Predictive algorithms for neuromuscular control of human locomotion.

The problem of quantifying muscular activity of the human body can be formulated as an optimal control problem. The current methods used with large-scale biomechanical systems are non-derivative techniques. These methods are costly, as they require numerous integrations of the equations of motion. Additionally, the convergence is slow, making them impractical for use with large systems. We apply an efficient numerical algorithm to the biomechanical optimal control problem. Using direct collocation with a trapezoidal discretization, the equations of motion are converted into a set of algebraic constraint equations. An augmented Lagrangian formulation is used for the optimization problem to handle both equality and inequality constraints. The resulting min-max problem is solved with a generalized Newton method. In contrast to the prevalent optimal control implementations, we calculate analytical first- and second-derivative information and obtain local quadratic convergence. To demonstrate the efficacy of the method, we solve a steady-state pedaling problem with 7 segments and 18 independent muscle groups. The computed muscle activations compare well with experimental EMG data. The computational effort is significantly reduced and solution times are a fraction of those of the non-derivative techniques.     

A model of the neuro-musculo-skeletal system for human locomotion

The generation of human locomotion was examined by linking computational neuroscience with biomechanics from the perspective of nonlinear dynamical theory. We constructed a model of human locomotion, which includes a musculo-skeletal system with 8 segments and 20 muscles, a neural rhythm generator composed of 7 pairs of neural oscillators, and mechanisms for processing and transporting sensory and motor signals. Using a computer simulation, we found that locomotion emerged as a stable limit cycle that was generated by the global entrainment between the musculo-skeletal system, the neural system, and the environment. Moreover, the walking movements of the model could be compared quantitatively with those of experimental studies in humans.Part of this paper was presented to IVth International Symposium on Computer Simulation in Biomechanics, Paris, France, July 1, 1993     

Adiabatic transformability hypothesis of human locomotion

It is hypothesized that metabolic and mechanical changes in human locomotion associated with changes in speed v are constrained by two attractive strategies: $Q_{{\text{metab}}} = 1{\text{ and }}\Delta Q_{{\text{metab}}} /\Delta v = {\text{a}}$ positive definite constant. $Q_{{\text{metab}}} = \Delta {\rm E}_{\text{k}} {\text{s}}^{{\text{ - 1}}} /{\text{ml O}}_{\text{2}} {\text{s}}^{{\text{ - 1}}} $ where ΔEs^?1 is the summed increments and decrements per unit time in the translational and rotational kinetic energies of the body's segments and ml O₂s^?1 is the rate at which chemical energy is dissipated. The expected constancy of ΔQ _metab/Δv _metab was derived from an extension of Ehrenfest's adiabatic hypothesis by which transformations (increases, decreases) in locomotion v can be considered as adiabatic, even though the biological conditions are nonconservative and non-rate-limited. The expected significance of Q _metab=1 was derived from stability considerations of the symmetry per stride of stored and dissipated energy. An experimental evaluation was provided by collecting metabolic and mechanical measures on walking (10 subjects) and running (9 subjects) at progressively greater treadmill speeds but within the aerobic limit. Results revealed that walking was restricted to ometab ? 1 with a nonlinear trajectory in v×Q _metab coordinates shaped by Q _metab=1 (primarily) and the constancy of ΔQ _metab/Δv. Running satisfied Q _metab > 1, with a linear trajectory in v×Q _metab coordinates conforming to ΔQ _metab/_Δv=a constant, with the constant predicted from invariants in the mechanical space v×ΔE _ks^?1. Results also suggested that the metabolic costs of running might be predictable from measures made in the v×ΔE _ks^?1 space.     

Spinal reciprocal inhibition in human locomotion.

The purpose of this paper was to study spinal inhibition during several different motor tasks in healthy human subjects. The short-latency, reciprocal inhibitory pathways from the common peroneal (CP) nerve to the soleus muscle and from the tibial nerve to the tibialis anterior muscle were studied as a depression of ongoing voluntary electromyograph (EMG) activity. First, the effect of stimulus intensity on the amount of inhibition was examined to decide an appropriate stimulation to study the task-dependent modulation of inhibition. Then, the inhibition at one level of stimulation (1.5 x motor threshold) was investigated during standing, walking, and running. The change in slope of inhibition vs. EMG level, which approximates the fraction of ongoing activity that is inhibited, decreased with CP stimulation from 0.52 during standing to 0.30 during fast walking (6 km/h) to 0.17 during running at 9 km/h. Similarly, the slope decreased with tibial nerve stimulation from 0.68 (standing) to 0.42 (fast walking) to 0.35 (running at 9 km/h). All differences, except the last one, were highly significant (P < 0.01, Student's t-test). However, the difference between walking (0.42) and running (0.36) at the same speed (6 km/h) was not significant with tibial nerve stimulation and only significant at P < 0.05 with CP nerve stimulation (0.30, 0.20). Also, the difference between standing (0.52) and slow walking (3 km/h; 0.41) with CP stimulation was not significant, but it was significant (P < 0.01) with tibial nerve stimulation (0.68, 0.49). In conclusion, our findings indicate that spinal reciprocal inhibition decreases substantially with increasing speed and only changes to a lesser extent with task.     

