The Choice of Reference Frame Alters Interpretations of Turning Gait and Stability

Abstract

Humans regularly follow curvilinear trajectories during everyday ambulation. However, globally-defined and locally-defined reference frames fall out of alignment during turning gait, which complicates spatiotemporal and biomechanical analyses. Thus, the choice of the locally-defined reference frame is an important methodological consideration. This study investigated how different definitions of reference frame change the results and interpretations of common gait measures during turning. Nine healthy adults completed two walking trials around a circular track. Kinematic data were collected via motion capture and used to calculate step length, step width, anteroposterior margin of stability, and mediolateral margin of stability using three different locally-defined reference frames: walkway-fixed, body-fixed, and trajectory-fixed. Linear-mixed effects models compared the effect of reference frame on each gait measure, and the effect of reference frame on conclusions about a known effect of turning gait – asymmetrical stepping patterns. All four gait measures differed significantly across the three reference frames. A significant interaction of reference frame and step type (i.e. inside vs outside step) on step length (p<0.001), anteroposterior margin of stability (p<0.001), and mediolateral margin of stability (p<0.001) indicated conclusions about asymmetry differed based on the choice of reference frame. The choice of reference frame will change the calculated gait measures and may alter the conclusions of studies investigating turning gait. Care should be taken when comparing studies that used different reference frames, as results cannot be easily harmonized. Future studies of turning gait need to justify and detail their choice of reference frame.

1. INTRODUCTION

Defining the reference frame of a locomotor environment is a critical step in reporting consistent and comparable measures of gait, with internationally accepted standards defined during straight gait (Wu and Cavanagh, 1995). However, turning is common during locomotion because humans routinely walk where there is no clear, pre-defined direction of travel (Glaister et al., 2007a). Compared to straight-line walking, analysis of this curvilinear gait is more difficult because the globally-defined and locally-defined reference frames fall out of alignment (Huxham et al., 2006; Kainz et al., 2016); measures from globally- and locally-defined reference frames can vary dramatically, yielding inconsistent interpretations and conclusions based on the choice of coordinate reference frame (Schache et al., 2008). Several different locally-defined references frames have been used to study turning gait (Imai et al., 2001; Kainz et al., 2016; Nolasco et al., 2019; Schache et al., 2008; Taylor et al., 2005; Wu et al., 2002; Wu and Cavanagh, 1995). But, there are no guidelines on how to choose a locally-defined frame (Glaister et al., 2007b; Wu et al., 2002; Wu and Cavanagh, 1995), or whether results from different locally-defined reference frames can be combined across studies, despite turning gait being increasingly studied.

To help provide guidance when choosing a locally-defined reference frame for turning gait, our aim was to investigate how the choice of reference frame influences spatial measures of gait and affects conclusions about turning gait and asymmetry - a well-described characteristic of turning (Fino et al., 2015; Orendurff et al., 2006; Strike and Taylor, 2009).

2. MATERIALS and METHODS

2.1. Participants

Nine healthy adults [5 female, 4 male; mean (SD) age: 22.9 (3.1) years; height: 172.6 (10.7) cm; mass: 64.7 (9.7) kg; 9 right-limb dominant] were recruited from the local community and provided informed written consent for participation in this IRB-approved study. Participants had no balance problems or unresolved injuries that may affect balance or locomotion.

2.2. Procedure

As part of a larger protocol, participants completed two, one-minute long walking trials around a 0.4m-wide circular track (inner radius: 1.2m, outer radius: 1.6m): one clockwise and one counter-clockwise trial. The circular track was constructed of 2.5cm-thick plywood to ensure no participant deviated outside of the inner or outer radius. Prior to the first trial, participants were asked to walk around the track at a normal pace to measure self-selected walking speed. Using the time of their initial laps, they were paced with a metronome delivered at each quarter-lap to maintain a consistent walking speed throughout all trials. Retroreflective markers were placed bilaterally on the posterior superior iliac spine (PSIS), anterior superior iliac spine (ASIS), iliac crest, heel, second metatarsophalangeal (MTP) joint, and fifth MTP joint. Kinematic data were collected via motion capture (Vicon Nexus ver. 2.12) at a rate of 200 Hz.

2.3. Data Processing

Custom MATLAB codes were used for data processing and statistical analysis (ver. R2020b, The Mathworks Inc., Natick MA, USA). Raw positional marker data were filtered using a 4^th-order phaseless, 6 Hz low-pass Butterworth filter. The position of the body center of mass (CoM) and feet in a globally-fixed reference frame were estimated from the ASIS and PSIS markers and the heel, second MTP, and fifth MTP markers, respectively (Havens et al., 2018). The velocity of the CoM was calculated using the central difference formula. Temporal gait events of heel contact and toe-off were identified using the methods of Ulrich et al. (2019). Steps were categorized as either inside or outside steps (e.g., clockwise: right is inside; counterclockwise: left is inside).

