Formation and control of optimal trajectory in human multijoint arm movement

In this paper, we study trajectory planning and control in voluntary, human arm movements. When a hand is moved to a target, the central nervous system must select one specific trajectory among an infinite number of possible trajectories that lead to the target position. First, we discuss what criterion is adopted for trajectory determination. Several researchers measured the hand trajectories of skilled movements and found common invariant features. For example, when moving the hand between a pair of targets, subjects tended to generate roughly straight hand paths with bell-shaped speed profiles. On the basis of these observations and dynamic optimization theory, we propose a mathematical model which accounts for formation of hand trajectories. This model is formulated by defining an objective function, a measure of performance for any possible movement: square of the rate of change of torque integrated over the entire movement. That is, the objective function CT is defined as follows: (formula; see text) We overcome this difficult by developing an iterative scheme, with which the optimal trajectory and the associated motor command are simultaneously computed. To evaluate our model, human hand trajectories were experimentally measured under various behavioral situations. These results supported the idea that the human hand trajectory is planned and controlled in accordance with the minimum torque-change criterion.     

Trajectory formation of arm movement by cascade neural network model based on minimum torque-change criterion

We proposed that the trajectory followed by human subject arms tended to minimize the time integral of the square of the rate of change of torque (Uno et al. 1987). This minimum torque-change model predicted and reproduced human multi-joint movement data quite well (Uno et al. 1989). Here, we propose a neural network model for trajectory formation based on the minimum torque-change criterion. Basic ideas of information representation and algorithm are(i) spatial representation of time,(ii) learning of forward dynamics and kinetics model and(iii) relaxation computation based on the acquired model. The model can resolve ill-posed inverse kinematics and inverse dynamics problems for redundant controlled object as well as ill-posed trajectory formation problems. By computer simulation, we show that the model can produce a multi-joint arm trajectory while avoiding obstacles or passing through viapoints.     

Lower extremity joint torque predicted by using artificial neural network during vertical jump

The purpose of this study was to develop an artificial neural network (ANN) for predicting lower extremity joint torques using the ground reaction force (GRF) and related parameters derived by the GRF during counter-movement jump (CMJ) and squat jump (SJ). Ten student athletes performed CMJ and SJ. Force plate and kinematic data were recorded. Joint torques were calculated using inverse dynamics and ANN. We used a fully connected, feed-forward network. The network comprised of one input layer, one hidden layer and one output layer. It was trained by error back-propagation algorithm using Steepest Descent Method. Input parameters of the ANN were GRF measurements and related parameters. Output parameters were three lower extremity joint torques. ANN model fitted well with the results of the inverse dynamics output. Our observations indicate that the model developed in this study can be used to estimate three lower extremity joint torques for CMJ and SJ based on ground reaction force data and related parameters.     

Four neural circuit models and their role in the organization of voluntary movement

Four neural circuit models and their role in the organization of voluntary movement are presented here. These circuits collectively control a ballistic type biped voluntary movement. The structure of each circuit, and its function is discussed. Three of the circuits are central and contribute to the construction of two classes of inputs, analogous to the α signals and γ signals in biological systems. The fourth circuit plays a role in stabilization of the movement, and in compensation for the receptors. Digital computer simulations are undertaken to demonstrate the construction of all the intermediate signals and the response of a two link biped to these efferent signals.     

Biomechanical outcomes and neural correlates of cutaneous reflexes evoked during rhythmic arm cycling

