Limits in reliability of leg-spring and joint stiffness measures during single-leg hopping within a sled-based system

Research examining the reliability of stiffness measures during hopping has shown strong consistency in leg-spring stiffness (kleg), but high variability in joint stiffness (kjoint) measures. Sled-based systems (SBS) reduce movement degrees-of-freedom and are used to examine stretch-shortening cycle (SSC) function under controlled conditions. The aim of this study was to examine the reliability of kleg and kjoint during single-leg hopping within an SBSKinematic and kinetic data were collected on four occasions (Day_1, Day_2, Day_3 and Day_3Offset). Participants completed two trials of single-leg hopping at different frequencies (1.5, 2.2 and 3.0 Hz) while attached to an inclined-SBS. Stiffness was determined using models of leg-spring (kleg) and torsional (kjoint) stiffness. Statistical analysis identified absolute and relative measures of reliability. Results showed moderate reliability for kleg at 1.5 Hz between inter-day testing bouts, and weak consistency at 2.2 and 3.0 Hz. Examination of intra-day comparisons showed weak agreement for repeated measures of kleg at 1.5 and 2.2 Hz, but moderate agreement at 3.0 Hz. Limits in kleg reliability were accompanied by weak-to-moderate agreement in kjoint measures across inter- and intra-day testing bouts. Results showed limits in the reliability of stiffness measures relative to previous reports on overground hopping. Lack of consistency in kleg and kjoint may be due to the novelty of hopping within the current inclined-SBS. Constraints imposed on the hopping task resulting from SBS design (e.g. additional chair mass, restricting upper body movement) may have also influenced limits in kleg and kjoint reliability. Researchers should consider these findings when employing inclined-SBS of a similar design to examine SSC function.


Introduction
Stretch-shortening cycle (SSC) tasks are characterised by eccentric lengthening immediately followed by concentric shortening [1]. These actions are typical of human movement (e.g. walking, running, jumping and throwing) and serve to enhance concentric force output and a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 Flanagan and Harrison [19] reported strong reliability (Cronbach's α > 0.95) for repeated measures of k leg during jumping tasks (Cronbach's α > 0.95) within an SBS.
Given the purpose of the SBS is to reduce extraneous upper body movement to encourage landing and measurement consistency, it is possible that stiffness measures (esp. k joint ) achieved during hopping within an SBS might demonstrate strong reliability. To date, the consistency of k leg and k joint measures recorded during hopping within an SBS has not been examined. The aim of this study was to examine the reliability of stiffness measures during hopping within an inclined-SBS. It was hypothesized that restricting extraneous upper body movement would facilitate strong consistency for k leg and k joint variables during hopping tasks.

Participant characteristics
Thirty-two students (16 males and 16 females; mean ± SD age 21.3 ± 2.9 years; stature 1.70 ± 0.08 m; mass 69.9 ± 10.0 kg) volunteered to participate. Volunteers were recruited via e-mail circulated to the campus community. All participants were physically active as members of a university sports club, attending bi-weekly practices and represented the university at varsity level. Participants were injury free for at least six months prior to testing as determined via health screening questionnaire. Procedures were approved by the research ethics committee of the Faculty of Education and Health Science at the University of Limerick, and all participants provided written informed consent. To limit the effects of fatigue on stiffness measurement, participants were instructed to abstain from vigorous physical activity 24 hours before testing bouts.

Experimental procedures
Participants completed a familiarization session one week prior to initial testing to acquaint them with procedures (Day_0) [31]. Following this, participants underwent testing on four occasions. The first (Day_1), second (Day_2) and third (Day_3) testing bouts took place at the same time of day, spaced three to seven days apart [23,32]. On the final test day, participants completed procedures twice; at their typically scheduled time (Day_3) and six hours prior to or following their scheduled time (Day_3 Offset ) [22].
For each test, participants wore dark, tight-fitting clothing. Retro-reflective markers (14 mm) were placed at six anatomical locations on participants' right side (acromion process, greater trochanter, lateral epicondyle of the femur, lateral malleolus, calcaneus and fifth metatarsal). Marker placement was conducted by the same tester throughout for consistency. During all test bouts (Day_0 -Day_3), participants completed two 10 second trials of single-leg hopping at each of 1.5, 2.2 and 3.0 Hz in time with a digital metronome (TempoPerfect Metronome, NCH Software, Greenwood Village, CO, USA) while secured within an SBS (Fig 1). The design of the SBS was described previously [12,19]. As previous research suggests little effect of leg dominance on k leg or k joint [23], participants were instructed to land as close as possible to the force plate center (AMTI OR6-5; AMTI, Watertown, MA, USA) in time with the metronome, using their right leg and natural hopping technique. Trials were accepted for analysis if participants hopped within ± 5% of the target frequency [33,34]. The order of hopping trials was randomly assigned, and participants received 60 seconds recovery between each trial to limit fatigue effects. An analogue triggering device was used to initiate 3D kinematic and kinetic data acquisition simultaneously. Kinematic data were recorded using three MAC Eagle cameras (MotionAnalysis Corporation, Santa Rosa CA, USA) operating at 200 Hz. Kinetic data were recorded at 1 kHz over the 10 second duration.

