This study reports for the first time, at our knowledge, the comparison of the main smoothness measures from both temporal and frequency domains on different sets (with or without pause) and types of actual point-to-point movements (forward and backward) in healthy subjects. The 4 smoothness parameters, N0C, NARJ, LDLC and SPARC, were sensitive to movement type, but the SPARC behaved differently than the temporal domain smoothness metrics (TDSM), finding backward movements to be less smooth than forward movements instead of the opposite. Only the TDSM were sensitive to movement set. TDSM strongly correlated with movement duration, whereas the SPARC did not. Within-subject repeatability was highest and between-subject variability was lowest for the SPARC. No difference in movement velocity nor smoothness was found across sides but movements were slightly straighter with the dominant arm. A normative dataset was built for each metric and is now available.
Different behavior between temporal domain smoothness measures and the SPARC- to be or not to be time-connected?
The most striking finding in this study is that temporal domain smoothness measures found backward movements to be smoother than forward movements. In particular there was only about one zero crossing on the acceleration profile in backward movements without pause while the SPARC found backward movements to be less smooth. Except for the fact that backward movements were faster than forward movements (movement time-dependence of metrics measured in the temporal domain), this opposite behavior between the two types of metrics is challenging to interpret.
Interestingly, TDSM were strongly correlated amongst them, while the SPARC was not correlated with any other metrics (low convergent validity) nor to movement duration (strong divergent validity). Besides, TDSM were strongly correlated with movement time. Thus, the changes in smoothness perceived by TDSM across sets (with vs without pause) might reflect the sensitivity of those metrics to movement duration. From mathematical models, Balasubramanian suggested shortcomings for temporal domain smoothness measures, including precisely their sensitivity to movement duration (and to noise in measurements) with a risk of lack of reliability and validity.12 Intellectually though, it may be tempting to speculate that a movement that loses smoothness should also lose speed in the process. It may therefore seem natural that a smoothness metric be somewhat correlated with movement time, at least in pathological or complex movements. Yet, it is also obvious that if no correction means is brought, for instance in adjusting the sampling frequency of the movement recording to movement time, noise is bound to emerge in those metrics that depend on movement time.5 On the other hand, a metric that involves the frequency domain only may allow bypassing the down-sampling issue and therefore seem more satisfactory. A number of such frequency-domain metrics have been proposed in the literature, for example the determination of the fast frequency to the movement frequency ratio in the acceleration power spectrum (FF/MF ratio), which has provided interesting results when comparing parkinsonian with simulated bradykinesia.5
It may be that the temporal domain and the frequency domain smoothness metrics may be irreconcilable. The question as to whether the appropriate smoothness metric should or should not be connected to movement time may come down to the way we wish to define smoothness. Perhaps there should be at least two different types of smoothness, depending on whether we connect smoothness to the braking effects of smoothness reduction or not. Future studies comparing those metrics in pathological movements could provide useful insight on their respective behavior and interest.
Coherence of the present smoothness data with previous literature
For forward movements, the present SPARC values (-1.43 to -1.45 ± 0.03) were consistent with recent findings: -1.45 to -1.48 for Engdahl et al. (2016)18 and − 1.44 ± 0.04 for Saes et al. (2021)19 in reach to grasp movements. Although themovement type was different in those studies (reach-to-grasp vs reach-to-point), the reaching phase was predominant in both types of movement, allowing the comparison. As for LDLJ values, the present data are also consistent with those reported by Engdahl et al. (2019)17 The N0C values in our findings (3 to 6 ± 3) seem relatively high, as only one zero crossing per movement is expected in healthy and even in some pathologic movements.18,19 As for the present NARJ values, they were also consistent with previous literature5 and varied more than twofold (20193 to 46378 ± 17085) depending on the movement type, possibly reflecting both noise and movement duration sensitivity of jerk-related metrics (artefacts in trajectories when movements stopped or during the plateau phase).
Similar observations can be made for backward movements, even though we could not find data in the literature for comparisons. SPARC values were also remarkably consistent across sets (-1.48 ± 0.06), LDLJ shows some differences (-6.64 ± 0.52 to -5.58 ± 0.53), whereas NARJ and N0C values again ranged from single to double depending on the movement type.
