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Article

Classifying Post-Stroke Gait Propulsion Impairment Beyond Walking Speed: A Clinically Feasible Approach Using the Functional Gait Assessment

by
Jeffrey Paskewitz
1,2,†,
Jie Fei
1,†,
Ruoxi Wang
1 and
Louis N. Awad
1,*
1
Department of Physical Therapy, Sargent College of Health and Rehabilitation Sciences, Boston University, Boston, MA 02215, USA
2
Department of Physical Therapy, Arcadia University, Glenside, PA 19038, USA
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Appl. Sci. 2026, 16(1), 134; https://doi.org/10.3390/app16010134
Submission received: 6 November 2025 / Revised: 17 December 2025 / Accepted: 17 December 2025 / Published: 22 December 2025
(This article belongs to the Special Issue Current Advances in Rehabilitation Technology)
Browse Figures
Versions Notes

Abstract

Post-stroke gait dysfunction is biomechanically heterogeneous, yet biomechanically informed classifications of functional walking remain underdeveloped. In particular, there is a lack of clinically accessible methods for classifying gait deficits that account for propulsion impairments—a historically laboratory-dependent gait parameter requiring measurement with force plate systems. This study examined whether propulsion impairment can be classified by combining a global measure of walking function (i.e., the 10 m walk test speed) with specific measures of dynamic walking ability derived from the Functional Gait Assessment (FGA). Forty participants >6 months post-stroke completed biomechanical evaluations quantifying propulsion during walking and clinical assessments including the FGA. Multivariable stepwise regression identified the FGA items most strongly associated with paretic propulsion. Models augmented with these FGA items explained 15% greater variance in the paretic propulsion peak and 7% greater variance in paretic propulsion impulse compared with models using Comfortable Walking Speed (CWS) alone. Incorporating FGA items also yielded the highest overall accuracy (72.5% vs. 60% with CWS alone) and best per-class performance in propulsion severity classification. These findings establish the co-assessment of walking speed and targeted FGA items as a clinically feasible approach to biomechanically informed classification of post-stroke gait dysfunction.

1. Introduction

Stroke affects more than 795,000 individuals annually in the United States [1] and remains one of the leading causes of long-term disability worldwide. The direct and indirect costs of stroke amount to an estimated USD 56 billion per year in the United States alone [1]. Mobility is reduced in more than half of survivors aged 65 and older [2]. Given its strong association with independence and quality of life, recovery of walking function is a central goal of rehabilitation [3,4,5,6]. However, although rehabilitation interventions can improve walking after stroke, outcomes remain highly variable, with many remaining substantially and functionally limited after completing formal rehabilitation [7,8,9,10,11,12,13].
A major contributor to this variability is the heterogeneity of post-stroke gait impairment. The most common gait classification approach used is based on baseline deficits in walking speed, where cutoffs of 0.80 m/s [14] and 0.93 m/s [15] have been proposed to differentiate limited and unlimited community ambulators. Although this approach is valuable, it overlooks the distinct biomechanical strategies individuals use to achieve a given speed [14]. Indeed, any two individuals post-stroke who walk at similar speeds may rely on profoundly different locomotor patterns to compensate for distinct biomechanical deficits. Prior work suggests that predictions of an intervention’s therapeutic effects improve substantially when both walking speed and gait biomechanics are considered [16]. This underscores the need for individualized biomechanically informed classification of post-stroke gait dysfunction, with emphasis on approaches that can be implemented clinically.
Propulsion is a key biomechanical subtask that enables stable and efficient forward progression during gait [17,18,19,20,21]. Propulsion arises from the interaction of kinematic and kinetic factors that are difficult to measure in clinical settings, historically requiring laboratory-based motion capture and force plate systems. Although experienced clinicians can grossly estimate propulsion deficits based on walking speed and observable (i.e., kinematic and spatiotemporal) gait deviations [22,23], observational gait analysis has considerable limitations [24,25,26]. While very large propulsion deficits may be visually apparent, clinically accessible methods for classifying walking deficits based on subtle yet meaningful deficits in gait propulsion are lacking [16,27,28]. Such methods are essential for guiding intervention selection and detecting treatment-related biomechanical changes [16,28].
The Functional Gait Assessment (FGA) is a reliable and valid measure of dynamic walking function that evaluates ten ambulatory tasks, each scored from 0 (severe impairment) to 3 (no impairment) [3,29,30,31,32,33]. Like walking speed, the FGA is feasible to administer in routine clinical practice and provides insight into gait quality, suggesting potential value in characterizing biomechanical impairments [30]. The purpose of this study was to examine the extent to which co-assessment of walking speed and the FGA can characterize propulsion impairment after stroke. We hypothesized that walking speed and specific FGA items together would improve the classification of propulsion impairment beyond walking speed alone, supporting the development of a clinically feasible, biomechanically informed framework for walking assessment.

2. Materials and Methods

2.1. Recruitment

Forty individuals were recruited from a registry of individuals who had previously sustained a stroke and expressed interest in participating in research studies. The inclusion criteria were as follows: age 18 years or older, prior history of stroke, medically stable, ability to walk without another individual supporting the person’s body weight for at least two minutes (assistive devices such as a cane were allowed), ability to communicate with investigators and follow instructions, and medical clearance provided by a physician. The exclusion criteria were as follows: inability to communicate, a score > 1 on question 1b and >0 on question 1c of the NIH Stroke Scale, pain that impaired walking ability, presence of neglect and hemianopia, unexplained dizziness in the last six months, serious comorbidities that may interfere with participation (musculoskeletal, cardiovascular, pulmonary, and neurological), and history of more than two falls in the previous month. All study procedures were approved by the Boston University Institutional Review Board. Written informed consent was obtained from all participants.

2.2. Experimental Settings

All data collection took place in an indoor university research laboratory (see Figure 1). During the study visit, each participant completed the FGA, three trials of the time-scored 10 m walk test (10MWT) at a comfortable speed, and one trial of the 6 min walk test (6MWT) [34]. The FGA and Fugl-Meyer Assessment for the Lower-Extremity (FMA-LE) [35,36] were administered and scored by licensed physical therapists. For the 10MWT, participants walked along a 10 m straight section of a 26.6 m oval indoor track, and the time required to complete was measured using a digital stopwatch [37]. For the 6MWT, participants walked around the entire track while ground reaction forces (GRFs) were captured each time they passed the straight section containing six floor-embedded force plates (Bertec Corp., Columbus, OH, USA). GRF data for both legs were collected at a sampling rate of 2000 Hz [38]. The use of assistive devices was allowed during all assessments, if needed.