Each position and velocity vector was rotated from the globally-fixed reference frame to three different reference frames: a walkway-fixed frame (Chang and Kram, 2007; Wu and Cavanagh, 1995), a body-fixed frame (Rasmussen et al., 2022; Schache et al., 2008; Taylor et al., 2005; Wu et al., 2002), and a trajectory-fixed frame (Fino et al., 2020; Glaister et al., 2007b; Imai et al., 2001; Kainz et al., 2016; Nolasco et al., 2019) [Figure 1]. The walkway-fixed frame was defined using the radial vector from the center of the circular walkway to the position of the CoM (+Z_W), vertical (+Y_W), and the right-handed orthogonal cross-product of the two (+X_W), with +X_W pointed in the direction of travel. The body-fixed frame was defined by the vector from the average position of the PSIS markers to the average position of the ASIS markers (+X_B), vertical (+Y_B), and their cross-product (+Z_B). The trajectory-fixed frame was defined by the vector of the instantaneous velocity of the CoM in the transverse plane (+X_T), vertical (+Y_T), and their cross-product (+Z_T).

Figure 1:

Visualization of the walkway-fixed (green, solid), body-fixed (pink, dotted), and trajectory-fixed (purple, dashed) reference frames. The ML aspect of the walkway-fixed frame (+Z_W) was defined by the radial vector from the origin of the circular track to the body CoM. The AP aspect of the walkway-fixed frame (+X_W) was defined by the orthogonal cross-product of +Z_W and a vertical vector (+Y). The AP aspect of the body-fixed frame (+X_B) was defined by the vector from the average position of the PSIS to the average position of the ASIS. The ML aspect of the body-fixed frame (+Z_B) was defined by the orthogonal cross-product of +Z_B and +Y. The AP aspect of the trajectory-fixed frame was defined by the vector of the instantaneous velocity of the CoM (+X_T). The ML aspect of the trajectory-fixed frame was defined by the orthogonal cross-product of +X_T and +Y. Each reference frame was calculated at initial heel strike for measuring step length and step width, and at contralateral toe-off for measuring AP and ML MoS.

Step length and step width vectors were extracted at the instant of the initial heel strike connecting the heel markers of successive heel strikes and calculated within each reference frame, which were defined at the moment of contralateral toe-off. The positive directions for each step pointed in the local +X direction and along the medial direction of the local Z axis from the initial heel strike (i.e., a negative step width indicates a crossover step). Anteroposterior (AP) and mediolateral (ML) margins of stability (MoS) were calculated at the time of contralateral toe-off, with the pendulum length defined by the mean CoM height of each participant (Hof, 2008; Hof et al., 2005; Watson et al., 2021). The most anterior and lateral boundaries of the base of support (BoS) were calculated by defining a piece-wise linear boundary from the second MTP marker to the fifth MTP marker and from the fifth MTP marker to the calcaneus marker (2MTP-5MTP-Calcaneus). For each reference frame, separate AP and ML BoS boundaries were defined as the points along that piecewise 2MTP-5MTP-Calcaneus line that were furthest from the extrapolated center of mass (xCoM) in the local AP and ML directions, respectively. The positive directions for MoS pointed in the local −X direction (AP) and along the medial direction of the local Z axis (ML) from the borders of the BoS (e.g., a negative AP MoS indicates the xCoM is anterior to the anterior border of the BoS; a positive ML MoS indicates the xCoM is medial to the lateral border of the BoS).

2.4. Statistical Analysis

To test the effects of reference frame on stability measures within subjects, linear mixed models were fit for each outcome measure with fixed effects of reference frame, stepping limb (inside vs outside), and their interaction. Models were also adjusted for the covariate of walking direction (clockwise vs. counter-clockwise) and random intercepts by subject. Overall effects of reference frame and the interaction with stepping limb were examined using a type 3 test for fixed effects (i.e., F-test). Post-hoc contrasts followed the F-tests and tested for pairwise differences between reference frames. For each model, significance was assessed at an alpha of 0.05, and a Benjamini-Hochberg correction (Benjamini and Hochberg, 1995) was used to account for multiple comparisons.

3. RESULTS

Participants took an average of 89.7 (SD=6.2; min=78; max=101) steps per trial, which were all included in the analyses. The average walking speed across all participants was 0.937 m/s (SD=0.099 m/s; min=0.766m/s; max=1.095m/s).

