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.     

A model of the neuro-musculo-skeletal system for anticipatory adjustment of human locomotion during obstacle avoidance

Theoretical studies on human locomotion have shown that a stable and flexible gait emerges from the dynamic interaction between the rhythmic activity of a neural system composed of a neural rhythm generator (RG) and the rhythmic movement of the musculo-skeletal system. This study further explores the mechanism of the anticipatory control of locomotion based on the emergent properties of a neural system that generates the basic pattern of gait. A model of the neuro-musculo-skeletal system to execute the task of stepping over a visible obstacle with both limbs during walking is described. The RG in the neural system was combined with a system referred to as a discrete movement generator (DM), which receives both the output of the RG and visual information regarding the obstacle and generates discrete signals for modification of the basic gait pattern. A series of computer simulations demonstrated that an obstacle placed at an arbitrary position can be cleared by sequential modifications of gait: (1) modulating the step length when approaching the obstacle and (2) modifying the trajectory of the swing limbs while stepping over it. This result suggests that anticipatory adjustments are produced not by the unidirectional flow of the information from visual signals to motor commands but by the bi-directional circulation of information between the DM and the RG. The validity of this model is discussed in relation to motor cortical activity during anticipatory modifications in cats and the ecological psychology of visuo-motor control in humans. Received: 19 September 1996 / Accepted in revised form: 21 March 1997     

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     

Resonance tuning in a neuro-musculo-skeletal model of the forearm

In rhythmic movements, humans activate their muscles in a robust and energy efficient way. These activation patterns are oscillatory and seem to originate from neural networks in the spinal cord, called central pattern generators (CPGs). Evidence for the existence of CPGs was found for instance in lampreys, cats and rats. There are indications that CPGs exist in humans as well, but this is not proven yet. Energy efficiency is achieved by resonance tuning: the central nervous system is able to tune into the resonance frequency of the limb, which is determined by the local reflex gains. The goal of this study is to investigate if the existence of a CPG in the human spine can explain the resonance tuning behavior, observed in human rhythmic limb movement. A neuro-musculo-skeletal model of the forearm is proposed, in which a CPG is organized in parallel to the local reflexloop. The afferent and efferent connections to the CPG are based on clues about the organization of the CPG, found in literature. The model is kept as simple as possible (i.e., lumped muscle models, groups of neurons are lumped into half-centers, simple reflex model), but incorporates enough of the essential dynamics to explain behavior—such as resonance tuning—in a qualitative way. Resonance tuning is achieved above, at and below the endogenous frequency of the CPG in a highly non-linear neuro- musculo-skeletal model. Afferent feedback of muscle lengthening to the CPG is necessary to accomplish resonance tuning above the endogenous frequency of the CPG, while feedback of muscle velocity is necessary to compensate for the phase lag, caused by the time delay in the loop coupling the limb to the CPG. This afferent feedback of muscle lengthening and velocity represents the Ia and II fibers, which—according to literature—is the input to the CPG. An internal process of the CPG, which integrates the delayed muscle lengthening and feeds it to the half-center model, provides resonance tuning below the endogenous frequency. Increased co-contraction makes higher movement frequencies possible. This agrees with studies of rhythmic forearm movements, which have shown that co-contraction increases with movement frequency. Robustness against force perturbations originates mainly from the CPG and the local reflex loop. The CPG delivers an increasing part of the necessary muscle activation for increasing perturbation size. As far as we know, the proposed neuro-musculo-skeletal model is the first that explains the observed resonance tuning in human rhythmic limb movement.     

Numerical model for the locomotion of spirilla

The swimming of trailing, leading, and bipolar spirilla (with realistic flagellar centerline geometries) is considered. A boundary element method is used to predict the instantaneous swimming velocity, counter-rotation angular velocity, and power dissipation of a given organism as functions of time and the geometry of the organism. Based on such velocities, swimming trajectories have been deduced enabling a realistic definition of mean swimming speeds. The power dissipation normalized in terms of the square of the mean swimming speed is considered to be a measure of hydrodynamic efficiency. In addition, kinematic efficiency is defined as the extent of deviation of the swimming motion from that of a previously proposed ideal corkscrew mechanism. The dependence of these efficiencies on the organism's geometry is examined giving estimates of its optimum dimensions. It is concluded that appreciable correlation exists between the two alternative definitions for many of the geometrical parameters considered. Furthermore, the organism having the deduced optimum dimensions closely resembles the real organism as experimentally observed.     

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.     

