Implementation of relative phase analysis to evaluate continuous interlimb coordination and stability in individuals with lower limb loss: Design and protocol for a retrospective analysis


Metabolic and biomechanical outcomes are primary factors used to evaluate effectiveness of a prosthetic device for individuals with lower limb loss during walking. However, previous research analysing these parameters has shown mixed results on the impact of different prosthetic devices. For example, a 2018 Cochrane review on the effectiveness for prosthetic intervention concluded that the current scientific literature does not provide sufficient high-quality research to allow strong conclusions.1

Therefore, a more sensitive quantitative measure should be used to supplement traditional biomechanical analysis to aid in determining the impact of the different devices on gait. Continuous movement coordination, the movement relationship between joints or body limb segments,2 is a non-traditional biomechanical measure of gait rooted in dynamical systems theory. For gait-related, cyclical activities, this relationship is best described as continuous coordination, which differs from discrete coordination. Discrete coordination refers to the coupling of different components during a task with a fixed beginning and end, measures the tendency of synchronisation, is usually measured at the peak of a movement at a given time, and is most often reported using basic spatiotemporal measures.3–5 However, continuous coordination measures the movement relationship between limbs throughout a cyclical movement, such as walking.2 6 While previous literature suggested that the principles of coordination may originate from various anatomical structures and neural mechanisms at the level of the movement patterns, these patterns can change based on internal constraints, such as musculoskeletal pathology or external constraints, such as walking with a prosthetic device that causes a less consistent, and therefore less stable, gait pattern.6 7 Therefore, appropriate interlimb coordination may differ between individuals due to a person’s intrinsic and extrinsic constraints, such as limb loss and different prosthetic devices. Importantly, when a person achieves appropriate coordination, stability is optimised during motor skill performance.8 While variability is traditionally used in the description of movement patterns, continuous coordination is associated with the measure of stability instead. Stability represents the system’s ability to offset a perturbation (internal or external) and remain in its coordinative pattern,8 while variability emerges from the many degrees of freedom inherent in the system.9 In this context, stability represents a more informative measure than variability when evaluating continuous movement coordination.

Superior coordination has been linked to increased physical activity and strength, as well as improved clinical outcome measures in both healthy10 11 and mobility-challenged populations.12 Such evidence makes optimisation of this parameter one potential target to improve whole-body dynamics. Optimal stability provides control over internal and external perturbations, allowing the system to quickly recover to a stable state.13 Optimal coordination and stability are pertinent to function in individuals with lower limb loss. Since different prosthetic devices may produce external perturbations to their system (ie, gait pattern), it is critical to determine the device that minimises these perturbations and allows the individual to reach his or her most stable walking pattern. While previous literature describes the application of relative phase (RP) analysis to individuals with lower limb loss,14–17 most of the studies focus on coordination between the pelvis and trunk,14 15 17 and one describes the intralimb (ie, within limb) coordination of the lower extremities.16 To date, only one study has investigated continuous gait interlimb (ie, between limbs) coordination and stability in individuals with lower limb loss.18 Deficits in both parameters were observed in individuals with lower limb loss compared with intact individuals.18 However, this study included a limited sample size (n=7) of individuals with transfemoral (ie, above the knee) limb loss and did not explore these parameters for individuals with transtibial limb loss (ie, below the knee). Though the majority of participants used different prosthetic devices, all participants were grouped together for analysis, which removed the ability to compare coordination and stability between devices. Furthermore, the speed at which participants walked (0.1–0.9 m/s) was slower than the range of speeds required to safely cross a street (0.9–1.2 m/s),19 reducing the functional applicability of the results. Because of these significant limitations, a gap in the literature exists, as no research has identified the continuous gait interlimb coordination and stability between the upper and lower extremities at functional speeds in individuals with transtibial limb loss or determined the effect of different prosthetic devices on interlimb coordination and stability.

