Comparison of three-dimensional body centre of mass trajectories during locomotion through zero- and one-dimensional statistics.

The trajectory of the body centre of mass (BCoM) during locomotion differs through speeds, gaits and pathological states; statistical methods are needed to compare it among different conditions. Here, ten participants walked on treadmill at 1.1 and 1.4 m/s; BCoM trajectories were obtained through stereophotogrammetry and expressed as Fourier series. Trajectories were compared among speeds using (i) zero-dimensional (0D) linear and circular tests for difference on amplitudes and phases of Fourier series harmonic, (ii) one-dimensional statistical parametric mapping (1D-SPM) t-tests on the anteroposterior, mediolateral and vertical axial components of the BCoM trajectory and (iii) 1D-SPM Hotelling's T test on the three-dimensional BCoM trajectory. Increasing speed increased the amplitude and decreased the phase of the fundamental (2nd) vertical harmonic. Coherently, the BCoM vertical trajectory featured greater displacement and a forward-shift, combined with greater displacement along the anteroposterior axis. Hotelling's T 1D-SPM on the whole trajectory featured supra-threshold clusters at the transition between double and single support, and mid of the single support. 0D and 1D test yielded coherent and complementary results: 1D-SPM Hotelling's T is suitable to compare whole three-dimensional BCoM trajectories; however, when researchers hypothesize that conditions may impact specific harmonics or axial components, 0D or 1D-SPM t-tests are recommended.