A hexapedal jointed-leg model for insect locomotion in the horizontal plane

We develop a simple model for insect locomotion in the horizontal (ground) plane. As in earlier work by Seipel et al. (Biol Cybern 91(0):76–90, 2004) we employ six actuated legs that also contain passive springs, but the legs, with “hip” and ‘knee’ joints, better represent insect morphology. Actuation is provided via preferred angle inputs at each joint, corresponding to zero torques in the hip and knee springs. The inputs are determined from estimates of foot forces in the cockroach Blaberus discoidalis via an inverse problem. The head–thorax–body is modeled as a single rigid body, and leg masses, inertia and joint dissipation are ignored. The resulting three degree-of-freedom dynamical system, subject to feedforward joint inputs, exhibits stable periodic gaits that compare well with observations over the insect’s typical speed range. The model’s response to impulsive perturbations also matches that of freely-running cockroaches (Jindrich and Full, J Exp Biol 205:2803–2823, 2002), and stability is maintained in the face of random foot touchdowns representative of real insects. We believe that this model will allow incorporation of realistic muscle models driven by a central pattern generator in place of the joint actuators, and that it will ultimately permit the study of proprioceptive feedback pathways involving leg force and joint angle sensing.     

Exotendons for assistance of human locomotion

Background  

Powered robotic exoskeletons for assistance of human locomotion are currently under development for military and medical applications. The energy requirements for such devices are excessive, and this has become a major obstacle for practical applications. Legged locomotion in many animals, however, is very energy efficient. We propose that poly-articular elastic mechanisms are a major contributor to the economy of locomotion in such specialized animals. Consequently, it should be possible to design unpowered assistive devices that make effective use of similar mechanisms.     

A mathematical model of the human thermal system

This paper describes a mathematical model developed to simulate the physical characteristics of the human thermal system in the transient state. Physiological parameters, such as local metabolic heat generation rates, local blood flow rates, and rates of sweating, must be specified as input data. Automatic computation of these parameters will be built into the model at a later date when it is used to study thermal regulation in the human. Finite-difference techniques have been used to solve the heat conduction equation on a Control Data Corporation 1604 computer. Since numerical techniques were used, it was possible to include many more factors in this model than in previous ones. The body was divided into 15 geometric regions, which were the head, the thorax, the abdomen, and the proximal, medial, and distal segments of the arms and legs. Axial gradients in a given segment were neglected. In each segment, the large arteries and veins were approximated by an arterial pool and a venous pool which were distributed radially throughout the segment. Accumulation of heat in the blood of the large arteries and veins, and heat transfer from the large arteries and veins to the surrounding tissue were taken into account. The venous streams were collected together at the heart before flowing into the capillaries of the lungs. Each of the segments was subdivided into 15 radial sections, thereby allowing considerable freedom in the assignment of physical properties such as thermal conductivity and rate of blood flow to the capillaries. The program has been carefully checked for errors, and it is now being used to analyze some problems of current interest. This study was supported by the office of the Surgeon General, U.S. Army, under contract no. DA 49-193-MD-2005.     

A computational model of ameboid deformation and locomotion

Traditional continuum models of ameboid deformation and locomotion are limited by the computational difficulties intrinsic in free boundary conditions. A new model using the immersed boundary method overcomes these difficulties by representing the cell as a force field immersed in fluid domain. The forces can be derived from a direct mechanical interpretation of such cell components as the cell membrane, the actin cortex, and the transmembrane adhesions between the cytoskeleton and the substratum. The numerical cytoskeleton, modeled as a dynamic network of immersed springs, is able to qualitatively model the passive mechanical behavior of a shear-thinning viscoelastic fluid (Bottino 1997). The same network is used to generate active protrusive and contractile forces. When coordinated with the attachment-detachment cycle of the cell's adhesions to the substratum, these forces produce directed locomotion of the model ameba. With this model it is possible to study the effects of altering the numerical parameters upon the motility of the model cell in a manner suggestive of genetic deletion experiments. In the context of this ameboid cell model and its numerical implementation, simulations involving multicellular interaction, detailed internal signaling, and complex substrate geometries are tractable. Received: 5 January 1998 / Revised version: 23 March 1998 / Accepted: 26 March 1998     

A dual-mode dynamic model of the human accommodation system

The function of the accommodation system is to provide a clear retinal image of objects in the visual scene. The system was previously thought to be under simple continuous (i.e., single mode of operation) feedback control, but recent research has shown that it is under discontinuous (i.e., two stimulus-dependent modes of operation) feedback control by means of fast and slow processes. A model using MATLAB/SIMULINK was developed to simulate this dual-mode behavior. It consists of fast and slow components in a feedback loop. The fast component responds to step target disparity with an open-loop movement to nearly reach the desired level, and then the slow component uses closed-loop feedback to reduce the residual error to an acceptable small level. For slow ramps, the slow component provides smooth tracking of the stimulus, whereas for fast ramps, the fast component provides accurate staircase-like step responses. Simulation of this model using a variety of stimuli, including pulse, step, ramp, and sinusoid, showed good agreement with experimental results. Thus, this represents the first dynamic model of accommodation that can accurately simulate the complex dual-mode behavior seen experimentally. The biological significance of this model is that it can be used to quantitatively analyze clinical deficits such as amblyopia and accommodative insufficiency.     