Quantifying coordination continuously throughout a movement is not easily accomplished using spatiotemporal measures, which lack information about the relationship between the limbs throughout movement.20 Consequently, spatiotemporal analysis may miss changes in patterns because it only analyses a single point, instead of the entire movement cycle, and relies on conventional time-series presentations that fail to reveal direct relationships between velocity changes and positions.21 Measures of RP analysis are more sensitive to detecting gait irregularities than spatiotemporal measures and detect changes at a greater resolution by providing a low-dimensional term (ie, phasing relationship) that incorporates two measures of movement (velocity and displacement) into one term.7 The advantages of RP analysis stem from the mathematical calculation of the relationship between two body segments (eg, an arm and a leg). Unlike spatiotemporal measurements, RP analysis determines the continuous RP (CRP) between two segments by identifying phase angles, which quantify the location of each segment’s trajectory as time progresses. Phase angles of the two segments are then subtracted at each given time point throughout the entire movement to evaluate the coordinative relationship between segments.7 Therefore, CRP represents the dynamic interaction of two segments for every point during a movement,21 as opposed to the snapshot of information provided by spatiotemporal analysis. Thus, when attempting to ascertain even subtle features of gait patterns, the higher-grade quantification of RP captures information that is not obtainable using basic spatiotemporal data. RP analysis can provide a comprehensive description of kinematic behaviour that may improve the understanding of emergent behaviour, which is especially important when evaluating coordination of mobility challenged populations, such as those with lower limb loss.

The goal of this study is to quantify interlimb coordination and stability of individuals with lower limb loss. The first specific aim is to determine the continuous gait interlimb coordination and stability of individuals with transtibial limb loss. It is hypothesised that individuals with transtibial limb loss will indicate lower levels of coordination and stability compared with individuals without lower limb loss. The second specific aim is to determine the extent to which continuous interlimb coordination and stability of individuals with transtibial limb loss are influenced by different prosthetic device types (energy storing and return (ESR), articulating ESR, and powered ESR). It is expected that RP analysis will provide higher resolution data compared with traditional spatiotemporal biomechanical measures for greater insight into even subtle changes in gait patterns. Further, it is hypothesised that a powered ESR device will allow individuals to achieve better continuous interlimb coordination and stability compared with the ESR and articulating ESR devices.

Methods and analysis

Patient and public involvement statement

No patients were involved in this retrospective analysis.

Study overview

This study is a retrospective companion study of an ongoing, randomised, cross-over clinical trial (Congressionally Directed Medical Research Programs–Orthotics and Prosthetics Outcomes Research Program grant W81XWH-17-2-0014).22 The start and end dates for this study are June 2020 to May 2024, respectively, with data collection of the original study expected to be completed by June 2023. For this investigation, the continuous gait interlimb coordination and stability in individuals with transtibial limb loss will be analysed to identify deficits in these individuals compared with individuals without limb loss. RP analysis will also be used to determine which ankle-foot prosthetic device type (ESR, articulating ESR, powered ESR) will be associated with the highest levels of coordination and stability in individuals with transtibial limb loss. In brief, analysis will be conducted on 30 individuals with transtibial limb loss who were fit and trained with three different types of prosthetic ankle-foot devices. Participants then separately used each prosthetic foot for one week at home. Following each one-week period, participants underwent biomechanical evaluations during level-ground walking. Additionally, a group of 10 individuals without limb loss completed the same biomechanical analysis to compare coordination and stability between control participants and individuals with transtibial limb loss. Data will be analysed using a novel approach of RP analysis, which has been shown to be more sensitive to detecting changes in motor patterns compared with traditional biomechanical measures.21 A detailed description of the study design follows.

Participant population

This retrospective analysis will include 30 participants with transtibial limb loss collected during an ongoing Department of Defense-funded clinical trial (W81XWH-17-2-0014).22 Eligibility criteria for the ongoing clinical trial are listed in table 1.

