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Edited by: Valerie Moyra Pomeroy, University of East Anglia, United Kingdom

Reviewed by: Denise Taylor, Auckland University of Technology, New Zealand; Andrew Kerr, University of Strathclyde, United Kingdom

This article was submitted to Stroke, a section of the journal Frontiers in Neurology

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Smoothness is a main characteristic of goal-directed human movements. The suitability of approaches quantifying movement smoothness is dependent on the analyzed signal's structure. Recently, activities of daily living (ADL) received strong interest in research on aging and neurorehabilitation. Such tasks have complex signal structures and kinematic parameters need to be adapted. In the present study we examined four different approaches to quantify movement smoothness in ADL. We tested the appropriateness of these approaches, namely the number of velocity peaks per meter (NoP), the spectral arc length (SAL), the speed metric (SM) and the log dimensionless jerk (LDJ), by comparing movement signals from eight healthy elderly (67.1a ± 7.1a) with eight healthy young (26.9a ± 2.1a) participants performing an activity of daily living (making a cup of tea). All approaches were able to identify group differences in smoothness (Cohen's d NoP = 2.53, SAL = 1.95, SM = 1.69, LDJ = 4.19), three revealed high to very high sensitivity (z-scores: NoP = 1.96 ± 0.55, SAL = 1.60 ± 0.64, SM = 3.41 ± 3.03, LDJ = 5.28 ± 1.52), three showed low within-group variance (NoP = 0.72, SAL = 0.60, SM = 0.11, LDJ = 0.71), two showed strong correlations between the first and the second half of the task execution (intra-trial R^{2}s: NoP = 0.22 n.s., SAL = 0.33, SM = 0.36, LDJ = 0.91), and one was independent of other kinematic parameters (SM), while three showed strong models of multiple linear regression (R^{2}s: NoP = 0.61, SAL = 0.48, LDJ = 0.70). Based on our results we make suggestion toward use examined smoothness measures. In total the log dimensionless jerk proved to be the most appropriate in ADL, as long as trial durations are controlled.

Despite the great importance of analyzing ecologically valid activities in clinical research and diagnostics, the quantification of activities of daily living (ADL) was typically limited to subjective scorings of videos (

For different types of movement tasks, trajectories and corresponding velocity profiles differ in the signals' structures (

In this study we assessed the validity of different smoothness parameters by comparing the hand movements of young and elderly participants in an ADL. We investigated to what degree the used parameters were sensitive, variable, and independent of general movement characteristics like velocities, trial durations, path lengths, or the activity level. Further, we examined if the parameters are quantifying a general ability to produce smooth movements. ADL offer a way to examine behavior in the context of disease and aging in an ecological valid way and should therefore be considered in research and clinical assessment (

We compared the movements of the dominant hand of 8 healthy young adults (26.9a ± 2.1a) with the movements of the dominant hand of 8 healthy elderly participants (67.1a ± 7.1a). The ADL task was to unimanually prepare a cup of tea with milk and sugar (

The experimental set-up was similar to the one in Gulde et al. (

The positional data of the dorsum of the hand was obtained by a Qualisys motion capturing system (Qualisys Inc. Gothenburg, Sweden) incorporating 5 Oqus cameras sampling with a frequency of 120 Hz. There were no gaps in the recordings. All post-processing was computed with MatLab (MATLAB R2017a, MathWorks, MA). After differentiation the data were smoothed using a 0.1s local regression filter (“loess”) (

The used smoothness parameters were the spectral arc length (

Calculation of the spectral arc length based on a velocity profile v, with [0, ω

For the number of velocity peaks per meter all peaks of the velocity profile, which exceed a prominence of 0.05 m/s, are counted and divided by the traveled path length. The resulting number is inverted, so that higher values indicate smoother movements (

Calculation of the number of velocity peaks per meter based on a velocity profile v and peaks being maxima with a prominence exceeding 0.05 m/s (

The speed metric is obtained by dividing the average velocity by the maximum velocity (

Calculation of the speed metric based on a velocity profile v (

The log dimensionless jerk results from the logarithm naturalis of the sum of the squared acceleration multiplied with the trial duration to the power of three and divided by the squared peak velocity (

Calculation of the log dimensionless jerk based on a velocity profile _{1} to _{2} (

Note that all parameters but the speed metric output negative values, and for every parameter values closer to zero represent smoother movements. These four parameters were considered as prototypical agents for the different classes of smoothness measures listed in the introduction. The speed metric was added, since its computation strongly differs from the peaks metric and therefore its behavior could not have been derived.

The smoothness parameters were compared between groups using ^{*}Power (G^{*}Power 3.192, 2014, HHU Düsseldorf, Germany).

The comparison of the groups revealed significant differences for all four parameters (Table ^{2}s ranging from 0.22 to 0.91. Note, that only the speed metric and the log dimensionless jerk reached significance and delivered power estimates of at least 0.80. The models of multiple linear regression showed significant models for number of velocity peaks per meter, spectral arc length, and log dimensionless jerk. The models for speed metric were all non-significant (Table

The means, standard deviations, effect-sizes,

Number of peaks per meter | −5.43 ± 0.67 | −7.82 ± 1.22 | < 0.01 | 2.53 | 1.00 |

Spectral arc length | −12.55 ± 2.16 | −17.97 ± 3.39 | < 0.01 | 1.95 | 0.95 |

Speed metric | 0.12 ± 0.04 | 0.08 ± 0.01 | 0.02 | 1.69 | 0.88 |

Log dimensionless jerk | −12.03 ± 0.70 | −14.47 ± 0.46 | 0.01 | 4.19 | 1.00 |

The means and standard deviations for the sensitivity measure and the within-group variability index for the four smoothness parameters.