Data processing
Analysis of data revealed an inconsistent delay in the initiation of kinematic and kinetic recordings. Whittlesey and Robertson [35] noted that kinematic and kinetic input signals must be temporally aligned to facilitate valid inverse dynamics analysis. Work in our laboratory has shown that maximum rate of change in fifth metatarsal marker acceleration profiles (i.e. peak jerk), coincide with ground contact to within 3.83 (± 1.06) ms of force plate criterion measures during overground hopping. Fifth metatarsal vertical coordinate data were subsequently differentiated to jerk [36]. The time of peak jerk was determined, and kinematic data were subsequently aligned with the time at which the vertical force increased above 5 N.
Marker trajectories were digitized using Cortex motion analysis software (version 2.1; MotionAnalysis Corporation, Santa Rosa, CA, USA). 3D kinematic and kinetic data were subsequently exported and analyzed using customized MS Excel macros. Recorded kinematic and kinetic data were concurrently filtered using a fourth-order Butterworth Low-Pass digital filter with an optimal cut-off of 11 Hz determined via residual analysis [36]. 3D coordinate data were subsequently interpolated to 1 kHz using a cubic spline. Filtered kinematic and kinetic data were used to calculate resultant joint moments occurring about ankle (M ankle ), knee (M knee ) and hip (M hip ) joints throughout the ground contact phase of each trial using inverse dynamics [7,23,37]. Segment inertia and mass characteristics were determined using the standards of Dempster [38]. Having calculated resultant moments, average torsional stiffness of the ankle (k ankle ), knee (k knee ) and hip (k hip ) were calculated as a ratio of changes in joint moment (ΔM joint ) and angle (Δϴ joint ) for respective lower limb joints [7,23].
In addition, k leg was recorded throughout the ground contact phase of all hopping trials using the spring-mass model [21]. Thus k leg was calculated as the ratio of F z max and maximum leg compression (ΔLeg L ) occurring during ground contact as measured from video records [39], where leg length represented the distance between the greater trochanter and the centerof-force [40]. In all analyzed trials, the temporal occurrence of discrete events of F z max and ΔLeg L coincided to within 10% of the hop period.

