Artificial neural network model for the generation of muscle activation patterns for human locomotion.

Skilled locomotor behaviour requires information from various levels within the central nervous system (CNS). Mathematical models have permitted researchers to simulate various mechanisms in order to understand the organization of the locomotor control system. While it is difficult to adequately characterize the numerous inputs to the locomotor control system, an alternative strategy may be to use a kinematic movement plan to represent the complex inputs to the locomotor control system based on the possibility that the CNS may plan movements at a kinematic level. We propose the use of artificial neural network (ANN) models to represent the transformation of a kinematic plan into the necessary motor patterns. Essentially, kinematic representation of the actual limb movement was used as the input to an ANN model which generated the EMG activity of 8 muscles of the lower limb and trunk. Data from a wide variety of gait conditions was necessary to develop a robust model that could accommodate various environmental conditions encountered during everyday activity. A total of 120 walking strides representing normal walking and ten conditions where the normal gait was modified in terms of cadence, stride length, stance width or required foot clearance. The final network was assessed on its ability to predict the EMG activity on individual walking trials as well as its ability to represent the general activation pattern of a particular gait condition. The predicted EMG patterns closely matched those recorded experimentally, exhibiting the appropriate magnitude and temporal phasing required for each modification. Only 2 of the 96 muscle/gait conditions had RMS errors above 0.10, only 5 muscle/gait conditions exhibited correlations below 0.80 (most were above 0.90) and only 25 muscle/gait conditions deviated outside the normal range of muscle activity for more than 25% of the gait cycle. These results indicate the ability of single network ANNs to represent the transformation between a kinematic movement plan and the necessary muscle activations for normal steady state locomotion but they were also able to generate muscle activation patterns for conditions requiring changes in walking speed, foot placement and foot clearance. The abilities of this type of network have implications towards both the fundamental understanding of the control of locomotion and practical realizations of artificial control systems for use in rehabilitation medicine.     

Legged insects select the optimal locomotor pattern based on the energetic cost

 The gait transition in legged animals has attracted many researchers, and its relation to metabolic cost and mechanical work has been discussed in recent decades. We assumed that the energetic cost during locomotion is given by the sum of positive mechanical work and the heat energy loss that is proportional to the square of joint torque and examined the optimal locomotor pattern based on the energetic cost in a simple dynamical model of a hexapod by computer simulations. The obtained results well agree with characteristics in the locomotor patterns in legged animals; for example, the leg protraction time, step length, and the metabolic cost of transport are almost constant for many velocities, the leg cycling period decreases with velocity, and the energetic cost of locomotion induced by carrying loads linearly increases with mass loaded. This correspondence of the results of calculation to experimental results suggest that the heat energy loss for torque generation is proportional to the square of the torque during locomotion, and that the locomotor pattern in legged animals is highly optimized based on the energetic cost. Received: 22 December 1998 / Accepted: 14 April 2000     

Mechanisms of locomotion in mammals

From biochemical studies of the hindlimb locomotor cycle in the cat, it appears that joint angle excursions are more simple at hip than at more distal joints. The pattern of EMG activity for the different hindlimb muscles is not simple but detailed and is roughly kept the same in the deafferented preparation and in the chronic spinal preparation too: these results show the central and spinal origin of the basic rhythm generation of the locomotor pattern. What is added to this basic mechanism by the supraspinal levels is: (1) a tonic activation which is necessary for the locomotor bursting to be initiated and maintained; (2) an adjustment of four limb posture to ensure equilibrium throughout a locomotor episode. The cerebellum is likely a leader in latter control. The basic spinal pattern is also controlled by peripheral feed-back signals which operate at spinal level and can delay the next locomotor cycle as long as the limb is loaded. On the other hand, a gain control of simple spinal reflexes is achieved by the spinal locomotion generator versus the phase of the locomotor cycle.     

