op-control and NTF). Thus the frequency of expression of some response types was modified by injury and to a lesser extent by training. Force pattern laminar distribution differed in spinal cats compared with intact, with more responses obtained dorsally (0-1,000 microm) and fewer ventrally (3,200-5,200 microm). EMG analysis demonstrated that muscle activity highly predicted some force pattern types and was independent of hindlimb position. We conclude that spinal motor output modularity is preserved after injury.

Endpoint force fluctuations reveal flexible rather than synergistic patterns of muscle cooperation.

We developed a new approach to investigate how the nervous system activates multiple redundant muscles by studying the endpoint force fluctuations during isometric force generation at a multi-degree-of-freedom joint. We hypothesized that, due to signal-dependent muscle force noise, endpoint force fluctuations would depend on the target direction of index finger force and that this dependence could be used to distinguish flexible from synergistic activation of the musculature. We made high-gain measurements of isometric forces generated to different target magnitudes and directions, in the plane of index finger metacarpophalangeal joint abduction-adduction/flexion-extension. Force fluctuations from each target were used to calculate a covariance ellipse, the shape of which varied as a function of target direction. Directions with narrow ellipses were approximately aligned with the estimated mechanical actions of key muscles. For example, targets directed along the mechanical action of the first dorsal interosseous (FDI) yielded narrow ellipses, with 88% of the variance directed along those target directions. It follows the FDI is likely a prime mover in this target direction and that, at most, 12% of the force variance could be explained by synergistic coupling with other muscles. In contrast, other target directions exhibited broader covariance ellipses with as little as 30% of force variance directed along those target directions. This is the result of cooperation among multiple muscles, based on independent electromyographic recordings. However, the pattern of cooperation across target directions indicates that muscles are recruited flexibly in accordance with their mechanical action, rather than in fixed groupings.

Use of intrinsic thumb muscles may help to improve lateral pinch function restored by tendon transfer

Background For surgical reconstruction of lateral pinch following tetraplegia, the function of the paralyzed flexor pollicis longus is commonly restored. The purpose of this study was to investigate if one of the intrinsic muscles could generate a more suitably directed thumb-tip force during lateral pinch than that of flexor pollicis longus. Methods Endpoint force resulting from 10 N applied to each thumb muscle was measured in eleven upper extremity cadaveric specimens. We utilized the Kruskal–Wallis test ( α = 0.05) to determine whether thumb-tip forces of intrinsic muscles were less directed toward the base of the thumb, i.e., proximally directed, than the thumb-tip force produced by flexor pollicis longus. Additionally, a biomechanical model was used to assess the effect of an increase in tendon force on intrinsic muscle endpoint forces. Findings All of the intrinsic muscles produced thumb-tip force vectors, ranging from 127° to 156°, that were significantly ( P < 0.009) less proximally directed than that of flexor pollicis longus (66° (46°)). A biomechanical model predicted that intrinsic muscle thumb-tip forces would vary non-linearly with tendon force. A 2-fold increase in tendon force produced, on average, a 2.3-fold increase in force magnitude and an 8° shift in force direction across all intrinsic muscles. Interpretation This study suggests the possibility of using an intrinsic muscle, e.g., the flexor pollicis brevis (ulnar head), instead of flexor pollicis longus, to produce a more advantageously directed thumb-tip force during lateral pinch in the surgically-reconstructed tetraplegic thumb and thus potentially enhance function.

Reduction of neuromuscular redundancy for postural force generation using an intrinsic stability criterion

Postural control requires the coordination of multiple muscles to achieve both endpoint force production and postural stability. Multiple muscle activation patterns can produce the required force for standing, but the mechanical stability associated with any given pattern may vary, and has implications for the degree of delayed neural feedback necessary for postural stability. We hypothesized that muscular redundancy is reduced when muscle activation patterns are chosen with respect to intrinsic musculoskeletal stability as well as endpoint force production. We used a three-dimensional musculoskeletal model of the cat hindlimb with 31 muscles to determine the possible contributions of intrinsic muscle properties to limb stability during isometric force generation. Using dynamic stability analysis we demonstrate that within the large set of activation patterns that satisfy the force requirement for posture, only a reduced subset produce a mechanically stable limb configuration. Greater stability in the frontal-plane suggests that neural control mechanisms are more highly active for sagittal-plane and for ankle joint control. Even when the limb was unstable, the time-constants of instability were sufficiently great to allow long-latency neural feedback mechanisms to intervene, which may be preferential for movements requiring maneuverability versus stability. Local joint stiffness of muscles was determined by the stabilizing or destabilizing effects of moment-arm versus joint angle relationships. By preferentially activating muscles with high local stiffness, muscle activation patterns with feedforward stabilizing properties could be selected. Such a strategy may increase intrinsic postural stability without co-contraction, and may be useful criteria in the force-sharing problem.