2.3. Data Processing

Raw GRF data collected during the 6MWT were exported from Qualisys Track Manager Version 2024.3 (Qualisys AB, Göteborg, Sweden) and processed using MATLAB Version R2024a (MathWorks Inc., Natick, MA, USA). A second-order low-pass Butterworth filter with a cutoff frequency of 10 Hz was applied to filter the raw GRF data. Gait events of heel strike and toe-off were identified based on a force threshold of 5% body weight (BW). GRF data were then segmented from heel strike to toe-off to represent the stance phase of walking [39]. Any segmented GRF data identified as abnormal due to crossover strides on the force plates were excluded. Anteriorly directed GRF for both legs was extracted to compute three gait propulsion point metrics, including the paretic propulsion peak, paretic propulsion impulse, and propulsion impulse symmetry [40]. The paretic propulsion peak was calculated as the maximum anteriorly directed GRF normalized by body weight, reported in the unit of %BW, while the paretic propulsion impulse was calculated as the integral of the anteriorly directed GRF normalized by body weight [39]. Propulsion impulse symmetry was determined using Equation (1):
P r o p u l s i o n   I m p u l s e   S y m m e t r y = | P a r e t i c   P r o p u l s i o n   I m p u l s e P a r e t i c   P r o p u l s i o n   I m p u l s e + N o n   P a r e t i c   P r o p u l s i o n   I m p u l s e − 0.5 |
Data points were identified as outliers and excluded if they exceeded three standard deviations from the mean [41]. The remaining point metrics data were then averaged for analysis. Higher paretic propulsion peak and impulse and lower propulsion impulse symmetry indicate less severe gait impairment [14,16]. The CWS was calculated as the average gait speed across three 10MWT trials. The gait speed for each trial was calculated by dividing the distance of steady-state walking (6 m, excluding the 2 m acceleration and 2 m deceleration phases) by the time taken to complete the distance.

2.4. Data Analysis

All data analyses and figure generation were performed in MATLAB Version R2024a (MathWorks Inc., Natick, MA, USA). Pearson correlations were calculated to examine associations between propulsion point metrics and both the FGA total score (FGA Total) and CWS [42,43]. Univariable linear regression models were first constructed with CWS as the sole predictor for each of the three propulsion metrics: paretic propulsion peak, paretic propulsion impulse, and propulsion impulse symmetry [44]. To evaluate whether the inclusion of FGA statistically improved model performance, two multivariable regression models were developed to estimate the same propulsion point metrics using (1) CWS and the FGA Total and (2) CWS in combination with individual FGA items selected via stepwise regression based on the Bayesian Information Criterion (BIC) [45,46].
Two pairs of nested models were compared using F-tests: the univariable model (CWS-only) versus the multivariable model 1 (CWS + FGA Total) and the univariable model versus the multivariable model 2 (CWS + stepwise-selected FGA items). Variance inflation factors (VIFs) [47,48] were calculated to assess multicollinearity among predictors, with variables exceeding a VIF of 5 removed. Model performance was evaluated using R-squared (R2), adjusted R-squared (adj R2) [46], Root Mean Square Error (RMSE), and model-level p-values. Regression coefficients and corresponding p-values were reported for all retained predictors. F-statistics, degrees of freedom, and p-values from the F-tests were reported for nested model comparisons. Model generalizability was assessed using 10-fold cross-validation (CV) [49,50], with cross-validated R2 and RMSE reported.
To further examine whether FGA-augmented models improved the classification of propulsion severity beyond CWS alone, participants were divided into three hemiparetic severity groups (severe, moderate, and mild) based on tertiles of a force plate-derived paretic propulsion peak. Group differences in paretic propulsion peak and impulse were tested using one-way ANOVA, followed by Bonferroni-corrected post hoc comparisons [51]. Predicted paretic propulsion peak values from each of the three regression models were then used to classify participants into severity groups using the same tertile cutoffs. These predicted classifications were compared with force plate-derived ground-truth classifications. Model classification performance was summarized using overall accuracy, confusion matrices, and class-specific sensitivity, specificity, and precision.

