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Article

The Mechanistic Causes of Increased Walking Speed After a Strength Training Program in Stroke Patients: A Musculoskeletal Modeling Approach

by
Georgios Giarmatzis
1,*,
Nikolaos Aggelousis
1,
Erasmia Giannakou
1,
Ioanna Karagiannakidou
1,
Evangelia Makri
1,
Anna Tsiakiri
2,
Foteini Christidi
2,
Paraskevi Malliou
1 and
Konstantinos Vadikolias
2
1
Department of Physical Education and Sport Science, Democritus University of Thrace, 69100 Komotini, Greece
2
Department of Neurology, School of Medicine, Democritus University of Thrace, 68100 Alexandroupolis, Greece
*
Author to whom correspondence should be addressed.
Biomechanics 2025, 5(4), 97; https://doi.org/10.3390/biomechanics5040097 (registering DOI)
Submission received: 15 October 2025 / Revised: 19 November 2025 / Accepted: 24 November 2025 / Published: 1 December 2025
(This article belongs to the Special Issue Gait and Balance Control in Typical and Special Individuals: Second Edition)
Browse Figures
Versions Notes

Abstract

Background/Objectives: While strength training interventions improve walking performance in stroke survivors, the underlying neuromuscular mechanisms remain poorly understood. This study investigated muscle-level adaptations following a 12-week moderate-to-high-intensity strength training program in ten chronic stroke survivors using comprehensive musculoskeletal modeling analysis. Methods: Three-dimensional gait analysis was performed pre- and post-intervention, with subject-specific OpenSim models estimating individual muscle forces, powers, and work capacities throughout stance phase. Results: Non-paretic hip flexor negative work capacity increased significantly (0.033 to 0.042 J/kg, p = 0.033, Cohen’s d = 0.47), driven by enhanced rectus femoris power absorption during late stance that mechanistically facilitated trunk acceleration through leg deceleration. Knee extensor force generation showed increasing trends during loading response in both limbs. During push-off, ankle plantar flexor force generation showed trends toward bilateral improvements, primarily through paretic soleus and gastrocnemius contributions, though power output remained unchanged, indicating persistent velocity-dependent muscular deficits. Conclusions: Improved gait performance in both limbs demonstrates that strength training produces functionally beneficial bilateral muscle-level reorganization. The absence of a control group limits causal inference, though the observed biomechanical adaptations align with functional improvements, supporting the integration of strength training into comprehensive stroke rehabilitation protocols targeting locomotor recovery.