During walking cutaneous stimulation of the foot yields neural and mechanical reflexes that serve a functional purpose to correct or assist the ongoing movement. Concurrently, while cutaneous stimulation of the hand during rhythmic arm movement parallel the neural responses observed in the legs, studies of rhythmic arm movement have only limited mechanical measurements. Therefore it is difficult to determine whether reflex responses in the arms during rhythmic arm movement serve a functional purpose similar to those seen in the lower limbs. The purpose of this study was to explore the mechanical outcomes of stimulating a cutaneous nerve innervating the hand during arm cycling. We hypothesized that there would be measurable mechanical effects to cutaneous stimulation during arm cycling that function to correct or assist the task of arm cycling. Specifically, kinetic responses measured at the handle would be considered assistive if they were tangential to the arm cycling path in the direction of forward progression. Also, limb kinematic responses would be considered corrective if they allowed limb movement that would result in removal of the limb from stimulus while not altering the kinetic profile at the handle necessary for arm cycling progression. Participants performed seated arm cycling while EMG was recorded from the arm and trunk muscles, kinematic data was recorded from the right arm, and kinetic data was recorded from the handle. Cutaneous reflexes were evoked by stimulating the superficial radial nerve. The results show that there are observable mechanical responses to cutaneous stimulation of the hand during arm cycling. Subjects responded to cutaneous stimulation of the hand during arm cycling with significant changes in backward and lateral forces at the handle as well as wrist abduction/adduction and wrist flexion/extension kinematics. These responses, related to the task and phase of movement, are consistent with the anatomical location of the stimulus and are correlated to the neural responses. Therefore, these responses are comparable to functionally relevant responses in the legs during rhythmic movement. However, while there is a single observation of a kinematic corrective strategy, the kinetics measured at the handle are not tangential to the arm cycling path and therefore not considered an assistive response. Therefore, unlike the observations in the lower limbs, the mechanical responses during arm cycling are not clearly related to the functional context of the ongoing task.     

Interaction between the vertical posture and movement control systems during a quick voluntary arm raise

The study was aimed at a deeper understanding of the interaction between the system of vertical posture control and the system of voluntary movement control based on the analysis of postural muscle activity components resulting from the action of the former or the latter system. For this purpose, a quick arm raise was performed in the standing and sitting positions with body fixation at different levels, when the task of maintaining a vertical posture was simplified or completely eliminated. Under these conditions, the muscle activity associated with posture control was supposed to change, while the activity of muscles raising the arm was supposed to remain invariable. The results showed that the simplification of the posture control resulted in a decrease or elimination of anticipatory changes in the activity of some muscles. However, most of the muscle activity variations were retained even in the sitting position, and these variations appeared simultaneously with the activity of muscles raising the arm. The so-called “anticipatory postural activity” during an arm raise in a normal standing position is supposed to consist of two components: an initial component reflecting the work of the posture control system and a later component reflecting the work of the movement control system. It is suggested that the planning of muscle activity and exchange of information between these two systems take place only before the beginning of the movement; after that, they act independently and in parallel.     

Protein symmetry and the co-operative ligand-binding behaviour predicted by allosteric Koshland models

It is shown that the nearest-neighbour interaction two-conformation allosteric models of Koshland, Nemethy & Filmer (1966) predict binding curves with a centre of symmetry when the protein is also symmetrical and induced-fit is assumed. When nonexclusive binding to both conformations is assumed, the models predict that the family of homotropic binding curves obtained by varying the heterotropic ligand has a centre of symmetry. It is argued that the symmetry or asymmetry of binding curves is the main experimentally verifiable prediction of allosteric models insofar as they are models of interaction between protein subunits.Symmetry in a binding curve greatly simplifies the analysis of cooperative behaviour. The co-operative features possible with a symmetric binding curve for a four-site protein are analysed. The sign of co-operativity may either be uniform or change twice as saturation increases; the conditions for the various possibilities are given. For example, in terms of the intrinsic binding constants per site A^∥₁, A2, etc. the necessary and sufficient condition for positive macroscopic co-operativity over the whole symmetric binding curve is A^∥₁≤ A2, A ^∥₁ ≤ A3 which should be contrasted with the obvious A^∥₁ ≤ Al, AZ ≤A^∥₃ (positive microscopic co-operativity) which is only a sufficient but not a necessary condition. A symmetric curve may have one or three, but no more, extrema of the “Hill coefficient” h. For three extrema a change of sign of microscopic (but not necessarily macroscopic) co-operativity is necessary but not sufficient. In the case where there are off-centre maxima of h, then h < 2 everywhere on the curve.The Koshland models predict qualitative and quantitative restrictions on the forms of binding curves additional to that of symmetry. In tetrameric induced fit models, negative co-operativity in the mid-region of the curve and positive co-operativity in the outside regions is possible, but not the opposite, and three extrema of h are possible with uniform positive but not with uniform negative co-operativity.Thus by recognising the importance of symmetry it has been possible to describe and categorise all the co-operativity behaviour possible with the most plausible Koshland tetrameric models. Several experimental examples of probable non-exclusive binding to proteins and enzymes are discussed, and it is shown how the symmetry point of view illuminates their interpretation.     