Number of peaks per meter | 1.96 ± 0.55 | 0.72 |

Spectral arc length | 1.60 ± 0.64 | 0.60 |

Speed metric | 3.41 ± 3.03 | 0.11 |

Log dimensionless jerk | 5.28 ± 1.52 | 0.71 |

The ^{2}-values of the intra-trial correlation, its

Number of peaks per meter | ^{2} = 0.22 |
0.07 | |

Spectral arc length | ^{2} = 0.33 |
0.02 | 0.75 |

Speed metric | ^{2} = 0.36 |
0.01 | 0.80 |

Log dimensionless jerk | ^{2} = 0.91 |
< 0.01 | 1.00 |

The corrected ^{2}-values of models of multiple linear regression, their p-values, power estimates, and the models' factors for three of the four smoothness parameters.

^{2} |
||||
---|---|---|---|---|

Number of peaks per meter | ^{2} = 0.61 |
< 0.01 | 0.98 | Path length (ß = −0.36, |

Spectral arc length | ^{2} = 0.48 |
< 0.01 | 0.87 | Trial duration (ß = −0.86, |

Log dimensionless jerk | ^{2} = 0.70 |
< 0.01 | 1.00 | Trial duration (ß = −0.85, |

Correlations between the four different smoothness parameters.

Log dimensionless jerk | |||

Speed metric | |||

Spectral arc length |

In the present study, we analyzed movement smoothness that is known as a highly characteristic aspect of task performance. Since measures of smoothness were typically established for simple continuous or discrete movements, we here analyzed the suitability of various measures for the evaluation of the complex activity of daily living of tea making.

The comparison of the four smoothness parameters revealed that all of the methods were able to detect the differences in smoothness between young and elderly participants in the ADL of tea making. With mean z-scores between 1.60 and 5.28 all four parameters proved to be highly sensitive. Three of the parameters showed a within-group variance index above or equal 0.6, meaning that within group variability was low in the number of velocity peaks per meter, the spectral arc length, and the log dimensionless jerk, while it was very high in the speed metric. The intra-trial comparisons (first half vs. second half) further revealed that three of the parameters were significantly correlated between the two halves with the strength of the correlations being strong. Note, that in one case the statistical power was lower than 0.80 (spectral arc length). High correlations between the two halves support a generalization beyond this specific ADL. By splitting, two different tasks were artificially created and in case of high intra-trial correlations, the metric shows the capability to estimate the participant's general and not task restricted movement smoothness. Lastly, the models of multiple linear regression revealed an impact of kinematic parameters on three of the parameters. All of the models were strong (

Table

Color-coded overview of the interpreted outcomes of the parameter analysis.

Number of velocity peaks per meter | Yes | High | Low | No | Strong (–) path length (+) mean peak velocity |

Spectral arc length | Yes | High | Low | Strong (power < 0.8) | Strong (–) trial duration (+) mean peak velocity |

Speed metric | Yes | Very high | Very high | Strong | None |

Log dimensionless jerk | Yes | Very high | Low | Strong | Strong (–) trial duration |

Of the four parameters, none proved to be fully suited for a general quantification of smoothness in the tested ADL, although log dimensionless jerk did reveal good characteristics except its very strong association with trial duration. The number of velocity peaks per meter was able to detect the group differences, showed high sensitivity, low within-group variance, but the correlation between the first and the second half of the trial was non-significant (although a trend was observed,

The analysis of the four smoothness parameters revealed that there is still the necessity for a novel, well-suited parameter for the analysis of movement smoothness in ADL. Still, three of the four parameters proved to deliver good estimates, when controlling for certain aspects of an experiment. Since the sample size was relatively small, our findings have to be interpreted with care, although the statistical power was mostly high. In addition, we tested only one ADL task and the question is how much our findings can be extended to ADL in general. However, certain patterns and combinations of actions, for instance phases of inactivity, grasping, or transporting, repeatedly appear in ADL. This is particularly true in an ADL that demands manual interactions with serval objects like the one analyzed here. We therefore believe that our findings can be generalized to a broad class of ADL and draw the following recommendations for the use of smoothness parameters in ADL: The number of velocity peaks per meter needs comparisons with equal lengths of the trajectories and comparable quantities of performed actions in a task. The spectral arc length needs tasks with comparable trial durations and movement speeds. The log dimensionless jerk, having a very strong intra-trial correlation, very high sensitivity, low within-group variability, but a very strong dependence on trial duration, should deliver good estimates on a wide range of ADL tasks, as long as the trial durations are controlled for. Given these prerequisites, these three parameters (number of velocity peaks per meter, spectral arc length & log dimensionless jerk) can deliver appropriate estimates of movement smoothness in complex motor tasks like ADL. Future research should examine the different sub-types of those measures and different ADL tasks to see if the behavior of the parameter class and the ADL (tea making) are generalizable.

The search for a universal smoothness parameter for ADL should have a high priority in neurorehabilitational research in order to assess motor capacity and supervise the rehabilitation process of patients suffering from neurological diseases like stroke, Parkinson's disease, or cerebral palsy. So far, comparisons of movement smoothness with control groups or in patient groups with high (kinematic) variabiliy and during the supervision of the rehabilitation process with changes in trial durations, mean peak velocities, or path lengths, are limited. A promising approach could be using wavelet transformation in order to estimate the complexity of the signal (analog to the spectral arc length metric).

There are clear limitations in this study. Although examining an ADL, ecological validity was limited by the unimanual execution of the task. However, previous research has shown that the transfer from bimanual to unimanual performance has no interaction with age (

PG and JH designed the study. PG performed the lab testing and the kinematic and statistical analyses. All authors contributed to the coordination of the study and the final draft of the manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.