American Society of Biomechanics Journal of Biomechanics Award 2018: Adaptive motor planning of center-of-mass trajectory during goal-directed walking in novel environments

To aid in the successful execution of goal-directed walking (discrete movement from a start location to an end target) the central nervous system forms a predictive motor plan. For the motor plan to be effective, it must be adapted in response to environmental changes. Despite motor planning being inherent to goal-directed walking, it is not understood how the nervous system adapts these plans to interact with changing environments. Our objective was to understand how people adapt motor plans of center of mass (COM) trajectory during goal-directed walking in response to a consistent change in environmental dynamics. Participants preformed a series of goal-directed walking trials in a novel environment created by a cable robot that applied a lateral force field to their COM. We hypothesized that participants would adapt to the environment by forming an internal model of their COM trajectory within the force field. Our findings support this hypothesis. Initially, we found COM trajectory significantly deviated in the same direction as the applied field, relative to baseline (no field) (p = 0.002). However, with practice in the field, COM trajectory adapted back to the baseline (p = 0.6). When we unexpectedly removed the field, participants demonstrated after-effects, COM trajectory deviated in the direction opposite of the field relative to baseline (p < 0.001). Our findings suggest that when performing a goal-directed walking task, people adapt a motor plan that predicts the COM trajectory that will emerge from the interaction between a specific set of motor commands and the external environment.     

Postural control system

The postural control system has two main functions: first, to build up posture against gravity and ensure that balance is maintained; and second, to fix the orientation and position of the segments that serve as a reference frame for perception and action with respect to the external world. This dual function of postural control is based on four components: reference values, such as orientation of body segments and position of the center of gravity (an internal representation of the body or postural body scheme); multisensory inputs regulating orientation and stabilization of body segments; and flexible postural reactions or anticipations for balance recovery after disturbance, or postural stabilization during voluntary movement. The recent data related to the organization of this system will be discussed in normal subjects (during ontogenesis), the elderly and in patients with relevant deficits.     

Center of mass motion in swimming fish: effects of speed and locomotor mode during undulatory propulsion

Studies of center of mass (COM) motion are fundamental to understanding the dynamics of animal movement, and have been carried out extensively for terrestrial and aerial locomotion. But despite a large amount of literature describing different body movement patterns in fishes, analyses of how the center of mass moves during undulatory propulsion are not available. These data would be valuable for understanding the dynamics of different body movement patterns and the effect of differing body shapes on locomotor force production. In the present study, we analyzed the magnitude and frequency components of COM motion in three dimensions (x: surge, y: sway, z: heave) in three fish species (eel, bluegill sunfish, and clown knifefish) swimming with four locomotor modes at three speeds using high-speed video, and used an image cross-correlation technique to estimate COM motion, thus enabling untethered and unrestrained locomotion. Anguilliform swimming by eels shows reduced COM surge oscillation magnitude relative to carangiform swimming, but not compared to knifefish using a gymnotiform locomotor style. Labriform swimming (bluegill at 0.5 body lengths/s) displays reduced COM sway oscillation relative to swimming in a carangiform style at higher speeds. Oscillation frequency of the COM in the surge direction occurs at twice the tail beat frequency for carangiform and anguilliform swimming, but at the same frequency as the tail beat for gymnotiform locomotion in clown knifefish. Scaling analysis of COM heave oscillation for terrestrial locomotion suggests that COM heave motion scales with positive allometry, and that fish have relatively low COM oscillations for their body size.     

Rotating horizontal ground reaction forces to the body path of progression

When studying the biomechanics of a transient turn, the orientation of the body will change relative to the orientation of the force plates over the progression of the turn. To express ground reaction forces relative to the body, this study investigated possible origin locations and axis alignments of body reference frames. The gait patterns of 10 subjects were recorded as subjects negotiated a 90 degrees hallway corner. Body reference frames were chosen whose origins were the center of mass (COM) and the pelvis origin (PEL). A finite-difference method was used to align the axes of the reference frames according to the horizontal paths of the COM and PEL. The ground reaction impulses (GRIs) were calculated relative to the COM and PEL reference frames. GRI differences were small between the PEL and COM frames, suggesting that either is acceptable for turning studies. Based on an investigation of finite-difference parameters, the COM frame should be used when using a kinematic sampling rate of 60 Hz. Either frame is acceptable when sampling at higher rates.     