Rectus femoris and vastus intermedius fiber excursions predicted by three-dimensional muscle models

Computer models of the musculoskeletal system frequently represent the force-length behavior of muscle with a lumped-parameter model. Lumped-parameter models use simple geometric shapes to characterize the arrangement of muscle fibers and tendon; this may inaccurately represent changes in fiber length and the resulting force-length behavior, especially for muscles with complex architecture. The purpose of this study was to determine the extent to which the complex features of the rectus femoris and vastus intermedius architectures affect the fiber changes in length ("fiber excursions"). We created three-dimensional finite-element models of the rectus femoris and vastus intermedius muscles based on magnetic resonance (MR) images, and compared the fiber excursions predicted by the finite-element models with fiber excursions predicted by lumped-parameter models of these muscles. The finite-element models predicted rectus femoris fiber excursions (over a 100 degrees range of knee flexion) that varied from 55% to 70% of the excursion of the muscle-tendon unit and vastus intermedius fiber excursions that varied from 55% to 98% of the excursion muscle-tendon unit. In contrast, the lumped-parameter model of the rectus femoris predicted fiber excursions that were 86% of the excursion of the muscle-tendon unit and vastus intermedius fiber excursions that were 97% of the excursion of the muscle-tendon unit. These results suggest that fiber excursions of many fibers are overestimated in lumped-parameter models of these muscles. These new representations of muscle architecture can improve the accuracy of computer simulations of movement and provide insight into muscle design.     

Effects of neck flexion on contingent negative variation and anticipatory postural control during arm movement while standing

We investigated the effects of neck flexion on contingent negative variation (CNV) and anticipatory postural control using an arm flexion task in standing. CNV was adopted to evaluate the state of activation of brain areas related to anticipatory postural control. Subjects were required to flex the arms in response to a sound stimulus preceded by a warning sound stimulus. Two different intervals (2.0 and 3.5 s) between these two stimuli were used in neck position in quiet standing (neck resting) and neck position at 80% angle of maximal neck flexion. The mean amplitude of CNV 100-ms before the response stimulus, recorded from a Cz electrode, was calculated. Onset timing of activation of the postural muscles (lumbar paraspinal, biceps femoris and gastrocnemius) with respect to the anterior deltoid was analyzed. Reaction time at the anterior deltoid was significantly shorter in the 2.0 s period than in the 3.5 s period, and in the neck flexion than in the neck resting in both periods. In the 2.0 s, but not in the 3.5 s period, neck flexion resulted in an increased CNV amplitude and an increased duration of preceding activation of the postural muscles, and the correlation between these increases was significant.     

Active leg stiffness and energy stored in the muscles during maximal counter movement jump in the aged

The purpose of this study was to examine the effects of age on active leg stiffness adjustment, electromyogram (EMG) activities and energy stored during eccentric and concentric phases in performing a maximal functional task involving stretch-shorten cycle. Ten young (24.3 ± 2 years) and 10 old (68.6 ± 5 years) healthy male subjects were filmed during maximal performance of counter movement jump (CMJ) and squat jump (SJ) on force plate. Integrated EMG (IEMG), ground reaction force (GRF), active leg stiffness, energy stored/returned and active work done by the muscles were compared between two groups on eccentric (ECC) and concentric (CON) phases of CMJ. The GRF, leg stiffness and energy stored in ECC and GRF, IEMG, energy returned and active work in CON were less in the elderly (p < 0.05). These results demonstrate that the neuromuscular function of adjusting active stiffness, storing elastic energy and optimizing the performance may decrease with age during CMJ.     

