Stabilizing PID controllers for a single-link biomechanical model with position, velocity, and force feedback

In this paper we address the problem of PID stabilization of a single-link inverted pendulum-based biomechanical model with force feedback, two levels of position and velocity feedback, and with delays in all the feedback loops. The novelty of the proposed model lies in its physiological relevance, whereby both small and medium latency sensory feedbacks from muscle spindle (MS), and force feedback from Golgi tendon organ (GTO) are included in the formulation. The biomechanical model also includes active and passive viscoelastic feedback from Hill-type muscle model and a second-order low-pass function for muscle activation. The central nervous system (CNS) regulation of postural movement is represented by a proportional-integral-derivative (PID) controller. Padé approximation of delay terms is employed to arrive at an overall rational transfer function of the biomechanical model. The Hermite-Biehler theorem is then used to derive stability results, leading to the existence of stabilizing PID controllers. An algorithm for selection of stabilizing feedback gains is developed using the linear matrix inequality (LMI) approach.     

Destabilizing and stabilizing forces to assess equilibrium during everyday activities

Postural stability is essential to functional activities. This paper presents a new model of dynamic stability which takes into account both the equilibrium associated with the body position over the base of support (destabilizing force) and the effort the subject needs to produce to keep his/her centre of mass inside the base of support (stabilizing force). The ratio between these two forces (destabilizing over stabilizing) is calculated to provide an overall index of stability for an individual. Preliminary results from data collected during walking at preferred and maximal safe speed in four older adults (aged from 64 to 84 yr) showed that both forces are lower for subjects with reduced maximal gait speed. In addition, the stabilizing force increases by 2–3 times from preferred to maximal speed, while the destabilizing force barely changes with gait speed. Overall, the model through the index of stability attributes lower dynamic stability to subjects with lower maximal gait speed. These preliminary results call for larger-scale studies to pursue the development and validation of the model and its application to different functional tasks.     

A model of the smooth pursuit eye movement system

Human, horizontal, smooth-pursuit eye movements were recorded by the search coil method in response to Rashbass step-ramp stimuli of 5 to 30 deg/s. Eye velocity records were analyzed by measuring features such as the time, velocity and acceleration of the point of peak acceleration, the time and velocity of the peaks and troughs of ringing and steady-state velocity. These values were averaged and mean responses reconstructed. Three normal subjects were studied and their responses averaged. All showed a peak acceleration-velocity saturation. All had ringing frequencies near 3.8 Hz and the mean steady-state gain was 0.95.It is argued that a single, linear forward path with any transfer function G(s) and a 100 ms delay (latency) cannot simultaneously simulate the initial rise of acceleration and ring at 3.8 Hz based on a Bode analysis. Also such a simple negative feedback model cannot have a steady-state gain greater than 1.0; a situation that occurs frequently experimentally. L.R. Young's model, which employs internal positive feedback to eliminate the built-in unity negative feedback, was felt necessary to resolve this problem and a modification of that model is proposed which simulates the data base. Acceleration saturation is achieved by borrowing the idea of the local feedback model for saccades so that one nonlinearity can account for the acceleration-velocity saturation: the main sequence for pursuit. Motor plasticity or motor learning, recently demonstrated for pursuit, is also incorporated and simulated.It was noticed that the offset of pursuit did not show the ringing seen in the onset so this was quantified in one subject. Offset velocity could be characterized by a single exponential with a time constant of about 90 ms. This observation suggests that fixation is not pursuit at zero velocity and that the pursuit system is turned on when needed and off during fixation.     

Optimization and evaluation of a proportional derivative controller for planar arm movement

In most clinical applications of functional electrical stimulation (FES), the timing and amplitude of electrical stimuli have been controlled by open-loop pattern generators. The control of upper extremity reaching movements, however, will require feedback control to achieve the required precision. Here we present three controllers using proportional derivative (PD) feedback to stimulate six arm muscles, using two joint angle sensors. Controllers were first optimized and then evaluated on a computational arm model that includes musculoskeletal dynamics. Feedback gains were optimized by minimizing a weighted sum of position errors and muscle forces. Generalizability of the controllers was evaluated by performing movements for which the controller was not optimized, and robustness was tested via model simulations with randomly weakened muscles. Robustness was further evaluated by adding joint friction and doubling the arm mass. After optimization with a properly weighted cost function, all PD controllers performed fast, accurate, and robust reaching movements in simulation. Oscillatory behavior was seen after improper tuning. Performance improved slightly as the complexity of the feedback gain matrix increased.     

