Martin Lakie

Direct measurement of human ankle stiffness during quiet standing: the intrinsic mechanical stiffness is insufficient for stability

During quiet standing the human ‘inverted pendulum’ sways irregularly. In previous work where subjects balanced a real inverted pendulum, we investigated what contribution the intrinsic mechanical ankle stiffness makes to achieve stability. Using the results of a plausible model, we suggested that intrinsic ankle stiffness is inadequate for providing stability. Here, using a piezo‐electric translator we applied small, unobtrusive mechanical perturbations to the foot while the subject was standing freely. These short duration perturbations had a similar size and velocity to movements which occur naturally during quiet standing, and they produced no evidence of any stretch reflex response in soleus, or gastrocnemius. Direct measurement confirms our earlier conclusion; intrinsic ankle stiffness is not quite sufficient to stabilise the body or pendulum. On average the directly determined intrinsic stiffness is 91 ± 23 % (mean ±s.d.) of that necessary to provide minimal stabilisation. The stiffness was substantially constant, increasing only slightly with ankle torque. This stiffness cannot be neurally regulated in quiet standing. Thus we attribute this stiffness to the foot, Achilles’ tendon and aponeurosis rather than the activated calf muscle fibres. Our measurements suggest that the triceps surae muscles maintain balance via a spring‐like element which is itself too compliant to guarantee stability. The implication is that the brain cannot set ankle stiffness and then ignore the control task because additional modulation of torque is required to maintain balance. We suggest that the triceps surae muscles maintain balance by predictively controlling the proximal offset of the spring‐like element in a ballistic‐like manner.

Human balancing of an inverted pendulum: position control by small, ballistic‐like, throw and catch movements

In standing, there are small sways of the body. Our interest is to use an artificial task to illuminate the mechanisms underlying the sways and to account for changes in their size. Using the ankle musculature, subjects balanced a large inverted pendulum. The equilibrium of the pendulum is unstable and quasi‐regular sway was observed like that in quiet standing. By giving full attention to minimising sway subjects could systematically reduce pendulum movement. The pendulum position, the torque generated at each ankle and the soleus and tibialis anterior EMGs were recorded. Explanations about how the human inverted pendulum is balanced usually ignore the fact that balance is maintained over a range of angles and not just at one angle. Any resting equilibrium position of the pendulum is unstable and in practice temporary; movement to a different resting equilibrium position can only be accomplished by a biphasic ‘throw and catch’ pattern of torque and not by an elastic mechanism. Results showed that balance was achieved by the constant repetition of a neurally generated ballistic‐like biphasic pattern of torque which can control both position and sway size. A decomposition technique revealed that there was a substantial contribution to changes in torque from intrinsic mechanical ankle stiffness; however, by itself this was insufficient to maintain balance or to control position. Minimisation of sway size was caused by improvement in the accuracy of the anticipatory torque impulses. We hypothesise that examination of centre of mass and centre of pressure data for quiet standing will duplicate these results.

Human postural sway results from frequent, ballistic bias impulses by soleus and gastrocnemius

It has been widely assumed for nearly a century, that postural muscles operate in a spring‐like manner and that muscle length signals joint angle (the mechano‐reflex mechanism). Here we employ automated analysis of ultrasound images to resolve calf muscle (soleus and gastrocnemius) length changes as small as 10 μm in standing subjects. Previously, we have used balancing of a real inverted pendulum to make predictions about human standing. Here we test and confirm these predictions on 10 subjects standing quietly. We show that on average the calf muscles are actively adjusted 2.6 times per second and 2.8 times per unidirectional sway of the body centre of mass (CoM). These alternating, small (30–300 µm) movements provide impulsive, ballistic regulation of CoM movement. The timing and pattern of these adjustments are consistent with multisensory integration of all information regarding motion of the CoM, pattern recognition, prediction and planning using internal models and are not consistent with control solely by local reflexes. Because the system is unstable, errors in stabilization provide a perturbation which grows into a sway which has to be reacted to and corrected. Sagittal sway results from this impulsive control of calf muscle activity rather than internal sources (e.g. the heart, breathing). This process is quite unlike the mechano‐reflex paradigm. We suggest that standing is a skilled, trial and error activity that improves with experience and is automated (possibly by the cerebellum). These results complement and extend our recent demonstration that paradoxical muscle movements are the norm in human standing.