Statistical analysis
The mean of 5 consecutive hops occurring within the middle of each 10-second trial was calculated for dependent variables and compared within and between experimental bouts. Differences between the means recorded for each experimental bout were established for each hopping frequency (HopFreq) using repeated measures ANOVA (parametric variables) or Friedman's test (non-parametric variables). Reliability analysis employed both 'absolute' and 'relative' measures. A two-way random effects intra-class correlation coefficient (ICC) model examined the relative agreement between parametric and log-transformed dependent variables, while measurement consistency was established from effect size (ES) and ICC 95% confidence interval results [31,41,42]. Variables were considered strong when ICC � 0.90 [43], the lower-bound level of the ICC 95% confidence interval (ICC Lower ) > 0.80 [31] and Cohen's ES < 0.50 (moderate effect) [44]. Moderate reliability occurred if ICC ranged from 0.80 to 0.89, ICC Lower � 0.70 and ES < 0.50, while 'weak' reliability occurred if the previous criteria were not met. Within-participant variation in dependent variables were also examined using typical error (TE) [41], however these statistics were not included in reliability indexing. All statistical analysis was conducted using SPSS (version 23.0, IBM Corporation, Armonk, NY, USA). Friedman's test revealed no significant change in k leg (χ 2 (5) = 0.68-10.23; p > 0.05) across Day_1, Day_2 and Day_3 testing bouts at any HopFreq. Despite exhibiting little change between days, reliability indices showed k leg exhibited weak-to-moderate consistency (ICC = 0.71-0.89; ICC Lower = 0.29-0.73; ES = 0.08-0.26) between inter-day bouts across all HopFreq ( Table 2). Examination of kinematic and kinetic variables (Table 3) shows limits in k leg measurement agreement originated from limits in F z max and ΔLeg L measurement consistency. Limits in k leg measurement agreement, were accompanied by weak consistency in k knee and k hip between Day_1, Day_2 and Day_3 across all HopFreq (ICC = 0.62-0.84; ICC Lower = 0.02-0.61; ES = 0.10-0.70). Only k ankle exhibited moderate-to-strong consistency at slower HopFreq (ICC = 0.91-0.94; ICC Lower = 0.76-0.83; ES = 0.17-0.18). Examination of kinematic and kinetic variables (Table 3) shows that despite limits to k knee and k hip at 1.5 Hz, participants exhibited weak-to-strong consistency for joint kinetic and kinematic variables. At 2.2 and 3.0 Hz, limits in k knee and k hip resulted from weak-to-moderate agreement for joint kinetics and kinematics. Data show that strong consistency in k ankle measures at 1.5 Hz was accompanied by strong consistency in M ankle max and Δϴ ankle . Limits in k ankle measurement agreement at 2.2 and 3.0 Hz were accompanied by varied consistency in ankle kinematic and kinetic measures. Joint kinetics and kinematics showed no change (p > 0.05) between inter-day test bouts at any hopping frequency.

Results
Examination of intra-day testing comparisons (Table 2)  Limits in k leg reliability originated from strong and weak consistency in F z max and ΔLeg L respectively at all HopFreq. Repeated measure ANOVA results showed no change in k joint variables between Day_3 and Day_3 Offset (F (1.1, 22.6) = 0.17-1.07; p > 0.05). Despite this, k knee and k hip exhibited weak-to-moderate consistency between Day_3 and Day_3 Offset (ICC = 0.29-0.89; ICC Lower = 0.00-0.72; ES = 0.02-0.50). In contrast, k ankle exhibited strong consistency at 3.0 Hz but weak consistency at other hopping frequencies. Examination of kinematic and kinetic data (Table 4) showed limits in k joint reliability originated from largely weak-to-moderate consistency in joint kinematic and kinetic inputs between Day_3 and Day_3 Offset . Limits in Table 1. Descriptive and reliability statistics (mean ± s) for control variables of CT, FT, and HopFreq recorded between inter-and intra-day testing bouts during hopping within a SBS.

Discussion
SBS are used to examine SSC function under controlled conditions. Sled design regulates eccentric loading and limits extraneous movement to improve landing and measurement Limits in reliability of leg-spring+joint stiffness consistency. During overground hopping and running, k leg has demonstrated good reliability [22,23]. In contrast, k joint measures have demonstrated limited consistency. The reliability of k leg and k joint while hopping within an SBS had not been examined. This study provides a comprehensive analysis of the inter-and intra-day reliability of k leg and k joint achieved during hopping within an SBS. Similar to the findings of Hobara and colleagues [21] k leg and k joint increased with increases in HopFreq in the present study. Values of 13.9-28.9 kN.m -1 have been reported for k leg during natural hopping conditions on different surfaces and at different frequencies [22,23,30,45,46]. In addition, values of 6.9-12.0 Nm.deg -1 have been reported for k ankle during natural hopping [45]. In the present study, stiffness values are lower than reported during natural hopping [22,23]. This can be explained by the orientation of the frame of the SBS (i.e. 30˚to the horizontal) which reduces (half) the effect of gravitational acceleration [12,19]. Therefore, lower Table 3 Abbreviations: ICC = intraclass correlation coefficient; 95% CI = 95% confidence interval; TE = typical error; ES = effect size; Index = reliability index resulting from absolute and relative reliability statistics; F z max = maximum ground reaction force; M ankle max , M knee max , and M hip max = maximum resultant moments recorded for ankle, knee, and hip joints, respectively; Δϴ ankle , Δϴ knee , and Δϴ hip = relative angular displacement at ankle, knee, and hip joints, respectively; ΔLeg L = change in leg length. Note. Central statistics represent the mean (± s) of 5 consecutive hops recorded for 2 trials across Day_1, Day_2, and Day_3 experimental bouts.

