Testing hypotheses and the advancement of science: recent attempts to falsify the equilibrium point hypothesis

Inverting a model of neuromuscular control to estimate descending activation patterns that generate fast-reaching movements

Reaching movements generally show smooth kinematic profiles that are invariant across varying movement speeds even as interaction torques and muscle properties vary nonlinearly with speed. How the brain brings about these invariant profiles is an open question. We developed an analytical inverse dynamics method to estimate descending activation patterns directly from observed joint angle trajectories based on a simple model of the stretch reflex, and of muscle and biomechanical dynamics. We estimated descending activation patterns for experimental data from eight different planar two-joint movements performed at two movement times (fast: 400 ms; slow: 800 ms). The temporal structure of descending activation differed qualitatively across speeds, consistent with the idea that the nervous system uses an internal model to generate anticipatory torques during fast movement. This temporal structure also depended on the cocontraction level of antagonistic muscle groups. Comparing estimated muscle activation and descending activation revealed the contribution of the stretch reflex to movement generation that was found to set in after about 20% of movement time.NEW & NOTEWORTHY By estimating descending activation patterns directly from observed movement kinematics based on a model of the dynamics of the stretch reflex, of muscle force generation, and of the biomechanics of the limb, we observed how brain signals must be temporally structured to enable fast movement.

The Role of Imitation, Primitives, and Spatial Referent Coordinates in Motor Control: Implications for Writing and Reading

We review a body of literature related to the drawing and recognition of geometrical two-dimensional linear drawings including letters. Handwritten letters are viewed not as two-dimensional geometrical objects but as one-dimensional trajectories of the tip of the implement. Handwritten letters are viewed as composed of a small set of kinematic primitives. Recognition of objects is mediated by processes of their creation (actual or imagined)-the imitation principle, a particular example of action-perception coupling. The concept of spatial directional field guiding the trajectories is introduced and linked to neuronal population vectors. Further, we link the kinematic description to the theory of control with spatial referent coordinates. This framework allows interpreting a number of experimental observations and clinical cases of agnosia. It also allows formulating predictions for new experimental studies of writing.

Is There a Deficit in Product and Process of Handwriting in Children with Attention Deficit Hyperactivity Disorder? A Systematic Review and Recommendations for Future Research

Handwriting abnormalities in children with attention deficit hyperactivity disorder (ADHD) have sometimes been reported both (i) at the product level (i.e., quality/legibility of the written trace and speed of writing) and (ii) at the process level (i.e., dynamic and kinematic features, such as on-paper and in-air durations, pen pressure and velocity peaks, etc.). Conversely, other works have failed to reveal any differences between ADHD and typically developing children. The question of the presence and nature of handwriting deficits in ADHD remains open and merits an in-depth examination. The aim of this systematic review was, therefore, to identify studies that have investigated the product and/or process of handwriting in children with ADHD compared to typically developing individuals. This review was conducted and reported in accordance with the PRISMA statement. A literature search was carried out using three electronic databases. The methodological quality of the studies was systematically assessed using the Critical Appraisal Skills Program (CASP) criteria. Twenty-one articles were identified. Of these, 17 described handwriting quality/legibility, 12 focused on speed and 14 analyzed the handwriting process. All the studies (100%) with satisfactory methodology procedures reported an impaired product and process in children with ADHD, while 25% evidenced a difference in the speed of production. Most importantly, the studies differed widely in their methodological approaches. Substantial gaps remain, particularly with regard to ascertaining comorbidities, ADHD subtypes and the medical status of the included children. The lack of overall homogeneity in the samples calls for higher quality studies. We conclude with recommendations for further studies.

Physics-based character animation and human motor control

Motor neuroscience and physics-based character animation (PBCA) approach human and humanoid control from different perspectives. The primary goal of PBCA is to control the movement of a ragdoll (humanoid or animal) applying forces and torques within a physical simulation. The primary goal of motor neuroscience is to understand the contribution of different parts of the nervous system to generate coordinated movements. We review the functional principles and the functional anatomy of human motor control and the main strategies used in PBCA. We then explore common research points by discussing the functional anatomy and ongoing debates in motor neuroscience from the perspective of PBCA. We also suggest there are several benefits to be found in studying sensorimotor integration and human-character coordination through closer collaboration between these two fields.

Unintentional force drifts in the lower extremities

We explored the phenomenon of unintentional force drift seen in the absence of visual feedback during knee extension contractions in isometric conditions. Based on the importance of knee extensors for the anti-gravity function, we hypothesized that such force drifts would be slower and smaller compared to those reported for the upper extremities. We also explored possible effects of foot dominance and gender on the force drifts. Young healthy persons produced isometric knee extension contractions to different levels, ranging from 15 to 25% of maximal voluntary contraction force, with the help of visual feedback, and then, the visual feedback was turned off. Force change over the time interval without visual feedback was quantified. In the absence of visual feedback, force drifted to smaller magnitudes. The drift magnitude expressed in percent of the initial force magnitude was smaller for smaller initial force levels, ranging between 8 and 15% of the initial force for the initial force magnitude of 15% and 25% of maximal voluntary contraction force. The time exponent of the force drift was independent of the initial force magnitude and was, on average, 6.45 s. There were no significant effects of foot dominance or gender, although the male subjects tended to show stronger scaling of the drift magnitude with the initial force level compared to the female subjects. The results show that unintentional force drift is a common phenomenon across limbs and muscle groups. This conclusion fits the theory of control with spatial referent coordinates and the general tendency of all natural systems to drift to states with lower potential energy.

The legacy of Gerald L. Gottlieb in human movement neuroscience

In this paper, we review the legacy of Gerald (Gerry) Gottlieb in various fields related to the neural control of human movement. His studies on the myotatic (stretch) reflex and postmyotatic responses to ankle joint perturbations paved the way for current explorations of long-loop reflexes and their role in the control of movement. The dual-strategy hypothesis introduced order into a large body of literature on the triphasic muscle activation patterns seen over a variety of voluntary movements in healthy persons. The dual-strategy hypothesis continues to be important for understanding the performance of subjects with disordered motor control. The principle of linear synergy (covariance of joint torques) was an attempt to solve one of the notorious problems of motor redundancy, which remains an important topic in the field. Gerry's attitude toward the equilibrium-point hypothesis varied between rejection and using it to explore patterns of hypothetical control variables and movement variability. The discovery of reciprocal excitation in healthy neonates fostered other studies of changes in spinal cord physiology as motor skills develop. In addition, studies of people with spasticity and the effects of treatment with intrathecal baclofen were crucial in demonstrating the possibility of unmasking voluntary movements after suppression of the hyperreflexia of spasticity. Gerry Gottlieb contributed a significant body of knowledge that formed a solid foundation from which to study a variety of neurological diseases and their treatments, and a more comprehensive and parsimonious foundation to describe the neural control of human movement.

