Intrinsic ankle stiffness is associated with paradoxical calf muscle movement but not postural sway or age.

Due to Achilles tendon compliance, passive ankle stiffness is insufficient to stabilise the body when standing. This results in 'paradoxical' muscle movement, whereby calf muscles tend to shorten during forward body sway. Natural variation in stiffness may affect this movement. This may have consequences for postural control, with compliant ankles placing greater reliance upon active neural control rather than stretch reflexes. Previous research also suggests ageing reduces ankle stiffness, possibly contributing to reduced postural stability. Here we determine the relationship between ankle stiffness and calf muscle movement during standing, and whether this is associated with postural stability or age. Passive ankle stiffness was measured during quiet stance in 40 healthy volunteers ranging from 18 to 88 years of age. Medial gastrocnemius muscle length was also recorded using ultrasound. We found a significant inverse relationship between ankle stiffness and paradoxical muscle movement, that is, more compliant ankles were associated with greater muscle shortening during forward sway (r ≥ 0.33). This was seen during both quiet stance as well as voluntary sway. However, we found no significant effects of age upon stiffness, paradoxical motion or postural sway. Furthermore, neither paradoxical muscle motion nor ankle stiffness was associated with postural sway. These results show that natural variation in ankle stiffness alters the extent of paradoxical calf muscle movement during stance. However, the absence of a clear relationship to postural sway suggests that neural control mechanisms are more than capable of compensating for a lack of inherent joint stiffness.

Idiosyncratic Characteristics of Postural Sway in Normal and Perturbed Standing.

OBJECTIVE: Are people with a characteristically large physiological sway rendered particularly unstable when standing on a moving surface? Is postural sway in standing individuals idiosyncratic? In this study, we examine postural sway in individuals standing normally, and when subtle continuous sinusoidal disturbances are applied to their support platform. We calculate consistency between conditions to verify if sway can be considered characteristic of each individual. We also correlate two different aspects of participants' responses to disturbance; their sway velocity and their regulation of body orientation. METHODS: Nineteen healthy adults (age 29.2 ± 3.2 years) stood freely on footplates coaxially aligned with their ankles and attached to a motorized platform. They had their eyes closed, and hips and knees locked with a light wooden board attached to their body. Participants either stood quietly on a fixed platform or on a slowly tilting platform (0.1 Hz sinusoid; 0.2 and 0.4 deg). Postural sway size was separated into two entities: (1) the spontaneous sway velocity component (natural random relatively rapid postural adjustments, RMS body angular velocity) and (2) the evoked tilt gain component (much slower 0.1 Hz synchronous tilt induced by the movement of the platform, measured as peak-to-peak (p-p) gain, ratio of body angle to applied footplate rotation). RESULTS: There was no correlation between the velocity of an individual's sway and their evoked tilt gain (r = 0.34, p = 0.15 and r = 0.30, p = 0.22). However, when considered separately, each of the two measurements showed fair to good absolute agreement within conditions. Spontaneous sway velocity consistently increased as participants were subjected to increasing disturbance. Participants who swayed more (or less) did so across all conditions [ICC(3,k) = 0.95]. Evoked tilt gain also showed consistency between conditions [ICC(3,k) = 0.79], but decreased from least to most disturbed conditions. CONCLUSION: The two measurements remain consistent between conditions. Consistency between conditions of two very distinct unrelated measurements reflects the idiosyncratic nature of postural sway. However, sway velocity and tilt gain are not related, which supports the idea that the short-term regulation of stability and the longer-term regulation of orientation are controlled by different processes.

Individual differences in intrinsic ankle stiffness and their relationship to body sway and ankle torque.