Table 1

Inclusion/exclusion criteria

Categories of prosthetic devices

The prosthetic ankle-foot devices included in this investigation were systematically selected and categorised at the time of the original study initiation by a diverse panel of experts in the limb loss field.22 Device structure, componentry, function and biomechanical properties were considered to create ankle-foot device categories. This process is in accordance with recommendations from previous literature to standardise the categorisation of devices according to specific features.23 Based on the developed criteria, all devices were placed into one of the following three categories: non-articulating ESR, powered (active plantarflexion) ESR, or articulating ESR.

Non-articulating ESR devices are the current gold standard for prescription in the Department of Veterans Affairs and provide energy storage and return during the gait cycle.24 This group includes any qualifying non-articulating ESR ankle-foot device that is commercially available. For the articulating ESR group, 14 devices have been included in this study (table 2). These devices provide energy storage and return properties, as well as articulation at the ankle. This group included all commercially available options in the K3 Medicare Functional Classification System category that have an articulating ankle and ESR properties at the time of study initiation. For the Powered ESR group, the Empower (Ottobock, Duderstadt, Germany) is currently the only commercially available device. The Powered ESR device provides active plantarflexion through an onboard motor.

Table 2

Ankle-foot prosthetic devices included in clinical trial

Description of data collection procedures

Due to the retrospective nature of this study, all data are collected as part of the ongoing clinical trial.22 Analysis for this companion study will be performed as participants complete all clinical trial protocol activities. A computer-generated algorithm that randomly selects from all available devices and then assigns the order will be used to indicate the sequence in which the prosthetic device will be evaluated. Randomization will be performed prior to study enrollment to ensure each combination of device order is used an equal number of times. During data collection procedures of the clinical trial, participants are fit and aligned with each device by a certified prosthetist and undergo device specific training by a qualified clinician using each foot to ensure their ability to appropriately use the device. All participants must score a 6 (modified independence) or 7 (complete independence) on two aspects of the Functional Independence Measures (ability to walk over level ground and ability to ascend and descend stairs). If a participant does not meet these criteria, guided rehabilitation to enhance the use of the ankle-foot device is provided until the participant meets the minimum standard of performance. Once met, participants return home with the first randomised prosthetic device for a 1-week acclimation period. Following each acclimation period, participants will complete biomechanical gait analysis. In brief, biomechanical data collection procedures include a total of 78 reflective markers placed on each participant to allow for creation of a three-dimensional (3D) model of all individuals. The specific markers used in this study include: acromion processes of the right and left shoulders, lateral epicondyles of the right and left humeri, ulnar styloid processes of the right and left wrists, iliac crests of the right and left hips, lateral point of the right and left knee joint spaces, and lateral malleolus of the right and left ankles. After performance of static trials to calculate lower limb joint centers, participants perform overground walking at their comfortable walking speed. Walking trials are continued until a total of 15 walking cycles are completed.

Data processing

Trials are recorded using an 11-camera Qualysis (Gothenburg, Sweden) passive, optical motion capture system. Once marker trajectories are labelled and gap-filled, the data will be imported into Visual 3D (C-Motion, Germantown, Maryland, USA), where the trajectories will be filtered using a Butterworth Filter with a cut-off Frequency of 6 Hz. Gait events, including heelstrike and toe-off, will then be labelled, and the trajectories of the listed markers for each cycle, defined as prosthetic-side heelstrike to heelstrike, will be exported into MatLab 2019a (The Mathworks, Natick, Massachusetts, USA) for further analysis. Each cycle will be normalized on a scale of 0%–100% of the gait cycle.

Segment angles will be calculated rather than joint angles, as calculating relative to an external reference frame removes coupling from adjacent joints and lends more interpretable phase relationships.25 To accomplish this, segment angles will be calculated by their position relative to the limb’s proximal joint (ie, wrist and elbow segments are both calculated relative to the shoulder marker, figure 1). This can be seen in equation 1, calculating the segment angle for the ith segment, Embedded Image

where Embedded Image and Embedded Image represent the proximal and distal planar marker trajectories.

Figure 1
Figure 1

Illustration of segmental angle of upper extremity used for calculation.