Effect of Object Texture and Weight on Ipsilateral Corticospinal Influences During Bimanual Holding in Humans

We tested the hypothesis that the ipsilateral corticospinal system, like the contralateral corticospinal system, controls the threshold muscle length at which wrist muscles and the stretch reflex begin to act during holding tasks. Transcranial magnetic stimulation was applied over the right primary motor cortex in 21 healthy subjects holding a smooth or coarse block between the hands. Regardless of the lifting force, motor evoked potentials in right wrist flexors were larger for the smooth block. This result was explained based on experimental evidence that motor actions are controlled by shifting spatial stretch reflex thresholds. Thus, the ipsilateral corticospinal system is involved in threshold position control by modulating facilitatory influences of hand skin afferents on motoneurons of wrist muscles during bimanual object manipulation.

Motor learning in neurological rehabilitation

While most upper limb training interventions in neurological rehabilitation are based on established principles of motor learning and neural plasticity, recovery potential may be improved if the focus includes remediating an individual's specific motor impairment within the framework of a motor control theory. This paper reviews current theories of motor control and motor learning and describes how they can be incorporated into training programs to enhance sensorimotor recovery in patients with neurological lesions. An emphasis is placed on dynamical systems theory and the use of new technologies such as virtual, augmented and mixed reality applications for rehabilitation to facilitate learning.Implications for RehabilitationKinematic abundance allows the healthy nervous system to produce different combinations of joint rotations to perform a desired task.The structure of practice to improve the movement repertoire in rehabilitation should take into account the kinematic abundance of the system.Learning can be enhanced by varied practice with feedback about key movement elements.Virtual reality environments provide opportunities to manipulate the structure and schedule of practice and feedback.

Understanding and Synergy: A Single Concept at Different Levels of Analysis?

Biological systems differ from the inanimate world in their behaviors ranging from simple movements to coordinated purposeful actions by large groups of muscles, to perception of the world based on signals of different modalities, to cognitive acts, and to the role of self-imposed constraints such as laws of ethics. Respectively, depending on the behavior of interest, studies of biological objects based on laws of nature (physics) have to deal with different salient sets of variables and parameters. Understanding is a high-level concept, and its analysis has been linked to other high-level concepts such as "mental model" and "meaning". Attempts to analyze understanding based on laws of nature are an example of the top-down approach. Studies of the neural control of movements represent an opposite, bottom-up approach, which starts at the interface with classical physics of the inanimate world and operates with traditional concepts such as forces, coordinates, etc. There are common features shared by the two approaches. In particular, both assume organizations of large groups of elements into task-specific groups, which can be described with only a handful of salient variables. Both assume optimality criteria that allow the emergence of families of solutions to typical tasks. Both assume predictive processes reflected in anticipatory adjustments to actions (motor and non-motor). Both recognize the importance of generating dynamically stable solutions. The recent progress in studies of the neural control of movements has led to a theory of hierarchical control with spatial referent coordinates for the effectors. This theory, in combination with the uncontrolled manifold hypothesis, allows quantifying the stability of actions with respect to salient variables. This approach has been used in the analysis of motor learning, changes in movements with typical and atypical development and with aging, and impaired actions by patients with various neurological disorders. It has been developed to address issues of kinesthetic perception. There seems to be hope that the two counter-directional approaches will meet and result in a single theoretical scheme encompassing biological phenomena from figuring out the best next move in a chess position to activating motor units appropriate for implementing that move on the chessboard.

Unintentional Force Drifts as Consequences of Indirect Force Control with Spatial Referent Coordinates

We explored the phenomenon of unintentional force drifts in the absence of visual feedback. Based on the idea of direct force control with internal models and on the idea of indirect force control with referent coordinates to the involved muscle groups, contrasting predictions were drawn for changes in the drift magnitude when acting against external spring loads. Fifteen young subjects performed typical accurate force production tasks by pressing with the Index finger at 20% of maximal voluntary contraction (MVC) in isometric conditions and while acting against one of the three external springs with different stiffness. The visual feedback on the force was turned off after 5 s. At the end of each 20-s trial, the subjects relaxed and then tried to reproduce the final force level. The force drifts were significantly smaller in the spring conditions, particularly when acting against more compliant springs. The subjects were unaware of the force drifts and, during force matching, produced forces close to the initial force magnitude, which were not different across the conditions. There was a trend toward larger drifts during performance by the dominant hand. We view these observations as strong arguments in favor of the theory of control with spatial referent coordinates. In particular, force drifts were likely consequences of drifts of referent coordinates to both agonist and antagonist muscles. The lack of drift effects on both perception-to-report and perception-to-act fit the scheme of kinesthetic perception based on the interaction of efferent (referent coordinate) and afferent processes.

Effect of Neck Muscle Fatigue on Hand Muscle Motor Performance and Early Somatosensory Evoked Potentials

Even on pain free days, recurrent neck pain alters sensorimotor integration (SMI) measured via somatosensory evoked potentials (SEPs). Neck muscle fatigue decreases upper limb proprioception, and thus may interfere with upper limb motor task acquisition and SMI. This study aimed to determine the effect of cervical extensor muscle (CEM) fatigue on upper limb motor acquisition and retention; and SMI, measured via early SEPs. Twenty-four healthy right-handed individuals were randomly assigned to control or CEM fatigue. Baseline SEPs were elicited via median nerve stimulation at the wrist. Participants then lay prone on a padded table. The fatigue group supported a 2 kg weight until they could no longer maintain the position. The control group rested their neck in neutral for 5 min. Participants completed pre- and post-motor skill acquisition while seated, SEPs were again collected. Task retention was measured 24 h later. Accuracy improved post acquisition and at retention for both groups (p < 0.001), with controls outperforming the fatigue group (p < 0.05). The fatigue group had significantly greater increases in the N24 (p = 0.017) and N30 (p = 0.007) SEP peaks. CEM fatigue impaired upper limb motor learning outcomes in conjunction with differential changes in SEP peak amplitudes related to SMI.