A model of neuro-musculo-skeletal system for human locomotion under position constraint condition

The human locomotion was studied on the basis of the interaction of the musculo-skeletal system, the neural system and the environment. A mathematical model of human locomotion under position constraint condition was established. Besides the neural rhythm generator, the posture controller and the sensory system, the environment feedback controller and the stability controller were taken into account in the model. The environment feedback controller was proposed for two purposes, obstacle avoidance and target position control of the swing foot. The stability controller was proposed to imitate the self-balancing ability of a human body and improve the stability of the model. In the stability controller, the ankle torque was used to control the velocity of the body gravity center. A prediction control algorithm was applied to calculate the torque magnitude of the stability controller. As an example, human stairs climbing movement was simulated and the results were given. The simulation result proved that the mathematical modeling of the task was successful.     

Postural stability of the human mandible during locomotion

Movements of the head and of the mandible relative to the head were measured in human subjects walking and running on a treadmill at various speeds and inclinations. A miniature magnet and piezo-electric accelerometer assembly was mounted on the mandibular incisors, and a Hall-effect sensor along with a second accelerometer mounted on a maxillary incisor along a common vertical axis. Signals from these sensors provided continuous records of vertical head and mandible acceleration, and relative jaw position. Landing on the heel or on the toe in different forms of locomotion was followed by rapid deceleration of the downward movement of the head and slightly less rapid deceleration of the downward movement of the mandible, i.e., the mandible moved downwards relative to the maxilla, then upwards again to near its normal posture within 200 ms. No tooth contact occurred in any forms of gait at any inclination. The movement of the mandible relative to the maxilla depended on the nature and velocity of the locomotion and their effects on head deceleration. The least deceleration and hence mandibular displacement occurred during toe-landing, for example, during "uphill" running. The maximum displacement of the mandible relative to the head was less than 1mm, even at the fastest running speed. The mechanisms that limit the vertical movements of the jaw within such a narrow range are not known, but are likely to include passive soft-tissue visco-elasticity and stretch reflexes in the jaw-closing muscles.     

Physiological determinants of best performances in human locomotion

In human locomotion, the metabolic power required (E) to cover a given distance d, in the time t is set by the product of the energy cost of the locomotion (C), i.e. the amount of metabolic energy spent to move over one unit of distance, and the speed (v = d t(-1)): E = Cv = Cdt(-1). Since, for any given d, v is a decreasing function of t and C is either constant or increases with v, it necessarily follows that E is larger the smaller the value of t. Thus, for any given distance and subject, the shortest time will be achieved when E is equal to the individual maximal metabolic power (Emax). In turn, Emax is a decreasing function of t: it depends upon the subject's maximal aerobic power (MAP) and on the maximal amount of energy derived from the full utilisation of anaerobic energy stores (AnS). So, if the relationship between C and (v) in the locomotion at stake and the subject's MAP and AnS are known, his best performance time (BPT) over any given distance can be obtained by solving the equality Emax(t) = E(t). This approach has been applied to estimate individual BPTs in running and cycling. In this paper, the above approach will be used to quantify the role of C, MAP, and AnS in determining BPTs for running, track cycling and swimming. This has been achieved by calculating the changes in BPT obtained when each variable, or a combination thereof, is changed by a given percentage. The results show that in all the three types of locomotion, regardless of the speed, the changes in BPT brought about by changes of C alone account for 45-55% of the changes obtained when all three variables (C, MAP and AnS) are changed by the same amount.     