Interaction between Visual and Proprioceptive Analyzers in Vertical Posture Control

The CNS can precisely assess the spatial position of the human body only by simultaneously processing and integrating the visual, proprioceptive, and vestibular inputs. Postural stability data make it possible to estimate changes taking place in the function of analyzers involved in the maintenance of the upright posture. The vertical posture stability was assessed in healthy children and children with spastic diplegic cerebral palsy from their postural responses to the presentation of single optokinetic or somatosensory stimuli. The visual analyzer was found to play a significant role in maintaining the upright position under natural gravity conditions in healthy children. A single exposure of the proprioceptive system to variable forces directed with the gravity of the earth (vertical) decreased the contribution of the visual analyzer. Healthy children maintained the upright position relying on the direction of movement of the optokinetic stimuli, which, however, produced no effect on the maintenance of posture in the patients. A hypothesis is proposed that prenatal or early postnatal CNS lesions decrease the contribution of phylogenetically newer brain structures to the regulation of upright posture.     

Individual muscle contributions to knee joint impedance following a sudden perturbation: An in vivo inverted pendulum model

Previous research has suggested that muscle forces, generated by reflexes, contribute to joint stability prior to the more coordinated voluntary muscle forces. The purpose of the current study was to quantify the behaviour of the leg muscles, through the calculation of individual muscle contributions to joint rotational impedance (MJRI), with a specific interest in the neuromuscular contribution in the period following shortly after a sudden knee extension perturbation. The knee was selected as an in vivo system to represent an inverted pendulum model. Kinematic and sEMG data were collected while subjects were in a prone position and exposed to sudden knee extension perturbations. A biomechanical model was used to estimate muscle forces and moments about the knee and these data were then used to calculate instantaneous MJRI. Data indicated that pre-voluntary muscle forces do contribute significantly to MJRI following a sudden knee extension perturbation as there was a 40% increase in total MJRI in the flexion/extension and valgus/varus axes immediately following the perturbation, suggesting their importance in stabilizing the joint immediately after a disturbance. Additionally, knowledge of perturbation timing was shown to increase anticipatory MJRI levels, pre-perturbation (p < 0.05), indicating that it is advantageous for the neuromuscular system to prepare for a sudden disturbance. In conclusion, the data show that the neuromuscular feedback system significantly contributes to MJRI and it is believed that this behaviour enhances joint impedance following a sudden knee extension perturbation.     

Using three-dimensional kinematics to identify feedback for the Snatch: a case study

This case study evaluated the importance of peak bar velocity and starting posture adopted by a novice weightlifter to the outcome of a Snatch lift. Multiple observations of both successful and unsuccessful attempts were captured using 3D motion analysis (VICON MX: 500 Hz). The following data analysis was then used to derive feedback. In total, 133 attempts of loads ranging from 75 to 100% of 1 repetition maximum (1RM) were performed by the subject (age = 25 years, stature = 171 cm, mass = 74.8 kg, Snatch 1RM = 80 kg). Variables included peak bar velocity, pelvis, hip, knee and ankle joint angles at the starting position for the right side and the difference between (left minus right) sides. No main effects for load, success, or their interactions were found for peak bar velocity. Starting position kinematics were mostly nonsignificant between the outcome of Snatch attempts. Right ankle joint angle was the only exception, where unsuccessful attempts displayed greater (p = 0.0228) dorsiflexion. A more comprehensive finding was achieved through the partition modeling; this analysis provided valuable insight and coaching feedback for the subject in relation to his lower body kinematics at the starting position. Furthermore, the accuracy of this feedback was verified using a holdback data set. Specifically, anterior pelvic tilt (>17.6°) and hip joint (<89.6°) angle were identified as the key features to increasing the likelihood of success. In conclusion, this case study outlines a method of data collection and analysis to assist coaching feedback for an individual.     