Central pattern generator and human locomotion in the context of referent control of motor actions

Unperturbed human locomotion presumably results from feedforward shifts in stable body equilibrium in the environment, thus avoiding falling and subsequent catching considered in alternative theories of locomotion. Such shifts are achieved by relocation of the referent body configuration at which multiple muscle recruitment begins. Rather than being directly specified by a central pattern generator, multiple muscles are activated depending on the extent to which the body is deflected from the referent, threshold body configuration, as confirmed in previous studies. Based on the referent control theory of action and perception, solutions to classical problems in motor control are offered, including the previously unresolved problem of the integration of central and reflex influences on motoneurons and the problem of how posture and movement are related. The speed of locomotion depends on the rate of shifts in the referent body configuration. The transition from walking to running results from increasing the rate of referent shifts. It is emphasised that there is a certain hierarchy between reciprocal and co-activation of agonist and antagonist muscles during locomotion and other motor actions, which is also essential for the understanding of how locomotor speed is regulated. The analysis opens a new avenue in neurophysiological approaches to human locomotion with clinical implications.

One more time about motor (and non-motor) synergies

We revisit the concept of synergy based on the recently translated classical book by Nikolai Bernstein (On the construction of movements, Medgiz, Moscow 1947; Latash, Bernstein's Construction of Movements, Routledge, Abingdon 2020b) and progress in understanding the physics and neurophysiology of biological action. Two aspects of synergies are described: organizing elements into stable groups (modes) and ensuring dynamical stability of salient performance variables. The ability of the central nervous system to attenuate synergies in preparation for a quick action-anticipatory synergy adjustments-is emphasized. Recent studies have demonstrated synergies at the level of hypothetical control variables associated with spatial referent coordinates for effectors. Overall, the concept of synergies fits naturally the hierarchical scheme of control with referent coordinates with an important role played by back-coupling loops within the central nervous system and from peripheral sensory endings. Further, we review studies showing non-trivial changes in synergies with development, aging, fatigue, practice, and a variety of neurological disorders. Two aspects of impaired synergic control-impaired stability and impaired agility-are introduced. The recent generalization of the concept of synergies for non-motor domains, including perception, is discussed. We end the review with a list of unresolved and troubling issues.

Computational reproductions of external force field adaption without assuming desired trajectories

Optimal feedback control is an established framework that is used to characterize human movement. However, it is not fully understood how the brain computes optimal gains through interactions with the environment. In the past study, we proposed a model of motor learning that identifies a set of feedback and feedforward controllers and a state predictor of the arm musculoskeletal system to control free reaching movements. In this study, we applied the model to force field adaptation tasks where normal reaching movements are disturbed by an external force imposed on the hand. Without a priori knowledge about the arm and environment, the model was able to adapt to the force field by generating counteracting forces to overcome it in a manner similar to what is reported in the behavioral literature. The kinematics of the movements generated by our model share characteristic features of human movements observed before and after force field adaptation. In addition, we demonstrate that the structure and learning algorithm introduced in our model induced a shift in the end-point's equilibrium position and a static force modulation, accompanied by a fast and a slow learning process. Importantly, our model does not require desired trajectories, yields movements without specifying movement duration, and predicts force generation patterns by exploring the environment. Our model demonstrates a possible mechanism through which the central nervous system may control and adapt a point-to-point reaching movement without specifying a desired trajectory by continuously updating the body's musculoskeletal model.

Efference copy in kinesthetic perception: a copy of what is it?

A number of notions in the fields of motor control and kinesthetic perception have been used without clear definitions. In this review, we consider definitions for efference copy, percept, and sense of effort based on recent studies within the physical approach, which assumes that the neural control of movement is based on principles of parametric control and involves defining time-varying profiles of spatial referent coordinates for the effectors. The apparent redundancy in both motor and perceptual processes is reconsidered based on the principle of abundance. Abundance of efferent and afferent signals is viewed as the means of stabilizing both salient action characteristics and salient percepts formalized as stable manifolds in high-dimensional spaces of relevant elemental variables. This theoretical scheme has led recently to a number of novel predictions and findings. These include, in particular, lower accuracy in perception of variables produced by elements involved in a multielement task compared with the same elements in single-element tasks, dissociation between motor and perceptual effects of muscle coactivation, force illusions induced by muscle vibration, and errors in perception of unintentional drifts in performance. Taken together, these results suggest that participation of efferent signals in perception frequently involves distorted copies of actual neural commands, particularly those to antagonist muscles. Sense of effort is associated with such distorted efferent signals. Distortions in efference copy happen spontaneously and can also be caused by changes in sensory signals, e.g., those produced by muscle vibration.

Exploring Stiffness Modulation in Prosthetic Hands and Its Perceived Function in Manipulation and Social Interaction

To physically interact with a rich variety of environments and to match situation-dependent requirements, humans adapt both the force and stiffness of their limbs. Reflecting this behavior in prostheses may promote a more natural and intuitive control and, consequently, improve prostheses acceptance in everyday life. This pilot study proposes a method to control a prosthetic robot hand and its impedance, and explores the utility of variable stiffness when performing activities of daily living and physical social interactions. The proposed method is capable of a simultaneous and proportional decoding of position and stiffness intentions from two surface electro-myographic sensors placed over a pair of antagonistic muscles. The feasibility of our approach is validated and compared to existing control modalities in a preliminary study involving one prosthesis user. The algorithm is implemented in a soft under-actuated prosthetic hand (SoftHand Pro). Then, we evaluate the usability of the proposed approach while executing a variety of tasks. Among these tasks, the user interacts with other 12 able-bodied subjects, whose experiences were also assessed. Several statistically significant aspects from the System Usability Scale indicate user's preference of variable stiffness control over low or high constant stiffness due to its reactivity and adaptability. Feedback reported by able-bodied subjects reveal a general tendency to favor soft interaction, i.e., low stiffness, which is perceived more human-like and comfortable. These combined results suggest the use of variable stiffness as a viable compromise between firm control and safe interaction which is worth investigating further.