Embedded Image


Calculation of RP analysis

RP analysis will be used to calculate the CRP, SD of CRP, mean absolute RP (MARP) and deviation phase (DP) for all pairs of limbs of interest. Six limb pairings will be included in this analysis (figure 2): (1) arm to arm, (2) leg to leg, (3) ipsilateral intact-side arm and intact-side leg, (4) ipsilateral prosthetic-side arm and prosthetic-side leg, (5) contralateral intact-side arm and prosthetic-side leg and (6) contralateral prosthetic-side arm and intact-side leg.

Figure 2
Figure 2

Pairs of limbs evaluated using relative phase analysis. Illustration of the phasing relationships analysed between the (A) arms and legs, (B) ipsilateral intact-side and prosthetic-side arms and legs, respectively, and (C) contralateral prosthetic-side arm and intact-side leg, and intact-side arm and prosthetic side leg, respectively.

Because RP analysis encompasses angular displacement and velocity within one variable, it provides a better measure of the organization of the neuromuscular system than other spatiotemporal measures.26 27 Additionally, continuous measures of RP allow quantification of the phase relationship across all points of the cycle.26 Therefore, all limb movement within a cycle will be included in the analysis.

Upper and lower extremity trajectory data will be prepared for analysis using normalization techniques to keep the calculated segmental angles and corresponding velocity within a −1 and+1 range.21 25 28 29 Given the trajectories, segment angles, Embedded Image

will be calculated in MATLAB, as given by equation 1. The segment angular velocity, Embedded Image, is determined by the time derivative. Both segment angle and angular velocity are normalized, given by equations 2 and 3, respectively, according to method A in Lamb and Stöckl.25

Embedded Image


Embedded Image


The extrema used in equations 2 and 3 are the absolute extrema across all cycles, to avoid overnormalization of individual trials. Using the normalized segment angle and angular velocity, the segment phase angle, Embedded Image

, is then calculated, given by equation 4. This calculation is repeated eight times, for the intact and prosthetic side limbs, calculating separate segment angles, velocities and phase angle, based off the trajectory of each listed distal marker.

Embedded Image


Phase angles, which quantify the location of the trajectory in the phase portrait (angular position vs angular velocity) as time progresses, illustrate the behaviour of the segments and will be used to calculate RP.7 An example of a phase portrait is shown in figure 3.

Figure 3
Figure 3

Phase portrait. Example phase portrait which illustrates the cyclical movement of the prosthetic ankle. Both angluar displacement and angular velocity are normalized, given in equations 2 and 3, respectively.

RP provides a measure of the coordination of two segments during the movement30 and will be calculated by subtracting the phase angles of the segments at each given time point throughout the movement. When RP is calculated throughout the entire movement, it is known as the CRP. The CRP will be calculated using equation 5:

Embedded Image


where ẋ1(t) and ẋ2(t) denote the angular velocity of each segment and x1 and x2 represent the angular displacement.25

CRP represents the dynamic interactions of two segments (eg, forearm and foot) for every point during the movement28 and refers to the phasing relationships between the segments.7 Phasing relationships are evaluated as being in-phase (ie, oscillating segments move in the same direction at the same time) or antiphase (ie, oscillating segments move in opposite directions at the same time), are measured in degrees, and range from 0° (perfectly in-phase) to 180° (perfectly antiphase).31 The test–retest reliability of the assessment of CRP was demonstrated in a repeated measures study design32 where young, healthy adults were assessed 24 times within 4 months. Results showed no main effect of assessment for both CRP and the SD of CRP at different walking velocities with a SD of CRP of 8.8°.

To determine the coordination of individuals during walking, the CRP data will be calculated in three subsets: CRP between the upper and lower limb pairs (ie, prosthetic side arm to intact side arm), the upper to lower ipsilateral limb CRP (ie, prosthetic side arm to prosthetic side leg) and the upper to lower contralateral limb CRP (ie, prosthetic side arm to intact side leg). As the most distal markers on the limbs have the greatest magnitude of travel and the clearest signal, only the segment angles determined by the ankle marker and wrist marker will be used to calculate the CRP.