Effect of arm swinging on lumbar spine and hip joint forces

During level walking, arm swing plays a key role in improving dynamic stability. In vivo investigations with a telemeterized vertebral body replacement showed that spinal loads can be affected by differences in arm positions during sitting and standing. However, little is known about how arm swing could influence the lumbar spine and hip joint forces and motions during walking. The present study aims to provide better understanding of the contribution of the upper limbs to human gait, investigating ranges of motion and joint reaction forces.A three-dimensional motion analysis was carried out via a motion capturing system on six healthy males and five patients with hip instrumented implant. Each subject performed walking with different arm swing amplitudes (small, normal, and large) and arm positions (bound to the body, and folded across the chest). The motion data were imported in a commercial musculoskeletal analysis software for kinematic and inverse dynamic investigation.The range of motion of the thorax with respect to the pelvis and of the pelvis with respect to the ground in the transversal plane were significantly associated with arm position and swing amplitude during gait. The hip external-internal rotation range of motion statistically varied only for non-dominant limb. Unlike hip joint reaction forces, predicted peak spinal loads at T12-L1 and L5-S1 showed significant differences at approximately the time of contralateral toe off and contralateral heel strike.Therefore, arm position and swing amplitude have a relevant effect on kinematic variables and spinal loads, but not on hip loads during walking.     

A New Auditory Multi-Class Brain-Computer Interface Paradigm: Spatial Hearing as an Informative Cue

Most P300-based brain-computer interface (BCI) approaches use the visual modality for stimulation. For use with patients suffering from amyotrophic lateral sclerosis (ALS) this might not be the preferable choice because of sight deterioration. Moreover, using a modality different from the visual one minimizes interference with possible visual feedback. Therefore, a multi-class BCI paradigm is proposed that uses spatially distributed, auditory cues. Ten healthy subjects participated in an offline oddball task with the spatial location of the stimuli being a discriminating cue. Experiments were done in free field, with an individual speaker for each location. Different inter-stimulus intervals of 1000 ms, 300 ms and 175 ms were tested. With averaging over multiple repetitions, selection scores went over 90% for most conditions, i.e., in over 90% of the trials the correct location was selected. One subject reached a 100% correct score. Corresponding information transfer rates were high, up to an average score of 17.39 bits/minute for the 175 ms condition (best subject 25.20 bits/minute). When presenting the stimuli through a single speaker, thus effectively canceling the spatial properties of the cue, selection scores went down below 70% for most subjects. We conclude that the proposed spatial auditory paradigm is successful for healthy subjects and shows promising results that may lead to a fast BCI that solely relies on the auditory sense.     

Mathematical model for the fluidized bed biofilm reactor

A mathematical model is proposed for the fluidized bed biofilm reactor (FBBR). For individual biofilm-covered particles (bioparticles) within the reactor, an analysis of intrabiofilm mass transfer and simultaneous intrinsic zero order reaction yields an effectiveness factor expression which is a function of the modified, zero order Thiele modulus, Φ_0,m. This expression is linked to a one-dimensional reactor flow model and a fluidization model to yield an overall reactor model describing convective transport and simultaneous biochemical conversion of substrate within a FBBR. For Φ_0,m<1.15, FBBR is mass transfer limited and 0.45 order kinetics are observed. For Φ_0,m<1.15, mass transfer limitations are insignificant and intrinsic zero order kinetics are observed. A sensitivity analysis using the proposed mathematical model indicates that biofilm thickness and media size are the two most important operating parameters. These two parameters can be optimized simultaneously for a specific application. The proposed model provides a rational approach for FBBR design.     