Mechanical performance of aquatic rowing and flying

Aquatic flight, performed by rowing or flapping fins, wings or limbs, is a primary locomotor mechanism for many animals. We used a computer simulation to compare the mechanical performance of rowing and flapping appendages across a range of speeds. Flapping appendages proved to be more mechanically efficient than rowing appendages at all swimming speeds, suggesting that animals that frequently engage in locomotor behaviours that require energy conservation should employ a flapping stroke. The lower efficiency of rowing appendages across all speeds begs the question of why rowing occurs at all. One answer lies in the ability of rowing fins to generate more thrust than flapping fins during the power stroke. Large forces are necessary for manoeuvring behaviours such as accelerations, turning and braking, which suggests that rowing should be found in slow-swimming animals that frequently manoeuvre. The predictions of the model are supported by observed patterns of behavioural variation among rowing and flapping vertebrates.     

Early development of locomotor behavior in vervet monkeys

The locomotor development of three vervet infants across approximately the first 2 months of life is described. Fairly normal-looking walking movements (as compared to adults) were seen in all the animals by approximately 1 month of age and galloping was observed by 2 months. Early locomotor footfall patterns were often aberrant and bounding-type gaits were sometimes exhibited. Most of the symmetrical gaits observed were classifiable as lateral sequence. Across the 2-month period the animals showed decreased three- and four-foot support and improvements in joint angular displacement patterns. From their earliest locomotor movements the infants showed significant linear relationship between both cycle duration and swing and stance durations of the limbs. We suggest that locomotor control mechanisms are probably fairly mature at birth but that weight support and postural control problems explain the initial locomotor difficulties exhibited by these infants.     

Modeling and optimal control of an energy-storing prosthetic knee

Advanced prosthetic knees for transfemoral amputees are currently based on controlled damper mechanisms. Such devices require little energy to operate, but can only produce negative or zero joint power, while normal knee joint function requires alternative phases of positive and negative work. The inability to generate positive work may limit the user's functional capabilities, may cause undesirable adaptive behavior, and may contribute to excessive metabolic energy cost for locomotion. In order to overcome these problems, we present a novel concept for an energy-storing prosthetic knee, consisting of a rotary hydraulic actuator, two valves, and a spring-loaded hydraulic accumulator. In this paper, performance of the proposed device will be assessed by computational modeling and by simulation of functional activities. A computational model of the hydraulic system was developed, with methods to obtain optimal valve control patterns for any given activity. The objective function for optimal control was based on tracking of joint angles, tracking of joint moments, and the energy cost of operating the valves. Optimal control solutions were obtained, based on data collected from three subjects during walking, running, and a sit-stand-sit cycle. Optimal control simulations showed that the proposed device allows near-normal knee function during all three activities, provided that the accumulator stiffness was tuned to each activity. When the energy storage mechanism was turned off in the simulations, the system functioned as a controlled damper device and optimal control results were similar to literature data on human performance with such devices. When the accumulator stiffness was tuned to walking, simulated performance for the other activities was sub-optimal but still better than with a controlled damper. We conclude that the energy-storing knee concept is valid for the three activities studied, that modeling and optimal control can assist the design process, and that further studies using human subjects are justified.     

Symmetry-breaking bifurcation: A possible mechanism for 2:1 frequency-locking in animal locomotion

The generation and control of animal locomotion is believed to involve central pattern generators — networks of neurons which are capable of producing oscillatory behavior. In the present work, the quadrupedal locomotor central pattern generator is modelled as four distinct but symmetrically coupled nonlinear oscillators. We show that the typical patterns for two such networks of oscillators include 2:1 frequency-locked oscillations. These patterns, which arise through symmetry-breaking Hopf bifurcation, correspond in part to observed patterns of 2:1 frequency-locking of limb movements during electrically elicited locomotion of decerebrate and spinal quadrupeds. We briefly describe how our theoretical predictions could be tested experimentally.     