Eye and head movements and vestibulo-ocular reflex in the context of indirect, referent control of motor actions

Conventional explanations of the vestibulo-ocular reflex (VOR) and eye and head movements are revisited by considering two alternative frameworks addressing the question of how the brain controls motor actions. Traditionally, biomechanical and/or computational frameworks reflect the views of several prominent scholars of the past, including Helmholtz and von Holst, who assumed that the brain directly specifies the desired motor outcome and uses efference copy to influence perception. However, empirical studies resulting in the theory of referent control of action and perception (an extension of the equilibrium-point hypothesis) revealed that direct specification of motor outcome is inconsistent with nonlinear properties of motoneurons and with the physical principle that the brain can control motor actions only indirectly, by changing or maintaining the values of neurophysiological parameters that influence, but can remain independent of, biomechanical variables. Some parameters are used to shift the origin (referent) points of spatial frames of reference (FRs) or system of coordinates in which motor actions emerge without being predetermined. Parameters are adjusted until the emergent motor actions meet the task demands. Several physiological parameters and spatial FRs have been identified, supporting the notion of indirect, referent control of movements. Instead of integration of velocity-dependent signals, position-dimensional referent signals underlying head motion can likely be transmitted to motoneurons of extraocular muscles. This would produce compensatory eye movement preventing shifts in gaze during head rotation, even after bilateral destruction of the labyrinths. The referent control framework symbolizes a shift in the paradigm for the understanding of VOR and eye and head movement production.

Linear and Non-linear Dimensionality-Reduction Techniques on Full Hand Kinematics

The purpose of this study was to find a parsimonious representation of hand kinematics data that could facilitate prosthetic hand control. Principal Component Analysis (PCA) and a non-linear Autoencoder Network (nAEN) were compared in their effectiveness at capturing the essential characteristics of a wide spectrum of hand gestures and actions. Performance of the two methods was compared on (a) the ability to accurately reconstruct hand kinematic data from a latent manifold of reduced dimension, (b) variance distribution across latent dimensions, and (c) the separability of hand movements in compressed and reconstructed representations derived using a linear classifier. The nAEN exhibited higher performance than PCA in its ability to more accurately reconstruct hand kinematic data from a latent manifold of reduced dimension. Whereas, for two dimensions in the latent manifold, PCA was able to account for 78% of input data variance, nAEN accounted for 94%. In addition, the nAEN latent manifold was spanned by coordinates with more uniform share of signal variance compared to PCA. Lastly, the nAEN was able to produce a manifold of more separable movements than PCA, as different tasks, when reconstructed, were more distinguishable by a linear classifier, SoftMax regression. It is concluded that non-linear dimensionality reduction may offer a more effective platform than linear methods to control prosthetic hands.

On Primitives in Motor Control

The concept of primitives has been used in motor control both as a theoretical construct and as a means of describing the results of experimental studies involving multiple moving elements. This concept is close to Bernstein’s notion of engrams and level of synergies. Performance primitives have been explored in spaces of peripheral variables but interpreted in terms of neural control primitives. Performance primitives reflect a variety of mechanisms ranging from body mechanics to spinal mechanisms and to supraspinal circuitry. This review suggests that primitives originate at the task level as preferred time functions of spatial referent coordinates or at mappings from higher level referent coordinates to lower level, frequently abundant, referent coordinate sets. Different patterns of performance primitives can emerge depending, in particular, on the external force field.

A computational scheme for internal models not requiring precise system parameters

Utilization by humans of a precise and adaptable internal model of the dynamics of the body in generating movements is a well-supported concept. The prevailing opinion is that such an internal model ceaselessly develops through long-term repetition and accumulation in the central nervous system (CNS). However, a long-term learning process would not be absolutely necessary for the formation of internal models. It is possible to estimate the dynamics of the system by using a motor command and its resulting output, instead of constructing a model of the dynamics with precise parameters. In this study, a computational model is proposed that uses a motor command and its corresponding output to estimate the dynamics of the system and it is examined whether the proposed model is capable of describing a series of empirical movements. The proposed model was found to be capable of describing humans' fast movements which require compensation for system dynamics as well as sensory delays. In addition, the proposed model shows equifinality under inertial perturbations as seen in several experimental studies. This satisfactory reproducibility of the proposed computation raises the possibility that humans make a movement by estimating the system dynamics with a copy of motor command and sensory output on a momentary basis, without the need to identify precise system parameters.

Real-time slacking as a default mode of grip force control: implications for force minimization and personal grip force variation

During trial-to-trial movement adaptation, the motor system systematically reduces extraneous muscle forces when kinematic errors experienced on previous movements are small, a phenomenon termed "slacking." There is also growing evidence that the motor system slacks continuously (i.e., in real-time) during arm movement or grip force control, but the initiation of this slacking is not well-characterized, obfuscating its physiological cause. Here, we addressed this issue by asking participants ( n = 32) to track discrete force targets presented visually using isometric grip force, then applying a brief, subtle error-clamp to that visual feedback on random trials. Participants reduced their force in an exponential fashion, on these error-clamp trials, except when the target force was <10% maximum voluntary contraction (MVC). This force drift began <250 ms after the onset of the error-clamp, consistent with slacking being an ongoing process unmasked immediately after the motor system finished reacting to the last veridical feedback. Above 10% MVC, the slacking rate increased linearly with grip force magnitude. Grip force variation was approximately 50-100% higher with veridical feedback, largely due to heightened signal power at ~1 Hz, the band of visuomotor feedback control. Finally, the slacking rate measured for each participant during error-clamp trials correlated with their force variation during control trials. That is, participants who slacked more had greater force variation. These results suggest that real-time slacking continuously reduces grip force until visual error prompts correction. Whereas such slacking is suited for force minimization, it may also account for ~30% of the variability in personal grip force variation. NEW & NOTEWORTHY We provide evidence that a form of slacking continuously conditions real-time grip force production. This slacking is well-suited to promote efficiency but is expected to increase force variation by triggering additional feedback corrections. Moreover, we show that the rate at which a person slacks is substantially correlated with the variation of their grip force. In combination, at the neurophysiological level, our results suggest slacking is caused by one or more relatively smooth neural adaptations.

Energy exchanges at contact events guide sensorimotor integration

The brain must consider the arm’s inertia to predict the arm's movements elicited by commands impressed upon the muscles. Here, we present evidence suggesting that the integration of sensory information leading to the representation of the arm's inertia does not take place continuously in time but only at discrete transient events, in which kinetic energy is exchanged between the arm and the environment. We used a visuomotor delay to induce cross-modal variations in state feedback and uncovered that the difference between visual and proprioceptive velocity estimations at isolated collision events was compensated by a change in the representation of arm inertia. The compensation maintained an invariant estimate across modalities of the expected energy exchange with the environment. This invariance captures different types of dysmetria observed across individuals following prolonged exposure to a fixed intermodal temporal perturbation and provides a new interpretation for cerebellar ataxia.

