Timing is everything: the effect of measurement timing on trailing limb angle in gait analysis

1 Introduction

Forward movement of the body, known as propulsion, is essential for normal human locomotion and walking speed, enabling efficient movement from point A to point B. When propulsion is impaired, it can significantly reduce walking speed and energy efficiency (1). To understand how propulsion contributes to forward motion, the dynamic model of walking highlights the balance of positive and negative work performed on the body's center of mass (COM) by the leading and trailing limbs (2). During double limb support, the trailing limb generates propulsive forces (positive work) while the leading limb manages the collision forces of weight acceptance (negative work) (3). By overcoming the negative work of the leading limb, the trailing limb ensures smooth and efficient forward progression.

In gait analysis, propulsive forces are often quantified using the anterior component of the ground reaction force (AGRF) (4), which reflects the body's ability to generate sufficient muscular force, range of motion, and positioning to achieve propulsion during walking. Previous studies have shown that AGRF parameters are associated with gait speed (5), severity of hemiparesis (6), and plantar flexor muscle activity (7). Both the impulse and peak magnitude of the AGRF has been used to assess the effectiveness of gait training protocols after stroke as a biofeedback parameter (8–9).

Because most patients with propulsion deficits will be treated outside the research setting, trailing limb angle (10, 11) could be a more accessible point-of-care estimate of propulsion (1). TLA is defined as the angle between the vertical axis of a laboratory and the vector connecting the greater trochanter to the fifth metatarsal head (12). It is a valid estimate of propulsive forces (13), can be measured using a simple set of inertial measurement units (14), is an independent predictor of walking speed (15), and has been effectively used as a biofeedback metric during gait rehabilitation protocols (8). These characteristics make it a viable measure of propulsion as part of a suite of outcomes related to gait function; however, approaches to TLA measurement vary across the literature, particularly in relation to the time at which it is calculated (8, 11, 12, 14–16).

Differences in the timing of TLA calculations in each of these studies (e.g., pre-swing, toe-off, double support, terminal stance) may reflect broad assumptions about the timing of peak propulsion that are not yet supported by the evidence. There is evidence to support the theory that peak propulsion occurs just before contralateral heel strike (HS) (17). The energy cost of human walking decreases when propulsion of the trailing limb occurs just before contralateral HS and increases if it occurs after contralateral HS (17). Generating propulsion at the appropriate time relative to contralateral HS plays a critical role in coordinating the step-to-step transition, and deviations from optimal timing may reflect underlying deficits in motor control quality. Supporting this notion is a study by Malcom et al. which reported optimum energy efficiency when a pneumatic exoskeleton provided propulsive forces prior to contralateral HS rather than after (18). In contrast, a more recent study found that peak AGRF occurred after contralateral HS in young, unimpaired adults, even at varying walking speeds (19).

With conflicting evidence on the timing of peak propulsion and the variability in the timing of TLA calculation methods, it is essential to investigate when propulsion occurs relative to key gait events, such as peak propulsion, contralateral HS, and ipsilateral toe-off (TO). Prior studies characterizing TLA in unimpaired adults have predominantly recruited young adults with mean ages in their mid-twenties (8, 12, 19), limiting the generalizability of their findings to middle-aged populations. The first objective of this study was to describe the timing of peak propulsion in middle-aged, unimpaired adults relative to contralateral HS and ipsilateral TO. The second objective of this study was to determine whether peak TLA occurs at the time of peak AGRF and whether different approaches to TLA calculations result in statistically significant different measurements. Clarifying the timing of peak propulsion and refining TLA measurement methods could enhance gait rehabilitation strategies and improve clinical assessments.

2 Methods

A power analysis for this study was completed a priori to determine sample size based on a previous study (11). The minimal detectable change (MDC) of AGRF reported was 2.8% body weight and a standard deviation of 4.4% (11). For the current study, the effect size for change in AGRF was set at 0.60 and was calculated using G*Power (Version 3.1.9.4). With the significance criterion of alpha = 0.05 and power = 0.80, the minimum sample size required for this study was 19.