1. Introduction

Stroke remains the second-leading cause of death and the third-leading cause of long-term disability worldwide, with approximately 12.2 million new strokes occurring annually [1]. The resulting neurological damage leads to significant impairments in motor control [2], sensory perception [3], and cognitive function [4], severely compromising patients’ quality of life and independence [5]. Among the numerous functional limitations faced by stroke survivors, reduced gait speed emerges as a particularly critical indicator of overall recovery, often termed the “sixth vital sign” due to its strong predictive value for mortality, hospital length of stay, discharge disposition, health status, and community reintegration [6,7]. Walking speed serves as a discriminative clinical measure that reflects the complex interplay of multiple physiological systems, including muscle strength, motor control, balance, and cardiovascular fitness [8]. Despite significant advances in rehabilitation strategies that have shifted from compensatory approaches to evidence-based interventions targeting neurophysiological and muscular mechanisms [9], up to 80% of chronic stroke patients continue to exhibit gait abnormalities and reduced walking speeds even after conventional rehabilitation [10]. These gait deficits significantly impact community participation, increase fall risk, and contribute to secondary complications such as cardiovascular deconditioning and metabolic disorders [11]. As the estimated global cost of stroke is expected to increase further from $721 billion (2019 estimate [1]), there is an urgent need for evidence-based interventions that effectively address the underlying biomechanical and neuromuscular impairments limiting functional recovery in this population.
Recent evidence from our laboratory demonstrated that a 12-week moderate-to-high-intensity strength training program can significantly improve gait parameters in chronic stroke survivors, even without direct gait-specific training [12]. Following the intervention, participants achieved bilateral improvements in walking speed (paretic limb: 0.61 to 0.69 m/s; non-paretic limb: 0.62 to 0.69 m/s), with the most notable changes occurring in spatial rather than temporal gait parameters. Correlation analyses revealed that walking speed improvements were strongly associated with increases in stride length on both sides, indicating that strength training primarily influenced force production capabilities that enabled longer steps.
Despite the demonstrated efficacy of strength training interventions in improving gait function post-stroke [13,14,15], particularly when high intensity is applied [16], the underlying neuromuscular mechanisms driving these improvements remain poorly understood. Traditional gait analysis approaches focus primarily on kinematic and spatiotemporal outcomes, providing limited insight into the muscle-level adaptations that enable functional recovery [17,18]. While increased muscle strength and joint power has been identified as a significant predictor of gait improvements [19,20], previous research has shown that stroke survivors often maintain altered muscle activation patterns [21,22], reduced force generation capacity [23], and impaired intermuscular coordination [24] during walking. These deficits usually come along with reduced ankle plantar flexor power generation during push-off, hip flexor power during swing initiation and hip extensor power during early stance [21,22,25] after training.
Few studies have directly examined how changes in individual muscle function and coordination patterns translate to enhanced walking performance [26], mainly because traditional gait analysis lacks the capability to isolate the specific contributions of individual muscles to walking function. Musculoskeletal modeling offers a powerful computational framework for addressing this limitation by decomposing complex multi-joint movements into individual muscle contributions [27]. Modeling studies have demonstrated that hemiparetic individuals show reduced paretic soleus and gastrocnemius contributions to forward propulsion and swing initiation, with limited compensation from the non-paretic limb during pre-swing [28]. Hip and knee muscle deficits identified through musculoskeletal modeling include hip flexor and extensor weakness leading to reduced swing initiation and early stance power generation, respectively [28,29], gluteus medius dysfunction causing hip circumduction [30], hamstring weakness resulting in extended knee during early stance [17], knee extensor weakness contributing to hyperextension [31], and rectus femoris spasticity causing stiff-knee gait patterns [32,33]. Despite the potential of these methods, a recent scoping review revealed that only 19 published studies have utilized musculoskeletal modeling to explore stroke locomotion, with the majority focusing on movement deficit assessment rather than training-induced adaptations [34].
Therefore, the primary objective of this study was to investigate the specific muscle force and power adaptations that underlie the functional gait improvements observed following our 12-week strength training intervention in chronic stroke survivors. We hypothesized that strength training would result in increased muscle force production capabilities, particularly in ankle plantar flexors and hip flexors/extensors, which would translate to enhanced walking performance through improved coordination and power generation patterns. The findings from this investigation will provide novel mechanistic insights into how strength training interventions modify individual muscle function during walking and advance our understanding of the neuromuscular basis of motor recovery in stroke survivors.

2. Materials and Methods

2.1. Study Design and Participants

This study represents a secondary biomechanical analysis of data collected from participants in our previously published 12-week strength training intervention [12]. The original study was a non-randomized trial conducted at the Neurological Rehabilitation Unit, University Hospital of Alexandroupolis, Greece, between January and December 2022. Ten chronic stroke survivors (age: 61 ± 7.4 years, 9 males, BMI: 28 ± 4.24 kg/m2) completed the full intervention protocol. Inclusion criteria were: (1) chronic stroke (≥6 months post-stroke), (2) age > 18 years, (3) walking speed > 0.2 m/s, (4) independent ambulation (without the use of mobility aids such as canes, walkers, or ankle–foot orthoses), and (5) confirmed hemiparesis with observable motor impairment. According to the National Institutes of Health Stroke Scale [35], almost all patients had a score between 1 and 4 (minor stroke), with one patient scoring 7 (moderate stroke).

2.2. Intervention Protocol

The exercise dosage for key lower-limb muscle groups was standardized as follows: hip extensors, knee extensors, ankle plantar flexors, and hip flexors each received 2–3 targeted exercises per session, with 2–3 sets performed to volitional fatigue. Upper-body musculature also received a similar dosage. Exercise progression was guided exclusively by Rated Perceived Exertion (RPE) monitoring, with resistance levels (spring settings on Pilates equipment) adjusted to maintain target RPE ranges as participants’ strength improved. A detailed description of the intervention according to the TIDieR checklist is provided in Table 1.

2.3. Data Collection

Three-dimensional gait analysis was performed at two points: pre-intervention and post-intervention (following 12-week training completion). During each session, participants were instructed to walk across a 10 m corridor at their self-selected comfortable pace until five successful trials for each leg were recorded. A successful trial was defined as one in which the participant’s foot made complete contact with the force plate without targeting and showed no visible gait deviations or interruptions. All recorded gait cycles from each session (pre- and post-intervention) were incorporated into a single musculoskeletal model for each subject. Retroreflective markers were positioned on specific anatomical landmarks according to the full-body Conventional Gait Model protocol [36]. Marker trajectories were recorded using a 10-camera Vicon motion analysis system (Vicon Motion Systems Ltd., Oxford, UK) operating at 100 Hz sampling frequency. All data processing was conducted using Vicon Nexus 2.12.1® software, with marker trajectories subjected to low-pass filtering at 6 Hz cutoff frequency to eliminate high-frequency noise artifacts. Ground reaction forces were collected using two force plates (Model FP4060, Bertec Corporation, Columbus, OH, USA, and Type 9281CA, Kistler Instruments AG, Winterthur, Switzerland) embedded in the walkway, sampled at 1000 Hz and synchronized with the motion capture system. Walking speed consistency was monitored across all trials. As reported in our previous publication [12], walking speed and its variability were within acceptable ranges for stroke populations, ensuring consistent gait conditions between pre- and post-intervention sessions.

