The curvature peaks of the trajectory of the body centre of mass during walking: A new index of dynamic balance

During walking, falling is most likely to occur towards the side of the supporting lower limb during the single stance. Timely lateral redirection of the centre of mass (CoM) preceding the no-return position is necessary for balance. We analysed the curvature peaks (the inverse of the radius of curvature) of the three-dimensional path of the CoM during the entire stride. Twelve healthy adults walked on a force-sensorized treadmill at constant velocities from 0.4 to 1.2 m s−1, in 0.2 m s−1 increments. The three-dimensional displacements of the CoM, the muscular power sustaining the CoM motion with respect to the ground, and the efficiency of the pendulum-like transfer of the CoM were computed via the double integration of the ground reaction forces. The curvatures of the CoM trajectory were measured (Frenet–Serret formula). During the single stance, the curvature showed a bell-shaped increment, lasting a few tenths of a millisecond, and peaking at 365–683 m−1 (radius of 2.7–1.4 mm, respectively), the higher the walking velocity. The CoM was redirected towards the swinging lower limb. The curvature increment was sustained by muscle-driven braking of the CoM. Smoother increments of curvature (peaking at approximately 37–150 m−1), further orienting the CoM towards the leading lower limb, were observed during the double stance. The peaks of the curvatures were symmetric between the two sides. The high curvature peaks during the single stance may represent an index of dynamic balance during walking. This index might be useful for both rehabilitation and sports training purposes.