Computational model of motor learning and perceptual change

Motor learning in the context of arm reaching movements has been frequently investigated using the paradigm of force-field learning. It has been recently shown that changes to somatosensory perception are likewise associated with motor learning. Changes in perceptual function may be the reason that when the perturbation is removed following motor learning, the hand trajectory does not return to a straight line path even after several dozen trials. To explain the computational mechanisms that produce these characteristics, we propose a motor control and learning scheme using a simplified two-link system in the horizontal plane: We represent learning as the adjustment of desired joint-angular trajectories so as to achieve the reference trajectory of the hand. The convergence of the actual hand movement to the reference trajectory is proved by using a Lyapunov-like lemma, and the result is confirmed using computer simulations. The model assumes that changes in the desired hand trajectory influence the perception of hand position and this in turn affects movement control. Our computer simulations support the idea that perceptual change may come as a result of adjustments to movement planning with motor learning.     

A Real-Time Brain-Machine Interface Combining Motor Target and Trajectory Intent Using an Optimal Feedback Control Design

Real-time brain-machine interfaces (BMI) have focused on either estimating the continuous movement trajectory or target intent. However, natural movement often incorporates both. Additionally, BMIs can be modeled as a feedback control system in which the subject modulates the neural activity to move the prosthetic device towards a desired target while receiving real-time sensory feedback of the state of the movement. We develop a novel real-time BMI using an optimal feedback control design that jointly estimates the movement target and trajectory of monkeys in two stages. First, the target is decoded from neural spiking activity before movement initiation. Second, the trajectory is decoded by combining the decoded target with the peri-movement spiking activity using an optimal feedback control design. This design exploits a recursive Bayesian decoder that uses an optimal feedback control model of the sensorimotor system to take into account the intended target location and the sensory feedback in its trajectory estimation from spiking activity. The real-time BMI processes the spiking activity directly using point process modeling. We implement the BMI in experiments consisting of an instructed-delay center-out task in which monkeys are presented with a target location on the screen during a delay period and then have to move a cursor to it without touching the incorrect targets. We show that the two-stage BMI performs more accurately than either stage alone. Correct target prediction can compensate for inaccurate trajectory estimation and vice versa. The optimal feedback control design also results in trajectories that are smoother and have lower estimation error. The two-stage decoder also performs better than linear regression approaches in offline cross-validation analyses. Our results demonstrate the advantage of a BMI design that jointly estimates the target and trajectory of movement and more closely mimics the sensorimotor control system.     

Postural Strategies and Sensory Integration: No Turning Point between Childhood and Adolescence

In this study, we investigated the sensory integration to postural control in children and adolescents from 5 to 15 years of age. We adopted the working hypothesis that considerable body changes occurring during these periods may lead subjects to under-use the information provided by the proprioceptive pathway and over-use other sensory systems such as vision to control their orientation and stabilize their body. It was proposed to determine which maturational differences may exist between the sensory integration used by children and adolescents in order to test the hypothesis that adolescence may constitute a specific phase in the development of postural control. This hypothesis was tested by applying an original protocol of slow oscillations below the detection threshold of the vestibular canal system, which mainly serves to mediate proprioceptive information, to the platform on which the subjects were standing. We highlighted the process of acquiring an accurate sensory and anatomical reference frame for functional movement. We asked children and adolescents to maintain a vertical stance while slow sinusoidal oscillations in the frontal plane were applied to the support at 0.01 Hz (below the detection threshold of the semicircular canal system) and at 0.06 Hz (above the detection threshold of the semicircular canal system) with their eyes either open or closed. This developmental study provided evidence that there are mild differences in the quality of sensory integration relative to postural control in children and adolescents. The results reported here confirmed the predominance of vision and the gradual mastery of somatosensory integration in postural control during a large period of ontogenesis including childhood and adolescence. The youngest as well as the oldest subjects adopted similar qualitative damping and segmental stabilization strategies that gradually improved with age without reaching an adult''s level. Lastly, sensory reweighting for postural strategies as assessed by very slow support oscillations presents a linear development without any qualitative turning point between childhood and adolescence.     