Deciphering the Palimpsest: Studying the Relationship Between Morphological Integration and Phenotypic Covariation

Organisms represent a complex arrangement of anatomical structures and individuated parts that must maintain functional associations through development. This integration of variation between functionally related body parts and the modular organization of development are fundamental determinants of their evolvability. This is because integration results in the expression of coordinated variation that can create preferred directions for evolutionary change, while modularity enables variation in a group of traits or regions to accumulate without deleterious effects on other aspects of the organism. Using our own work on both model systems (e.g., lab mice, avians) and natural populations of rodents and primates, we explore in this paper the relationship between patterns of phenotypic covariation and the developmental determinants of integration that those patterns are assumed to reflect. We show that integration cannot be reliably studied through phenotypic covariance patterns alone and argue that the relationship between phenotypic covariation and integration is obscured in two ways. One is the superimposition of multiple determinants of covariance in complex systems and the other is the dependence of covariation structure on variances in covariance-generating processes. As a consequence, we argue that the direct study of the developmental determinants of integration in model systems is necessary to fully interpret patterns of covariation in natural populations, to link covariation patterns to the processes that generate them, and to understand their significance for evolutionary explanation.     

Inferior olive mirrors joint dynamics to implement an inverse controller

To produce smooth and coordinated motion, our nervous systems need to generate precisely timed muscle activation patterns that, due to axonal conduction delay, must be generated in a predictive and feedforward manner. Kawato proposed that the cerebellum accomplishes this by acting as an inverse controller that modulates descending motor commands to predictively drive the spinal cord such that the musculoskeletal dynamics are canceled out. This and other cerebellar theories do not, however, account for the rich biophysical properties expressed by the olivocerebellar complex’s various cell types, making these theories difficult to verify experimentally. Here we propose that a multizonal microcomplex’s (MZMC) inferior olivary neurons use their subthreshold oscillations to mirror a musculoskeletal joint’s underdamped dynamics, thereby achieving inverse control. We used control theory to map a joint’s inverse model onto an MZMC’s biophysics, and we used biophysical modeling to confirm that inferior olivary neurons can express the dynamics required to mirror biomechanical joints. We then combined both techniques to predict how experimentally injecting current into the inferior olive would affect overall motor output performance. We found that this experimental manipulation unmasked a joint’s natural dynamics, as observed by motor output ringing at the joint’s natural frequency, with amplitude proportional to the amount of current. These results support the proposal that the cerebellum—in particular an MZMC—is an inverse controller; the results also provide a biophysical implementation for this controller and allow one to make an experimentally testable prediction.     

Contribution of NMDA and non-NMDA glutamate receptors to locomotor pattern generation in the neonatal rat spinal cord.

The motor programme executed by the spinal cord to generate locomotion involves glutamate-mediated excitatory synaptic transmission. Using the neonatal rat spinal cord as an in vitro model in which the locomotor pattern was evoked by 5-hydroxytryptamine (5-HT), we investigated the role of N-methyl-D-aspartate (NMDA) and non-NMDA glutamate receptors in the generation of locomotor patterns recorded electrophysiologically from pairs of ventral roots. In a control solution, 5-HT (2.5-30 microM) elicited persistent alternating activity in left and right lumbar ventral roots. Increasing 5-HT concentration within this range resulted in increased cycle frequency (on average from 8 to 20 cycles min-1). In the presence of NMDA receptor antagonism, persistent alternating activity was still observed as long as 5-HT doses were increased (range 20-40 microM), even if locomotor pattern frequency was lower than in the control solution. In the presence of non-NMDA receptor antagonism, stable locomotor activity (with lower cycle frequency) was also elicited by 5-HT, albeit with doses larger than in the control solution (15-40 microM). When NMDA and non-NMDA receptors were simultaneously blocked, 5-HT (5-120 microM) always failed to elicit locomotor activity. These data show that the operation of one glutamate receptor class was sufficient to express locomotor activity. As locomotor activity developed at a lower frequency than in the control solution after pharmacological block of either NMDA or non-NMDA receptors, it is suggested that both receptor classes were involved in locomotor pattern generation.     