3. Results

Eleven female and twenty-nine male participants completed the study. In two participants, due to time constraints, the FGA was performed during a second study visit completed within 7 days of the first study visit. All other participants completed the study according to the described methods. Participant demographics are summarized in Table 1. The mean (±sd) age was 61.52 ± 9.95 years, with a BMI of 28.77 ± 5.79 kg/m2, and stroke chronicity of 7.97 ± 4.18 years. Twenty-two participants presented with left-sided paresis and eighteen with right-sided paresis. The FMA-LE motor function scores were available for 34 participants, with a mean of 22.32 ± 6.16; the mean CWS was 0.85 ± 0.29 m/s, and the mean FGA Total was 16.62 ± 6.09. During FGA, eight participants used an Ankle-Foot Orthosis (AFO) or Assistive Device (AD), twenty-nine ambulated without support, and usage data were unavailable for three participants.
The distribution of propulsion point metrics is illustrated in Figure 2a. The paretic propulsion peak averages 9.37 ± 5.81%BW, ranging from −0.72 to 21.06%BW. The paretic propulsion impulse is 2.46 ± 1.42%BW, with values ranging from 0.01 to 5.19%BW. The propulsion impulse symmetry shows a mean of 0.17 ± 0.15, with values ranging from 0.00 to 0.50. A stacked bar plot showing the frequency of participant scores (0–3) across 10 items of the FGA is shown in Supplementary Figure S1. Several items (e.g., FGA 2, 5, and 10) were predominantly scored 2–3, indicating better performance, whereas items such as FGA 1 and especially 7 and 8 showed a high proportion of scores 0–1, reflecting greater impairment. Figure 2b illustrates moderate positive correlations between CWS and both paretic propulsion peak (r = 0.68, p < 0.001) and paretic propulsion impulse (r = 0.68, p < 0.001) and propulsion impulse symmetry (r = −0.50, p < 0.001) [36]. Figure 2c shows similar patterns for the FGA Total. A strong positive correlation is observed between the FGA Total and the paretic propulsion peak (r = 0.73, p < 0.001), and moderate correlations are observed between FGA Total and both paretic propulsion impulse (r = 0.65, p < 0.001) and propulsion impulse symmetry (r = −0.48, p < 0.01).
Regression analysis of the paretic propulsion peak is summarized in Table 2. Univariable regression using CWS as the sole predictor explains 45% of the variance in the paretic propulsion peak (Adj R2 = 0.45, RMSE = 4.32%BW, p < 0.001), demonstrating a significant positive relationship between CWS and paretic propulsion peak (β = 13.55, p < 0.001). Adding the FGA Total in multivariable model 1 improves the explained variance to 56% (Adj R2 = 0.56, RMSE = 3.87%BW, p < 0.001), with the FGA Total emerging as a significant predictor (β = 0.48, p < 0.01), and significantly improving model performance compared to the CWS-only model (F(1, 37) = 10.38, p < 0.01). Multivariable model 2 using stepwise-selected FGA items (FGA 7 and FGA 10) yields the best model performance, explaining 60% of the variance (Adj R2 = 0.60, RMSE = 3.68%BW, p < 0.001). This model also significantly improves model performance compared to the CWS-only model (F(2, 36) = 8.26, p < 0.01). Both selected FGA items are statistically significant (p < 0.05), along with CWS (β = 8.31, p < 0.01). Cross-validation confirms the improved performance of this model (CV R2 = 0.57, CV RMSE = 3.77%BW).
A regression analysis modeling paretic propulsion impulse is shown in Table 3. The univariable model with CWS alone explains 45% of the variance (Adj R2 = 0.45, RMSE = 1.05%BW, p < 0.001), with CWS being a significant predictor (β = 3.33, p < 0.001). The addition of the FGA Total slightly improves model fit (Adj R2 = 0.49, RMSE = 1.01%BW, p < 0.001), although the FGA Total is not statistically significant (p = 0.071) and the improvement over the CWS-only model is not significant (F(1, 37) = 3.45, p = 0.071). Multivariable model 2, selected via stepwise regression, includes CWS and FGA 10 as predictors, explaining 52% of the variance (Adj R2 = 0.52, RMSE = 0.98%BW, p < 0.001). This model significantly outperforms the CWS-only model (F(1, 37) = 6.66, p < 0.05), with all predictors reaching statistical significance (p < 0.05), and cross-validation supports improved generalizability (CV R2 = 0.50, CV RMSE = 0.99%BW).
In contrast with regression models of the paretic propulsion peak and propulsion impulse, regression models for propulsion impulse symmetry show a weaker predictive performance (see Table 4). The univariable model with CWS explains 20% of the variance (Adj R2 = 0.20, RMSE = 0.14, p = 0.002), with a significant positive association (β = 0.26, p < 0.01). Incorporating the FGA Total does not improve model performance (Adj R2 = 0.20, RMSE = 0.14), and neither predictor reaches statistical significance in the multivariable model. The improvement over the CWS-only model is also not significant (F(1, 37) = 0.91, p = 0.345). Stepwise regression does not select additional FGA items, and the resulting model is identical to the univariable model. The cross-validation results are consistent across models (CV R2 = 0.17, CV RMSE = 0.14–0.15). Notably, FGA 6 is excluded from all stepwise regression analyses due to a high VIF value (VIF = 5.30).
Using cutoff values of 7.02%BW and 10.86%BW, derived from tertiles of a force plate-derived paretic propulsion peak, participants may be divided into three groups: severe (<7.02%BW), moderate (>7.02%BW and <10.86%BW), and mild (>10.86%BW) groups, as shown in Figure 3a. A one-way ANOVA reveals significant differences in the paretic propulsion peak across the three groups (F(2, 37) = 65.60, p < 0.001). Post hoc pairwise comparisons with Bonferroni correction confirm that all group differences are statistically significant (see Supplementary Table S1). Similarly, another one-way ANOVA finds significant differences in paretic propulsion impulse among the same groups (F(2, 37) = 67.90, p < 0.001), with post hoc Bonferroni-corrected pairwise comparisons confirming that all group differences are statistically significant (see Supplementary Figure S2 and Table S2).
The confusion matrices in Figure 3b summarize the classification performance of the three models in predicting the propulsion severity group using the estimated paretic propulsion peak. The model using CWS achieves an overall accuracy of 60.0%. Adding the FGA Total improves accuracy to 70.0%. The model including CWS with two stepwise-selected FGA items (FGA 7 and FGA 10) yields the highest accuracy (72.5%). Detailed per-class classification metrics are shown in Figure 3c. For the severe class, sensitivity is 0.62 in the CWS-only model and 0.69 in both the CWS + FGA Total and CWS + stepwise-selected FGA items models; specificity is 0.85, 0.85, and 0.89 across the three models; and precision increases from 0.67 (CWS-only) to 0.69 and 0.75, respectively. For the moderate class, sensitivity is 0.50 in both the CWS-only and CWS + FGA Total models, and 0.57 in the CWS + stepwise-selected FGA items models; specificity improves from 0.73 to 0.85 in both FGA models; the precision is 0.50, 0.64, and 0.67. For the mild class, sensitivity is 0.69 in the CWS-only model and 0.92 in both FGA models; specificity is 0.81 in the CWS-only model and 0.85 in both FGA models; and precision increases from 0.64 to 0.75 in both FGA models.
The estimation equations derived from the multivariable models are as follows, with severity groups determined as described above using cutoffs of 7.02%BW and 10.86%BW:
(1)
Paretic propulsion peak = −3.8817 + 6.0963 × CWS + 0.4837 × FGA Total.
(2)
Paretic propulsion peak = −4.3901 + 8.3050 × CWS + 1.3739 × FGA 7 + 2.9257 × FGA 10.