2.1 Participants

This study was approved by the University of Houston Institutional Review Board in accordance with the Declaration of Helsinki. Adults between 50 and 65 years of age, who were independent community ambulators and able to consent were recruited to participate in the study. Individuals were excluded if any of the following conditions were present: chronic ankle instability, history of recent (<6 months) ankle sprain, history of orthopedic ankle surgery, chronic foot, ankle, or leg pain, pregnancy, neuropathy, arthritis (osteoarthritis, rheumatoid arthritis, lupus, psoriatic arthritis), inflammation disorders (ankylosing spondylitis, gout), type I or type II diabetes, peripheral vascular disease, stroke, traumatic brain injury, multiple sclerosis, Huntington's disease, post-polio syndrome, Alzheimer's disease or other dementia diagnoses, myasthenia gravis, muscular dystrophy, limb amputation, open ulcer on the lower extremity, Charcot-Marie-Tooth disorder or other hereditary neuropathies, or if the subject requires an assistive device for ambulation. Participants were recruited from the greater Houston area and provided with written informed consent.

2.2 Procedures

The data collection session consisted of anthropometric measurements, determination of self-selected walking speed (SSWS) via the 10-meter walk test (10MWT) (20), and three-dimensional (3D) gait analysis. Gait analysis was conducted after a familiarization trial on a split-belt Bertec (Columbus, OH, USA) instrumented treadmill. Participants ambulated using a harness and the treadmill speed was adjusted above or below overground SSWS to accommodate subject comfort prior to data collection trials. A handrail was present during data collection; however, participants were instructed to walk without using the handrail. During data collection, a 16-camera Vicon (Oxford, ENG, UK) motion capture system was used to collect 3D positions of reflective markers of the right and left lower extremities while participants walked at their SSWS for a single three-minute trial. Data collected for analysis was captured from the second minute of the full trial. Ankle, knee, and hip kinematics were collected bilaterally using the Vicon Plug-in Gait Model with the Oxford Foot Model extension. As the Plug-in Gait Model does not include a marker over the greater trochanter (GT), one additional marker captured the proximal landmark used for TLA calculations.

2.3 Data processing

Data processing was conducted using custom MATLAB (R2023b, Mathworks Inc., Natick, MA, USA) code. Marker data was captured at 100 Hz and GRF data was captured at 2,000 Hz. All data were time normalized to 100% of the gait cycle (both stance and swing phases) using interpolation. Marker trajectories were smoothed using a Woltring filter in Vicon Nexus software. GRF data was filtered at 10 Hz using a second order Butterworth filter (21). Contralateral heel strike (HS%) and ipsilateral toe-off (TO%) events were identified using a GRF threshold of 30 N (21). All complete gait cycles for the left and right legs within the 1-minute walking trial were included in the analysis.

2.4 Dependent variables

Complete definitions of all dependent variables can be found in Table 1. Peak propulsion was defined as the peak amplitude of the AGRF expressed as a percentage of body weight (AGRF_Peak) for the right and left lower extremities of each participant. TLA was calculated using the two most used definitions: (1) TLA_5M = the angle between the vertical axis of the laboratory and a vector connecting the greater trochanter (GT) and the 5th metatarsal head (5M), and (2) TLA_LM = the angle between the vertical axis of the laboratory and a vector connecting the GT to the lateral malleolus. Peak amplitude was calculated for AGRF and each TLA measurement technique (AGRF_Peak, TLA_5MPeak, and TLA_LMPeak).

Table 1. Variable labels and definitions.

The timing of the peak value of each variable was expressed as a percentage of the gait cycle (AGRF_Peak%, TLA_5MPeak%, and TLA_LMPeak%). In addition, each TLA measurement was calculated at the time of AGRF_Peak (TLA_5MAGRFPeak%, TLA_LMAGRFPeak%).