The influence of lower leg configurations on muscle force variability

The maintenance of steady contractions is required in many daily tasks. However, there is little understanding of how various lower limb configurations influence the ability to maintain force. The purpose of the current investigation was to examine the influence of joint angle on various lower-limb constant force contractions. Nineteen adults performed knee extension, knee flexion, and ankle plantarflexion isometric force contractions to 11 target forces, ranging from 2 to 95% maximal voluntary contraction (MVC) at 2 angles. Force variability was quantified with mean force, standard deviation, and the coefficient of variation of force output. Non-linearities in force output were quantified with approximate entropy. Curve fitting analyses were performed on each set of data from each individual across contractions to further examine whether joint angle interacts with global functions of lower-limb force variability. Joint angle had significant effects on the model parameters used to describe the force-variability function for each muscle contraction (p < 0.05). Regularities in force output were more explained by force level in smaller angle conditions relative to the larger angle conditions (p < 0.05). The findings support the notion that limb configuration influences the magnitude and regularities in force production. Biomechanical factors, such as joint angle, along with neurophysiological factors should be considered together in the discussion of the dynamics of constant force production.

Muscle coactivation: definitions, mechanisms, and functions

The phenomenon of agonist-antagonist muscle coactivation is discussed with respect to its consequences for movement mechanics (such as increasing joint apparent stiffness, facilitating faster movements, and effects on action stability), implication for movement optimization, and involvement of different neurophysiological structures. Effects of coactivation on movement stability are ambiguous and depend on the effector representing a kinematic chain with a fixed origin or free origin. Furthermore, coactivation is discussed within the framework of the equilibrium-point hypothesis and the idea of hierarchical control with spatial referent coordinates. Relations of muscle coactivation to changes in one of the basic commands, the c-command, are discussed and illustrated. A hypothesis is suggested that agonist-antagonist coactivation reflects a deliberate neural control strategy to preserve effector-level control and avoid making it degenerate and facing the necessity to control at the level of signals to individual muscles. This strategy, in particular, allows stabilizing motor actions by covaried adjustments in spaces of control variables. This hypothesis is able to account for higher levels of coactivation in young healthy persons performing challenging tasks and across various populations with movement impairments.

Control of wrist movement in deafferented man: evidence for a mixed strategy of position and amplitude control

There is a continuing debate about control of voluntary movement, with conflicted evidence about the balance between control of movement vectors (amplitude control) that implies knowledge of the starting position for accuracy, and equilibrium point or final position control, that is independent of the starting conditions. We tested wrist flexion and extension movements in a man with a chronic peripheral neuronopathy that deprived him of proprioceptive knowledge of his wrist angles. In a series of experiments, we demonstrate that he could scale the amplitude of his wrist movements in flexion/extension, even without visual feedback, and appeared to adopt a strategy of moving via a central wrist position when asked to reach target angles from unknown start locations. When examining the relationship between positional error at the start and end of each movement in long sequences of movements, we report that he appears to have three canonical positions that he can reach relatively successfully, in flexion, in extension and in the centre. These are consistent with end-point or position control. Other positions were reached with errors that suggest amplitude control. Recording wrist flexor and extensor EMG confirmed that the flexion and extension canonical positions were reached by strong flexor and extensor activity, without antagonist activity, and other positions were reached with graded muscle activation levels. The central canonical position does not appear to be reached by either maximal co-contraction or by complete relaxation, but may have been reached by matched low-level co-contraction.

Threshold position control of anticipation in humans: a possible role of corticospinal influences

KEY POINTS

Sudden unloading of preloaded wrist muscles elicits motion to a new wrist position. Such motion is prevented if subjects unload muscles using the contralateral arm (self-unloading). Corticospinal influences originated from the primary motor cortex maintain tonic influences on motoneurons of wrist muscles before sudden unloading but modify these influences prior to the onset and until the end of self-unloading. Results are interpreted based on the previous finding that intentional actions are caused by central, particularly corticospinal, shifts in the spatial thresholds at which wrist motoneurons are activated, thus predetermining the attractor point at which the neuromuscular periphery achieves mechanical balance with environment forces. By maintaining or shifting the thresholds, descending systems let body segments go to the equilibrium position in the respective unloading tasks without the pre-programming of kinematics or muscle activation patterns. The study advances the understanding of how motor actions in general, and anticipation in particular, are controlled.

ABSTRACT

The role of corticospinal (CS) pathways in anticipatory motor actions was evaluated using transcranial magnetic stimulation (TMS) of the primary motor cortex projecting to motoneurons (MNs) of wrist muscles. Preloaded wrist flexors were suddenly unloaded by the experimenter or by the subject using the other hand (self-unloading). After sudden unloading, the wrist joint involuntarily flexed to a new position. In contrast, during self-unloading the wrist remained almost motionless, implying that an anticipatory postural adjustment occurred. In the self-unloading task, anticipation was manifested by a decrease in descending facilitation of pre-activated flexor MNs starting ∼72 ms before changes in the background EMG activity. Descending facilitation of extensor MNs began to increase ∼61 ms later. Conversely, these influences remained unchanged before sudden unloading, implying the absence of anticipation. We also tested TMS responses during EMG silent periods produced by brief muscle shortening, transiently resulting in similar EMG levels before the onset and after the end of self-unloading. We found reduced descending facilitation of flexor MNs after self-unloading. To explain why the wrist excursion was minimized in self-unloading due to these changes in descending influences, we relied on previous demonstrations that descending systems pre-set the threshold positions of body segments at which muscles begin to be activated, thus predetermining the equilibrium point to which the system is attracted. Based on this notion, a more consistent explanation of the kinematic, EMG and descending patterns in the two types of unloading is proposed compared to the alternative notion of direct pre-programming of kinematic and/or EMG patterns.

Spasticity Measurement Based on Tonic Stretch Reflex Threshold in Children with Cerebral Palsy Using the PediAnklebot

Nowadays, objective measures are becoming prominent in spasticity assessment, to overcome limitations of clinical scales. Among others, Tonic Stretch Reflex Threshold (TSRT) showed promising results. Previous studies demonstrated the validity and reliability of TSRT in spasticity assessment at elbow and ankle joints in adults. Purposes of the present study were to assess: (i) the feasibility of measuring TSRT to evaluate spasticity at the ankle joint in children with Cerebral Palsy (CP), and (ii) the correlation between objective measures and clinical scores. A mechatronic device, the pediAnklebot, was used to impose 50 passive stretches to the ankle of 10 children with CP and 3 healthy children, to elicit muscles response at 5 different velocities. Surface electromyography, angles, and angular velocities were recorded to compute dynamic stretch reflex threshold; TSRT was computed with a linear regression through angles and angular velocities. TSRTs for the most affected side of children with CP resulted into the biomechanical range (95.7 ± 12.9° and 86.7 ± 17.4° for Medial and Lateral Gastrocnemius, and 75.9 ± 12.5° for Tibialis Anterior). In three patients, the stretch reflex was not elicited in the less affected side. TSRTs were outside the biomechanical range in healthy children. However, no correlation was found between clinical scores and TSRT values. Here, we demonstrated the capability of TSRT to discriminate between spastic and non-spastic muscles, while no significant outcomes were found for the dorsiflexor muscle.