Velocity-Based Planning of Rapid Elbow Movements Expands the Control Scheme of the Equilibrium Point Hypothesis

According to the equilibrium point hypothesis of voluntary motor control, control action of muscles is not explicitly computed, but rather arises as a consequence of interaction between moving equilibrium position, current kinematics and stiffness of the joint. This approach is attractive as it obviates the need to explicitly specify the forces controlling limb movements. However, many debatable aspects of this hypothesis remain in the manner of specification of the equilibrium point trajectory and muscle activation (or its stiffness), which elicits a restoring force toward the planned equilibrium trajectory. In this study, we expanded the framework of this hypothesis by assuming that the control system uses the velocity measure as the origin of subordinate variables scaling descending commands. The velocity command is translated into muscle control inputs by second order pattern generators, which yield reciprocal command and coactivation commands, and create alternating activation of the antagonistic muscles during movement and coactivation in the post-movement phase, respectively. The velocity command is also integrated to give a position command specifying a moving equilibrium point. This model is purely kinematics-dependent, since the descending commands needed to modulate the visco-elasticity of muscles are implicitly given by simple parametric specifications of the velocity command alone. The simulated movements of fast elbow single-joint movements corresponded well with measured data performed over a wide range of movement distances, in terms of both muscle excitations and kinematics. Our proposal on a synthesis for the equilibrium point approach and velocity command, may offer some insights into the control scheme of the single-joint arm movements.     

Posturographic analysis through markerless motion capture without ground reaction forces measurement

The ability of the central nervous system to control posture and balance has been used with increasing frequency for the diagnosis and/or treatment evaluation of various neuromuscular diseases. Typically this analysis (Posturographic Analysis) is based on tracking the motion of the center of mass (COM) during quiet standing, however direct measurement of the COM has been commonly approximated using the movement of the center of pressure (COP). The purpose of this study was to apply and validate a new method to track the COM (center of mass) and COP (center of pressure) from a visual hull measured using a markerless motion capture (MMC) method. The method was tested by comparing the calculation of the COP from direct measurements of the COP. The deviations between the methods, below 2 mm, were small relative to the average range of movement guaranteeing a satisfactory signal to noise ratio. This new method requires only kinematic data through MMC method and without the need of a force plate can identify the influence of individual body segments to motion of the COM.     

Temporal pattern of the control actions accomplishing stabilization of the vertical posture of man

The problem of determination of the temporal patterns of control actions, which accomplish the process of the vertical posture stabilization, was considered. On the basis of stabilogram analysis, it was concluded that the temporal pattern of the trajectory components of pressure center (PC) motion consists of interval sequences. Motion velocity is practically constant within each interval. Transition to the following interval is accompanied by a spasmodic change not only in the velocity magnitude but also in its sign. It was shown that velocity constancy at the linear interval is the result of linear time change in control actions. A conclusion was drawn about the presence of two separate mechanisms realizing the process of stabilization of the vertical posture. They form independent control actions oriented in the frontal and sagittal planes.     

