Modeling of postural stability borders during heel–toe rocking

To maintain balance during movements such as bending and reaching, the CNS must generate muscle forces to counteract destabilizing torques produced by gravitational (position-dependent) and inertial (acceleration-dependent) forces. This may create a trade-off between the attainable frequency and amplitude of movements. We used experiments and mathematical modeling to examine this relationship during the task of heel–toe rocking. During the experiments, participants (n = 15) rocked about the ankles in the sagittal plane with maximum attainable amplitude at a frequency of 0.33 Hz or 0.66 Hz. As the frequency doubled, the maximum anterior position of the whole-body centre-of-gravity (COG) with respect to the ankle decreased by 11% of foot length (from 11.9 cm (S.D. 1.6) to 9.2 cm (S.D. 1.2); p < 0.001), the minimum anterior position of the COG increased by 8% of foot length (from 1.6 cm to 3.5 cm in front on the ankle; p < 0.0005), and the ankle stiffness increased from 787 Nm/rad (S.D. 156) to 1625 Nm/rad (S.D. 339). However, there was no difference between conditions in the maximum anterior position of the COP (p = 0.51), the minimum anterior position of the COP (p = 0.23), or the peak ankle torque (p = 0.39). An inverted pendulum model driven by a rotational spring predicted the measured ankle stiffness to within 0.9% (S.D. 6.8), and the maximum anterior COG position to within 1.2% (S.D. 4.0). These results indicate that COG amplitude decreases with increasing rocking frequency, due to (a) invariability in peak ankle torque and (b) the need to allocate torque between gravitational and inertial components, the latter of which scales with the square of frequency.