4. Discussion

Precise identification and classification of propulsion impairment is of great clinical significance; not only are propulsion deficits associated with the stability and efficiency of walking, but propulsion is a modifiable biomechanical gait subtask that, when improved, leads to meaningful increases in walking speed and functional mobility [14,15,16,52].
A key observation in this study is that gait propulsion and walking speed are only moderately correlated in people post-stroke. This finding underlies why some may walk with slow gait speeds despite relatively minimal propulsion impairments, while individuals with substantial propulsion impairment may achieve a relatively fast gait speed through compensatory biomechanical strategies. This finding illustrates the limitation of using walking speed alone when classifying propulsion impairments after stroke.
Our regression analyses demonstrate that combining walking speed with clinically derived measurements of dynamic walking ability from the FGA—captured through either the FGA total score or select FGA items—is a clinically feasible means of characterizing propulsion impairment after stroke. Linear regression models derived from stepwise regression using CWS and FGA items # 7 (“gait with narrow base of support”) and # 10 (“steps”) offered the best quantitative prediction of paretic propulsion peak, improving classification accuracy by 12.5% compared to CWS alone. Notably, this improvement was driven primarily by enhanced differentiation among individuals with mild to moderate impairment, for whom propulsion deficits are often visually subtle. Thus, co-assessment of the FGA and walking speed extends the diagnostic precision of traditional clinic-based gait assessments and supports the broader goal of developing function-centered, biomechanical classifications of post-stroke walking ability. Interestingly, combining FGA metrics with CWS did not substantially enhance the characterization of either paretic propulsion impulse or propulsion impulse symmetry. One explanation for this is that, similar to CWS, scoring the FGA is based on global performance rather than specific kinetic subtasks, which appears to limit its sensitivity to some propulsion parameters.
Other classification approaches have grouped individuals according to self-selected walking speed [14], walking activity [32], and balance self-efficacy [32]; all of these approaches consider functional mobility without regard for gait biomechanics [14,32]. Biomechanics-informed characterization is required to inform treatment-based classifications required to guide physical rehabilitation and to distinguish between gait recovery versus compensation [15]. Classification of the paretic propulsion peak using the FGA involves a function-centered examination approach that highlights biomechanical deficits associated with a variety of gait-related tasks. FGA scores have shown excellent intra-rater and inter-rater reliability during assessment of individuals post-stroke [30]. Good to excellent concurrent validity of the FGA has been established with other measures such as the Functional Ambulation Category, Berg Balance Scale, Rivermead Mobility Index, Barthel Index, and Dynamic Gait Index [30,31,32]. Additionally, the FGA has been shown to predict physical activity in individuals post-stroke and to correlate with kinematic gait parameters [3,32]. The current findings demonstrate that the FGA—an already standardized, reliable clinical tool—can be repurposed to identify specific biomechanical deficits when analyzed through a function-centered lens. In clinical practice, this dual use preserves feasibility while enabling more precise, mechanism-informed treatment selection. Furthermore, focused subsets of the FGA may efficiently capture key biomechanical deficits when time or testing burden limit full administration. With this function-centered biomechanical classification approach, essential biomechanical impairments contributing to gait dysfunction can be identified and targeted to optimize rehabilitation and contribute to improved ambulation quality and capacity. After biomechanical capacity for gait is restored, it is possible that psychosocial and cognitive profiles that affect gait participation in community environments may be more meaningfully altered [32].
This study has several limitations. While this work provides evidence that the classification accuracy of gait propulsion impairment may be enhanced with the combined assessment of walking speed and FGA, the generalizability of this conclusion would be enhanced if externally validated with a larger and more diverse multi-site sample. The sample size of this study may limit the statistical power of the regression models with multiple predictors [53]. It is possible that, with a larger sample size, some FGA items that were not significant in the models would have been found to be significant. However, this limitation does not detract from the primary conclusion of this study, that the co-assessment of walking speed and FGA items produces superior estimates of gait propulsion impairment compared to the assessment of walking speed alone. Despite this limitation, we have reported adjusted R-squared to more appropriately and conservatively characterize the performance of our multivariable models and employed 10-fold cross-validation to further assess model robustness. In addition, classification thresholds were defined using sample-based tertiles of a paretic propulsion peak, which may limit generalizability to populations with different propulsion characteristics. Another limitation is that this analysis focused on propulsion, while other biomechanical subtasks, such as foot clearance, single-limb support, and gait adaptability, undoubtedly contribute to overall walking function. While propulsion impairment is associated with impairment in other biomechanical subtasks of gait, such as foot clearance [54], incorporating other elements into a unified classification system could yield a more comprehensive framework for clinical decision-making. Future studies may also build on our work by examining foot clearance deficits at multiple lower-extremity joints [24]. Lastly, the omission of formal cognitive assessment and description of lesion location introduces the possibility of subtle cognitive impairment and variability in lesion location to confound our results and may limit the generalizability of our findings.

5. Conclusions

This work advances a clinically feasible and biomechanically grounded method for characterizing post-stroke gait propulsion. Specifically, the combined assessment of walking speed and select Functional Gait Assessment items improved the estimation and classification of paretic propulsion impairment compared with walking speed alone. By demonstrating that established clinical assessments can be integrated to classify patients based on salient, quantitatively derived kinetic measurements, it lays the foundation for scalable, mechanism-driven rehabilitation strategies that target the biomechanical sources of walking dysfunction. Importantly, future work may incorporate machine learning and other artificial intelligence approaches to further refine classification accuracy and generate additional insights.

Supplementary Materials

The following supporting information can be downloaded at https://www.mdpi.com/article/10.3390/app16010134/s1, Figure S1: Distribution of FGA item scores among participants; Figure S2: Box and whisker plots illustrating group differences in paretic propulsion impulse; Table S1: One-way ANOVA and post hoc comparisons for paretic propulsion peak across severity groups; Table S2: One-way ANOVA and post hoc comparisons for paretic propulsion impulse across severity groups.