Inter-day Comparisons
ground reaction forces (i.e. F z max ) are expected in the present study relative to published reports on overground hopping. This is supported by the work of Harrison et al. [25] and Flanagan and Harrison [19] who reported lower values for k leg during DJ and RBJ tasks (3.4-8.5 kN.m -1 ) performed within the current SBS, relative to natural conditions. The stiffness data recorded during the present study are in line with previous data reported for SSC tasks performed within an inclined-SBS. Hobara et al. [21] showed increases in k leg with increases in HopFreq. Thus, regulation of HopFreq between testing bouts was important to reliability analysis. In the current study Hop-Freq displayed weak-to-moderate consistency across all trials despite CT and FT variables showing strong agreement at all HopFreq between Day_3 and Day_3 Offset . Inter-day comparisons showed strong consistency for CT throughout. In contrast, FT exhibited strong agreement at 1.5 and 3.0 Hz but moderate consistency at 2.2 Hz. Hopkins and colleagues [41]  Abbreviations: ICC = intraclass correlation coefficient; 95% CI = 95% confidence interval; TE = typical error; ES = effect size; Index = reliability index resulting from absolute and relative reliability statistics; F z max = maximum ground reaction force; M ankle max , M knee max , and M hip max = maximum resultant moments recorded for ankle, knee, and hip joints, respectively; Δϴ ankle , Δϴ knee , and Δϴ hip = relative angular displacement at ankle, knee, and hip joints, respectively; ΔLeg L = change in leg length. Note. Central statistics represent the mean (± s) of 5 consecutive hops recorded for 2 trials across Day_3 and Day_3 Offset experimental bouts. https://doi.org/10.1371/journal.pone.0225664.t004 Limits in reliability of leg-spring+joint stiffness suggested low ICC's occur in situations where between participant variation is low for a given variable. In the present study, HopFreq was regulated to within 5% of the target frequency. Thus, low levels of variability may have produced spurious reliability indices in HopFreq and in FT measures during hopping at 2.2 Hz. The low TE (0.01-0.02) and ES (� 0.31) for CT, FT and HopFreq support this. Thus, HopFreq was controlled adequately throughout. Despite regulation of HopFreq in the present study, k leg exhibited moderate reliability at 1.5 Hz and weak reliability at 2.2 and 3.0 Hz (ICC = 0.59-0.89) between inter-day test bouts. These reliability indexes were accompanied by strong consistency for k ankle at 1.5 Hz only. Remaining k joint variables demonstrated weak-to-moderate agreement between Day_1, Day_2 and Day_3 testing bouts. Between Day_3 and Day_3 Offset , k leg exhibited moderate reliability at 3.0 Hz but weak consistency at the other frequencies. The moderate index for k leg at 3.0 Hz was accompanied by strong consistency for k ankle . Variables of k knee and k hip however, exhibited weak-to-moderate consistency throughout. Examination of kinematic and kinetic inputs (Tables 3 and 4) showed that limits in k leg reliability occurred due to limits in ΔLeg L reliability, while F z max exhibited moderate-to-strong consistency. The present data also showed that limits in k joint measurement agreement resulted from inconsistencies in M joint max and Δϴ joint at the highest hopping frequencies (2.2 and 3.0 Hz).
While the present study did not include a control condition, previous work in our lab examined the reliability of k leg and k joint measures in overground hopping [22]. This study employed the same methodology and used physically active participants consistent with the current work. Our work showed strong agreement (ICC = 0.95-0.98) for k leg and k ankle measures at different hopping frequencies [22]. In contrast, k knee and k hip exhibited weak-to-moderate agreement. Given our previous findings, that many stiffness variables showed weak-tomoderate agreement in the present study is surprising. Particularly since the primary function of the current inclined-SBS is to limit extraneous upper body movement to enhance landing and measurement consistency during SSC tasks [8,19].
It is understood that in biological measurement, observed scores are composed of a true score and additional error [42]. Weir [42] suggests that errors in measurement data result from instrumentation errors associated with equipment used, in addition to participant / tester error, modelling error and biological variability. In the context of the current work, instrumentation errors arise from equipment (force plate and video) use and protocol adherence between testing bouts. It is important to note that participants were instructed refrain from physical activity prior to data collection. Furthermore, force plate and video equipment were calibrated as per the manufacturer's guidelines prior to each data collection period. In addition, equipment set-up and protocols used were consistent with published works showing strong reliability for k leg and k ankle during overground hopping [22]. Consequently, deteriorations in measurement consistency relative to published reports are not due to differences in testing protocols between studies.