When standing, intrinsic ankle stiffness is smaller when measured using large perturbations, when sway size is large, and when background torque is low. However, there is a large variation in individual intrinsic ankle stiffness. Here we determine if individual variation has consequences for postural control. We examined the relationship between ankle stiffness, ankle torque and body sway across different individuals. Ankle stiffness was estimated in 19 standing participants by measuring torque responses to small, brief perturbations. Perturbation sizes of 0.2 & 0.9 degrees (both lasting 140 ms) measured short- and long-range stiffness respectively, while participants either stood quietly on a fixed platform or were imperceptibly tilted to reduce stability (0.1 Hz sinusoid; 0.2 & 0.4 deg). The spontaneous body sway component (natural random relatively rapid postural adjustments) and background ankle torque were averaged from sections immediately before perturbations. The results show that, first, intrinsic ankle stiffness is positively associated with ankle torque, and that this relationship is stronger for long-range stiffness. Second, intrinsic ankle stiffness is negatively associated with body sway, but, in contrast to the relationship with torque, this relationship is stronger for short-range stiffness. We conclude that high short-range intrinsic ankle stiffness is associated with reduced spontaneous sway, although the causal relationship between these two parameters is unknown. These results suggest that, in normal quiet standing where sway is very small, the most important determinant of intrinsic ankle stiffness may be stillness. In less stable conditions, intrinsic ankle stiffness may be more dependent on ankle torque.

Muscle thixotropy-where are we now?

Relaxed skeletal muscle has an inbuilt resistance to movement. In particular, the resistance manifests itself as a substantial stiffness for small movements. The stiffness is impermanent, because it forms only when the muscle is stationary for some time and is reduced upon active or passive movement. Because the resistance to movement increases with time at rest and is reduced by movement, this behavior has become known as muscle thixotropy. In this short review, we describe the phenomenon of thixotropy and illustrate its significance in postural control with particular emphasis on human standing. We show how thixotropy came to be unambiguously associated with muscle mechanics and we review present knowledge of the molecular basis of thixotropic behavior. Specifically, we examine how recent knowledge about titin, and about the control of cross-bridge cycling, has impacted on the role of non-cross-bridge mechanisms and cross-bridge mechanisms in explaining thixotropy. We describe how thixotropic changes in muscle stiffness that occur during transitions from posture to movement can be tracked by analyzing physiological tremor. Finally, because skeletal muscle contains sensory receptors, and because some of these receptors are themselves thixotropic, we outline some of the consequences of muscle thixotropy for proprioception.

Intrinsic ankle stiffness during standing increases with ankle torque and passive stretch of the Achilles tendon.

Individuals may stand with a range of ankle angles. Furthermore, shoes or floor surfaces may elevate or depress their heels. Here we ask how these situations impact ankle stiffness and balance. We performed two studies (each with 10 participants) in which the triceps surae, Achilles tendon and aponeurosis were stretched either passively, by rotating the support surface, or actively by leaning forward. Participants stood freely on footplates which could rotate around the ankle joint axis. Brief, small stiffness-measuring perturbations (<0.7 deg; 140 ms) were applied at intervals of 4-5 s. In study 1, participants stood at selected angles of forward lean. In study 2, normal standing was compared with passive dorsiflexion induced by 15 deg toes-up tilt of the support surface. Smaller perturbations produced higher stiffness estimates, but for all perturbation sizes stiffness increased with active torque or passive stretch. Sway was minimally affected by stretch or lean, suggesting that this did not underlie the alterations in stiffness. In quiet stance, maximum ankle stiffness is limited by the tendon. As tendon strain increases, it becomes stiffer, causing an increase in overall ankle stiffness, which would explain the effects of leaning. However, stiffness also increased considerably with passive stretch, despite a modest torque increase. We discuss possible explanations for this increase.

Visuo-manual tracking: does intermittent control with aperiodic sampling explain linear power and non-linear remnant without sensorimotor noise?