Inter- and intra-subject reliability and sensitivity to change of smoothness metrics
Can smoothness characterize one individual’s movement, or can it change between two different movements made by one person? Among the smoothness metrics tested here, SPARC showed the least intra- and between-subject variability for all tested movements (e.g. FPMCoVinter 1.6 to 2.2%) followed by the LDLJ (with higher CoVinter6.8 to 8.7%). On the other hand, the NARJ and N0C were characterized by high levels of inter-subject differences, i.e., High CoVinter. Similarly, the SPARC was characterized by higher intra-subject repeatability (FPM CoVintra1.6 to 1.9%) than TDSM (FPM CoVintra 5.0-6.4% for the LDLJ, 18–30% for the NARJ and 27–40% for the N0C).
In our protocol, each movement was repeated four times, the first attempt being considered as training and thus not retained for computation. We assumed this number of repetitions to be sufficient in healthy subjects for the SPARC computation. Indeed, no differences were observed in the literature when using 7 or 10 repetitions.20,21 For TDSM, due to their greater variability/sensitivity to changes in movements and/or in movement durations, a higher number of repetitions might have to be used to obtain a reliable mean smoothness value, such as 7–8 movements.5 This lower number of repetitions needed for the SPARC computation can be interesting in very impaired subjects for whom only fewer movement repetitions may be possible.21
Smoothness and laterality - is there an ‘optimal’ smoothness?
If movements on the dominant side were slightly straighter, as previously described,22 we did not find smoothness differences between sides. Reaching movements are relatively simple, largely used, thus trained, in most daily activities. In more complex tasks like transferring an object with chopsticks, movements have been shown to be longer and less smooth on the non-dominant side, but trainable to become as smooth as on the dominant side.23 Finally, in healthy subjects, simple movements are expected to be optimally smooth; thus, a ceiling effect should be expected from smoothness measures, as shown in Fig. 3 for the SPARC, the NARJ and the N0C. By applying a logarithmic transformation to normalize the Dimensionless Jerk, the LDLJ displays an artificially normal distribution, which might make interpretations of changes in smoothness more difficult than it is with the other metrics.
Subjects were asked to complete each task at their preferred speed, and yet found differences in movement durations across movement types and sets, suggesting an explanation for changes in smoothness reported by TDSM. It would have been useful to add sets of movements of various imposed speeds, including ballistic movements at maximal speed, to better explore sensitivity of the four metrics to movement duration.5
Reach-to-point movements were tested to aim for normative smoothness data that could be of interest in clinical routine. Pointing movements requiring multi-joint coordination are often used in clinical practice, especially in neurorehabilitation to assess patient progression, as these are simple to assess, reproducible,24 and frequently used in daily living activities.25 Moreover, reach-to-point movements are more easily performed than reach-to-grasp movements, especially in numerous neurological disorders that can prevent patients from grasping (stroke, advanced parkinsonism, severe peripheral neuropathies, myopathies…) and have been recommended in more impaired patients.4 However, smoothness of other movements of interest still needs to be quantified, especially of single-joint movements with the hope of better differentiation between recovery and compensation.20
To date, there is no clear consensus on how to determine with precision the onset and the end of a reaching movement. As explained in the Methods section, a single assessor visually inspected each recorded trajectory twice and standardized the beginnings of FPM as the first ascending point of the projection of the trajectory in the vertical direction, and the end of FPM (which also was the beginning of the BPM) as the most forward point of the trajectory in the antero-posterior direction; the end of the BPM being the last point of the descending trajectory in the vertical direction. This method is time-consuming and might have resulted in errors, in contrast with other methods that rely on the detection of changes in maximum tangential speed during the various phases of the movement.20,25,26 However, those definitions for the starting and ending points of trajectories allow considering more trajectory points at critical stages of movements (such as when nearing the target, where accuracy is needed), with thus perhaps more accurate estimations of smoothness across the whole movement.