Neural control of Caenorhabditis elegans forward locomotion: the role of sensory feedback

This paper presents a simple yet biologically-grounded model for the neural control of Caenorhabditis elegans forward locomotion. We identify a minimal circuit within the C. elegans ventral cord that is likely to be sufficient to generate and sustain forward locomotion in vivo. This limited subcircuit appears to contain no obvious central pattern generated control. For that subcircuit, we present a model that relies on a chain of oscillators along the body which are driven by local and proximate mechano-sensory input. Computer simulations were used to study the model under a variety of conditions and to test whether it is behaviourally plausible. Within our model, we find that a minimal circuit of AVB interneurons and B-class motoneurons is sufficient to generate and sustain fictive forward locomotion patterns that are robust to significant environmental perturbations. The model predicts speed and amplitude modulation by the AVB command interneurons. An extended model including D-class motoneurons is included for comparison. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. John Bryden and Netta Cohen contributed equally to this work.     

Predictability of phenotypic differentiation across flow regimes in fishes

Fish inhabit environments greatly varying in intensity of water velocity, and these flow regimes are generally believed to be of major evolutionary significance. To what extent does water flow drive repeatable and predictable phenotypic differentiation? Although many investigators have examined phenotypic variation across flow gradients in fishes, no clear consensus regarding the nature of water velocity's effects on phenotypic diversity has yet emerged. Here, I describe a generalized model that produces testable hypotheses of morphological and locomotor differentiation between flow regimes in fishes. The model combines biomechanical information (describing how fish morphology determines locomotor abilities) with ecological information (describing how locomotor performance influences fitness) to yield predictions of divergent natural selection and phenotypic differentiation between low-flow and high-flow environments. To test the model's predictions of phenotypic differentiation, I synthesized the existing literature and conducted a meta-analysis. Based on results gathered from 80 studies, providing 115 tests of predictions, the model produced some accurate results across both intraspecific and interspecific scales, as differences in body shape, caudal fin shape, and steady-swimming performance strongly matched predictions. These results suggest that water flow drives predictable phenotypic variation in disparate groups of fish based on a common, generalized model, and that microevolutionary processes might often scale up to generate broader, interspecific patterns. However, too few studies have examined differentiation in body stiffness, muscle architecture, or unsteady-swimming performance to draw clear conclusions for those traits. The analysis revealed that, at the intraspecific scale, both genetic divergence and phenotypic plasticity play important roles in phenotypic differentiation across flow regimes, but we do not yet know the relative importance of these two sources of phenotypic variation. Moreover, while major patterns within and between species were predictable, we have little direct evidence regarding the role of water flow in driving speciation or generating broad, macroevolutionary patterns, as too few studies have addressed these topics or conducted analyses within a phylogenetic framework. Thus, flow regime does indeed drive some predictable phenotypic outcomes, but many questions remain unanswered. This study establishes a general model for predicting phenotypic differentiation across flow regimes in fishes, and should help guide future studies in fruitful directions, thereby enhancing our understanding of the predictability of phenotypic variation in nature.     

A Method for Numerical Simulation of Single Limb Ground Contact Events: Application to Heel-Toe Running

The objective of this work was to develop a method to simulate single-limb ground contact events, which may be applied to study musculoskeletal injuries associated with such movements. To achieve this objective, a three-dimensional musculoskeletal model was developed consisting of the equations of motion for the musculoskeletal system, and models for the muscle force generation and ground contact elements. An optimization framework and a weighted least-squares objective function were presented that generated muscle stimulation patterns that optimally reproduced subject-specific movement data. Experimental data were collected from a single subject to provide initial conditions for the simulation and tracking data for the optimization. As an example application, a simulation of the stance phase of running was generated. The results showed that the average difference between the simulation and subject's ground reaction force and joint angle data was less than two inter-trial standard deviations. Further, there was good agreement between the model's muscle excitation patterns and experimentally collected electromyography data. These results give confidence in the model to examine musculoskeletal loading during a variety of landing movements and to study the effects of various factors associated with injury. Limitations were examined and areas of improvement for the model were presented.     