Author Contributions

Conceptualization, L.N.A.; Methodology, L.N.A., J.P. and J.F.; Software, L.N.A., R.W. and J.F.; Validation, L.N.A., J.P., J.F. and R.W.; Formal Analysis, J.F., R.W. and J.P.; Investigation, J.F. and L.N.A.; Resources, L.N.A.; Data Curation, L.N.A., J.F., J.P. and R.W.; Writing—Original Draft Preparation, J.P. and J.F.; Writing—Review and Editing, J.F., J.P., L.N.A. and R.W.; Visualization, J.F.; Supervision, J.P., L.N.A. and J.F.; Project Administration, L.N.A., J.P. and J.F.; Funding Acquisition, not applicable. All authors have read and agreed to the published version of the manuscript.

Funding

No external funding was provided to support this work.

Institutional Review Board Statement

The study was conducted according to the guidelines of the Declaration of Helsinki and approved by the Boston University (Charles River Campus) Institutional Review Board (protocol number: #4440, approval date: 4 October 2016).

Informed Consent Statement

Informed consent was obtained from all subjects involved in the study.

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Acknowledgments

The authors acknowledge the members of the Neuromotor Recovery Laboratory for their assistance with data collection.

Conflicts of Interest

The authors declare no conflicts of interest.

References

  1. Martin, S.S.; Aday, A.W.; Almarzooq, Z.I.; Anderson, C.A.M.; Arora, P.; Avery, C.L.; Baker-Smith, C.M.; Barone Gibbs, B.; Beaton, A.Z.; Boehme, A.K.; et al. 2024 Heart Disease and Stroke Statistics: A Report of US and Global Data from the American Heart Association. Circulation 2024, 149, e347–e913. [Google Scholar] [CrossRef] [PubMed]
  2. Benjamin, E.J.; Blaha, M.J.; Chiuve, S.E.; Cushman, M.; Das, S.R.; Deo, R.; de Ferranti, S.D.; Floyd, J.; Fornage, M.; Gillespie, C.; et al. American Heart Association Statistics Committee and Stroke Statistics Subcommittee. Heart Disease and Stroke Statistics-2017 Update: A Report from the American Heart Association. Circulation 2017, 135, e146–e603. [Google Scholar] [CrossRef] [PubMed]
  3. Price, R.; Choy, N.L. Investigating the Relationship of the Functional Gait Assessment to Spatiotemporal Parameters of Gait and Quality of Life in Individuals with Stroke. J. Geriatr. Phys. Ther. 2019, 42, 256–264. [Google Scholar] [CrossRef] [PubMed]
  4. Rand, D.; Eng, J.J.; Tang, P.F.; Hung, C.; Jeng, J.S. Daily physical activity and its contribution to the health-related quality of life of ambulatory individuals with chronic stroke. Health Qual. Life Outcomes 2010, 8, 80. [Google Scholar] [CrossRef]
  5. Muren, M.A.; Hütler, M.; Hooper, J. Functional capacity and health-related quality of life in individuals post stroke. Top. Stroke Rehabil. 2008, 15, 51–58. [Google Scholar] [CrossRef]
  6. Schmid, A.; Duncan, P.W.; Studenski, S.; Lai, S.M.; Richards, L.; Perera, S.; Wu, S.S. Improvements in Speed-Based Gait Classifications Are Meaningful. Stroke 2007, 38, 2096–2100. [Google Scholar] [CrossRef]
  7. Awad, L.N.; Reisman, D.S.; Kesar, T.M.; Binder-Macleod, S.A. Targeting paretic propulsion to improve poststroke walking function: A preliminary study. Arch. Phys. Med. Rehabil. 2014, 95, 840–848. [Google Scholar] [CrossRef]
  8. Ordahan, B.; Karahan, A.Y.; Basaran, A.; Turkoglu, G.; Kucuksarac, S.; Cubukcu, M.; Tekin, L.; Polat, A.D.; Kuran, B. Impact of exercises administered to stroke patients with balance trainer on rehabilitation results: A randomized controlled study. Hippokratia 2015, 19, 125–130. [Google Scholar]
  9. Kim, J.O.; Lee, J.; Lee, B.H. Effect of Scapular Stabilization Exercise during Standing on Upper Limb Function and Gait Ability of Stroke Patients. J. Neurosci. Rural. Pract. 2017, 8, 540–544. [Google Scholar]
  10. Kim, K.; Lee, D.K.; Kim, E.K. Effect of aquatic dual-task training on balance and gait in stroke patients. J. Phys. Ther. Sci. 2016, 28, 2044–2047. [Google Scholar] [CrossRef][Green Version]
  11. Srivastava, S.; Kao, P.C.; Reisman, D.S.; Scholz, J.P.; Agrawal, S.K.; Higginson, J.S. Robotic Assist-As-Needed as an Alternative to Therapist-Assisted Gait Rehabilitation. Int. J. Phys. Med. Rehabil. 2016, 4, 370. [Google Scholar] [CrossRef] [PubMed]
  12. Lee, J.; Kim, J.O.; Lee, B.H. The effects of posterior talar glide with dorsiflexion of the ankle on mobility, muscle strength and balance in stroke patients: A randomised controlled trial. J. Phys. Ther. Sci. 2017, 29, 452–456. [Google Scholar] [CrossRef] [PubMed]
  13. Park, J.; Park, S.; Kim, Y.; Woo, Y. Comparison between treadmill training with rhythmic auditory stimulation and ground walking with rhythmic auditory stimulation on gait ability in chronic stroke patients: A pilot study. NeuroRehabilitation 2015, 37, 193–202. [Google Scholar] [CrossRef] [PubMed]
  14. Bowden, M.G.; Balasubramanian, C.K.; Behrman, A.L.; Kautz, S.A. Validation of a speed-based classification system using quantitative measures of walking performance poststroke. Neurorehabil. Neural Repair. 2008, 22, 672–675. [Google Scholar] [CrossRef]
  15. Awad, L.N.; Lewek, M.D.; Kesar, T.M.; Franz, J.R.; Bowden, M.G. These legs were made for propulsion: Advancing the diagnosis and treatment of post-stroke propulsion deficits. J. Neuroeng. Rehabil. 2020, 17, 139. [Google Scholar] [CrossRef]