Quantitative genetic variability maintained by mutation-stabilizing selection balance: sampling variation and response to subsequent directional selection

A model of genetic variation of a quantitative character subject to the simultaneous effects of mutation, selection and drift is investigated. Predictions are obtained for the variance of the genetic variance among independent lines at equilibrium with stabilizing selection. These indicate that the coefficient of variation of the genetic variance among lines is relatively insensitive to the strength of stabilizing selection on the character. The effects on the genetic variance of a change of mode of selection from stabilizing to directional selection are investigated. This is intended to model directional selection of a character in a sample of individuals from a natural or long-established cage population. The pattern of change of variance from directional selection is strongly influenced by the strengths of selection at individual loci in relation to effective population size before and after the change of regime. Patterns of change of variance and selection responses from Monte Carlo simulation are compared to selection responses observed in experiments. These indicate that changes in variance with directional selection are not very different from those due to drift alone in the experiments, and do not necessarily give information on the presence of stabilizing selection or its strength.     

Countermovement strategy changes with vertical jump height to accommodate feasible force constraints

In this study, we developed a curve-fit model of countermovement dynamics and examined whether the characteristics of a countermovement jump can be quantified using the model parameter and its scaling; we expected that the model-based analysis would facilitate an understanding of the basic mechanisms of force reduction and propulsion with a simplified framework of the center of mass (CoM) mechanics. Ten healthy young subjects jumped straight up to five different levels ranging from approximately 10% to 35% of their body heights. The kinematic and kinetic data on the CoM were measured using a force plate system synchronized with motion capture cameras. All subjects generated larger vertical forces compared with their body weights from the countermovement and sufficiently lowered their CoM position to support the work performed by push-off as the vertical elevations became more challenging. The model simulation reasonably reproduced the trajectories of vertical force during the countermovement, and the model parameters were replaced by linear and polynomial regression functions in terms of the vertical jump height. Gradual scaling trends of the individual model parameters were observed as a function of the vertical jump height with different degrees of scaling, depending on the subject. The results imply that the subjects may be aware of the jumping dynamics when subjected to various vertical jump heights and may select their countermovement strategies to effectively accommodate biomechanical constraints, i.e., limited force generation for the standing vertical jump.     

The influence of natural selection and sexual selection on the tails of sea-snakes (Laticauda colubrina)

Many phenotypic traits perform more than one function, and so can influence organismal fitness in more than one way. Sexually dimorphic traits offer an exceptional opportunity to clarify such complexity, especially if the trait involved is subject to natural as well as sexual selection, and if the sexes differ in ecology as well as reproductive behaviour. Relative tail length in sea-snakes fulfils these conditions. Our field studies on a Fijian population of yellow-lipped sea kraits ( Laticauda colubrina ) show that relative tail lengths in male sea kraits have strong consequences for individual fitness, both via natural and sexual selection. Males have much longer tails (relative to snout-vent length) than do females. Mark-recapture studies revealed a trade-off between growth and survival: males with relatively longer tails grew more slowly, but were more likely to survive, than were shorter-tailed males. A male snake's tail length relative to body length influenced not only his growth rate and probability of survival, but also his locomotor ability and mating success. Relative tail length in male sea kraits was thus under a complex combination of selective forces. These forces included directional natural selection (through effects on survival, growth and swimming speed) as well as stabilizing natural selection (males with average-length tails swam faster) and stabilizing sexual selection (males with average-length tails obtained more matings). In contrast, our study did not detect significant selection on relative tail length in females. This sex difference may reflect the fact that females use their tails primarily for swimming, whereas males also must frequently use the tail in terrestrial locomotion and in courtship as well as for swimming.     