Step length (p<0.001), step width (p<0.001), AP MoS (p<0.001), and ML MoS (p<0.001) all differed across reference frames [Figure 2A–D]. Altering reference frame did not change the observed asymmetry (i.e., inside vs outside) of stepping limb of step width (p=0.993), but it did change the observed asymmetry of stepping limb on step length (p<0.001), AP MoS (p<0.001), and ML MoS (p<0.001), as indicated by the interaction between reference frame and stepping limb. Pair-wise contrasts failed to detect significant differences in ML MoS (p=0.136) when measured in the body-fixed frame and when measured in the walkway-fixed frame. All other pair-wise comparisons were significantly different (Tables 1, 2).

Figure 2A-D:

Results for each gait measure in walkway-fixed, body-fixed, and trajectory-fixed reference frames, and between inside (white) versus outside (grey) steps. Each participant’s gait measures are represented in separate colors. Each step is represented by individual scatter points. Open diamonds represent the within-participant means. Each panel includes measures from every trial (both clockwise and counterclockwise). Negative AP MoS denotes an xCoM anterior to the BoS and negative ML MoS denotes an xCoM lateral to the BoS.

Table 1:

Means, standard deviations and results from the linear mixed models for step length, step width, AP MoS, and ML MoS measured at contralateral toe-off. Fixed effects included reference frame, stepping limb, walking direction, and the reference frame*stepping limb interaction. The walkway-fixed reference frame and inside stepping limb were the reference condition for each model. Each gait measure differed both by reference frame and stepping limb. The interaction of reference frame*stepping limb on step length and AP MoS was significant across all reference frames. However, the interaction of reference frame*stepping limb did not alter interpretations of step width across all three reference frames, nor did it alter interpretations of ML MoS when comparing the walkway-fixed frame to the body-fixed frame. Pair-wise contrasts indicate differences from the post-hoc contrasts (W = walkway-fixed; B = body-fixed; T = trajectory-fixed)

		Inner Limb		Outer Limb			Asymmetry (Outer Limb - Inner Limb)
Step Length	Reference Frame	Mean (mm)	SD (mm)	Mean (mm)	SD (mm)	Pair-wise Contrasts	Mean (mm)	SD (mm)	Pair-wise Contrasts
	Walkway-Fixed Frame	614.6	43.5	636.2	46.6	B, T	22.1	36.4	B, T
	Body-Fixed Frame	629.2	49.6	624.7	42.4	W, T	−3.6	38.9	W, T
	Trajectory-Fixed Frame	585.4	45.0	642.9	48.9	W, B	57.7	35.4	W, B
		Inner Limb		Outer Limb			Asymmetry (Outer Limb - Inner Limb)
Step Width	Reference Frame	Mean (mm)	SD (mm)	Mean (mm)	SD (mm)	Pair-wise Contrasts	Mean	SD	Pair-wise Contrasts
	Walkway-Fixed Frame	233.6	50.9	−93.4	54.7	B, T	−325.0	56.2	−
	Body-Fixed Frame	184.4	66.8	−143.1	77.6	W, T	−325.6	104.4	−
	Trajectory-Fixed Frame	299.8	46.5	−27.5	46.6	W, B	−325.4	54.9	−
		Inner Limb		Outer Limb			Asymmetry (Outer Limb - Inner Limb)
AP Margin of Stability	Reference Frame	Mean (mm)	SD (mm)	Mean (mm)	SD (mm)	Pair-wise Contrasts	Mean	SD	Pair-wise Contrasts
	Walkway-Fixed Frame	−22.2	31.7	−12.5	30.9	B, T	9.5	16.7	B, T
	Body-Fixed Frame	−18.5	30.8	−17.6	32.2	W, T	0.9	19.0	W, T
	Trajectory-Fixed Frame	−25.7	32.4	−4.4	28.9	W, B	21.0	17.3	W, B
		Inner Limb		Outer Limb			Asymmetry (Outer Limb - Inner Limb)
ML Margin of Stability	Reference Frame	Mean (mm)	SD (mm)	Mean (mm)	SD (mm)	Pair-wise Contrasts	Mean	SD	Pair-wise Contrasts
	Walkway-Fixed Frame	10.8	18.5	134.7	26.7	B, T	122.7	32.1	T
	Body-Fixed Frame	4.2	22.9	130.5	26.3	W, T	125.0	37.3	T
	Trajectory-Fixed Frame	19.2	17.5	139.6	29.6	W, B	119.2	31.9	W, B

Table 2:

Coefficients and results from the linear mixed models for step length, step width, AP MoS, and ML MoS measured at contralateral toe-off. Fixed effects included reference frame, stepping limb, walking direction, and the reference frame*stepping limb interaction. The walkway-fixed reference frame and inside stepping limb were the reference condition for each model. Each gait measure differed both by reference frame and stepping limb. The interaction of reference frame*stepping limb on step length and AP MoS was significant across all reference frames. However, the interaction of reference frame*stepping limb did not alter interpretations of step width when comparing the walkway-fixed frame to the trajectory-fixed frame, nor did it alter interpretations of ML MoS when comparing the walkway-fixed frame to the body-fixed frame.