  16. Awad, L.N.; Reisman, D.S.; Pohlig, R.T.; Binder-Macleod, S.A. Identifying candidates for targeted gait rehabilitation after stroke: Better prediction through biomechanics-informed characterization. J. Neuroeng. Rehabil. 2016, 13, 84. [Google Scholar] [CrossRef]
  17. Browne, M.G.; Franz, J.R. More push from your push-off: Joint-level modifications to modulate propulsive forces in old age. PLoS ONE 2018, 13, e0201407. [Google Scholar] [CrossRef]
  18. Hsiao, H.; Knarr, B.A.; Higginson, J.S.; Binder-Macleod, S.A. Mechanisms to increase propulsive force for individuals poststroke. J. Neuroeng. Rehabil. 2015, 12, 40. [Google Scholar] [CrossRef]
  19. Hsiao, H.; Knarr, B.A.; Higginson, J.S.; Binder-Macleod, S.A. The relative contribution of ankle moment and trailing limb angle to propulsive force during gait. Hum. Mov. Sci. 2015, 39, 212–221. [Google Scholar] [CrossRef]
  20. Roelker, S.A.; Bowden, M.G.; Kautz, S.A.; Neptune, R.R. Paretic propulsion as a measure of walking performance and functional motor recovery post-stroke: A review. Gait Posture 2019, 68, 6–14. [Google Scholar] [CrossRef]
  21. Awad, L.N.; Binder-Macleod, S.A.; Pohlig, R.T.; Reisman, D.S. Paretic propulsion and trailing limb angle are key determinants of long-distance walking function after stroke. Neurorehabil. Neural Repair. 2015, 29, 499–508. [Google Scholar] [CrossRef] [PubMed]
  22. McGinley, J.L.; Goldie, P.A.; Greenwood, K.M.; Olney, S.J. Accuracy and reliability of observational gait analysis data: Judgments of push-off in gait after stroke. Phys. Ther. 2003, 83, 146–160. [Google Scholar] [CrossRef] [PubMed]
  23. McGinley, J.L.; Morris, M.E.; Greenwood, K.M.; Goldie, P.A.; Olney, S.J. Accuracy of clinical observations of push-off during gait after stroke. Arch. Phys. Med. Rehabil. 2006, 87, 779–785. [Google Scholar] [CrossRef] [PubMed]
  24. Kawamura, C.M.; de Morais Filho, M.C.; Barreto, M.M.; de Paula Asa, S.K.; Juliano, Y.; Novo, N.F. Comparison between visual and three-dimensional gait analysis in patients with spastic diplegic cerebral palsy. Gait Posture 2007, 25, 18–24. [Google Scholar] [CrossRef]
  25. Brunnekreef, J.J.; Van Uden, C.J.; van Moorsel, S.; Kooloos, J.G. Reliability of videotaped observational gait analysis in patients with orthopedic impairments. BMC Musculoskelet. Disord. 2005, 6, 17. [Google Scholar] [CrossRef]
  26. Miyazaki, S.; Kubota, T. Quantification of gait abnormalities on the basis of continuous foot-force measurement: Correlation between quantitative indices and visual rating. Med. Biol. Eng. Comput. 1984, 22, 70–76. [Google Scholar] [CrossRef]
  27. Kesar, T.M.; Binder-Macleod, S.A.; Hicks, G.E.; Reisman, D.S. Minimal detectable change for gait variables collected during treadmill walking in individuals post-stroke. Gait Posture 2011, 33, 314–317. [Google Scholar] [CrossRef]
  28. Perry, J.; Garrett, M.; Gronley, J.K.; Mulroy, S.J. Classification of walking handicap in the stroke population. Stroke 1995, 26, 982–989. [Google Scholar] [CrossRef]
  29. Wrisley, D.M.; Marchetti, G.F.; Kuharsky, D.K.; Whitney, S.L. Reliability, internal consistency, and validity of data obtained with the functional gait assessment. Phys. Ther. 2004, 84, 906–918. [Google Scholar] [CrossRef]
  30. Thieme, H.; Ritschel, C.; Zange, C. Reliability and validity of the functional gait assessment (German version) in subacute stroke patients. Arch. Phys. Med. Rehabil. 2009, 90, 1565–1570. [Google Scholar] [CrossRef]
  31. Lin, J.H.; Hsu, M.J.; Hsu, H.W.; Wu, H.C.; Hsieh, C.L. Psychometric comparisons of 3 functional ambulation measures for patients with stroke. Stroke 2010, 41, 2021–2025. [Google Scholar] [CrossRef] [PubMed]
  32. Danks, K.A.; Pohlig, R.T.; Roos, M.; Wright, T.R.; Reisman, D.S. Relationship Between Walking Capacity, Biopsychosocial Factors, Self-efficacy, and Walking Activity in Persons Poststroke. J. Neurol. Phys. Ther. 2016, 40, 232–238. [Google Scholar] [CrossRef] [PubMed]
  33. Seamon, B.A.; Kautz, S.A.; Bowden, M.G.; Dean, J.C.; Gregory, C.M.; Neptune, R.R.; Velozo, C.A. Item-level psychometrics for the functional gait assessment in persons with stroke. Arch. Rehabil. Res. Clin. Transl. 2025, 7, 100452. [Google Scholar] [CrossRef]
  34. Hsieh, Y.W.; Wu, C.Y.; Lin, K.C.; Chang, Y.F.; Chen, C.L.; Liu, J.S. Responsiveness and validity of three outcome measures of motor function after stroke rehabilitation. Stroke 2009, 40, 1386–1391. [Google Scholar] [CrossRef] [PubMed]
  35. Fugl-Meyer, A.R.; Jääskö, L.; Leyman, I.; Olsson, S.; Steglind, S. The post-stroke hemiplegic patient. 1. a method for evaluation of physical performance. Scand. J. Rehabil. Med. 1975, 7, 13–31. [Google Scholar] [CrossRef]
  36. Gladstone, D.J.; Danells, C.J.; Black, S.E. The fugl-meyer assessment of motor recovery after stroke: A critical review of its measurement properties. Neurorehabil. Neural Repair. 2002, 16, 232–240. [Google Scholar] [CrossRef]
  37. Flansbjer, U.B.; Holmbäck, A.M.; Downham, D.; Patten, C.; Lexell, J. Reliability of gait performance tests in men and women with hemiparesis after stroke. J. Rehabil. Med. 2005, 37, 75–82. [Google Scholar]
  38. Bergamo, G.; Swaminathan, K.; Kim, D.; Chin, A.; Siviy, C.; Novillo, I.; Baker, T.C.; Wendel, N.; Ellis, T.D.; Walsh, C.J. Individualized Learning-Based Ground Reaction Force Estimation in People Post-Stroke Using Pressure Insoles. In Proceedings of the 2023 International Conference on Rehabilitation Robotics (ICORR), Singapore, 24–28 September 2023; pp. 1–6. [Google Scholar]