KEY POINTS: A human controlling an external system is described most easily and conventionally as linearly and continuously translating sensory input to motor output, with the inevitable output remnant, non-linearly related to the input, attributed to sensorimotor noise. Recent experiments show sustained manual tracking involves repeated refractoriness (insensitivity to sensory information for a certain duration), with the temporary 200-500 ms periods of irresponsiveness to sensory input making the control process intrinsically non-linear. This evidence calls for re-examination of the extent to which random sensorimotor noise is required to explain the non-linear remnant. This investigation of manual tracking shows how the full motor output (linear component and remnant) can be explained mechanistically by aperiodic sampling triggered by prediction error thresholds. Whereas broadband physiological noise is general to all processes, aperiodic sampling is associated with sensorimotor decision making within specific frontal, striatal and parietal networks; we conclude that manual tracking utilises such slow serial decision making pathways up to several times per second. ABSTRACT: The human operator is described adequately by linear translation of sensory input to motor output. Motor output also always includes a non-linear remnant resulting from random sensorimotor noise from multiple sources, and non-linear input transformations, for example thresholds or refractory periods. Recent evidence showed that manual tracking incurs substantial, serial, refractoriness (insensitivity to sensory information of 350 and 550 ms for 1st and 2nd order systems respectively). Our two questions are: (i) What are the comparative merits of explaining the non-linear remnant using noise or non-linear transformations? (ii) Can non-linear transformations represent serial motor decision making within the sensorimotor feedback loop intrinsic to tracking? Twelve participants (instructed to act in three prescribed ways) manually controlled two systems (1st and 2nd order) subject to a periodic multi-sine disturbance. Joystick power was analysed using three models, continuous-linear-control (CC), continuous-linear-control with calculated noise spectrum (CCN), and intermittent control with aperiodic sampling triggered by prediction error thresholds (IC). Unlike the linear mechanism, the intermittent control mechanism explained the majority of total power (linear and remnant) (77-87% vs. 8-48%, IC vs. CC). Between conditions, IC used thresholds and distributions of open loop intervals consistent with, respectively, instructions and previous measured, model independent values; whereas CCN required changes in noise spectrum deviating from broadband, signal dependent noise. We conclude that manual tracking uses open loop predictive control with aperiodic sampling. Because aperiodic sampling is inherent to serial decision making within previously identified, specific frontal, striatal and parietal networks we suggest that these structures are intimately involved in visuo-manual tracking.

Physiological tremor reveals how thixotropy adapts skeletal muscle for posture and movement.

People and animals can move freely, but they must also be able to stay still. How do skeletal muscles economically produce both movement and posture? Humans are well known to have motor units with relatively homogeneous mechanical properties. Thixotropic muscle properties can provide a solution by providing a temporary stiffening of all skeletal muscles in postural conditions. This stiffening is alleviated almost instantly when muscles start to move. In this paper, we probe this behaviour. We monitor both the neural input to a muscle, measured here as extensor muscle electromyography (EMG), and its output, measured as tremor (finger acceleration). Both signals were analysed continuously as the subject made smooth transitions between posture and movement. The results showed that there were marked changes in tremor which systematically increased in size and decreased in frequency as the subject moved faster. By contrast, the EMG changed little and reflected muscle force requirement rather than movement speed. The altered tremor reflects naturally occurring thixotropic changes in muscle behaviour. Our results suggest that physiological tremor provides useful and hitherto unrecognized insights into skeletal muscle's role in posture and movement.

Sway-dependent changes in standing ankle stiffness caused by muscle thixotropy.