Integration of Visual and Joint Information to Enable Linear Reaching Motions

A new dynamics-driven control law was developed for a robot arm, based on the feedback control law which uses the linear transformation directly from work space to joint space. This was validated using a simulation of a two-joint planar robot arm and an optimisation algorithm was used to find the optimum matrix to generate straight trajectories of the end-effector in the work space. We found that this linear matrix can be decomposed into the rotation matrix representing the orientation of the goal direction and the joint relation matrix (M_JRM) representing the joint response to errors in the Cartesian work space. The decomposition of the linear matrix indicates the separation of path planning in terms of the direction of the reaching motion and the synergies of joint coordination. Once the M_JRM is numerically obtained, the feedfoward planning of reaching direction allows us to provide asymptotically stable, linear trajectories in the entire work space through rotational transformation, completely avoiding the use of inverse kinematics. Our dynamics-driven control law suggests an interesting framework for interpreting human reaching motion control alternative to the dominant inverse method based explanations, avoiding expensive computation of the inverse kinematics and the point-to-point control along the desired trajectories.

Referent control and motor equivalence of reaching from standing

Motor actions may result from central changes in the referent body configuration, defined as the body posture at which muscles begin to be activated or deactivated. The actual body configuration deviates from the referent configuration, particularly because of body inertia and environmental forces. Within these constraints, the system tends to minimize the difference between these configurations. For pointing movement, this strategy can be expressed as the tendency to minimize the difference between the referent trajectory (R_T) and actual trajectory (Q_T) of the effector (hand). This process may underlie motor equivalent behavior that maintains the pointing trajectory regardless of the number of body segments involved. We tested the hypothesis that the minimization process is used to produce pointing in standing subjects. With eyes closed, 10 subjects reached from a standing position to a remembered target located beyond arm length. In randomly chosen trials, hip flexion was unexpectedly prevented, forcing subjects to take a step during pointing to prevent falling. The task was repeated when subjects were instructed to intentionally take a step during pointing. In most cases, reaching accuracy and trajectory curvature were preserved due to adaptive condition-specific changes in interjoint coordination. Results suggest that referent control and the minimization process associated with it may underlie motor equivalence in pointing.

NEW & NOTEWORTHY

Motor actions may result from minimization of the deflection of the actual body configuration from the centrally specified referent body configuration, in the limits of neuromuscular and environmental constraints. The minimization process may maintain reaching trajectory and accuracy regardless of the number of body segments involved (motor equivalence), as confirmed in this study of reaching from standing in young healthy individuals. Results suggest that the referent control process may underlie motor equivalence in reaching.

Feedback control of electrical stimulation electrode arrays

Electrical stimulation electrode arrays are an emerging technology that enables muscles to be artificially contracted through the activation of their associated motor neurons. A principal application of electrical stimulation is to assist human motion for orthotic or therapeutic purposes. This paper develops a framework for the design of model-based electrode array feedback controllers that balance joint angle tracking performance with the degree of disturbance and modeling mismatch that can exist in the true underlying biomechanical system. This framework is used to develop a simplified control design procedure that is suitable for application in a clinical setting. Experimental results evaluate the feasibility of the control design approach through tests on ten participants using both fabric and polycarbonate electrode arrays.

Active sensing without efference copy: referent control of perception

Although action and perception are different behaviors, they are likely to be interrelated, as implied by the notions of perception-action coupling and active sensing. Traditionally, it has been assumed that the nervous system directly preprograms motor commands required for actions and uses a copy of them called efference copy (EC) to also influence our senses. This review offers a critical analysis of the EC concept by identifying its limitations. An alternative to the EC concept is based on the experimentally confirmed notion that sensory signals from receptors are perceived relative to referent signals specified by the brain. These referents also underlie the control of motor actions by predetermining where, in the spatial domain, muscles can work without preprogramming how they should work in terms of motor commands or EC. This approach helps solve several problems of action and explain several sensory experiences, including position sense and the sense that the world remains stationary despite changes in its retinal image during eye or body motion (visual space constancy). The phantom limb phenomenon and other kinesthetic illusions are also explained within this framework.

Towards physics of neural processes and behavior

Behavior of biological systems is based on basic physical laws, common across inanimate and living systems, and currently unknown physical laws that are specific for living systems. Living systems are able to unite basic laws of physics into chains and clusters leading to new stable and pervasive relations among variables (new physical laws) involving new parameters and to modify these parameters in a purposeful way. Examples of such laws are presented starting from the tonic stretch reflex. Further, the idea of control with referent coordinates is formulated and merged with the idea of hierarchical control and the principle of abundance. The notion of controlled stability of behaviors is linked to the idea of structured variability, which is a common feature across living systems and actions. The explanatory and predictive power of this approach is illustrated with respect to the control of both intentional and unintentional movements, the phenomena of equifinality and its violations, preparation to quick actions, development of motor skills, changes with aging and neurological disorders, and perception.

A physiologically based hypothesis for learning proprioception and in approximating inverse kinematics

A long-standing problem in muscle control is the "curse of dimensionality". In part, this problem relates to the fact that coordinated movement is only achieved through the simultaneous contraction and extension of multitude muscles to specific lengths. Couched in robotics terms, the problem includes the determination of forward and inverse kinematics. Of the many neurophysiological discoveries in cortex is the existence of position gradients. Geometrically, position gradients are described by planes in Euclidean space whereby neuronal activity increases as the hand approaches locations that lie in a plane. This work demonstrates that position gradients, when coupled with known physiology in the spinal cord, allows for a way to approximate proprioception (forward kinematics) and to specify muscle lengths for goal-directed postures (inverse kinematics). Moreover, position gradients provide a means to learn and adjust kinematics as animals learn to move and grow. This hypothesis is demonstrated using computer simulation of a human arm. Finally, experimental predictions are described that might confirm or falsify the hypothesis.