A cycle is defined as one complete gait cycle (two consecutive heel strikes of the same foot). Invalid cycles are those in which all markers are not visible, or if the participant experiences a small trip or stumble during walking. In addition, the above calculations will initially be performed and checked for outlier cycles (eg, an atypical arm swing).

Outcome measures

The primary outcome measures for this study will be the coordination (defined by MARP) and stability (defined by DP) between the arms, between the legs, between ipsilateral arms and legs, and between contralateral arms and legs during overground walking.

MARP will be used to quantify the in-phase or antiphase relationship of the interacting segments33 34 and will be calculated using the following equation:

Embedded Image


where Embedded Image

is the relative phasing relationship between the two segments and N is the number of points in the RP mean ensemble curve.

The mean ensemble curve is created by adding the length of data points for all cycles included in analysis. A low MARP value (closer to 0°) indicates that the oscillating segments had a more in-phase relationship (ie, contralateral arms and legs), while a high MARP value (closer to 180°) indicates that the oscillating segments had a more antiphase relationship (ie, arms, legs, ipsilateral arms and legs). MARP calculation is necessary so that differences in RP curves can be quantified and statistically tested.7

Lastly, DP will be used to quantify the stability of the system throughout the movement.7 DP will be calculated using the following equation:

Embedded Image


where N is the number of points in the RP mean ensemble curve and SD is the SD of the mean ensemble curve at the ith point.

A low DP value (closer to 0°) indicates a more stable organization of the system and a high DP value (closer to 180°) indicates less stability in the organization of the neuromuscular system.7

Data analysis

A Kolmogorov-Smirnov test will determine normality of the data and Levene’s test of homogeneity will be used to determine the equality of variance. If both assumptions are satisfied, parametric statistical analyses will be employed. Descriptive statistical analyses will be used to summarize continuous coordination and stability values for both the participants with transtibial limb loss (n=30) and the participants without lower limb loss (n=10) groups. Two-sample t-tests will be used to compare means between groups.

The analysis will be based on repeated measure analysis of variance. The two outcomes are MARP (measure of coordination) and DP (measure of stability), and the aim has a single predictor (prosthetic device type). Repeated measures will be used to account for the fact that each participant will be tested with each prosthetic device type (three tests per participant). Post hoc tests with corrections for multiple tests will be used to further examine tests that show significant effects of prosthetic device type. Separate models will be run for each outcome.

If the data fail to meet normality and homogeneity assumptions, non-parametric analyses will be conducted. In this case, a Mann-Whitney U test will be used to compare means between experimental and control groups and the Friedman test will be implemented to determine differences in MARP and DP between the different prosthetic device types. If differences are identified, post hoc analysis with Wilcoxon signed-rank tests will be conducted with a Bonferroni correction applied. A Spearman correlation will be used to identify correlations.

Sample size estimation

This study will be a convenience sample of 30 participants with lower limb loss and 10 individuals without limb loss, which is supported by the power analyses. Due to the retrospective analysis of this study, sample size was determined a priori from the companion clinical study. The average effect size associated with the preliminary data from repeated measures analysis of variance of both MARP and DP was 0.77. Power analysis using the established number of participants with transtibial limb loss (n=30) was calculated with an alpha level of 0.05. The outcome of this calculation was a percent power of 97% with a large effect size of f=0.48. Therefore, the sample size of 30 participants with transtibial limb loss and 10 participants without lower limb loss will provide sufficient power to detect a true effect and will not be distorted by random or systematic error.

Ethics and dissemination

This study was approved by the local Department of Veterans Affairs Institutional Review Board (IRBNet #1573135, MIRB #1775). Informed consent from participants is not required due to the retrospective nature of this study. No personal identifiable information will be used in this study. Findings will be disseminated through peer-reviewed publications, academic conference presentations, invited workshops, webinars and seminars.

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