  39. Revi, D.A.; Alvarez, A.M.; Walsh, C.J.; De Rossi, S.M.M.; Awad, L.N. Indirect measurement of anterior-posterior ground reaction forces using a minimal set of wearable inertial sensors: From healthy to hemiparetic walking. J. Neuroeng. Rehabil. 2020, 17, 82. [Google Scholar] [CrossRef]
  40. Choe, D.K.; Aiello, A.J.; Spangler, J.E.; Walsh, C.J.; Awad, L.N. A Propulsion Neuroprosthesis Improves Overground Walking in Community-Dwelling Individuals After Stroke. IEEE Open J. Eng. Med. Biol. 2024, 5, 563–572. [Google Scholar] [CrossRef]
  41. Kwak, S.K.; Kim, J.H. Statistical data preparation: Management of missing values and outliers. Korean J. Anesthesiol. 2017, 70, 407–411. [Google Scholar] [CrossRef]
  42. Schober, P.; Boer, C.; Schwarte, L.A. Correlation Coefficients: Appropriate Use and Interpretation. Anesth. Analg. 2018, 126, 1763–1768. [Google Scholar] [CrossRef] [PubMed]
  43. Chan, Y.H. Biostatistics 104: Correlational analysis. Singapore Med. J. 2003, 44, 614–619. [Google Scholar] [PubMed]
  44. Marill, K.A. Advanced statistics: Linear regression, Part I: Simple linear regression. Acad. Emerg. Med. 2004, 11, 87–93. [Google Scholar] [CrossRef] [PubMed]
  45. Cataldo, A.R.; Fei, J.; Hutchinson, K.J.; Sloutsky, R.; Starr, J.; De Rossi, S.M.M.; Awad, L.N. Enhancing Heart Rate-Based Estimation of Energy Expenditure and Exercise Intensity in Patients Post Stroke. Bioengineering 2024, 11, 1250. [Google Scholar] [CrossRef]
  46. Varady, N.H.; Pareek, A.; Eckhardt, C.M.; Williams, R.J., 3rd; Madjarova, S.J.; Ollivier, M.; Martin, R.K.; Karlsson, J.; Nwachukwu, B.U. Multivariable regression: Understanding one of medicine’s most fundamental statistical tools. Knee Surg. Sports Traumatol. Arthrosc. 2023, 31, 7–11. [Google Scholar] [CrossRef]
  47. Kim, J.H. Multicollinearity and misleading statistical results. Korean J. Anesthesiol. 2019, 72, 558–569. [Google Scholar] [CrossRef]
  48. Austin, P.C. Informing power and sample size calculations when using inverse probability of treatment weighting using the propensity score. Stat. Med. 2021, 40, 6150–6163. [Google Scholar] [CrossRef]
  49. Bates, S.; Hastie, T.; Tibshirani, R. Cross-validation: What does it estimate and how well does it do it? J. Am. Stat. Assoc. 2024, 119, 1434–1445. [Google Scholar] [CrossRef]
  50. Efthimiou, O.; Seo, M.; Chalkou, K.; Debray, T.; Egger, M.; Salanti, G. Developing clinical prediction models: A step-by-step guide. BMJ 2024, 386, e078276. [Google Scholar] [CrossRef]
  51. Bender, R.; Lange, S. Adjusting for multiple testing—When and how? J. Clin. Epidemiol. 2001, 54, 343–349. [Google Scholar] [CrossRef]
  52. Hsiao, H.; Higginson, J.S.; Binder-Macleod, S.A. Baseline predictors of treatment gains in peak propulsive force in individuals poststroke. J. Neuroeng. Rehabil. 2016, 13, 2. [Google Scholar] [CrossRef]
  53. Anderson, S.F. Using prior information to plan appropriately powered regression studies: A tutorial using BUCSS. Psychol. Methods 2021, 26, 513–526. [Google Scholar] [CrossRef]
  54. Dean, J.C.; Bowden, M.G.; Kelly, A.L.; Kautz, S.A. Altered post-stroke propulsion is related to paretic swing phase kinematics. Clin. Biomech. 2020, 72, 24–30. [Google Scholar] [CrossRef]
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Figure 1. Experimental environment and data-collection setup. Participants performed overground walking on a 26.6 m indoor oval track equipped with six floor-embedded force plates used to measure ground reaction forces during the 6 min walk test.
Figure 1. Experimental environment and data-collection setup. Participants performed overground walking on a 26.6 m indoor oval track equipped with six floor-embedded force plates used to measure ground reaction forces during the 6 min walk test.
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Figure 2. Distribution of propulsion point metrics and their Pearson’s correlation analysis with CWS and FGA Total: (a) Distribution of paretic propulsion peak, paretic propulsion impulse, and propulsion impulse symmetry among participants. Green arrows point toward better propulsion performance. (b) Correlation between each propulsion point metric and CWS. (c) Correlation between each propulsion point metric and FGA Total.
Figure 2. Distribution of propulsion point metrics and their Pearson’s correlation analysis with CWS and FGA Total: (a) Distribution of paretic propulsion peak, paretic propulsion impulse, and propulsion impulse symmetry among participants. Green arrows point toward better propulsion performance. (b) Correlation between each propulsion point metric and CWS. (c) Correlation between each propulsion point metric and FGA Total.
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Figure 3. Classification of participants based on paretic propulsion peak and model performance in predicting the propulsion severity group. (a) Box plots illustrating group differences in paretic propulsion peak. *** indicates p < 0.001 for all pairwise comparisons. (b) Confusion matrices showing classification accuracy for three models predicting propulsion severity group using estimated paretic propulsion peak. (c) Bar plots summarizing per-class sensitivity, specificity, and precision for each model. Higher values indicate better performance across all metrics.