Fifty Years of Physics of Living Systems

The equilibrium-point hypothesis and its more recent version, the referent configuration hypothesis, represent the physical approach to the neural control of action. This hypothesis can be naturally combined with the idea of hierarchical control of movements and of synergic organization of the abundant systems involved in all actions. Any action starts with defining trajectories of a few referent coordinates for a handful of salient task-specific variables. Further, referent coordinates at hierarchically lower levels emerge down to thresholds of the tonic stretch reflex for the participating muscles. Stability of performance with respect to salient variables is reflected in the structure of inter-trial variance and phenomena of motor equivalence. Three lines of recent research within this framework are reviewed. First, synergic adjustments of the referent coordinate and apparent stiffness have been demonstrated during finger force production supporting the main idea of control with referent coordinates. Second, the notion of unintentional voluntary movements has been introduced reflecting unintentional drifts in referent coordinates. Two types of unintentional movements have been observed with different characteristic times. Third, this framework has been applied to studies of impaired movements in neurological patients. Overall, the physical approach searching for laws of nature underlying biological movement has been highly stimulating and productive.

Unintentional movements induced by sequential transient perturbations in a multi-joint positional task

We explored the phenomenon of unintentional movements of a multi-joint effector produced by multiple transient changes in the external force. The subjects performed a position-holding task against a constant bias force produced by a robot and were instructed not to intervene voluntarily with arm movements produced by changes in the robot force. The robot produced a smooth force increase leading to hand movement from the trunk, followed by a dwell time. Then, the force dropped to its initial value leading to hand movement toward the initial position but with an undershot. Such perturbation episodes were repeated four times in a row. The accumulated perturbation and undershoot distances kept increasing without saturation within the sequence of four perturbation episode. The limb apparent stiffness before dwell time increased over sequential perturbations while apparent stiffness after dwell time decreased. We interpret the results as consequences of a drift of the hand referent coordinate (RC) caused by a hypothesized RC-back-coupling mechanism and a coupled drift of the apparent stiffness. The results show that RC-back-coupling continues to lead to unintentional movements over repeated perturbations and is accompanied by a relatively slow re-setting process.

Synergies in the space of control variables within the equilibrium-point hypothesis

We use an approach rooted in the recent theory of synergies to analyze possible co-variation between two hypothetical control variables involved in finger force production based on the equilibrium-point (EP) hypothesis. These control variables are the referent coordinate (R) and apparent stiffness (C) of the finger. We tested a hypothesis that inter-trial co-variation in the {R; C} space during repeated, accurate force production trials stabilizes the fingertip force. This was expected to correspond to a relatively low amount of inter-trial variability affecting force and a high amount of variability keeping the force unchanged. We used the "inverse piano" apparatus to apply small and smooth positional perturbations to fingers during force production tasks. Across trials, R and C showed strong co-variation with the data points lying close to a hyperbolic curve. Hyperbolic regressions accounted for over 99% of the variance in the {R; C} space. Another analysis was conducted by randomizing the original {R; C} data sets and creating surrogate data sets that were then used to compute predicted force values. The surrogate sets always showed much higher force variance compared to the actual data, thus reinforcing the conclusion that finger force control was organized in the {R; C} space, as predicted by the EP hypothesis, and involved co-variation in that space stabilizing total force.

On the Origin of Muscle Synergies: Invariant Balance in the Co-activation of Agonist and Antagonist Muscle Pairs

Investigation of neural representation of movement planning has attracted the attention of neuroscientists, as it may reveal the sensorimotor transformation essential to motor control. The analysis of muscle synergies based on the activity of agonist–antagonist (AA) muscle pairs may provide insight into such transformations, especially for a reference frame in the muscle space. In this study, we examined the AA concept using the following explanatory variables: the AA ratio, which is related to the equilibrium-joint angle, and the AA sum, which is associated with joint stiffness. We formulated muscle synergies as a function of AA sums, positing that muscle synergies are composite units of mechanical impedance. The AA concept can be regarded as another form of the equilibrium-point (EP) hypothesis, and it can be extended to the concept of EP-based synergies. We introduce, here, a novel tool for analyzing the neurological and motor functions underlying human movements and review some initial insights from our results about the relationships between muscle synergies, endpoint stiffness, and virtual trajectories (time series of EP). Our results suggest that (1) muscle synergies reflect an invariant balance in the co-activation of AA muscle pairs; (2) each synergy represents the basis for the radial, tangential, and null movements of the virtual trajectory in the polar coordinates centered on the specific joint at the base of the body; and (3) the alteration of muscle synergies (for example, due to spasticity or rigidity following neurological injury) results in significant distortion of endpoint stiffness and concomitant virtual trajectories. These results indicate that muscle synergies (i.e., the balance of muscle mechanical impedance) are essential for motor control.

Unintentional changes in the apparent stiffness of the multi-joint limb

We explored the phenomenon of unintentional changes in the apparent stiffness of the human arm produced by transient changes in the external force. The subjects performed a positional task against a constant baseline force and were instructed not to react to changes in the force. A HapticMaster robot produced a smooth force increase (a perturbation) leading to a hand movement, followed by a dwell time. No visible hand drift was observed during the dwell time. After the robot force dropped to its initial baseline value, the hand moved toward the initial position but stopped short of it. Small perturbations were applied at different time intervals along different directions during the dwell time. Arm apparent stiffness distribution in a horizontal plane was approximated with an ellipse. The apparent stiffness magnitude along the main axis of the ellipse showed a non-monotonic increase with dwell time, while the apparent stiffness along the minor axis did not change significantly. We interpreted the early part of the changes in the apparent stiffness as due to peripheral muscle properties. The later part is interpreted as caused by a combination of two processes: a drift in the referent hand coordinate due to the hypothesized back-coupling between the referent and actual hand coordinates and an implicit instruction to keep the hand steady when no changes in robot-generated force took place. The data provide support for the idea of back-coupling between the referent and actual body configurations, which may be an important contributor to stability of motor actions.

