Harmonic ratios: a quantification of step to step symmetry.

The harmonic ratio (HR), derived from the Fourier analysis of trunk accelerations, has been described in various ways as a measure of walking smoothness, walking rhythmicity, or dynamic stability. There is an increasing interest in applying the HR technique to investigate the impact of various pathologies on locomotion; however, explanation of the method has been limited. The aim here is to present a clear description of the mathematical basis of HRs and an understanding of their interpretation. We present harmonic theory, the interpretation of the HR using sinusoidal signals, and an example using actual trunk accelerations and harmonic analyses during limb-loading conditions. We suggest that the HR method may be better defined, not as a measure of rhythmicity or stability, but as a measure of step-to-step symmetry within a stride.

Age- and speed-related differences in harmonic ratios during walking.

Harmonic ratios (HRs), derived from trunk accelerations, measure smoothness of trunk motion during gait; higher ratios indicate greater smoothness. Previous research indicates that young adults optimize HRs at preferred pace, exhibiting reduced HRs at speeds faster and slower than preferred. Recent studies examining HRs and other trunk acceleration measures challenge this finding. The purpose of this study was to examine age-related differences in HRs across a range of self-selected overground walking speeds. Anteroposterior (AP), vertical (VT), and mediolateral (ML) HRs were examined in 13 young adults (ages 20-23), 13 healthy older adults (ages 60-69), and 13 healthy old-old adults (ages 80-86) while walking overground at very slow, slow, preferred, fast, and very fast speeds. Young and older adults exhibited similar HRs in all directions of motion across speeds, while old-old adults exhibited lower AP- and VT-HRs. All groups exhibited reduced HRs at speeds slower than preferred. However, there were no differences in HRs between preferred and faster speeds, with the exception of reduced VT-HRs in the very fast condition for the older groups. The ML-HR was not different between groups, and varied less across speeds. Stride time variability exhibited inverse relations with, and independently contributed to, HRs across speeds; lower stride time variability was associated with greater smoothness of trunk motion. Older groups were not disproportionately affected by walking more slowly and smoothness of trunk motion did not show a clear pattern of optimization at preferred pace for any group.

Planning and control of sequential rapid aiming in adults with Parkinson's disease.

Eight people with Parkinson's disease (PD), 8 age-matched older adults, and 8 young adults executed 3-dimensional rapid aiming movements to 1, 3, 5, and 7 targets. Reaction time, flight time, and time after peak velocity to the 1st target indicated that both neurologically healthy groups implemented a plan on the basis of anticipation of upcoming targets, whereas the PD group did not. One suggested reason for the PD group's deficiency in anticipatory control is the greater variability in their initial force impulse. Although the PD group scaled peak velocity and time to peak velocity similarly to the other groups, their coefficients of variation were greater, making consistent prediction of the movement outcome difficult and thus making it less advantageous to plan too far in advance. A 2nd finding was that the PD group exhibited increased slowing in time after peak velocity in the final segments of the longest sequence, whereas the other 2 groups did not. The increased slowing could be the result of a different movement strategy, increased difficulty modulating the agonist and antagonist muscle groups later in the sequence, or both. The authors conclude that people with PD use more segmented planning and control strategies than do neurologically healthy older and young adults when executing movement sequences and that the locus of increased bradykinesia in longer sequences is in the deceleration phase of movement.

Modifications to recursion unfolding algorithms to find more appropriate neutron spectra.

Modifications were made to recursion unfolding algorithms which allow the incorporation of prior knowledge, such as cutoff energy or preferred spectral shape, into the solution. Using these modifications, more appropriate neutron spectra are obtained.