2.5 Statistical analysis

SPSS version 29.0 (SPSS IBM, New York, NY, US) was used to conduct statistical analyses. Means and standard deviations (SD) for all dependent variables were calculated for the left and right legs separately for each participant. Prior to pooling the data, the data were assessed for outliers for the left and right legs separately using boxplots and Q-Q plots. The following number of outliers were removed from the data set for the right leg: AGRF_Peak (1), AGRF_Peak% (1), HS% (1), TO% (1), TLA_LMPeak (1), TLA_LMAGRFPeak% (2). No outliers were identified for the left leg. Normality of data after outlier removal for each variable was confirmed via a Shapiro–Wilk test (P > 0.05). A paired t-test was calculated for each variable to determine if there were significant differences between the left and right legs. Significant differences were found between the left and right legs for HS% (P = 0.037), TLA_5MPeak (P = 0.033), TLA_5MPeakAGRF% (P = 0.031). For comparisons that included any of these three variables, an analysis of variance (ANOVA) was calculated with Side (left or right) as a factor with significance level set at P < 0.05. For comparisons that utilized the remaining variables without a significant difference between the left and right sides, data from both limbs were pooled prior to analysis. To describe the position of the ankle, knee, and hip joints of the leading and trailing limbs at the time of peak propulsion, means and SD of joint kinematics were calculated at AGRF_Peak% and across the entire gait cycle. Effect sizes were calculated using Cohen's d for paired t-tests and partial eta-squared (ηp2) for ANOVA models, with conventional thresholds applied (Cohen's d: small = 0.2, medium = 0.5, large = 0.8; ηp2: small = 0.01, medium = 0.06, large = 0.14).

3 Results

A total of 19 (11 female, 8 male) middle aged unimpaired adults participated in the study. Most study participants were White (n = 13) with the remaining participants reporting Asian (n = 4) or Hispanic (n = 2) ethnicities. Descriptive statistics of clinical assessment variables are summarized in Table 2.

Table 2. Participant clinical assessment variables.

SSWS, self-selected walking speed; SSTS, self-selected treadmill speed; SSTS-SSWS, difference between overground SSWS and SSTS; A1C, hemoglobin A1C test.

Each variable of interest occurred at statistically significantly different times throughout the gait cycle (Tables 3, 4) (Figure 1). There were also statistically significant differences in TLA amplitudes across varying measurement and timing approaches (Tables 3, 4) (Figure 1). There was a significant difference in timing among AGRF_Peak% and HS% [F_(1,32) = 296.260, P < 0.001] with a significant effect of side (F_(1,32) = 5.939, P = 0.021). For all other ANOVA tests, there was no effect of Side. Joint kinematics of both the trailing and leading limb are presented in Figure 2.

Table 3. Results of ANOVA.

Mean difference = first variable—second variable.

A significant effect of side was found, see text for full results.

Table 4. Results of paired t-tests.

Mean difference = first variable—second variable.

On average, at AGRF_Peak%, the trailing limb ankle was dorsiflexed (12.07°, ±6.0), the knee was flexed (11.68°, ±4.84), and the hip was extended (−10.24°, ±6.26). At the same time, the leading limb ankle was slightly dorsiflexed (1.81°, ±5.48), the knee was slightly flexed (7.14°, ±3.75), and the hip was flexed (22.18°, ±6.56).

4 Discussion

The results of this study showed that peak propulsion occurs just before contralateral HS in a sample of middle-aged unimpaired adults walking at a self-selected speed on a split-belt treadmill. Although the peak value of TLA is often utilized as a measure of peak propulsion (AGRF_Peak), the current study revealed that peak TLA occurs at a statistically significantly later time in the gait cycle than AGRF_Peak. The time at which TLA was measured had a significant effect on the resultant angle, regardless of whether the fifth metatarsal head or lateral malleolus was used as the distal landmark of the TLA.