Shoulder joint movement of the non-throwing arm during baseball pitch—comparison between skilled and unskilled pitchers

The shoulder of a non-throwing arm during a baseball pitch must be in a constant position while the shoulder of the throwing arm moves in a nearly circular path around it. However, it has not been investigated whether a skilled pitch requires less shoulder-joint movement. It was hypothesized that pitchers with less shoulder movement of the non-throwing arm can be considered to have higher skill and to attain higher initial ball velocity. Nine baseball pitchers were used as subjects. The coach classified them into a skilled and an unskilled group. The pitching motions were recorded using two high-speed cameras. The time series of three-dimensional landmark coordinates of the shoulder joint of the non-throwing arm during the baseball pitch were calculated using the direct linear transformation method. The shoulder-joint movement (SJM) index, which expresses the movement (displacement) of the shoulder joint of the non-throwing arm quantitatively, was proposed to compare the SJM at different skill levels and investigate the relationship between SJM and initial ball velocity. The SJM of the skilled pitchers was smaller than that of the unskilled pitchers, and the smaller value of the SJM led to faster initial ball velocity. The data suggest that the less SJM of the non-throwing arm is required to attain a skilled pitch and higher initial ball velocity.     

Femoral strength is better predicted by finite element models than QCT and DXA.

Clinicians and patients would benefit if accurate methods of predicting and monitoring bone strength in-vivo were available. A group of 51 human femurs (age range 21-93; 23 females, 28 males) were evaluated for bone density and geometry using quantitative computed tomography (QCT) and dual energy X-ray absorptiometry (DXA). Regional bone density and dimensions obtained from QCT and DXA were used to develop statistical models to predict femoral strength ex vivo. The QCT data also formed the basis of a three-dimensional finite element (FE) models to predict structural stiffness. The femurs were separated into two groups; a model training set (n = 25) was used to develop statistical models to predict ultimate load, and a test set (n = 26) was used to validate these models. The main goal of this study was to test the ability of DXA, QCT and FE techniques to predict fracture load non-invasively, in a simple load configuration which produces predominantly femoral neck fractures. The load configuration simulated the single stance phase portion of normal gait; in 87% of the specimens, clinical appearing sub-capital fractures were produced. The training/test study design provided a tool to validate that the predictive models were reliable when used on specimens with "unknown" strength characteristics. The FE method explained at least 20% more of the variance in strength than the DXA models. Planned refinements of the FE technique are expected to further improve these results. Three-dimensional FE models are a promising method for predicting fracture load, and may be useful in monitoring strength changes in vivo.     

Computer simulation of flagellar movement: VII. Conventional but functionally different cross-bridge models for inner and outer arm dyneins can explain the effects of outer arm dynein removal

Outer arm dynein removal from flagella by genetic or chemical methods causes decreased frequency and power, but little change in bending pattern. These results suggest that outer arm dynein operates within bends to increase the speed of bend propagation, but does not produce forces that alter the bending pattern established by inner arm dyneins. A flagellar model incorporating different cross-bridge models for inner and outer arm dyneins has been examined. The inner arm dynein model has a hyperbolic force-velocity curve, with a maximum average force at 0 sliding velocity of about 14 pN for each 96 nm group of inner arm dyneins. The outer arm dynein model has a very different force-velocity curve, with a maximum force at about 10-15% of V(max). The outer arm dynein model is adjusted so that the unloaded sliding velocity for a realistic mixture of inner and outer arm dyneins is twice the unloaded sliding velocity for the inner arm dynein model alone. With these cross-bridge models, a flagellar model can be obtained that reduces its sliding velocity and frequency by approximately 50% when outer arm dyneins are removed, with little change in bending pattern. The addition of outer arm dyneins, therefore, gives an approximately 4-fold increase in power output against viscous resistances, and outer arm dyneins may generate 90% or more of the power output. Cell Motil.     

Eye movement instabilities and nystagmus can be predicted by a nonlinear dynamics model of the saccadic system