Dynamic balance control during sit-to-stand movement: an examination with the center of mass acceleration

The purpose of this study was to establish the region of stability of balance control using the center of mass (COM) acceleration and to characterize age-related differences during sit-to-stand (STS) movement. Whole body motion data were collected from 10 young and 10 elderly subjects while performing STS at their self-selected manners. In addition, young subjects were asked to perform another block of trials with their trunk purposely bent forward prior to seat-off. With the use of a single-link-plus-foot inverted pendulum model, boundaries for the region of stability were determined based on the COM position at seat-off and its instantaneous velocity or its peak acceleration (ROSv or ROSa, respectively). No significant group differences were detected in COM velocities at seat-off. However, peak COM accelerations differed significantly between groups and conditions. This suggested that even though a similar COM momentum was observed at seat-off, this momentum was controlled differently prior to seat-off. Young and elderly subjects utilized similar strategies but with different COM acceleration profiles to perform STS. Furthermore, data from an elderly subject who complained of difficulty in STS during the experiment were located outside the forward boundary of the ROSa, demonstrating a potential use of ROSa to differentiate individuals with declined balance control ability. The ROSa could provide insights into how the COM is controlled prior to seat-off, which may allow us to better identify elderly individuals who are most likely at a risk for imbalance or falls.     

Retinal optic flow during natural locomotion

We examine the structure of the visual motion projected on the retina during natural locomotion in real world environments. Bipedal gait generates a complex, rhythmic pattern of head translation and rotation in space, so without gaze stabilization mechanisms such as the vestibular-ocular-reflex (VOR) a walker’s visually specified heading would vary dramatically throughout the gait cycle. The act of fixation on stable points in the environment nulls image motion at the fovea, resulting in stable patterns of outflow on the retinae centered on the point of fixation. These outflowing patterns retain a higher order structure that is informative about the stabilized trajectory of the eye through space. We measure this structure by applying the curl and divergence operations on the retinal flow velocity vector fields and found features that may be valuable for the control of locomotion. In particular, the sign and magnitude of foveal curl in retinal flow specifies the body’s trajectory relative to the gaze point, while the point of maximum divergence in the retinal flow field specifies the walker’s instantaneous overground velocity/momentum vector in retinotopic coordinates. Assuming that walkers can determine the body position relative to gaze direction, these time-varying retinotopic cues for the body’s momentum could provide a visual control signal for locomotion over complex terrain. In contrast, the temporal variation of the eye-movement-free, head-centered flow fields is large enough to be problematic for use in steering towards a goal. Consideration of optic flow in the context of real-world locomotion therefore suggests a re-evaluation of the role of optic flow in the control of action during natural behavior.     

Spatial coding of the predicted impact location of a looming object

Avoiding or intercepting looming objects implies a precise estimate of both time until contact and impact location. In natural situations, extrapolating a movement trajectory relative to some egocentric landmark requires taking into account variations in retinal input associated with moment-to-moment changes in body posture. Here, human observers predicted the impact location on their face of an approaching stimulus mounted on a robotic arm, while we systematically manipulated the relation between eye, head, and trunk orientation. The projected impact point on the observer's face was estimated most accurately when the target originated from a location aligned with both the head and eye axes. Eccentric targets with respect to either axis resulted in a systematic perceptual bias ipsilateral to the trajectory's origin. We conclude that (1) predicting the impact point of a looming target requires combining retinal information with eye position information, (2) that this computation is accomplished accurately for some, but not all, possible combinations of these cues, (3) that the representation of looming trajectories is not formed in a single, canonical reference frame, and (4) that the observed perceptual biases could reflect an automatic adaptation for interceptive/defensive actions within near peripersonal space.     