Moving a hand-held object: Reconstruction of referent coordinate and apparent stiffness trajectories

This study used the framework of the referent configuration hypothesis and slow changes in the external conditions during vertical oscillation of a hand-held object to infer the characteristics of hypothetical control variables. The study had two main objectives: (1) to show that hypothetical control variables, namely, referent coordinates and apparent stiffness of vertical hand position and grip force can be measured in an experiment; and (2) to establish relation(s) between these control variables that yield the classic grip-force-load-force coupling. Healthy subjects gripped a handle and performed vertical oscillations between visual targets at one of five metronome-prescribed frequencies. A HapticMaster robot was used to induce slow changes in the vertical force applied to the handle, while the size of the handle was changed slowly leading to changes in the grip aperture. The subjects were instructed not to react to possible changes in the external forces. A linear, second-order model was used to reconstruct the referent coordinate and apparent stiffness values for each phase of the vertical oscillation cycle using across-cycle regressions. The reconstructed time profiles of the referent coordinates and apparent stiffness showed consistent trends across subjects and movement frequencies. To validate the method, these values were used to predict the vertical force and the grip force applied to the handle for movement cycles that were not utilized in the reconstruction process. Analysis of the coupling between the four variables, two referent coordinates and two apparent stiffness values, revealed a single strong constraint reflecting the coupling between the grip force and vertical force. We view these data as providing experimental support for the idea of controlling natural, multi-muscle actions with shifts in a low-dimensional set of referent coordinates.

Positional errors introduced by transient perturbations applied to a multi-joint limb

We explored a recently discovered phenomenon that smooth transient perturbations applied to the hand can lead to violations of equifinality. Healthy subjects occupied an initial hand position against a bias force and tried not to interfere with hand displacements produced by changes in the force. The force changes were smooth and transient (ending up with the same bias force value), with or without a time interval (dwell time) between the force change application and removal. They could lead to an increase or a decrease in the bias force. The subjects performed the task with eyes open and closed. After the force change was over, the hand stopped consistently short of the initial position only when the initial force change increased the bias force. No consistent positional errors were seen for the opposite force change direction. These results were consistent across trials with and without dwell time performed with and without vision. We conclude that the positional errors were not due to muscle properties but reflected a drift in the hand referent coordinate within the central nervous system triggered by the perturbation and driven by the difference between the actual and referent hand coordinates during the dwell time.

Characteristics of unintentional movements by a multijoint effector

The authors explored the phenomenon of unintentional changes in the equilibrium state of a multijoint effector produced by transient changes in the external force. The subjects performed a position-holding task against a constant force produced by a robot and were instructed not to intervene voluntarily with movements produced by changes in the robot force. The robot produced a smooth force increase leading to a hand movement, followed by a dwell time. Then, the force dropped to its initial value leading to hand movement toward the initial position, but the hand stopped short of the initial position. The undershoot magnitude increased linearly with the peak hand displacement and exponentially with dwell time (time constant of about 1 s). For long dwell times, the hand stopped at about half the total distance to the initial position. The authors interpret the results as consequences of a drift of the referent hand coordinate. Our results provide support for back-coupling between the referent and actual body configurations during multijoint actions and produce the first quantitative analysis of this phenomenon. This mechanism can also explain the phenomena of slacking and force drop after turning visual feedback off during accurate force production task.

Stability of multifinger action in different state spaces

We investigated stability of action by a multifinger system with three methods: analysis of intertrial variance, application of transient perturbations, and analysis of the system's motion in different state spaces. The "inverse piano" device was used to apply transient (lifting-and-lowering) perturbations to individual fingers during single- and two-finger accurate force production tasks. In each trial, the perturbation was applied either to a finger explicitly involved in the task or one that was not. We hypothesized that, in one-finger tasks, task-specific stability would be observed in the redundant space of finger forces but not in the nonredundant space of finger modes (commands to explicitly involved fingers). In two-finger tasks, we expected that perturbations applied to a nontask finger would not contribute to task-specific stability in mode space. In contrast to our expectations, analyses in both force and mode spaces showed lower stability in directions that did not change total force output compared with directions that did cause changes in total force. In addition, the transient perturbations led to a significant increase in the enslaving index. We consider these results within a theoretical scheme of control with referent body configurations organized hierarchically, using multiple few-to-many mappings organized in a synergic way. The observed volatility of enslaving, greater equifinality of total force compared with elemental variables, and large magnitude of motor equivalent motion in both force and mode spaces provide support for the concept of task-specific stability of performance and the existence of multiple neural loops, which ensure this stability.

The lognormal handwriter: learning, performing, and declining

The generation of handwriting is a complex neuromotor skill requiring the interaction of many cognitive processes. It aims at producing a message to be imprinted as an ink trace left on a writing medium. The generated trajectory of the pen tip is made up of strokes superimposed over time. The Kinematic Theory of rapid human movements and its family of lognormal models provide analytical representations of these strokes, often considered as the basic unit of handwriting. This paradigm has not only been experimentally confirmed in numerous predictive and physiologically significant tests but it has also been shown to be the ideal mathematical description for the impulse response of a neuromuscular system. This latter demonstration suggests that the lognormality of the velocity patterns can be interpreted as reflecting the behavior of subjects who are in perfect control of their movements. To illustrate this interpretation, we present a short overview of the main concepts behind the Kinematic Theory and briefly describe how its models can be exploited, using various software tools, to investigate these ideal lognormal behaviors. We emphasize that the parameters extracted during various tasks can be used to analyze some underlying processes associated with their realization. To investigate the operational convergence hypothesis, we report on two original studies. First, we focus on the early steps of the motor learning process as seen as a converging behavior toward the production of more precise lognormal patterns as young children practicing handwriting start to become more fluent writers. Second, we illustrate how aging affects handwriting by pointing out the increasing departure from the ideal lognormal behavior as the control of the fine motricity begins to decline. Overall, the paper highlights this developmental process of merging toward a lognormal behavior with learning, mastering this behavior to succeed in performing a given task, and then gradually deviating from it with aging.

The distributed lambda (λ) model (DLM): a 3-D, finite-element muscle model based on Feldman's λ model; assessment of orofacial gestures

PURPOSE

The authors aimed to design a distributed lambda model (DLM), which is well adapted to implement three-dimensional (3-D), finite-element descriptions of muscles.

METHOD

A muscle element model was designed. Its stress-strain relationships included the active force-length characteristics of the λ model along the muscle fibers, together with the passive properties of muscle tissues in the 3-D space. The muscle element was first assessed using simple geometrical representations of muscles in the form of rectangular bars. It was then included in a 3-D face model, and its impact on lip protrusion was compared with the impact of a Hill-type muscle model.

RESULTS

The force-length characteristic associated with the muscle elements matched well with the invariant characteristics of the λ model. The impact of the passive properties was assessed. Isometric force variation and isotonic displacements were modeled. The comparison with a Hill-type model revealed strong similarities in terms of global stress and strain.

CONCLUSION

The DLM accounted for the characteristics of the λ model. Biomechanically, no clear differences were found between the DLM and a Hill-type model. Accurate evaluations of the λ model, based on the comparison between data and simulations, are now possible with 3-D biomechanical descriptions of the speech articulators because of the DLM.