4.1 Challenging assumptions around TLA and peak propulsion

Perhaps because previous studies identified TLA as an alternative measure of AGRF_Peak, there is an assumption that it is the peak value of TLA that represents peak propulsion. A recent state-of-the-art review of 39 studies utilizing TLA as a measure of propulsion found that 70% of the studies provided some timing indicator of measurement, but with substantial variation: toe-off, double support, terminal stance, pre-swing, or peak AGRF (16). The review identified a critical distinction, that none of the 12 studies measuring TLA at “peak TLA” reported measuring it at the time of peak AGRF, yet studies measuring TLA at peak AGRF avoided using the term “peak TLA”. The current study findings validate this important distinction, demonstrating that peak TLA occurs 10.38% later in the gait cycle than TLA measured at peak AGRF.

In the current study, TLA_5M at the time of AGRF_Peak was on average 16.09° (±1.77°), while the peak value of TLA_5M was on average 22.77° (±3.03°), a statistically significant difference. When measured using the lateral malleolus as the distal landmark for TLA, the difference was smaller, but still statistically significant at 4.20°. Additionally, the timing of peak values varied considerably; TLA_5M peaked 10.38% later than AGRF_Peak, and TLA_LM peaked 8.61% later. Incorrect timing during instrumented or video gait analysis could lead to a consistent overestimation of TLA, potentially resulting in false negatives. A patient’s propulsive capacity may appear adequate when measured at peak TLA but is actually impaired when measured at the clinical relevant time point of peak propulsion. Our results demonstrate the magnitude of this error: when TLA is measured at peak value rather than at peak AGRF, values are overestimated by an average of 6.69° (using the 5th metatarsal head landmark) or 4.20° (using the lateral malleolus landmark). This misclassification can delay or prevent diagnosis of true propulsive deficits and can obscure whether a gait impairment reflects genuine motor control deficiency or merely compensatory limb positioning. While peak TLA may be adequate for tracking relative progress within a single patient, precision remains critical for establishing normative data, comparing outcomes across facilities, and identifying whether propulsive deficits represent true motor control impairment or a measurement error due to inconsistent timing protocols. Additionally, the proportional relationship between peak TLA and TLA at peak AGRF may be fundamentally altered in individuals with movement disorders, potentially masking clinically meaningful changes in propulsive mechanics if peak TLA is used as a surrogate without verification in impaired populations.

Several studies in this area of research state in their methods sections that TLA was measured at the time of peak AGRF (9, 12, 13, 22–27). However, others reference a specific phase of gait such as toe-off (10, 11, 28–31), double support (15, 32), terminal stance (8, 33); and pre-swing (14). To clarify whether these approaches would create differences in TLA measurement, the current study described AGRF_Peak relative to ipsilateral TO, and described the kinematics of the hip, knee, and ankle at the time of AGRF_Peak. AGRF_Peak occurred approximately 2.49% before contralateral HS, and 9.88% before ipsilateral TO, suggesting that peak propulsion does not occur during the period of double support in middle-aged unimpaired adults. The peak value of TLA_5M and TLA_LM indeed peak very close to ipsilateral TO, with timing differences of only.50% and 1.27%, respectively. Pre-swing is often used interchangeably with TO, and the results show that if TLA is measured at either time, it is capturing the peak value of TLA, rather than TLA at the time of AGRF_Peak, as originally intended.

Diagrams of the lower limb joint positions in previous studies using TLA are also varied. Some images depict joint positions that are reflective of the double limb support period (10, 14, 24), while others reflect single limb support (23, 32, 34). Our analysis of the trailing and leading limb kinematics in this study lends further insight as to what is functionally happening at the time of peak propulsion in middle-aged unimpaired adults. The results demonstrated that at the time of AGRF_Peak, the trailing ankle is in a dorsiflexed position, the knee is slightly flexed, and the hip is near a position of maximum extension in the gait cycle. The leading limb ankle is approaching a neutral position for HS, the knee is slightly flexed, and the hip is in a flexed position. These joint positions are reflective of the diagrams that represent the terminal stance phase of gait that occurs during single limb support, just before contralateral HS. In clinical settings where force plates are typically unavailable, clinicians often resort to less rigorous methods like 2D video gait analysis to assess basic temporospatial parameters (35). Future studies should examine the feasibility of the use of wearable sensors to capture the timing of contralateral HS and leading limb joint kinematics as more clinically accessible indicators of peak propulsion.