Modeling biological motor control for human locomotion with functional electrical stimulation

This paper develops a novel control system for functional electrical stimulation (FES) locomotion, which aims to generate normal locomotion for paraplegics via FES. It explores the possibility of applying ideas from biology to engineering. The neural control mechanism of the biological motor system, the central pattern generator, has been adopted in the control system design. Some artificial control techniques such as neural network control, fuzzy logic, control and impedance control are incorporated to refine the control performance. Several types of sensory feedback are integrated to endow this control system with an adaptive ability. A musculoskeletal model with 7 segments and 18 muscles is constructed for the simulation study. Satisfactory simulation results are achieved under this FES control system, which indicates a promising technique for the potential application of FES locomotion in future.     

Fundamental patterns of bilateral muscle activity in human locomotion

Human gait is characterized by smooth, regular and repeating movements but the control system is complex: there are many more actuators (i.e. muscles) than degrees of freedom in the system. Statistical pattern-recognition techniques have been applied to examine muscle activity signals, but these have all concentrated exclusively on unilateral gait. We report here the application of factor analysis to the electromyographic patterns of 16 muscles (eight bilateral pairs) in ten normal subjects. Consistent with our prior work, we have established two factors, named loading response and propulsion, which correspond with important phases in the gait cycle. In addition, we have also discovered a third factor, which we have named the coordinating factor, that maintains the phase shift between the left and right sides. These findings suggest that the central nervous system solves the problem of high dimensionality by generating a few fundamental signals which control the major muscle groups in both legs.     

Experimental/analytical analysis of human locomotion using bondgraphs

A new vectorial bondgraph approach for modeling and simulation of human locomotion is introduced. The vectorial bondgraph is applied to an eight-segment gait model to derive the equations of motion for studying ground reaction forces (GRFs) and centers of pressure (COPs) in single and double support phases of ground and treadmill walking. A phase detection technique and accompanying transition equation is proposed with which the GRFs and COPs may be calculated for the transitions from double-to-single and single-to-double support phases. Good agreement is found between model predictions and experimental data obtained from force plate measurements. The bondgraph modeling approach is shown to be both informative and adaptable, in the sense that the model resembles the human body structure, and that modeled body segments can be easily added or removed.     

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.     

Video analysis of chemotactic locomotion of stored human polymorphonuclear leukocytes

Previous studies of the storage of polymorphonuclear leukocytes (PMNs) have used an empirical approach to define "optimal" conditions. To date, no storage conditions have been described which satisfactorily preserve the chemotactic function of PMNs beyond 24 h. In an effort to define the precise nature of the storage lesion, we studied the chemotactic locomotion of freshly isolated PMNs and PMNs which had been suspended in citrate-phosphate-dextrose-adenine (CPD-A1) plasma and stored in PVC bags, at 20-22 degrees C for 24 h. We used time-lapse video recording and computer image analysis to quantitate the motion of PMNs migrating under agarose. The positions of individual motile cells were traced at 1-min intervals for 5 min. The following parameters were used to quantitate migration: speed (distance/min), persistence of locomotion index (velocity/speed), orientation angle (the angle of the vector describing the next displacement of a cell relative to a direct line toward the chemoattractant), and chemotropic index (cosine of the orientation angle). After 24 h of storage, the following changes were observed: fewer cells migrated, the speed of migrating cells was reduced by 25%, the persistence of locomotion index decreased by 7%, which indicates that migrating cells made slightly more/wider turns, and the chemotropic index was decreased by 30%, which indicates that migrating cells were less accurate in their orientation toward the chemoattractant. Apparently, the storage of PMNs selectively impairs the ability of some cells to orient accurately in a chemotactic gradient and changes the distribution of these locomotor parameters within the population.     

Tripedal knuckle-walking: a proposal for the evolution of human locomotion and handedness.