Learning to walk with a robotic ankle exoskeleton

We used a lower limb robotic exoskeleton controlled by the wearer's muscle activity to study human locomotor adaptation to disrupted muscular coordination. Ten healthy subjects walked while wearing a pneumatically powered ankle exoskeleton on one limb that effectively increased plantar flexor strength of the soleus muscle. Soleus electromyography amplitude controlled plantar flexion assistance from the exoskeleton in real time. We hypothesized that subjects' gait kinematics would be initially distorted by the added exoskeleton power, but that subjects would reduce soleus muscle recruitment with practice to return to gait kinematics more similar to normal. We also examined the ability of subjects to recall their adapted motor pattern for exoskeleton walking by testing subjects on two separate sessions, 3 days apart. The mechanical power added by the exoskeleton greatly perturbed ankle joint movements at first, causing subjects to walk with significantly increased plantar flexion during stance. With practice, subjects reduced soleus recruitment by approximately 35% and learned to use the exoskeleton to perform almost exclusively positive work about the ankle. Subjects demonstrated the ability to retain the adapted locomotor pattern between testing sessions as evidenced by similar muscle activity, kinematic and kinetic patterns between the end of the first test day and the beginning of the second. These results demonstrate that robotic exoskeletons controlled by muscle activity could be useful tools for testing neural mechanisms of human locomotor adaptation.     

Modular neuromuscular control of human locomotion by central pattern generator

The central pattern generators (CPG) in the spinal cord are thought to be responsible for producing the rhythmic motor patterns during rhythmic activities. For locomotor tasks, this involves much complexity, due to a redundant system of muscle actuators with a large number of highly nonlinear muscles. This study proposes a reduced neural control strategy for the CPG, based on modular organization of the co-active muscles, i.e., muscle synergies. Four synergies were extracted from the EMG data of the major leg muscles of two subjects, during two gait trials each, using non-negative matrix factorization algorithm. A Matsuoka׳s four-neuron CPG model with mutual inhibition, was utilized to generate the rhythmic activation patterns of the muscle synergies, using the hip flexion angle and foot contact force information from the sensory afferents as inputs. The model parameters were tuned using the experimental data of one gait trial, which resulted in a good fitting accuracy (RMSEs between 0.0491 and 0.1399) between the simulation and experimental synergy activations. The model׳s performance was then assessed by comparing its predictions for the activation patterns of the individual leg muscles during locomotion with the relevant EMG data. Results indicated that the characteristic features of the complex activation patterns of the muscles were well reproduced by the model for different gait trials and subjects. In general, the CPG- and muscle synergy-based model was promising in view of its simple architecture, yet extensive potentials for neuromuscular control, e.g., resolving redundancies, distributed and fast control, and modulation of locomotion by simple control signals.     

Altered kinetic strategy for the control of swing limb elevation over obstacles in unilateral below-knee amputee gait.

Our goal was to document the kinetic strategies for obstacle avoidance in below-knee amputees. Kinematic data were collected as unilateral below-knee traumatic amputees stepped over obstacles of various heights in the walking path. Inverse dynamics were employed to calculate power profiles and work during the limb-elevation and limb-lowering phases. Limb elevation was achieved by employing a different strategy of intra-limb interaction for elevation of the prosthetic limb than for the sound limb, which was similar to that seen in healthy adult non-amputees. As obstacle height increased, prosthetic side knee flexion was increased by modulating the work done at the hip, and not the knee, as seen on the sound side. Although the strength of the muscles about the residual knee was preserved, the range of motion of that knee had previously been found to be somewhat limited. Perhaps more importantly, potential instability of the interface between the stump and the prosthetic socket, and associated discomfort at the stump could explain the altered limb-elevation strategy. Interestingly, the limb-lowering strategy seen in the sound limb and in non-amputees already features modulation of rotational and translational work at the hip, so an alternate strategy was not required. Thus, following a major insult to the sensory and neuromuscular system, the CNS is able to update the internal model of the locomotor apparatus as the individual uses the new limb in a variety of movements, and modify control strategies as appropriate.     

