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

Abstract

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.

Figure 1. Ankle stiffness measuring apparatus

A, ankle stiffness measurement. The left footplate is constructed of aluminium alloy, lightened by holes and cross-braced for rigidity. A piezo-electric transducer (PZT) produces a translation which rotates the footplate relative to the platform. Lengthening of the element raises the toe end of the footplate. The footplate rotation is registered by the contactless displacement transducer. The resulting force change is recorded by the torque cell. The contact face of the PZT is spherical to minimise off-axis forces. B, ankle rotation. A miniature laser range-finder operating by triangulation and insensitive to rotation measures the linear distance to a target attached to a mount attached to the subject's heel with dental wax. The laser can be attached to the footplate as shown or alternatively mounted on a snugly fitting calf mould securely taped to the leg. C, general view. The subject stands on two footplates. Both footplates are coupled to the platform by horizontally mounted load cells which record ankle torque. The platform is rigidly coupled to a heavy inverted pendulum. A piezo-electric, vibrating gyroscope mounted under the platform measures angular velocity. In free standing the platform and pendulum are immobilised and the apparatus remains stationary while the subject sways. In the torque generation and pendulum balancing tasks the subject is strapped at pelvis height to a solid back support (not shown) that prevents body movement. During pendulum balancing the pendulum and platform sway while the subject is static. The backward lean of the pendulum mimics the normal forward inclination of the body and is measured by a contactless, precision potentiometer. The ankles, platform and footplates have a common axis. Alignment and support are provided by six precision ball races and a substantial steel framework (omitted here for clarity).

Figure 7. Stiffness and compliance of the foot and ankle

A, rotation of the footplate relative to the calf (F) is taken up by angular deformation of the ball of the foot relative to the heel (f) and rotation of the heel relative to the calf (a) such that F =f+a. It is assumed that the calf does not move during the applied rotation of the footplate. The stiffness of the foot (K_f) can be thought of as being in series with the stiffness of the ankle (K_a). In both series elements, the torque (T) is the same. The foot stiffness is calculated from the torque increment per unit foot deformation, K_f =ΔT/Δf. Likewise the ankle stiffness is the torque increment per unit ankle rotation, K_a =ΔT/Δa. The combined stiffness (K) is the torque increment per unit footplate rotation, K =ΔT/ΔF. Compliance is the inverse of stiffness. The combined compliance (1/K) is the sum of the foot compliance (1/K_f) and ankle compliance (1/K_a) so 1/K = 1/K_f+ 1/K_a. Accordingly, K of the two series springs is less than the weakest spring in the chain. Usually researchers do not partition footplate rotation into foot and ankle components. K is usually regarded as ankle stiffness. So that we may compare our results with previous work we will refer to the combined stiffness (K) as the ankle stiffness and we refer to the stiffness related purely to ankle rotation (K_a) as the true ankle stiffness. B, we think K_f most likely resides in the soft tissues of the foot as well as the arch. The true ankle stiffness (K_a) includes all components acting in parallel at the ankle joint.

Figure 2. Averaging and calculation of mechanical response

For one representative standing subject, A shows the averaged footplate rotation (continuous), rotation of heel (calcanean tuberosity) about the ankle measured using the laser (dashed), and movement of the body CoM (dotted). The zero degree position is arbitrary. The footplate rotation starts at 0.4 s. B, the averaged velocity of the footplate (continuous trace) and the heel about the ankle (dashed trace). C, the unaveraged time record of left ankle torque. The asterisks mark the beginning of footplate rotations. D, the averaged record of left torque (continuous trace), left torque after subtraction of footplate component (dashed trace), the interpolated background torque during the perturbation (dot-dashed trace) and the right torque (dotted trace). E, the averaged mechanical response to the footplate rotation (continuous trace) and the torque computed from the elastic, viscous, inertial model (dotted trace).

Figure 3. Neurally modulated responses to perturbation

A, left torque (continuous trace) and right torque (dotted trace) record averaged from nine subjects while they maintained a variety of constant torque levels. B, the corresponding averaged integrated EMG records from soleus (Sol), gastrocnemius medialis (GM), gastrocnemius lateralis (GL) and tibialis anterior (TA) for the left leg. For the same nine subjects, C shows the averaged torque records while standing freely and D shows the corresponding averaged EMG records. The perturbations start at 0.4 s.

Figure 4. Stiffness during standing and balancing the pendulum

The intrinsic, mechanical left ankle stiffness, averaged from 15 subjects while they stood freely (1) and balanced the pendulum (2) is shown in A. B, combined stiffness of both legs relative to the toppling torque per unit angle of (1) the body CoM while standing (2) the pendulum CoM while balancing the inverted pendulum. A sway is defined as a unidirectional movement from one reversal point to the next. The median sway size and median sway speed, averaged from 13 subjects are shown in C and D, respectively, for standing (1) and balancing (2). The uncertainty bars represent standard errors in the mean values.

Figure 5. Variation of stiffness with ankle torque

For 15 subjects, the variation of intrinsic mechanical left ankle stiffness with ankle torque is shown in A. B and D show the variation with ankle torque of viscosity (ankle and apparatus) and inertia (foot), respectively. The error bars show the uncertainty associated with estimating the background torque during the perturbation. The continuous lines represent the mean quadratic line of best fit. C shows the variation of soleus EMG with ankle torque for 11 of the 15 subjects. For these experiments subjects were strapped at their normal standing ankle angle to a fixed vertical support. Subjects maintained constant ankle torque using visual feedback from an oscilloscope and repeated this at different levels of torque.

Figure 6. Partitioning stiffness into ankle and foot components

For one representative subject balancing the inverted pendulum, A shows the unaveraged record of footplate angle (continuous trace) and heel rotation about the ankle measured using the laser (dotted trace). The left axis scale shows angular changes of the footplate and heel in degrees about an arbitrary zero and the right axis scale shows linear movements of the heel relative to the calf in millimetres. B, for six subjects the mean, intrinsic, overall ankle stiffness while standing (1), and balancing the pendulum (2) is shown. The true ankle stiffness measured using the laser is shown for standing (3) and balancing the pendulum (4). For nine subjects the overall ankle stiffness while standing (6) and balancing the pendulum (7) is shown. The foot stiffness measured using the laser is shown for standing (8) and balancing the pendulum (9). For five subjects, C shows the variation of true ankle stiffness with ankle torque. D shows the variation of foot stiffness with ankle torque for nine subjects. For C and D the error bars show the uncertainty associated with estimating the background torque during the perturbation. The continuous lines represent the mean quadratic line of best fit.