KEY POINTS: The passive stiffness of the calf muscles contributes to standing balance, although the properties of muscle tissue are highly labile. We investigated the effect of sway history upon intrinsic ankle stiffness and demonstrated reductions in stiffness of up to 43% during conditions of increased baseline sway. This sway dependence was most apparent when using low amplitude stiffness-measuring perturbations, and the short-range stiffness component was smaller during periods of high sway. These characteristics are consistent with the thixotropic properties of the calf muscles causing the observed changes in ankle stiffness. Periods of increased sway impair the passive stabilization of standing, demanding more active neural control of balance. Quiet standing is achieved through a combination of active and passive mechanisms, consisting of neural control and intrinsic mechanical stiffness of the ankle joint, respectively. The mechanical stiffness is partly determined by the calf muscles. However, the viscoelastic properties of muscle are highly labile, exhibiting a strong dependence on movement history. By measuring the effect of sway history upon ankle stiffness, the present study determines whether this lability has consequences for the passive stabilization of human standing. Ten subjects stood quietly on a rotating platform whose axis was collinear with the ankle joint. Ankle sway was increased by slowly tilting this platform in a random fashion, or decreased by fixing the body to a board. Ankle stiffness was measured by using the same platform to simultaneously apply small, brief perturbations (<0.6 deg; 140 ms) at the same time as the resulting torque response was recorded. The results show that increasing sway reduces ankle stiffness by up to 43% compared to the body-fixed condition. Normal quiet stance was associated with intermediate values. The effect was most apparent when using smaller perturbation amplitudes to measure stiffness (0.1 vs. 0.6 deg). Furthermore, torque responses exhibited a biphasic pattern, consisting of an initial steep rise followed by a shallower increase. This transition occurred earlier during increased levels of ankle sway. These results are consistent with a movement-dependent change in passive ankle stiffness caused by thixotropic properties of the calf muscle. The consequence is to place increased reliance upon active neural control during times when increased sway renders ankle stiffness low.

The complete frequency spectrum of physiological tremor can be recreated by broadband mechanical or electrical drive.

Two frequency peaks of variable preponderance have been reported for human physiological finger tremor. The high-frequency peak (20-25 Hz, seen only in postural tremor) is generally attributed to mechanical resonance, whereas the lower frequency peak (8-12 Hz, seen in both postural and kinetic tremor) is usually attributed to synchronous central or reflexive neural drive. In this study, we determine whether mechanical resonance could generate both peaks. In relaxed subjects, an artificial finger tremor was evoked by random mechanical perturbations of the middle finger or random electrical muscular stimulation of the finger extensor muscle. The high and the low frequencies observed in physiological tremor could both be created by either type of artificial input at appropriate input intensity. Resonance, inferred from cross-spectral gain and phase, occurred at both frequencies. To determine any neural contribution, we compared truly passive subjects with those who exhibited some electromyographic (EMG) activity in the finger extensor; artificially created tremor spectra were almost identical between groups. We also applied electrical stimuli to two clinically deafferented subjects lacking stretch reflexes. They exhibited the same artificial tremor spectrum as control subjects. These results suggest that both typical physiological finger tremor frequencies can be reproduced by random artificial input; neither requires synchronized neural input. We therefore suggest that mechanical resonance could generate both dominant frequency peaks characteristic of physiological finger tremor. The inverse relationship between the input intensity and the resulting tremor frequency can be explained by a movement-dependent reduction in muscle stiffness, a conjecture we support using a simple computational model.

Does the motor system need intermittent control?

Explanation of motor control is dominated by continuous neurophysiological pathways (e.g., transcortical, spinal) and the continuous control paradigm. Using new theoretical development, methodology, and evidence, we propose intermittent control, which incorporates a serial ballistic process within the main feedback loop, provides a more general and more accurate paradigm necessary to explain attributes highly advantageous for competitive survival and performance.

Intermittent control models of human standing: similarities and differences.

Two architectures of intermittent control are compared and contrasted in the context of the single inverted pendulum model often used for describing standing in humans. The architectures are similar insofar as they use periods of open-loop control punctuated by switching events when crossing a switching surface to keep the system state trajectories close to trajectories leading to equilibrium. The architectures differ in two significant ways. Firstly, in one case, the open-loop control trajectory is generated by a system-matched hold, and in the other case, the open-loop control signal is zero. Secondly, prediction is used in one case but not the other. The former difference is examined in this paper. The zero control alternative leads to periodic oscillations associated with limit cycles; whereas the system-matched control alternative gives trajectories (including homoclinic orbits) which contain the equilibrium point and do not have oscillatory behaviour. Despite this difference in behaviour, it is further shown that behaviour can appear similar when either the system is perturbed by additive noise or the system-matched trajectory generation is perturbed. The purpose of the research is to come to a common approach for understanding the theoretical properties of the two alternatives with the twin aims of choosing which provides the best explanation of current experimental data (which may not, by itself, distinguish between the two alternatives) and suggesting future experiments to distinguish between the two alternatives.