2.4. Musculoskeletal Modeling Pipeline

Subject-specific musculoskeletal models were generated using the Rajagopal full-body model [37] implemented in OpenSim 4.0 (Stanford University, Stanford, CA, USA). Individual anthropometric scaling was performed using body mass data and marker distances generated during one static calibration trial for each experimental session. The scaled models incorporated 37 degrees of freedom and 80 muscle–tendon units representing the major muscle groups of the lower extremities. Joint angles throughout the stance phase (heel-strike to ipsilateral toe-off) were computed using OpenSim’s inverse kinematics algorithm, which minimized the weighted least-squares difference between experimental and virtual marker positions. The optimization procedure solved for generalized coordinates that best reproduced the experimental marker trajectories while respecting the kinematic constraints of the musculoskeletal model. Net joint moments were calculated using OpenSim’s inverse dynamics tool, incorporating measured ground reaction forces, joint kinematics, and segment anthropometric properties. Joint moments were normalized by individual body weight to account for inter-subject anthropometric differences. Individual muscle forces during stance phase were estimated using OpenSim’s static optimization algorithm, which solved the muscle redundancy problem by minimizing the sum of squared muscle activations while satisfying equilibrium constraints at each time instant. The optimization assumed that muscle activations could change instantaneously and that co-contraction was minimized. Muscle forces were subsequently normalized by body weight to enable cross-subject and cross-session comparisons. Muscle fiber lengths and contraction velocities were computed using OpenSim’s muscle analysis tool, which evaluated muscle–tendon dynamics based on Hill-type muscle models.

2.5. Data Processing and Analysis

Individual muscle forces were analyzed both separately and systematically grouped into functional anatomical categories based on their primary biomechanical actions: hip flexors (iliacus, psoas, rectus femoris, sartorius), hip extensors (extensor head of adductor magnus, gluteus maximus, semimembranosus, semitendinosus), hip abductors (gluteus medius, tensor fasciae latae), hip adductors (adductor brevis, adductor longus, adductor magnus), hip internal rotators (gluteus minimus), hip external rotators (piriformis), knee flexors (biceps femoris long and short heads, gracilis), knee extensors (vastus intermedius, vastus lateralis, vastus medialis), ankle dorsiflexors (extensor digitorum longus, extensor hallucis longus, tibialis anterior), and ankle plantar flexors (flexor digitorum longus, flexor hallucis longus, gastrocnemius, peroneus brevis, peroneus longus, soleus, tibialis posterior).
Instantaneous muscle power was calculated as the scalar product of muscle force and muscle fiber contraction velocity, providing measures of mechanical power generation (positive values) and absorption (negative values) throughout the stance phase. Muscle group powers were derived by summating individual muscle powers within each functional category. All kinematic, kinetic, and muscle force data were interpolated to 100 equally spaced data points representing percentages of stance phase duration using quadratic spline interpolation. This normalization procedure enabled ensemble averaging across trials and subjects for all variables. Statistical Parametric Mapping (SPM) was used to compare the stance phase time series to understand how the sub-phases of gait change pre and post training conditions. Depending on the data distribution (tested with D’Agostino–Pearson K2 test), parametric or non-parametric paired sample SPM paired t-tests were performed to determine the biomechanical differences between these two conditions. Where applicable, force and power data from separate bundles of a muscle were summed.
Peak values analysis was performed by extracting maximum absolute values during early stance (0–50%) and late stance (50–100%) phases for each parameter. Muscle work was calculated by integrating muscle power over the absolute time of the stance phase, with positive work representing energy generation and negative work representing energy absorption. Statistical significance was determined using paired t-tests or Wilcoxon signed-rank tests based on normality testing (Shapiro–Wilk), with significance set at p < 0.05. p-values were adjusted for multiple comparisons using the Benjamini–Hochberg false discovery rate (FDR) procedure [38,39]. Effect sizes were quantified using Cohen’s d, calculated as the mean difference divided by the pooled standard deviation, with values of 0.2, 0.5, and 0.8 interpreted as small, moderate, and large effects, respectively. Positive values indicate post-intervention increases while negative values indicate decreases.

3. Results

The 12-week strength training intervention produced comprehensive neuromuscular adaptations that enhanced locomotor capacity while preserving fundamental movement coordination patterns.