Effects of 6(5H)-phenanthridinone,an Inhibitor of Poly(ADP-ribose)Polymerase-1 Activity (PARP-1), on Locomotor Networks of the Rat Isolated Spinal Cord

Excitotoxicity is considered to be a major pathophysiological mechanism responsible for extensive neuronal death after acute spinal injury. The chief effector of such a neuronal death is thought to be the hyperactivation of intracellular PARP-1 that leads to cell energy depletion and DNA damage with the manifestation of non-apoptotic cell death termed parthanatos. An in vitro lesion model using the neonatal rat spinal cord has recently shown PARP-1 overactivity to be closely related to neuronal losses after an excitotoxic challenge by kainate: in this system the PARP-1 inhibitor 6(5H)-phenanthridinone (PHE) appeared to be a moderate histological neuroprotector. This article investigated whether PHE could actually preserve the function of locomotor networks in vitro from excitotoxicity. Bath-applied PHE (after a 60 min kainate application) failed to recover locomotor network function 24 h later. When the PHE administration was advanced by 30 min (during the administration of kainate), locomotor function could still not be recovered, while basic network rhythmicity persisted. Histochemical analysis showed that, even if the number of surviving neurons was improved with this protocol, it had failed to reach the threshold of minimal network membership necessary for expressing locomotor patterns. These results suggest that PARP-1 hyperactivity was a rapid onset mechanism of neuronal loss after an excitotoxic challenge and that more selective and faster-acting PARP-1 inhibitors are warranted to explore their potential neuroprotective role.     

An Experimental Analysis of Overcoming Obstacle in Human Walking

In this paper, an experimental analysis of overcoming obstacle in human walking is carried out by means of a motion capture system. In the experiment, the lower body of an adult human is divided into seven segments, and three markers are pasted to each segment with the aim to obtain moving trajectory and to calculate joint variation during walking. Moreover, kinematic data in terms of displacement, velocity and acceleration are acquired as well. In addition, ground reaction forces are measured using force sensors. Based on the experimental results, features of overcoming obstacle in human walking are ana- lyzed. Experimental results show that the reason which leads to smooth walking can be identified as that the human has slight movement in the vertical direction during walking; the reason that human locomotion uses gravity effectively can be identified as that feet rotate around the toe joints during toe-off phase aiming at using gravitational potential energy to provide propulsion for swing phase. Furthermore, both normal walking gait and obstacle overcoming gait are characterized in a form that can provide necessary knowledge and useful databases for the implementation of motion planning and gait planning towards overcoming obstacle for humanoid robots.     

An equilibrium-point model of electromyographic patterns during single-joint movements based on experimentally reconstructed control signals

The purpose of this work has been to develop a model of electromyographic (EMG) patterns during single-joint movements based on a version of the equilibrium-point hypothesis, a method for experimental reconstruction of the joint compliant characteristics, the dual-strategy hypothesis, and a kinematic model of movement trajectory. EMG patterns are considered emergent properties of hypothetical control patterns that are equally affected by the control signals and peripheral feedback reflecting actual movement trajectory. A computer model generated the EMG patterns based on simulated movement kinematics and hypothetical control signals derived from the reconstructed joint compliant characteristics. The model predictions have been compared to published recordings of movement kinematics and EMG patterns in a variety of movement conditions, including movements over different distances, at different speeds, against different-known inertial loads, and in conditions of possible unexpected decrease in the inertial load. Changes in task parameters within the model led to simulated EMG patterns qualitatively similar to the experimentally recorded EMG patterns. The model's predictive power compares it favourably to the existing models of the EMG patterns.