Of additional concern to the reliability of k leg and k joint scores is error derived from the use of mathematical models. Whittlesey and Hammill [47] noted that models are sensitive to the number of model components. Thus, small errors present early in the modelling process will propagate by the end of the simulation. This suggests that modelling errors will increase as calculations progress from distal to proximal joints. As k joint is the ratio of changes in M joint and ϴ joint , it is clear that errors in M joint (and k knee and k hip ) measures will increase as inverse dynamics analysis progresses from distal to proximal joints. It is important to consider that while these errors will influence k joint consistency, they are unlikely to influence k leg in the present work. In addition, as modelling procedures employed in the current work are consistent with previous works [22], it is unlikely that differences in measurement consistency between the current and previous works result from modelling errors.
Considering biological variability, our previous work on overground hopping noted the existence of k leg as an attractor state [22] where participants are drawn to the manipulation of leg compression (seen by variable k joint or ΔLeg L ) to maintain a consistent k leg under variable landing conditions [9,45]. These works also showed that stiffness variables were accompanied by mostly strong consistency for F z max and ΔLeg L variables. In the present study, it must be considered that while the reliability of F z max was strong, the reliability of ΔLeg L was weak-tomoderate across all testing bouts. As a result, the k leg exhibited weak-to-moderate consistency throughout. It is therefore difficult to establish a consistent outcome variable (i.e. attractor state) that participants are trying to regulate. Furthermore, considering limits in the reliability of kinematic and kinetic variables measured, and the limited pattern to the nature of this reliability, we feel that our data does not support the notion that limits in reliability are due to kinematic variability to achieve consistent outcomes.
It is important to consider the novelty of the hopping task and its impact on the present data. Our previous work showed that familiarizing participants with testing procedures prior to data collection enhanced measurement reliability relative to earlier reports [23]. In the present study however, participants completed a familiarization session prior to data collection. Thus, acquainting participants with procedures did not benefit the consistency of hopping dynamics within the current SBS. One reason for this is likely the design of the current SBS. The design of the current SBS requires participants to adopt a flexed torso position while secured to it. This novel hopping position would alter the functional length of lower limb musculature compared to upright hopping, which will have impacted participants' ability to achieve consistent hopping dynamics. In addition, the mass of the chair of the current SBS was 19.6 kg. The added mass may have made it difficult for participants to achieve consistency in their hopping patterns. This is partly supported by the work of Kramer et al. [48]. The authors demonstrated that participants achieved almost natural reactive jumps following this fourweek period (i.e. 12 sessions). While the instructions regarding landing dynamics differed from the current study, the design of the lightweight sled (5 kg) allowed participants to adopt natural movement patterns [27,48]. Although the authors did not report reliability indices for variables measured, the changes seen (38% increase) following four weeks of training (i.e. familiarizing) suggest the performance of SSC tasks within an SBS to be a novel task requiring extensive participant familiarization. The practicalities of including multiple familiarization sessions prior to data collection must also be considered.
Considering the lack of reliability evident in kinematics, kinetics and stiffness variables measured, it is appropriate to accept the null hypothesis. Limiting extraneous upper body movement by using an SBS during single-leg hopping did not improve the reliability of k leg and k joint measures relative to previous reports on overground hopping. In fact, use of the current SBS reduced consistency of stiffness measures relative to previous reports on natural conditions.

Conclusions
To summarize, the present data showed weak-to-moderate reliability for all stiffness measures during hopping using the current SBS. This was due largely to inconsistencies in leg compression (ΔLeg L ). Thus, reducing extraneous upper body movement using the current SBS did not encourage consistent stiffness regulation. In fact, hopping within the current inclined-SBS had adverse effects on measurement consistency relative to published reports on overground hopping. Limits in the consistency of stiffness measures may be due to constraints imposed by restricting upper body movement, which introduced novelty to the single-leg hopping task. A single familiarization session was therefore inadequate to achieve consistent landing mechanics. The influence of sled design on the current findings must also be considered, with chair mass and orientation likely making it difficult for participants to achieve consistent hopping patterns. Researchers should consider these findings and endeavour to construct a lightweight system with a chair orientation that replicates the functional length of the muscle-tendon units driving the SSC task being analysed.