The study of eye movements and oculomotor disorders has, for four decades, greatly benefitted from the application of control theoretic concepts. This paper is an example of a complementary approach based on the theory of nonlinear dynamical systems. Recently, a nonlinear dynamics model of the saccadic system was developed, comprising a symmetric piecewise-smooth system of six first-order autonomous ordinary differential equations. A preliminary numerical investigation of the model revealed that in addition to generating normal saccades, it could also simulate inaccurate saccades, and the oscillatory instability known as congenital nystagmus (CN). By varying the parameters of the model, several types of CN oscillations were produced, including jerk, bidirectional jerk and pendular nystagmus. The aim of this study was to investigate the bifurcations and attractors of the model, in order to obtain a classification of the simulated oculomotor behaviours. The application of standard stability analysis techniques, together with numerical work, revealed that the equations have a rich bifurcation structure. In addition to Hopf, homoclinic and saddlenode bifurcations organised by a Takens-Bogdanov point, the equations can undergo nonsmooth pitchfork bifurcations and nonsmooth gluing bifurcations. Evidence was also found for the existence of Hopf-initiated canards. The simulated jerk CN waveforms were found to correspond to a pair of post-canard symmetry-related limit cycles, which exist in regions of parameter space where the equations are a slow-fast system. The slow and fast phases of the simulated oscillations were attributed to the geometry of the corresponding slow manifold. The simulated bidirectional jerk and pendular waveforms were attributed to a symmetry invariant limit cycle produced by the gluing of the asymmetric cycles. In contrast to control models of the oculomotor system, the bifurcation analysis places clear restrictions on which kinds of behaviour are likely to be associated with each other in parameter space, enabling predictions to be made regarding the possible changes in the oscillation type that may be observed upon changing the model parameters. The analysis suggests that CN is one of a range of oculomotor disorders associated with a pathological saccadic braking signal, and that jerk and pendular nystagmus are the most probable oscillatory instabilities. Additionally, the transition from jerk CN to bidirectional jerk and pendular nystagmus observed experimentally when the gaze angle or attention level is changed is attributed to a gluing bifurcation. This suggests the possibility of manipulating the waveforms of subjects with jerk CN experimentally to produce waveforms with an extended foveation period, thereby improving visual resolution.     

Muscle forces during running predicted by gradient-based and random search static optimisation algorithms

Muscle forces during locomotion are often predicted using static optimisation and SQP. SQP has been criticised for over-estimating force magnitudes and under-estimating co-contraction. These problems may be related to SQP's difficulty in locating the global minimum to complex optimisation problems. Algorithms designed to locate the global minimum may be useful in addressing these problems. Muscle forces for 18 flexors and extensors of the lower extremity were predicted for 10 subjects during the stance phase of running. Static optimisation using SQP and two random search (RS) algorithms (a genetic algorithm and simulated annealing) estimated muscle forces by minimising the sum of cubed muscle stresses. The RS algorithms predicted smaller peak forces (42% smaller on average) and smaller muscle impulses (46% smaller on average) than SQP, and located solutions with smaller cost function scores. Results suggest that RS may be a more effective tool than SQP for minimising the sum of cubed muscle stresses in static optimisation.     

Muscle forces during running predicted by gradient-based and random search static optimisation algorithms

Muscle forces during locomotion are often predicted using static optimisation and SQP. SQP has been criticised for over-estimating force magnitudes and under-estimating co-contraction. These problems may be related to SQP's difficulty in locating the global minimum to complex optimisation problems. Algorithms designed to locate the global minimum may be useful in addressing these problems. Muscle forces for 18 flexors and extensors of the lower extremity were predicted for 10 subjects during the stance phase of running. Static optimisation using SQP and two random search (RS) algorithms (a genetic algorithm and simulated annealing) estimated muscle forces by minimising the sum of cubed muscle stresses. The RS algorithms predicted smaller peak forces (42% smaller on average) and smaller muscle impulses (46% smaller on average) than SQP, and located solutions with smaller cost function scores. Results suggest that RS may be a more effective tool than SQP for minimising the sum of cubed muscle stresses in static optimisation.     

Accuracy of gastrocnemius muscles forces in walking and running goats predicted by one-element and two-element Hill-type models

Hill-type models are commonly used to estimate muscle forces during human and animal movement—yet the accuracy of the forces estimated during walking, running, and other tasks remains largely unknown. Further, most Hill-type models assume a single contractile element, despite evidence that faster and slower motor units, which have different activation–deactivation dynamics, may be independently or collectively excited. This study evaluated a novel, two-element Hill-type model with “differential” activation of fast and slow contractile elements. Model performance was assessed using a comprehensive data set (including measures of EMG intensity, fascicle length, and tendon force) collected from the gastrocnemius muscles of goats during locomotor experiments. Muscle forces predicted by the new two-element model were compared to the forces estimated using traditional one-element models and to the forces measured in vivo using tendon buckle transducers. Overall, the two-element model resulted in the best predictions of in vivo gastrocnemius force. The coefficient of determination, r², was up to 26.9% higher and the root mean square error, RMSE, was up to 37.4% lower for the two-element model than for the one-element models tested. All models captured salient features of the measured muscle force during walking, trotting, and galloping (r²=0.26–0.51), and all exhibited some errors (RMSE=9.63–32.2% of the maximum in vivo force). These comparisons provide important insight into the accuracy of Hill-type models. The results also show that incorporation of fast and slow contractile elements within muscle models can improve estimates of time-varying, whole muscle force during locomotor tasks.     