Altered control of submaximal bite force during bruxism in humans

The control of bite force during varying submaximal loads was examined in patients suffering from bruxism compared to healthy humans not showing these symptoms. The subjects raised a bar (preload) with their incisor teeth and held it between their upper and lower incisors using the minimal bite force required to keep the bar in a horizontal position. Further loading was added during the preload phase. A sham load was also used. Depending on the session, the teeth were loaded by the experimenter or the subject and in one session the subject did not see the load (no visual feedback). The bite force was measured continuously using a calibrated force transducer. In all the subjects, the bite force increased with increasing load. Following the addition of the load, the level of the tonic bite force was reached rapidly with no marked overshoot. The patients with bruxism used significantly higher bite forces to hold the submaximal loads compared to the control subjects. In the control subjects, the holding forces for each submaximal load were identical in the men and the women and were independent of subject maximal bite force. Sham loading evoked no marked responses in biting force. Whether the subject or the experimenter added the load or whether the subject had visual feedback or not were not significant factors in determining the level of bite force. The results indicated that the patients with bruxism used excessively large biting forces for each given submaximal load. This study showed no evidence that the inappropriate control of bite force by patients with bruxism was due to an abnormality in the higher cortical circuits that regulates the function of trigeminal motoneurons in the brainstem. This was shown by a lack of abnormality in coordination of voluntary hand movement with biting force, a lack of abnormal anticipation response to a sham load and a lack of any effect of visual feedback. The results were in line with the hypothesis that afferent input from oral (periodontal or masticatory muscle) tissues does not provide an appropriate control of motor command in bruxism.     

A new integrated variable based on thermometry, actimetry and body position (TAP) to evaluate circadian system status in humans

The disruption of the circadian system in humans has been associated with the development of chronic illnesses and the worsening of pre-existing pathologies. Therefore, the assessment of human circadian system function under free living conditions using non-invasive techniques needs further research. Traditionally, overt rhythms such as activity and body temperature have been analyzed separately; however, a comprehensive index could reduce individual recording artifacts. Thus, a new variable (TAP), based on the integrated analysis of three simultaneous recordings: skin wrist temperature (T), motor activity (A) and body position (P) has been developed. Furthermore, we also tested the reliability of a single numerical index, the Circadian Function Index (CFI), to determine the circadian robustness. An actimeter and a temperature sensor were placed on the arm and wrist of the non-dominant hand, respectively, of 49 healthy young volunteers for a period of one week. T, A and P values were normalized for each subject. A non-parametric analysis was applied to both TAP and the separate variables to calculate their interdaily stability, intradaily variability and relative amplitude, and these values were then used for the CFI calculation. Modeling analyses were performed in order to determine TAP and CFI reliability. Each variable (T, A, P or TAP) was independently correlated with rest-activity logs kept by the volunteers. The highest correlation (r = −0.993, p<0.0001), along with highest specificity (0.870), sensitivity (0.740) and accuracy (0.904), were obtained when rest-activity records were compared to TAP. Furthermore, the CFI proved to be very sensitive to changes in circadian robustness. Our results demonstrate that the integrated TAP variable and the CFI calculation are powerful methods to assess circadian system status, improving sensitivity, specificity and accuracy in differentiating activity from rest over the analysis of wrist temperature, body position or activity alone.     

Effects of geometric individualisation of a human spine model on load sharing: neuro-musculoskeletal simulation reveals significant differences in ligament and muscle contribution

In spine research, two possibilities to generate models exist: generic (population-based) models representing the average human and subject-specific representations of individuals. Despite the increasing interest in subject specificity, individualisation of spine models remains challenging. Neuro-musculoskeletal (NMS) models enable the analysis and prediction of dynamic motions by incorporating active muscles attaching to bones that are connected using articulating joints under the assumption of rigid body dynamics. In this study, we used forward-dynamic simulations to compare a generic NMS multibody model of the thoracolumbar spine including fully articulated vertebrae, detailed musculature, passive ligaments and linear intervertebral disc (IVD) models with an individualised model to assess the contribution of individual biological structures. Individualisation was achieved by integrating skeletal geometry from computed tomography and custom-selected muscle and ligament paths. Both models underwent a gravitational settling process and a forward flexion-to-extension movement. The model-specific load distribution in an equilibrated upright position and local stiffness in the L4/5 functional spinal unit (FSU) is compared. Load sharing between occurring internal forces generated by individual biological structures and their contribution to the FSU stiffness was computed. The main finding of our simulations is an apparent shift in load sharing with individualisation from an equally distributed element contribution of IVD, ligaments and muscles in the generic spine model to a predominant muscle contribution in the individualised model depending on the analysed spine level.