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

Homeostasis, the physiological control of variables such as body position, is founded on negative feedback mechanisms. The default understanding, consistent with a wealth of knowledge related to peripheral reflexes, is that feedback mechanisms controlling body position act continuously. For more than fifty years, it has been assumed that sustained control of position is best interpreted using continuous paradigms from engineering control theory such as those which regulate speed in a vehicle ‘cruise control’ system. Using a joystick to control an unstable load that falls over like a person fainting, we show that control using intermittent gentle taps is natural, more effective and robust to unexpected changes than continuous hand contact, works best with two taps per second, and can explain the upper frequency limit of control by both methods. Serial ballistic control, limited to an optimum rate, provides a new physiological paradigm for interpreting sustained control of posture and movement.

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.

Active, non‐spring‐like muscle movements in human postural sway: how might paradoxical changes in muscle length be produced?

In humans, during standing the calf muscles soleus and gastrocnemius actively prevent forward toppling about the ankles. It has been generally assumed that these postural muscles behave like springs with dynamic stiffness reflecting their mechanical properties, reflex gain including higher derivatives, and central control. Here, for the first time, we have used an ultrasound scanner and automated image analysis to record the tiny muscular movements occurring in normal standing. This new, non‐invasive technique resolves changes in muscle length as small as 10 μm without disturbing the standing process. This technical achievement has allowed us to test the long‐established mechano‐reflex, muscle spring hypothesis that muscle length changes in a spring‐like way during sway of the body. Our results contradict that hypothesis. Muscle length changes in a non‐spring‐like manner: on average, shortening during forward sway and lengthening during backwards sway (paradoxical movements). This counter‐intuitive result is a consequence of the fact that calf muscles generate tension through a series elastic component (SEC, Achilles tendon and foot) which limits maximal ankle stiffness to 92 ± 20% of that required to balance the body. Paradoxical movements cannot be generated by stretch reflexes with constant intrafusal drive but might be produced by reflex coupling of extrafusal (α) and intrafusal (β, γ) drive or by positive force feedback. Standing requires the predictive ability to produce the observed muscle movements preceded (110 ± 50 ms) by corresponding changes in integrated EMG signal. We suggest higher level anticipatory control is more plausible.

Human balancing of an inverted pendulum: is sway size controlled by ankle impedance?

1 Using the ankle musculature, subjects balanced a large inverted pendulum. The equilibrium of the pendulum is unstable and quasi‐regular sway was observed like that in quiet standing. Two main questions were addressed. Can subjects systematically change sway size in response to instruction and availability of visual feedback? If so, do subjects decrease sway size by increasing ankle impedance or by some alternative mechanism? 2 The position of the pendulum, the torque generated at each ankle and the soleus and tibialis anterior EMG were recorded. 3 Results showed that subjects could significantly reduce the mean sway size of the pendulum by giving full attention to that goal. With visual feedback sway size could be minimised significantly more than without visual feedback. In changing sway size, the frequency of the sways was not changed. 4 Results also revealed that ankle impedance and muscle co‐contraction were not significantly changed when the sway size was decreased. As the ankle impedance and sway frequency do not change when the sway size is decreased, this implies no change in ankle stiffness or viscosity. 5 Increasing ankle impedance, stiffness or viscosity are not the only methods by which sway size could be reduced. A reduction in torque noise or torque inaccuracy via a predictive process which provides active damping could reduce sway size without changing ankle impedance and is plausible given the data. Such a strategy involving motion recognition and generation of an accurate motor response may require higher levels of control than changing ankle impedance by altering reflex or feedforward gain.

A cross-bridge mechanism can explain the thixotropic short-range elastic component of relaxed frog skeletal muscle