Figure 3. Classification of participants based on paretic propulsion peak and model performance in predicting the propulsion severity group. (a) Box plots illustrating group differences in paretic propulsion peak. *** indicates p < 0.001 for all pairwise comparisons. (b) Confusion matrices showing classification accuracy for three models predicting propulsion severity group using estimated paretic propulsion peak. (c) Bar plots summarizing per-class sensitivity, specificity, and precision for each model. Higher values indicate better performance across all metrics.
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Table 1. Participant demographics.
Table 1. Participant demographics.
Characteristic
Age (sd), y61.52 (9.95)
BMI (sd), kg/m228.77 (5.79)
Chronicity (sd), y7.97 (4.18)
Sex (M/F)29/11
Paretic leg (L/R)22/18
FMA-LE motor function scores (sd) *22.32 (6.16)
CWS (sd), m/s0.85 (0.29)
FGA Total (sd)16.62 (6.09)
AFO or AD use during FGA, (yes/no/missing) **8/29/3
* FMA-LE motor function scores were missing for 6 participants. ** AFO and AD usage data were missing for 3 participants. Abbreviations: sd = standard deviation; y = year; BMI = Body Mass Index; FMA-LE = Fugl-Meyer Assessment for Lower Extremity; CWS = Comfortable Walking Speed; FGA = Functional Gait Assessment; AFO = Ankle–Foot Orthosis; AD = Assistive Device.
Table 2. Univariable and multivariable regression analysis for the paretic propulsion peak.
Table 2. Univariable and multivariable regression analysis for the paretic propulsion peak.
Model StatisticsPredictor StatisticsCross-ValidationF-Test p
ModelR2Adj R2RMSEpPredictorβpR2RMSE
Univariable (CWS-only)0.460.454.320.000 ***Constant−2.210.3100.414.42N/A
CWS13.550.000 ***
Multivariable (CWS + FGA Total)0.580.563.870.000 ***Constant−3.880.0590.523.970.003 **
CWS6.100.060
FGA Total0.480.003 **
Multivariable (CWS + Stepwise-selected FGA items)0.630.603.680.000 ***Constant−4.390.0610.573.770.001 **
CWS8.310.001 **
FGA 71.370.024 *
FGA 102.930.014 *
* p < 0.05, ** p < 0.01, *** p < 0.001. Abbreviations: R2 = R-squared; Adj R2 = Adjusted R-squared; RMSE = Root Mean Square Error; p = p-value; β = Regression Coefficient Estimates; CWS = Comfortable Walking Speed; FGA = Functional Gait Assessment.
Table 3. Univariable and multivariable regression analysis for paretic propulsion impulse.
Table 3. Univariable and multivariable regression analysis for paretic propulsion impulse.
Model StatisticsPredictor StatisticsCross-ValidationF-Test p
ModelR2Adj R2RMSEpPredictorβpR2RMSE
Univariable (CWS-only)0.470.451.050.000 ***Constant−0.380.4680.411.08N/A
CWS3.330.000 ***
Multivariable (CWS + FGA Total)0.510.491.010.000 ***Constant−0.630.2320.441.050.071
CWS2.200.011 *
FGA Total0.070.071
Multivariable (CWS + Stepwise-selected FGA items)0.550.520.980.000 ***Constant−1.170.048 *0.500.990.014 *
CWS2.570.000 ***
FGA 100.750.014 *
* p < 0.05, *** p < 0.001. Abbreviations: R2 = R-squared; Adj R2 = Adjusted R-squared; RMSE = Root Mean Square Error; p = p-value; β = Regression Coefficient Estimates; CWS = Comfortable Walking Speed; FGA = Functional Gait Assessment.
Table 4. Univariable and multivariable regression analysis for propulsion impulse symmetry.
Table 4. Univariable and multivariable regression analysis for propulsion impulse symmetry.
Model StatisticsPredictor StatisticsCross-ValidationF-Test p
ModelR2Adj R2RMSEpPredictorβpR2RMSE
Univariable (CWS-only)0.220.200.140.002 **Constant0.120.1010.170.14N/A
CWS0.260.002 *
Multivariable (CWS + FGA Total)0.240.200.140.006 **Constant0.100.1780.170.150.345
CWS0.180.138
FGA Total0.010.345
Multivariable (CWS + Stepwise-selected FGA items)0.220.200.140.002 **Constant0.120.1010.170.14N/A
CWS0.260.002 *
* p < 0.05, ** p < 0.01. Abbreviations: R2 = R-squared; Adj R2 = Adjusted R-squared; RMSE = Root Mean Square Error; p = p-value; β = Regression Coefficient Estimates; CWS = Comfortable Walking Speed; FGA = Functional Gait Assessment.
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Paskewitz, J.; Fei, J.; Wang, R.; Awad, L.N. Classifying Post-Stroke Gait Propulsion Impairment Beyond Walking Speed: A Clinically Feasible Approach Using the Functional Gait Assessment. Appl. Sci. 2026, 16, 134. https://doi.org/10.3390/app16010134

AMA Style

Paskewitz J, Fei J, Wang R, Awad LN. Classifying Post-Stroke Gait Propulsion Impairment Beyond Walking Speed: A Clinically Feasible Approach Using the Functional Gait Assessment. Applied Sciences. 2026; 16(1):134. https://doi.org/10.3390/app16010134

Chicago/Turabian Style

Paskewitz, Jeffrey, Jie Fei, Ruoxi Wang, and Louis N. Awad. 2026. "Classifying Post-Stroke Gait Propulsion Impairment Beyond Walking Speed: A Clinically Feasible Approach Using the Functional Gait Assessment" Applied Sciences 16, no. 1: 134. https://doi.org/10.3390/app16010134

APA Style

Paskewitz, J., Fei, J., Wang, R., & Awad, L. N. (2026). Classifying Post-Stroke Gait Propulsion Impairment Beyond Walking Speed: A Clinically Feasible Approach Using the Functional Gait Assessment. Applied Sciences, 16(1), 134. https://doi.org/10.3390/app16010134

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