Interfacing sensory input with motor output: does the control architecture converge to a serial process along a single channel?

Modular organization in control architecture may underlie the versatility of human motor control; but the nature of the interface relating sensory input through task-selection in the space of performance variables to control actions in the space of the elemental variables is currently unknown. Our central question is whether the control architecture converges to a serial process along a single channel? In discrete reaction time experiments, psychologists have firmly associated a serial single channel hypothesis with refractoriness and response selection [psychological refractory period (PRP)]. Recently, we developed a methodology and evidence identifying refractoriness in sustained control of an external single degree-of-freedom system. We hypothesize that multi-segmental whole-body control also shows refractoriness. Eight participants controlled their whole body to ensure a head marker tracked a target as fast and accurately as possible. Analysis showed enhanced delays in response to stimuli with close temporal proximity to the preceding stimulus. Consistent with our preceding work, this evidence is incompatible with control as a linear time invariant process. This evidence is consistent with a single-channel serial ballistic process within the intermittent control paradigm with an intermittent interval of around 0.5 s. A control architecture reproducing intentional human movement control must reproduce refractoriness. Intermittent control is designed to provide computational time for an online optimization process and is appropriate for flexible adaptive control. For human motor control we suggest that parallel sensory input converges to a serial, single channel process involving planning, selection, and temporal inhibition of alternative responses prior to low dimensional motor output. Such design could aid robots to reproduce the flexibility of human control.

A dominant role for mechanical resonance in physiological finger tremor revealed by selective minimization of voluntary drive and movement.

There is a debate in the literature about whether the low- and high-frequency peaks of physiological finger tremor are caused by resonance or central drive. One way to address this issue is to examine the consequences of eliminating, as far as possible, the resonant properties or the voluntary drive. To study the effect of minimizing resonance, finger tremor was recorded under isometric conditions and compared with normal isotonic tremor. To minimize central drive, finger tremor was generated artificially by broad-band electrical stimulation. When resonance was minimized, tremor size declined almost monotonically with increasing frequency. There was no consistent large peak at a frequency characteristic of tremor. Although there was sometimes a peak around the tremor frequency during some isometric conditions, it was extremely small and variable; therefore, any contribution of central drive was minimal. In contrast, there was always a prominent peak in the isotonic frequency spectra. Resonance was, therefore, necessary to produce the characteristic tremor peaks. When central drive was minimized by replacing voluntary muscle activation with artificial stimulation, a realistic tremor spectrum was observed. Central drive is, therefore, not required to generate a characteristic physiological tremor spectrum. In addition, regardless of the nature of the driving input (voluntary or artificial), increasing the size of the input considerably reduced isotonic tremor frequency. We attribute the frequency reduction to a movement-related thixotropic change in muscle stiffness. From these results we conclude that physiological finger tremor across a large range of frequencies is produced by natural broad-band forcing of a nonlinear resonant system, and that synchronous central input is not required.

The resonant component of human physiological hand tremor is altered by slow voluntary movements.