     

Problems in heart rate and alpha electroencephalographic feedback

When a subject has demonstrated successful control over a feedback stimulus, the experimenter should not interpret this to mean that the subject has learned a specific correlated physiological function. Data from two types of experiments — attempted heart rate stoppage and alpha electro-encephalographic feedback control — demonstrate some of the problems. The apparent heart stoppage of one subject was caused by the decrease in arterial pressure which occurred during a Valsalva procedure. The successful control over feedback stimuli during an EEG feedback study led to confused results: in this case the alpha criterion was too broad and was satisfied by different alpha frequencies, amplitudes, phase relations, and toposcopic distributions. Grouped subject data would only confuse the interpretation further. Suggestions to avoid some EEG feedback pitfalls are given.     

Nonlinear muscles, passive viscoelasticity and body taper conspire to create neuromechanical phase lags in anguilliform swimmers

Locomotion provides superb examples of cooperation among neuromuscular systems, environmental reaction forces, and sensory feedback. As part of a program to understand the neuromechanics of locomotion, here we construct a model of anguilliform (eel-like) swimming in slender fishes. Building on a continuum mechanical representation of the body as an viscoelastic rod, actuated by a traveling wave of preferred curvature and subject to hydrodynamic reaction forces, we incorporate a new version of a calcium release and muscle force model, fitted to data from the lamprey Ichthyomyzon unicuspis, that interactively generates the curvature wave. We use the model to investigate the source of the difference in speeds observed between electromyographic waves of muscle activation and mechanical waves of body curvature, concluding that it is due to a combination of passive viscoelastic and geometric properties of the body and active muscle properties. Moreover, we find that nonlinear force dependence on muscle length and shortening velocity may reduce the work done by the swimming muscles in steady swimming.     

A mass-length scaling law for modeling muscle strength in the lower limb

Musculoskeletal computer models are often used to study muscle function in children with and without impaired mobility. Calculations of muscle forces depend in part on the assumed strength of each muscle, represented by the peak isometric force parameter, which is usually based on measurements obtained from cadavers of adult donors. The aim of the present study was twofold: first, to develop a method for scaling lower-limb peak isometric muscle forces in typically-developing children; and second, to determine the effect of this scaling method on model calculations of muscle forces obtained for normal gait. Muscle volumes were determined from magnetic resonance (MR) images obtained from ten children aged from 7 to 13yr. A new mass-length scaling law was developed based on the assumption that muscle volume and body mass are linearly related, which was confirmed by the obtained volume and body mass data. Two musculoskeletal models were developed for each subject: one in which peak isometric muscle forces were estimated using the mass-length scaling law; and another in which these parameters were determined directly from the MR-derived muscle volumes. Musculoskeletal modeling and quantitative gait analysis were then used to calculate lower-limb muscle forces in normal walking. The patterns of muscle forces predicted by the model with scaled peak isometric force values were similar to those predicted by the MR-based model, implying that assessments of muscle function obtained from these two methods are practically equivalent. These results support the use of mass-length scaling in the development of subject-specific musculoskeletal models of children.     

Stimulated and co-operative electron transfer in energy conversion and catalysis.

A new mechanism of electron transfer, stimulated electron transfer, is postulated, in which an electronic feedback is drastically increasing both the rate of electron transfer and the propagation of free energy along electron transferring molecular pathways. In principle, the idea of pushing a system far from equilibrium to achieve a high reaction rate and co-operative phenomena is applied to molecular electron transfer. The effect is calculated from a semiclassical kinetic model of a chain redox reaction with autocatalytic feedback on individual rate constants, where the steps have subsequently been minimized to obtain a continuous electron transfer pathway with electronic feedback. The influence of inhomogeneities and asymmetries in the electron transfer path and of vectorial components (electrical field, gradient of redox potential) are discussed as well as the acceleration of individual and multiple electron transfer as a function of feedback. Examples of autocatalytic feedback are provided including mechanisms involving electron transfer proteins and multi-centre electron transfer catalysts. Such a phenomenon can be described for molecular and interfacial electron transfer in analogy to stimulated and coherent light emission. The results suggest that autocatalytic or stimulated electron transfer may be a key to the understanding of efficient electron transfer and co-operative multi-electron transfer catalysis in biology and a challenge for fuel production mechanisms in artificial photosynthesis and fuel cycles.