1 The passive tension and sarcomere length of relaxed frog skeletal muscle fibres were measured in response to imposed length stretches. The tension response to a constant‐velocity stretch exhibited a clear discontinuity. Tension rose more rapidly during the initial ∼ 0.4 %L0 of the stretch than during the latter stages (where L0 is the resting length of the fibre). This initial tension response is attributed to the short‐range elastic component (SREC). 2 The use of paired triangular stretches revealed that the maximum tension produced during the SREC response of the second stretch was significantly reduced by the first stretch. This history‐dependent behaviour of the SREC reflects thixotropic stiffness changes that have been previously described in relaxed muscle. 3 The biphasic nature of the SREC tension response to movement was most apparent during the first imposed length change after a period at a fixed length, irrespective of the direction of movement. 4 If a relaxed muscle was subjected to an imposed triangular length change so that the muscle was initially stretched and subsequently shortened back to its original fibre length, the resting tension at the end of the stretch was reduced relative to its initial pre‐stretch value. Following the end of the stretch, tension slowly increased towards its initial value but the tension recovery was not accompanied by a contemporaneous increase in sarcomere length. This finding suggests that the resting tension of a relaxed muscle fibre is not entirely due to passive elasticity. The results are compatible with the suggestion that a portion of the resting tension ‐ the filamentary resting tension (FRT) ‐ is produced by a low level of active force generation. 5 If a second identical stretch was imposed on the muscle at a time when the resting tension was reduced by the previous stretch, the maximal tension produced during the second stretch was the same as that produced during the first, despite the second stretch commencing from a lower initial resting tension. 6 In experiments using paired triangular length changes, an inter‐stretch interval of zero did not produce a substantially greater thixotropic reduction in the second stretch elastic limit force than an inter‐stretch interval in the range 0.5‐1 s. 7 A theoretical model was developed in which the SREC and FRT arise as manifestations of a small number of slowly cycling cross‐bridges linking the actin and myosin filaments of a relaxed skeletal muscle. The predictions of the model are compatible with many of the experimental observations. If the SREC and FRT are indeed due to cross‐bridge activity, the model suggests that the cross‐bridge attachment rate must increase during interfilamentary movement. A mechanism (based on misregistration between the actin binding sites and the myosin cross‐bridges) by which this might arise is presented.

Human balancing of an inverted pendulum with a compliant linkage: neural control by anticipatory intermittent bias

These experiments were prompted by the recent discovery that the intrinsic stiffness of the ankle is inadequate to stabilise passively the body in standing. Our hope was that showing how a large inverted pendulum was manually balanced with low intrinsic stiffness would elucidate the active control of human standing. The results show that the pendulum can be satisfactorily stabilised when intrinsic stiffness is low. Analysis of sway size shows that intrinsic stiffness actually plays little part in stabilisation. The sway duration is also substantially independent of intrinsic stiffness. This suggests that the characteristic sway of the pendulum, rather than being dictated by stiffness and inertia, may result from the control pattern of hand movements. The key points revealed by these experiments are that with low intrinsic stiffness the hand provides pendulum stability by intermittently altering the bias of the spring and, on average, the hand moves in opposition to the load. The results lead to a new and testable hypothesis; namely that in standing, the calf muscle shortens as the body sways forward and lengthens as it sways backwards. These findings are difficult to reconcile with stretch reflex control of the pendulum and are of particular relevance to standing. They may also be relevant to postural maintenance in general whenever the CNS controls muscles which operate through compliant linkages. The results also suggest that in standing, rather than providing passive stability, the intrinsic stiffness acts as an energy efficient buffer which provides decoupling between muscle and body.

The passive, human calf muscles in relation to standing: the non‐linear decrease from short range to long range stiffness

During human standing, tonic ankle extensor torque is required to support the centre of mass (CoM) forward of the ankles, and dynamic torque modulation is required to maintain unstable balance. Passive mechanisms contribute to both but the extent is controversial. Some groups have revealed a substantial intrinsic stiffness (65–90%) normalized to load stiffness, ‘mgh’. Others regard their methodology as unsuitable for the low‐frequency conditions of quiet standing and believe the passive contribution to be small (10–15%). Here we applied low‐frequency ankle rotations to upright subjects who were supported at the waist allowing the leg muscles to be passive and we report normalized stiffness. The passive calf muscles provided: (i) an extensor torque capable of sustaining unstable balance without tonic activity at a mean CoM–ankle angle of 1.6 deg, (ii) a long range stiffness of 13 ± 2% and (iii) a short range (< 0.2 deg) stiffness of 67 ± 8%. Chordal ankle stiffness, derived from the torque versus angle relationship for 7 deg rotations, shows a non‐linear decrease (stiffness α rotation−0.33±0.04) from 101 ± 9% to 19 ± 5% for rotations of 0.03–7 deg, respectively. Thus, passive stiffness is well adapted for the continuum of postural and movement activity and has a substantial postural role eliminating the need for continuous muscle activity and increasing the unstable time constant of the human inverted pendulum. Ignoring the non‐linear dependence of passive stiffness on sway size could lead to serious misinterpretation of experiments using perturbations and sensory manipulations such as eye closure, sway referencing and altered support surfaces.