Limb resonance imparts a characteristic spectrum to hand tremor. Movement will alter the resonance. We have examined the consequences of this change. Rectified forearm extensor muscle EMG and physiological hand tremor were recorded. In postural conditions the EMG spectrum is relatively flat whereas the acceleration spectrum is sharply peaked. Consequently, the gain between EMG and acceleration is maximal at the frequency where the tremor is largest (∼8 Hz). The shape of the gain curve implies mechanical resonance. Substantial alterations in posture do not significantly change the characteristics of the tremor or the shape or size of the gain curve. By contrast, slow or moderately paced voluntary wrist flexion­extension movements dramatically increase the hand tremor size and lower its peak frequency. These changes in size and frequency of the tremor cannot be attributed to changes in the EMG. Instead they reflect a very large change in the size and shape of the gain curve relating EMG to acceleration. The gain becomes larger and the peak moves to a lower frequency (∼6 Hz). We suggest that a movement-related (thixotropic) alteration in resonant properties of the wrist provides a simple explanation for these changes. The mechanism is illustrated by a model. Our new findings confirm that resonance plays a major role in wrist tremor. We also demonstrate that muscles operate very differently under postural and dynamic conditions. The different coupling between EMG and movement in posture and when moving must pose a considerable challenge for neural predictive control of skeletal muscles.

A novel planar tracking technology for physiological image analysis.

Automated image tracking provides new insights in many physiological studies, but present methods are ad hoc and can be difficult to use. They are generally based on following the movement of one or more specific regions of interested - point tracking. We tested newly available novel planar tracking technology commercially developed for the special effects industry, which does not use point tracking. We validated the tracker and made two dynamic physiological measurements. Our validation measurements describe the accuracy and repeatability of the technique, and our physiological measurements demonstrate the flexibility of the software. Our results suggest that planar tracking may be of particular use with techniques that produce low quality images such as ultrasonography.

Intermittent control: a computational theory of human control.

The paradigm of continuous control using internal models has advanced understanding of human motor control. However, this paradigm ignores some aspects of human control, including intermittent feedback, serial ballistic control, triggered responses and refractory periods. It is shown that event-driven intermittent control provides a framework to explain the behaviour of the human operator under a wider range of conditions than continuous control. Continuous control is included as a special case, but sampling, system matched hold, an intermittent predictor and an event trigger allow serial open-loop trajectories using intermittent feedback. The implementation here may be described as "continuous observation, intermittent action". Beyond explaining unimodal regulation distributions in common with continuous control, these features naturally explain refractoriness and bimodal stabilisation distributions observed in double stimulus tracking experiments and quiet standing, respectively. Moreover, given that human control systems contain significant time delays, a biological-cybernetic rationale favours intermittent over continuous control: intermittent predictive control is computationally less demanding than continuous predictive control. A standard continuous-time predictive control model of the human operator is used as the underlying design method for an event-driven intermittent controller. It is shown that when event thresholds are small and sampling is regular, the intermittent controller can masquerade as the underlying continuous-time controller and thus, under these conditions, the continuous-time and intermittent controller cannot be distinguished. This explains why the intermittent control hypothesis is consistent with the continuous control hypothesis for certain experimental conditions.

Human control of an inverted pendulum: is continuous control necessary? Is intermittent control effective? Is intermittent control physiological?

Human motor control is often explained in terms of engineering 'servo' theory. Recently, continuous, optimal control using internal models has emerged as a leading paradigm for voluntary movement. However, these engineering paradigms are designed for high band-width, inflexible, consistent systems whereas human control is low bandwidth and flexible using noisy sensors and actuators. By contrast, engineering intermittent control was designed for bandwidth-limited applications. Our general interest is whether intermittent rather than continuous control is generic to human motor control. Currently, it would be assumed that continuous control is the superior and physiologically natural choice for controlling unstable loads, for example as required for maintaining human balance. Using visuo-manual tracking of an unstable load, we show that control using gentle, intermittent taps is entirely natural and effective. The gentle tapping method resulted in slightly superior position control and velocity minimisation, a reduced feedback time delay, greater robustness to changing actuator gain and equal or greater linearity with respect to the external disturbance. Control was possible with a median contact rate of 0.8±0.3 s(-1). However, when optimising position or velocity regulation, a modal contact rate of 2 s(-1) was observed. This modal rate was consistent with insignificant disturbance-joystick coherence beyond 1-2 Hz in both tapping and continuous contact methods. For this load, these results demonstrate a motor control process of serial ballistic trajectories limited to an optimum rate of 2 s(-1). Consistent with theoretical reasoning, our results suggest that intermittent open loop action is a natural consequence of human physiology.