A model of bipedal locomotion on compliant legs.

Simple mathematical models capable of walking or running are used to compare the merits of bipedal gaits. Stride length, duty factor (the fraction of the stride, for which the foot is on the ground) and the pattern of force on the ground are varied, and the optimum gait is deemed to be the one that minimizes the positive work that the muscles must perform, per unit distance travelled. Even the simplest model, whose legs have neither mass nor elastic compliance, predicts the changes of duty factor and force pattern that people make as they increase their speed of walking. It predicts a sudden change to running at a critical speed, but this is much faster than the speed at which people make the change. When elastic compliance is incorporated in the model, unnaturally fast walking becomes uncompetitive. However, a slow run with very brief foot contact becomes the optimum gait at low speeds, at which people would walk, unless severe energy dissipation occurs in the compliance. A model whose legs have mass as well as elastic compliance predicts well the relationship between speed and stride length in human walking.     

A theory for the locomotion of spirochetes

A hydrodynamic theory for the locomotion of spirochetes is presented. The theory is based on a possible arrangement of internal fibrils such that self rotation about a local body axis is possible. This self rotation is responsible for cancelling the torque produced by the traveling helical waves of the body.     

A mathematical model of adaptive behavior in quadruped locomotion

Locomotion involves repetitive movements and is often executed unconsciously and automatically. In order to achieve smooth locomotion, the coordination of the rhythms of all physical parts is important. Neurophysiological studies have revealed that basic rhythms are produced in the spinal network called, the central pattern generator (CPG), where some neural oscillators interact to self-organize coordinated rhythms. We present a model of the adaptation of locomotion patterns to a variable environment, and attempt to elucidate how the dynamics of locomotion pattern generation are adjusted by the environmental changes. Recent experimental results indicate that decerebrate cats have the ability to learn new gait patterns in a changed environment. In those experiments, a decerebrate cat was set on a treadmill consisting of three moving belts. This treadmill provides a periodic perturbation to each limb through variation of the speed of each belt. When the belt for the left forelimb is quickened, the decerebrate cat initially loses interlimb coordination and stability, but gradually recovers them and finally walks with a new gait. Based on the above biological facts, we propose a CPG model whose rhythmic pattern adapts to periodic perturbation from the variable environment. First, we design the oscillator interactions to generate a desired rhythmic pattern. In our model, oscillator interactions are regarded as the forces that generate the desired motion pattern. If the desired pattern has already been realized, then the interactions are equal to zero. However, this rhythmic pattern is not reproducible when there is an environmental change. Also, if we do not adjust the rhythmic dynamics, the oscillator interactions will not be zero. Therefore, in our adaptation rule, we adjust the memorized rhythmic pattern so as to minimize the oscillator interactions. This rule can describe the adaptive behavior of decerebrate cats well. Finally, we propose a mathematical framework of an adaptation in rhythmic motion. Our framework consists of three types of dynamics: environmental, rhythmic motion, and adaptation dynamics. We conclude that the time scale of adaptation dynamics should be much larger than that of rhythmic motion dynamics, and the repetition of rhythmic motions in a stable environment is important for the convergence of adaptation. Received: 10 July 1997 / Accepted in revised form: 13 March 1998     

A computational model of visually guided locomotion in lamprey

This study addresses mechanisms for the generation and selection of visual behaviors in anamniotes. To demonstrate the function of these mechanisms, we have constructed an experimental platform where a simulated animal swims around in a virtual environment containing visually detectable objects. The simulated animal moves as a result of simulated mechanical forces between the water and its body. The undulations of the body are generated by contraction of simulated muscles attached to realistic body components. Muscles are driven by simulated motoneurons within networks of central pattern generators. Reticulospinal neurons, which drive the spinal pattern generators, are in turn driven directly and indirectly by visuomotor centers in the brainstem. The neural networks representing visuomotor centers receive sensory input from a simplified retina. The model also includes major components of the basal ganglia, as these are hypothesized to be key components in behavior selection. We have hypothesized that sensorimotor transformation in tectum and pretectum transforms the place-coded retinal information into rate-coded turning commands in the reticulospinal neurons via a recruitment network mimicking the layered structure of tectal areas. Via engagement of the basal ganglia, the system proves to be capable of selecting among several possible responses, even if exposed to conflicting stimuli. The anatomically based structure of the control system makes it possible to disconnect different neural components, yielding concrete predictions of how animals with corresponding lesions would behave. The model confirms that the neural networks identified in the lamprey are capable of responding appropriately to simple, multiple, and conflicting stimuli.