Optimal control of antagonistic muscle stiffness during voluntary movements

This paper presents a study on the control of antagonist muscle stiffness during single-joint arm movements by optimal control theory with a minimal effort criterion. A hierarchical model is developed based on the physiology of the neuromuscular control system and the equilibrium point hypothesis. For point-to-point movements, the model provides predictions on (1) movement trajectory, (2) equilibrium trajectory, (3) muscle control inputs, and (4) antagonist muscle stiffness, as well as other variables. We compared these model predictions to the behavior observed in normal human subjects. The optimal movements capture the major invariant characteristics of voluntary movements, such as a sigmoidal movement trajectory with a bell-shaped velocity profile, an N-shaped equilibrium trajectory, a triphasic burst pattern of muscle control inputs, and a dynamically modulated joint stiffness. The joint stiffness is found to increase in the middle of the movement as a consequence of the triphasic muscle activities. We have also investigated the effects of changes in model parameters on movement control. We found that the movement kinematics and muscle control inputs are strongly influenced by the upper bound of the descending excitation signal that activates motoneuron pools in the spinal cord. Furthermore, a class of movements with scaled velocity profiles can be achieved by tuning the amplitude and duration of this excitation signal. These model predictions agree with a wide body of experimental data obtained from normal human subjects. The results suggest that the control of fast arm movements involves explicit planning for both the equilibrium trajectory and joint stiffness, and that the minimal effort criterion best characterizes the objective of movement planning and control.     

Analysis of kinematic invariances of multijoint reaching movement

 There is a no unique relationship between the trajectory of the hand, represented in cartesian or extrinsic space, and its trajectory in joint angle or intrinsic space in the general condition of joint redundancy. The goal of this work is to analyze the relation between planning the trajectory of a multijoint movement in these two coordinate systems. We show that the cartesian trajectory can be planned based on the task parameters (target coordinates, etc.) prior to and independently of angular trajectories. Angular time profiles are calculated from the cartesian trajectory to serve as a basis for muscle control commands. A unified differential equation that allows planning trajectories in cartesian and angular spaces simultaneously is proposed. Due to joint redundancy, each cartesian trajectory corresponds to a family of angular trajectories which can account for the substantial variability of the latter. A set of strategies for multijoint motor control following from this model is considered; one of them coincides with the frog wiping reflex model and resolves the kinematic inverse problem without inversion. The model trajectories exhibit certain properties observed in human multijoint reaching movements such as movement equifinality, straight end-point paths, bell-shaped tangential velocity profiles, speed-sensitive and speed-insensitive movement strategies, peculiarities of the response to double-step targets, and variations of angular trajectory without variations of the limb end-point trajectory in cartesian space. In humans, those properties are almost independent of limb configuration, target location, movement duration, and load. In the model, these properties are invariant to an affine transform of cartesian space. This implies that these properties are not a special goal of the motor control system but emerge from movement kinematics that reflect limb geometry, dynamics, and elementary principles of motor control used in planning. All the results are given analytically and, in order to compare the model with experimental results, by computer simulations. Received: 6 April 1994/Accepted in revised form: 25 April 1995     

Adaptive Postural Control for Joint Immobilization during Multitask Performance

Motor abundance is an essential feature of adaptive control. The range of joint combinations enabled by motor abundance provides the body with the necessary freedom to adopt different positions, configurations, and movements that allow for exploratory postural behavior. This study investigated the adaptation of postural control to joint immobilization during multi-task performance. Twelve healthy volunteers (6 males and 6 females; 21–29 yr) without any known neurological deficits, musculoskeletal conditions, or balance disorders participated in this study. The participants executed a targeting task, alone or combined with a ball-balancing task, while standing with free or restricted joint motions. The effects of joint configuration variability on center of mass (COM) stability were examined using uncontrolled manifold (UCM) analysis. The UCM method separates joint variability into two components: the first is consistent with the use of motor abundance, which does not affect COM position (V_UCM); the second leads to COM position variability (V_ORT). The analysis showed that joints were coordinated such that their variability had a minimal effect on COM position. However, the component of joint variability that reflects the use of motor abundance to stabilize COM (V_UCM) was significant decreased when the participants performed the combined task with immobilized joints. The component of joint variability that leads to COM variability (V_ORT) tended to increase with a reduction in joint degrees of freedom. The results suggested that joint immobilization increases the difficulty of stabilizing COM when multiple tasks are performed simultaneously. These findings are important for developing rehabilitation approaches for patients with limited joint movements.     