Postmovement changes in the frequency and amplitude of physiological tremor despite unchanged neural output.

Active or passive movement causes a temporary reduction in muscle stiffness that gradually returns to baseline levels when the muscle remains still. This effect, termed muscle thixotropy, alters the mechanical properties of the joint around which the muscle acts, reducing its resonant frequency. Because physiological tremor is affected by joint mechanics, this suggests that prior movement may alter tremor independently of neural output. To address this possibility, vertical acceleration of the outstretched prone hand was recorded in eight healthy subjects, along with EMG activity of the extensor digitorum communis muscle. A series of voluntary wrist flexion/extension movements was performed every 20 s, interspersed by periods during which hand position was maintained. Time-dependent changes in the amplitude and frequency of acceleration and EMG were analyzed using a continuous wavelet transform. Immediately following movement, acceleration displayed a significant increase in wavelet power accompanied by a reduction in peak frequency. During the postmovement period, power declined by 63%, and frequency increased from 7.2 to 8.0 Hz. These changes occurred with an exponential time constant of 2-4 s, consistent with a thixotropic mechanism. In contrast to acceleration, EMG activity showed no significant changes despite being strongly related to acceleration during the movement itself. These results show that prior movement transiently increases the amplitude and reduces the frequency of physiological tremor, despite unchanging neural output. This effect is best explained by a reduction in joint stiffness caused by muscle thixotropy, highlighting the importance of mechanical factors in the genesis of physiological tremor.

The influence of muscle tremor on shooting performance.

Shooting ability is compromised by involuntary movement. Some of this movement is physiological tremor. Tremor size has a demonstrable inverse correlation with shooting performance. Consequently, factors which affect tremor size should affect shooting ability. Adrenaline and local muscle warming markedly increase tremor size, whereas local muscle cooling reduces it. The physiological mechanisms behind these changes are not well understood, but they have the potential to affect shooting performance in subjects who exercise heavily and/or are exposed to extreme environments. The Olympic biathlon is an event in which vigorous physical exercise alternates with rifle shooting and it often takes place in a cold environment. The possible impact of exercise, temperature and other factors on the Olympic biathlete is considered here.

Predictive feedback in human simulated pendulum balancing.

In studies of human balance, it is common to fit stimulus-response data by tuning the time-delay and gain parameters of a simple delayed feedback model. Many interpret this fitted model, a simple delayed feedback model, as evidence that predictive processes are not required to explain existing data on standing balance. However, two questions lead us to doubt this approach. First, does fitting a delayed feedback model lead to reliable estimates of the time-delay? Second, can a non-predictive controller provide an explanation compatible with the independently estimated time delay? For methodological and experimental clarity, we study human balancing of a simulated inverted pendulum via joystick and screen. A two-step approach to data analysis is used: firstly a non-parametric model--the closed-loop impulse response--is estimated from the experimental data; second, a parametric model is fitted to the non-parametric impulse-response by adjusting time-delay and controller parameters. To support the second step, a new explicit formula relating controller parameters to closed-loop impulse response is derived. Two classes of controller are investigated within a common state-space context: non-predictive and predictive. It is found that the time-delay estimate arising from the second step is strongly dependent on which controller class is assumed; in particular, the non-predictive control assumption leads to time-delay estimates that are smaller than those arising from the predictive assumption. Moreover, the time-delays estimated using the non-predictive control assumption are not consistent with a lower-bound on the time-delay of the non-parametric model whereas the corresponding predictive result is consistent. Thus while the goodness of fit only marginally favoured predictive over non-predictive control, if we add the additional constraint that the model must reproduce the non-parametric time delay, then the non-predictive control model fails. We conclude (1) the time-delay should be estimated independently of fitting a low order parametric model, (2) that balance of the simulated inverted pendulum could not be explained by the non-predictive control model and (3) that predictive control provided a better explanation than non-predictive control.