4.2 Gait event detection and peak propulsion considerations

In the current study, the average timing of contralateral HS occurred at approximately 49.99% of the gait cycle while AGRF_Peak occurred at approximately 47.50% of the gait cycle. These results are in alignment with the dynamic model of walking that suggests that when push-off occurs before contralateral HS, the energy cost of walking is optimized (2). However, Kuhman et al. found that in a sample of young, unimpaired adults, all measures of propulsion (measured by AGRF_Peak, peak limb propulsive power, and peak ankle plantar flexion power) occurred after contralateral HS, regardless of walking speed (19). A potential explanation for the conflicting findings is related to data processing decisions, such as HS and TO event identification techniques. In the current study, vertical GRF thresholds (30 N) to identify HS and TO events were chosen in accordance with the study conducted by Revi et al., which validated the use of a minimal set of wearable sensors to provide indirect measurement of the AGRF in both healthy and impaired participants (21). While acceptable HS identification thresholds range from 10 N (36), 20 N (37), to 30 N (21), the choice of the threshold for basic gait events, and decreases in walking speed will impact the timing AGRF_Peak, and our results should be considered in light of this knowledge. A lower HS threshold (e.g., 10 N) would detect HS earlier, potentially shifting the timing relationships reported in this study. Additionally, individuals with slower walking speed, such as those with stroke, could delay AGRF_Peak. Therefore, future studies should examine whether the specific timing percentages reported in this study are consistent across unimpaired and impaired populations, and whether these methodological choices systematically change clinical interpretations.

4.3 Limitations

Participants in this study had a statistically significantly slower treadmill SSWS (1.2 m/s) than their overground SSWS (1.3 m/s). Although the difference in walking speeds may not be clinically significant, the slower treadmill walking speed suggests that walking on a split belt treadmill in a motion analysis lab could be a challenging task for middle-aged unimpaired adults. It is unknown whether the timing of HS and AGRF_Peak would be maintained during overground walking (38). Although self-reported physical activity levels were not measured, 14 of the 19 participants in this study were recruited from a local running club in Houston, Texas. As a result, this sample is not likely representative of the activity levels and overall health of the average adult between 55 and 70 years old, and the results may not be generalizable to middle-aged adults typically at risk of stroke. Notably, some participants showed greater discrepancies between overground SSWS and treadmill SSWS and may be individuals with lower baseline activity levels or general treadmill familiarity. The relatively fast mean SSWS observed in this sample (1.30 m/s) likely reflects the high physical activity levels of many of the participants. As walking speed modulates both TLA magnitude and propulsive force generation (12), the timing relationships described here should be replicated in samples walking at slower speeds. We did, however, capture metabolic health indicators such as waist-to-hip ratio and glycated hemoglobin (A_1c) levels for future analysis. Significant left-right differences were observed in this study despite participants being unimpaired. These asymmetries likely reflect natural biomechanical variation related to limb dominance or the unfamiliar task of split-belt treadmill walking.

5 Conclusion

The findings of this study underscore the critical importance of precise measurement and interpretation of TLA for assessing peak propulsion in gait analysis. This study provides important clarification that whether in the laboratory setting or the clinical setting, the maximum value of TLA is not methodologically equivalent to TLA measurements must be taken at the time of AGRF_Peak, which occurs just before contralateral HS in middle-aged unimpaired adults. Our findings provide concrete evidence supporting recommendations for standardized TLA reporting in future research and clinical practice.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

Publisher's note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Footnotes

Edited by: Abu Jor, Khulna University of Engineering & Technology, Bangladesh

Reviewed by: Yusuke Sekiguchi, Tohoku University Hospital, Japan

Julia Greenfield, Université Polytechnique Hauts-de-France, France