Role of signal-dependent noise during maintenance of isometric force

The assumption that signal-dependent noise during isometric force production controls the stabilization of voluntary isometric force is considered. To verify the assumption the trajectory of isometric force is decomposed into voluntary and involuntary components and the mathematical model describing the relationship between them is developed. It is shown that the integral of an involuntary component (signal-dependent noise) plays the role of the controlling parameter realizing the stabilization of a voluntary component. The stabilization is carried out both in the absence and in the presence of visual feedback. Changes of experimental conditions are accompanied by essential changes in the amplitude of the involuntary component oscillations.     

Fusion integration: COM trajectory from a force platform

A fusion integration algorithm is used to estimate the one-dimensional center of mass (COM) trajectory from force platform data. The resulting COM trajectory combines the best attributes of several established algorithms used to estimate the COM trajectory, and it appears to have the advantage of being robust, accurate, continuous in its higher derivatives, and fast to obtain. In current research projects, variations of the fusion integration algorithm have been adapted by the authors for the analysis of postural balance and the sensing of limb orientations with inertial measurement units.     

Spatial coding of visually guided arm movements in primate motor cortex

Previous studies of the motor cortex in behaving animals were focused on the relations between the activity of single cells, usually pyramidal tract neurons, and parameters of isometric contraction (e.g., intensity of force) or parameters of movement along one axis (e.g., flexion-extension) of a single joint (e.g., elbow or wrist). However, the commonly meaningful behavioral parameter is the trajectory of the hand in extrapersonal space, which is realized by simultaneous motions about two or three joints (e.g., elbow, shoulder, wrist) and concurrent engagement of several muscles. The spatial parameters of a straight trajectory are its direction and extent. We hypothesized that a major function of the motor cortex, among other possible roles, is the specification and control of the direction of the movement trajectory in space. This reference of motor cortical function to the control of spatial aspects of the trajectory differentiated our approach from the other approaches outlined above. We investigated the directional selectivity cells in the arm area of the motor cortex by recording their activity while monkeys moved their hands in various directions in space towards visual targets. There were two salient findings of these studies. First, the intensity of the discharge of single cells varies in an orderly fashion with the direction of movement in space, so that the discharge rate is highest with movements in a preferred direction, and decreases progressively with movements made in directions more and more away from the preferred one. Thus single cells are broadly tuned around a preferred direction which differs among different cells.(ABSTRACT TRUNCATED AT 250 WORDS)     

Control of lateral weight transfer is associated with walking speed in individuals post-stroke

Restoring functional gait speed is an important goal for rehabilitation post-stroke. During walking, transferring of one’s body weight between the limbs and maintaining balance stability are necessary for independent functional gait. Although it is documented that individuals post-stroke commonly have difficulties with performing weight transfer onto their paretic limbs, it remains to be determined if these deficits contributed to slower walking speeds. The primary purpose of this study was to compare the weight transfer characteristics between slow and fast post-stroke ambulators. Participants (N = 36) with chronic post-stroke hemiparesis walked at their comfortable and maximal walking speeds on a treadmill. Participants were stratified into 2 groups based on their comfortable walking speeds (≥0.8 m/s or <0.8 m/s). Minimum body center of mass (COM) to center of pressure (COP) distance, weight transfer timing, step width, lateral foot placement relative to the COM, hip moment, peak vertical and anterior ground reaction forces, and changes in walking speed were analyzed. Results showed that slow walkers walked with a delayed and deficient weight transfer to the paretic limb, lower hip abductor moment, and more lateral paretic limb foot placement relative to the COM compared to fast walkers. In addition, propulsive force and walking speed capacity was related to lateral weight transfer ability. These findings demonstrated that deficits in lateral weight transfer and stability could potentially be one of the limiting factors underlying comfortable walking speeds and a determinant of chronic stroke survivors’ ability to increase walking speed.