Visual Feedback Is Not Necessary for the Learning of Novel Dynamics

BackgroundWhen learning to perform a novel sensorimotor task, humans integrate multi-modal sensory feedback such as vision and proprioception in order to make the appropriate adjustments to successfully complete the task. Sensory feedback is used both during movement to control and correct the current movement, and to update the feed-forward motor command for subsequent movements. Previous work has shown that adaptation to stable dynamics is possible without visual feedback. However, it is not clear to what degree visual information during movement contributes to this learning or whether it is essential to the development of an internal model or impedance controller.Methodology/Principle FindingsWe examined the effects of the removal of visual feedback during movement on the learning of both stable and unstable dynamics in comparison with the case when both vision and proprioception are available. Subjects were able to learn to make smooth movements in both types of novel dynamics after learning with or without visual feedback. By examining the endpoint stiffness and force after learning it could be shown that subjects adapted to both types of dynamics in the same way whether they were provided with visual feedback of their trajectory or not. The main effects of visual feedback were to increase the success rate of movements, slightly straighten the path, and significantly reduce variability near the end of the movement.Conclusions/SignificanceThese findings suggest that visual feedback of the hand during movement is not necessary for the adaptation to either stable or unstable novel dynamics. Instead vision appears to be used to fine-tune corrections of hand trajectory at the end of reaching movements.

Functional muscle synergies constrain force production during postural tasks

We recently demonstrated that a set of five functional muscle synergies were sufficient to characterize both hindlimb muscle activity and active forces during automatic postural responses in cats standing at multiple postural configurations. This characterization depended critically upon the assumption that the endpoint force vector (synergy force vector) produced by the activation of each muscle synergy rotated with the limb axis as the hindlimb posture varied in the sagittal plane. Here, we used a detailed, 3D static model of the hindlimb to confirm that this assumption is biomechanically plausible: as we varied the model posture, simulated synergy force vectors rotated monotonically with the limb axis in the parasagittal plane ( r 2=0.94±0.08). We then tested whether a neural strategy of using these five functional muscle synergies provides the same force-generating capability as controlling each of the 31 muscles individually. We compared feasible force sets (FFSs) from the model with and without a muscle synergy organization. FFS volumes were significantly reduced with the muscle synergy organization ( F=1556.01, p≪0.01), and as posture varied, the synergy-limited FFSs changed in shape, consistent with changes in experimentally measured active forces. In contrast, nominal FFS shapes were invariant with posture, reinforcing prior findings that postural forces cannot be predicted by hindlimb biomechanics alone. We propose that an internal model for postural force generation may coordinate functional muscle synergies that are invariant in intrinsic limb coordinates, and this reduced-dimension control scheme reduces the set of forces available for postural control.

Explaining Patterns of Neural Activity in the Primary Motor Cortex Using Spinal Cord and Limb Biomechanics Models

What determines the specific pattern of activation of primary motor cortex (M1) neurons in the context of a given motor task? We present a systems level physiological model describing the transformation from the neural activity in M1, through the muscle control signal, into joint torques and down to endpoint forces and movements. The redundancy of the system is resolved by biologically plausible optimization criteria. The model explains neural activity at both the population, and single neuron, levels. Due to the model's relative simplicity and analytic tractability, it provides intuition as to the most salient features of the system as well as a possible causal explanation of how these determine the overall behavior. Moreover, it explains a large number of recent observations, including the temporal patterns of single-neuron and population firing rates during isometric and movement tasks, narrow tuning curves, non cosine tuning curves, changes of preferred directions during a task, and changes of preferred directions due to different experimental conditions.

Inter-joint coupling effects on muscle contributions to endpoint force and acceleration in a musculoskeletal model of the cat hindlimb

The biomechanical principles underlying the organization of muscle activation patterns during standing balance are poorly understood. The goal of this study was to understand the influence of biomechanical inter-joint coupling on endpoint forces and accelerations induced by the activation of individual muscles during postural tasks. We calculated induced endpoint forces and accelerations of 31 muscles in a 7 degree-of-freedom, three-dimensional model of the cat hindlimb. To test the effects of inter-joint coupling, we systematically immobilized the joints (excluded kinematic degrees of freedom) and evaluated how the endpoint force and acceleration directions changed for each muscle in 7 different conditions. We hypothesized that altered inter-joint coupling due to joint immobilization of remote joints would substantially change the induced directions of endpoint force and acceleration of individual muscles. Our results show that for most muscles crossing the knee or the hip, joint immobilization altered the endpoint force or acceleration direction by more than 90° in the dorsal and sagittal planes. Induced endpoint forces were typically consistent with behaviorally observed forces only when the ankle was immobilized. We then activated a proximal muscle simultaneous with an ankle torque of varying magnitude, which demonstrated that the resulting endpoint force or acceleration direction is modulated by the magnitude of the ankle torque. We argue that this simple manipulation can lend insight into the functional effects of co-activating muscles. We conclude that inter-joint coupling may be an essential biomechanical principle underlying the coordination of proximal and distal muscles to produce functional endpoint actions during motor tasks.