	Name (dF = 4838)	Estimate (mm)	SE (mm)	pValue	95% CI (mm)
Step Length	Intercept (Walkway-fixed Frame, Inside Step, CW)	614.2	11.2	< 0.001	[592.1, 636.2]
	Body-fixed Frame	14.6	1.6	< 0.001	[11.5, 17.7]
	Trajectory-fixed Frame	−29.2	1.6	< 0.001	[−32.2, −26.1]
	Stepping Limb (Outside Limb)	21.8	1.6	< 0.001	[18.7, 24.9]
	Walking Direction (CCW)	−1.2	0.9	0.177	[−3.0, 0.6]
	Body-fixed Frame*Stepping Limb	−26.0	2.2	< 0.001	[−30.4, −21.7]
	Trajectory-fixed Frame*Stepping Limb	35.9	2.2	< 0.001	[31.5, 40.2]
	Name (dF = 4838)	Estimate (mm)	SE (mm)	pValue	95% CI (mm)
Step Width	Intercept (Walkway-fixed Frame, Inside Step, CW)	238.4	6.4	< 0.001	[225.8, 250.9]
	Body-fixed Frame	−49.2	2.7	< 0.001	[−54.6, −43.8]
	Trajectory-fixed Frame	66.2	2.7	< 0.001	[60.8, 71.6]
	Stepping Limb (Outside Limb)	−327.1	2.7	< 0.001	[−332.5, −321.7]
	Walking Direction (CCW)	−8.5	1.6	< 0.001	[−11.7, −5.4]
	Body-fixed Frame*Stepping Limb	−0.5	3.9	0.907	[−8.1, 7.2]
	Trajectory-fixed Frame*Stepping Limb	−0.2	3.9	0.951	[−7.9, 7.4]
	Name (dF = 4838)	Estimate (mm)	SE (mm)	pValue	95% CI (mm)
AP Margin of Stability	Intercept (Walkway-fixed Frame, Inside Step, CW)	−19.6	8.4	0.019	[−36.1, −3.2]
	Body-fixed Frame	3.7	0.9	< 0.001	[1.8, 5.5]
	Trajectory-fixed Frame	−3.5	0.9	< 0.001	[−5.4, −1.7]
	Stepping Limb (Outside Limb)	9.5	0.9	< 0.001	[7.7, 11.4]
	Walking Direction (CCW)	−2.8	0.5	< 0.001	[−3.8, −1.7]
	Body-fixed Frame*Stepping Limb	−8.7	1.3	< 0.001	[−11.4, −6.1]
	Trajectory-fixed Frame*Stepping Limb	11.7	1.3	< 0.001	[9.1, 14.3]
	Name (dF = 4838)	Estimate (mm)	SE (mm)	pValue	95% CI (mm)
ML Margin of Stability	Intercept (Walkway-fixed Frame, Inside Step, CW)	10.7	3.6	0.003	[3.8, 17.7]
	Body-fixed Frame	−6.5	1.1	< 0.001	[−8.7, −4.4]
	Trajectory-fixed Frame	8.4	1.1	< 0.001	[6.3, 10.5]
	Stepping Limb (Outside Limb)	124.0	1.1	< 0.001	[121.9, 126.1]
	Walking Direction (CCW)	−0.6	0.6	0.347	[−1.8, 0.6]
	Body-fixed Frame*Stepping Limb	2.3	1.5	0.136	[−0.7, 5.3]
	Trajectory-fixed Frame*Stepping Limb	−3.5	1.5	0.020	[−6.5, −0.6]

4. DISCUSSION

This study investigated how the choice of reference frame influences spatial measures of gait and impacts conclusions about important effects of interest (e.g., asymmetry) during turning gait. Our results indicate that different locally-based reference frames change the resulting step length, step width, AP MoS, and ML MoS. Specifically, the body-fixed frame and the trajectory-fixed frame yielded opposing results when compared to the walkway-fixed frame for all four outcome measures.