A comparative morphological analysis of human and non-human hominoids was conducted in an attempt to determine the mode of locomotion of the protohominid. Although the generalized hominoid anatomy permits variation of locomotion: brachiation, knuckle-walking, etc., minor variations in structure determine which behavior is favored. Arboreal arm swinging requires a flexible forelimb while terrestrial fist or knuckle-walking demands more rigidity of the hand and wrist. It is demonstrated that the large human thumb accompanied by the strong adduction of the thenar, hypothenar, and palmar interosseous muscles offer powerful rigidity to the hand, while fusion of the os centrale with the scaphoid during gestation permits the formation of an arch of carpals which imbue the wrist with the stability necessary for weight bearing. Fascialization of the contrahentes and dorsiepitrochlearis muscles in the human as well as depilation of the middle phalanges; the webbing (syndactyly) of the palm; the direction of the fibers of the interosseous membrane of the forearm; the shape of the puerile annular ligament, and the direction of the human glenoid fossa strongly suggest that the ancestor of man used a knuckle-walking form of locomotion prior to becoming bipedal. A model is presented that suggests that bipedalism was attained through an intermediate stage of tripedalism. The model is based on the fact that man's anatomy is much more asymmetric than that of the great apes. A presumption is made that due to the absence of trees for climbing in the transition from forest to open plain, the protohominid needed to carry tools (stones) at all times for protection. Stones could be carried for long distances on the posterior iliac crest since the weight would be shifted posteriorly over the legs. Pick up, medial rotation and adduction of the stone would employ a two-muscle chain of biceps brachii and latissimus dorsi. On the iliac crest, the stone is posterior to the coronal plane of the glenohumeral joint, and with the contraction of this two-muscle chain, the shoulder on one side is moved posteriorly effecting a semi-erect posture. It is proposed that tripedalism of the protohominid may be an explanation for the handedness unique to hominids.     

Ground reaction forces during human locomotion on railroad ballast

Locomotion over ballast surfaces provides a unique situation for investigating the biomechanics of gait. Although much research has focused on level and sloped walking on a smooth, firm surface in order to understand the common kinematic and kinetic variables associated with human locomotion, the literature currently provides few if any discussions regarding the dynamics of locomotion on surfaces that are either rocky or uneven. The purpose of this study was to investigate a method for using force plates to measure the ground reaction forces (GRFs) during gait on ballast. Ballast is a construction aggregate of unsymmetrical rock used in industry for the purpose of forming track bed on which railway ties are laid or in yards where railroad cars are stored. It is used to facilitate the drainage of water and to create even running surfaces. To construct the experimental ballast surfaces, 31.75 mm (1 1/4 in.) marble ballast at depths of approximately 63.5 mm (2.5 in.) or 101.6 mm (4 in.) were spread over a carpeted vinyl tile walkway specially designed for gait studies. GRF magnitudes and time histories from a force plate were collected under normal smooth surface and under both ballast surface conditions for five subjects. GRF magnitudes and time histories during smooth surface walking were similar to GRF magnitudes and time histories from the two ballast surface conditions. The data presented here demonstrate the feasibility of using a force plate system to expand the scope of biomechanical analyses of locomotion on ballast surfaces.     

Generation of human bipedal locomotion by a bio-mimetic neuro-musculo-skeletal model

To emulate the actual neuro-control mechanism of human bipedal locomotion, an anatomically and physiologically based neuro-musculo-skeletal model is developed. The human musculo-skeletal system is constructed as seven rigid links in a sagittal plane, with a total of nine principal muscles. The nervous system consists of an alpha motoneuron and proprioceptors such as a muscle spindle and a Golgi tendon organ for each muscle. At the motoneurons, feedback signals from the proprioceptors are integrated with the signal induced by foot–ground contact and input from the rhythm pattern generator; a muscle activation signal is produced accordingly. Weights of connection in the neural network are optimized using a genetic algorithm, thus maximizing walking distance and minimizing energy consumption. The generated walking pattern is in remarkably good agreement with that of actual human walking, indicating that the locomotory pattern could be generated automatically, according to the musculo-skeletal structures and the connections of the peripheral nervous system, particularly due to the reciprocal innervation in the muscle spindles. Using the proposed model, the flow of sensory-motor information during locomotion is estimated and a possible neuro-control mechanism is discussed. Received: 03 December 1998 / Accepted in revised form: 09 June 2000     

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.     

Studies of human locomotion: past, present and future

The study of human locomotion and its applications are examined from a historical viewpoint. Several critical steps in the advancement of the discipline are considered in the context of addressing a particular need to answer fundamental questions regarding the process of human locomotion. In addition, changes in the methods of observation are discussed in terms of the advancement of the field. As an example, the application of a newly developed point cluster technique to reduce the artifact due to skin movement is described. The method was applied to a study of patients with anterior cruciate ligament (ACL) deficient knees. The results demonstrate that patients with ACL-deficient knees have significantly greater than normal anterior-posterior displacement of the femur relative to the tibia during walking. Many of the advancements in the tools for observation and interpretation have been driven by new demands on our fundamental knowledge. Future advancements in the study of human locomotion will likely be motivated by new treatment modalities that require an in depth understanding of the subtle complexities of human locomotion. Future directions are discussed in the context of new methods for reducing errors associated with skin movement combined with information obtained from other imaging methods, such as magnetic resonance imaging.