A numerical simulation of muscle spindle ensemble encoding during planar movement of the human arm: correlation sensitivity and parameter dependence

We extend the analysis developed in the preceding paper in which we correlated kinematic parameters of planar movements of the human arm made by subjects moving to a visual target with numerical estimates of the ensemble encoding of muscle spindles within some of the muscles of this limb. Three possible models for the inclusion of noise in the calculations of the ensemble encodings are considered: (i) random errors in the angular coordinates from which muscle fascicle, and hence spindle length are calculated, (ii) variability of spindle discharge rates, and (iii) variability in the calculation of the ensemble encoding. In each case the correlations between kinematic variables of the movements and the resultant ensemble encodings decrease as the contribution of the noise term to the calculation of the encodings increases. Subject to the constraint that the magnitude of the noise term remains within physiologically realistic limits, however, the observed correlations persist at statistically significant levels. We also investigate the dependence of the observed correlations on the choice of model parameters, namely (i) the absolute and relative contributions made by simulated spindle primary and secondary afferents to the ensemble encoding, (ii) the inclusion of explicit length-related terms in the model of muscle spindle discharge, and (iii) the fractional power of velocity experienced by the model spindles during movement. The resulting correlations are approximately independent of both the fractional power of velocity and absolute firing levels of both the primary and secondary afferents of the spindle model. The inclusion of explicit length-dependent terms in the model does result in differences in the observed correlation coefficients. In this case, however, the magnitudes of the differences are small. On the basis of these findings we conclude that the correlations between kinematic variables of movement and the associated ensemble encodings are robust with regard to both the choice of model parameters and noise inherent at all stages of the transduction and processing of proprioceptive information. The findings of the present study provide further evidence, therefore, to support the hypothesis that motor structures capable of deriving such an ensemble encoding would be provided with information regarding ongoing movements in both intrinsic (body-centered) and extrinsic (Cartesian) coordinate systems. Received: 17 November 1995 / Accepted in revised form: 17 June 1996     

Optimization of biopharmaceutical downstream processes supported by mechanistic models and artificial neural networks

Downstream process development is a major area of importance within the field of bioengineering. During the design of such a downstream process, important decisions have to be made regarding the type of unit operations as well as their sequence and their operating conditions. Current computational approaches addressing these issues either show a high level of simplification or struggle with computational speed. Therefore, this article presents a new approach that combines detailed mechanistic models and speed‐enhancing artificial neural networks. This approach was able to simultaneously optimize a process with three different chromatographic columns toward yield with a minimum purity of 99.9%. The addition of artificial neural networks greatly accelerated this optimization. Due to high computational speed, the approach is easily extendable to include more unit operations. Therefore, it can be of great help in the acceleration of downstream process development. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 33:696–707, 2017     

Sensory-motor cortex activity modulation by hypnotic susceptibility and hypnosis during finger movement

The aim of the experiment was to study whether the activity of the primary sensory-motor (S1/M1), supplementary motor (SMA) and pre-motor (PMA) areas during fingers movement is modulated by hypnotic susceptibility and hypnosis. Cortical activity was studied through functional Magnetic Resonance Imaging (fMRI) during a finger-to-thumb opposition task in awake (Highs) and hypnotized highly susceptible (H-Highs) as well as in awake non susceptible subjects (Lows). Results did not show any significant difference in sensory-motor areas activation between Highs and Lows (trait effect) and between Highs and H-Highs (state effect). The activation in 3 subjects among Highs and only 1 among Lows (out of 5) of the caudal S1, receiving the most part of the cutaneous input, appears noteworthy and prompts further investigation on possible hypnotizability-related differences in sensory-motor integration.