Different reference frames yielded different interpretations of asymmetry for step length and AP MoS across all three reference frames. For example, the difference in step length between inside and outside limbs was greater when using a trajectory-fixed frame compared to a walkway-fixed frame. However, the interpretation about inside vs. outside steps was not different for ML MoS in the body-fixed frame compared to the walkway-fixed frame, or for step width across any of the reference frames. While different reference frames will not universally impact every gait measure, our results indicate that any difference in reference frame will influence the interpretation of at least one outcome. Therefore, measures of turning gait should be interpreted with respect to the locally-defined reference frame. While the walkway-fixed, trajectory-fixed, and body-fixed frames can all be appropriate choices based on the aim of a study, it is imperative that future studies investigating turning gait detail and justify their choice of reference frame.

The definition of the walkway-fixed frame is the most similar to the globally-defined reference frame that is commonly used to study linear gait (Wu and Cavanagh, 1995). The walkway-fixed frame also consistently yielded results that were in-between the body-fixed and trajectory-fixed frames, indicating a desirable middle-ground for future studies on turning. This reference frame will likely be an intuitive choice for studies that employ a prescribed walking path [Figure 3]. However, not all turns are attached to a specific walkway, nor are they always performed about a consistent radius (Glaister et al., 2007a; Hase and Stein, 1999).

Figure 3:

Decision tree for determining which reference frame is appropriate for a given study.

The trajectory-fixed frame shares some similarity to the standard globally-defined frame used in linear gait; the trajectory-fixed frame is aligned with the instantaneous direction of travel, rather than the general direction of travel (Wu and Cavanagh, 1995). While similar, the instantaneous and general directions of travel differ to varying degrees throughout the step cycle as the CoM oscillates in the ML direction (Tesio et al., 2010). As a result, the trajectory-fixed frame oscillates between each side of the walkway-fixed frame, which makes results from this frame more dependent on the phase of the gait cycle at which they are extracted. The misalignment of these two reference frames due to the oscillatory motion of the CoM also has important implications on any analysis of the motion of the CoM during gait, particularly regarding ML motion. For example, the trajectory-fixed frame is inappropriate for studies examining ML velocity of the CoM; since the trajectory-fixed frame defines the AP direction as the CoM velocity vector, the ML velocity of the CoM will always be zero and a direction of instability defined perpendicular to the instantaneous velocity will be oblique to the anatomical AP and ML axes.

The body-fixed frame may yield more anatomically relevant results [Figure 3] because it is aligned with the orientation of the pelvis. A body-fixed frame may be more helpful when investigating muscle activation or joint range of motion, particularly surrounding the hip joints. However, the body-fixed frame removes a degree of freedom – axial rotation of the hip (i.e., yaw/heading angle of the pelvis) in the body-fixed transverse plane is zero at all points in time.

While we focused our analysis on MoS at contralateral toe-off, previous studies have reported MoS at different gait events (e.g., ipsilateral heel contact). Our conclusions - that changing reference frame will alter outcomes and interpretations about turning – extend to calculations at different temporal events (See Supplemental Material). As an ancillary analysis, we calculated each outcome measures at ipsilateral heel contact using reference frames defined at that instant in time. Similar to the primary analysis, reference frame still had significant effects on all outcomes and conclusions about asymmetry (See Supplemental Material), but the largest effects of reference frame switch limbs (inner to outer limb) when contrasting the results between toe-off and heel contact definitions.

An important consideration for future studies of turning gait is the definition of the BoS when calculating the MoS. Across a turn, individuals reorient their feet to face the new direction of travel (Bernardin et al., 2012), which can change the most anterior and lateral points on the BoS with respect to the xCoM. Consequently, an anatomically-fixed point may not consistently represent the lateral-most boundary of the BoS across all turning steps. While our study found that the anterior-most and lateral-most boundaries were consistent during every step, larger and/or more variable turn angles with greater internal or external rotation of the foot may find different results. We recommend calculating the boundary of the BoS for each step, rather than using a single anatomically-fixed point, when calculating MoS during turning.

The primary limitation is that this study only assessed the gait of healthy young adults. It is possible that the alignment or misalignment of reference frames varies depending on different pathological gaits. However, our conclusions – that reference frames can affect results and should be explicitly defined and justified – are likely relevant to both healthy and pathological populations. Additionally, participants walked at a self-selected speed that may have altered the magnitude of the centripetal force experienced by each participant throughout the trials. It is possible that faster or slower speeds may vary the degree to which reference frames alter gait outcomes. Similarly, each trial featured the same walkway with a single consistent radius. We expect the choice of reference frame would have a greater impact on gait measures at sharper turn angles with smaller radii. Finally, this study used a reduced marker set to estimate CoM dynamics. Future studies should investigate further with whole-body CoM measurement.