3.1. Joint Kinematics and Kinetics Adaptations

Analysis of joint angles and moments (Figure 1) throughout the stance phase revealed that the 12-week strength training intervention preserved fundamental movement patterns while producing selective biomechanical adaptations, although SPM analysis did not reveal significant bilateral adaptations. Our results suggest that the stride length increase found in our previous work was mainly caused by increasing hip extension during late stance in both limbs, although statistically non-significant. Hip sagittal moments showed a similar pattern, where hip flexor moments were increased during late stance phase for both limbs.
Ankle sagittal moments exhibited notable adaptations during late stance, with both limbs showing slightly enhanced plantar flexor moment generation during the push-off phase (60–80% stance). Knee sagittal moments maintained their characteristic biphasic pattern throughout stance in the non-paretic limb, with enhanced extensor moment generation observed in both the loading response and late stance phases post-intervention. Notably, the paretic limb demonstrated restoration of the typical biphasic extensor moment pattern following training.

3.2. Muscle Group Force Adaptations

Time profiles of muscle group forces (Figure 2) revealed bilateral neuromuscular adaptations, although SPM analysis did not find any statistically significant regions. Hip extensors showed decreases bilaterally post-intervention. Knee extensor forces demonstrated enhanced force generation during the loading response phase (0–20% stance) for both limbs, while non-paretic hip flexor forces exhibited enhanced force generation during late stance (70–90%) preparing for swing phase initiation. Individual muscle analysis (see Appendix A Figure A1) confirmed these group-level findings, with all vasti muscles and non-paretic rectus femoris–iliopsoas muscles showing enhanced force generation throughout early and late stance, respectively.
Paretic ankle dorsiflexors showed a more similar decreased activation to the non-paretic side post-intervention during mid and terminal stance. Ankle plantar flexor forces also exhibited adaptations, with analysis revealing slightly enhanced force generation during the push-off phase (60–85% stance) in both limbs. Individual muscle analysis (see Figure A1) revealed that gastrocnemius (both lateral and medial for non-paretic and only lateral for paretic) and soleus (paretic) contributed to these improvements, with enhanced force generation throughout their respective activation windows.

3.3. Muscle Group Power Adaptations

Time profiles of muscle group power (Figure 3) revealed that the strength training intervention enhanced both concentric (positive) and eccentric (negative) power capacities while maintaining the temporal coordination of power production and absorption phases, although SPM analysis did not find any statistically significant regions.
One notable change is seen in non-paretic hip flexor power profiles, which showed an increase in power absorption during late stance, while the paretic limb hip flexor power profiles remained largely unchanged. The driving force behind this finding is the non-paretic rectus femoris power profile (see Appendix A—Figure A2), which demonstrated statistically significant enhanced power absorption during late stance post-intervention. In addition, notable reductions in paretic limb muscle power were observed that resulted in more symmetrical bilateral power profiles. Specifically, paretic knee flexor and ankle dorsiflexor power showed reductions between 20–50 and 50–100% of the stance phase, respectively, post-intervention. These power reductions brought the paretic limb power profiles closer to those of the non-paretic limb, suggesting improved inter-limb coordination and reduced compensatory power generation strategies that were present pre-intervention. Last, although non-paretic hip extensor power profile remained largely unchanged, paretic hip extensor power generation decreased during 20–50% of the stance phase, going below the levels of the non-paretic side.

3.4. Muscle Work Capacity Adaptations

Analysis of muscle work capacity revealed that the strength training intervention enhanced both positive (concentric) and negative (eccentric) work capabilities, with distinct adaptation patterns between work types. Table 2 and Table 3 show the results of the peak analysis and Figure A3 and Figure A4 show individual trends.
Negative work performed by individual muscle groups during stance phase showed minimal changes following the 12-week strength training intervention. Only the non-paretic hip flexors demonstrated a statistically significant increase in negative work (Pre: 0.033 ± 0.017 J/kg vs. Post: 0.042 ± 0.021 J/kg; 95% CI [0.004, 0.018]; Cohen’s d = 0.47; p = 0.04). All other muscle groups on both the paretic and non-paretic sides showed non-significant changes after FDR correction. The largest effect sizes were observed for paretic hip extensors (Cohen’s d = −0.56) and paretic knee flexors (Cohen’s d = −0.49), suggesting moderate reductions in negative work that did not reach statistical significance. Hip extensors on the non-paretic side also showed a moderate effect size (Cohen’s d = −0.50, p = 0.645). Ankle plantar flexors remained essentially unchanged on both limbs (Paretic: 0.013 ± 0.007 J/kg vs. 0.013 ± 0.005 J/kg, Cohen’s d = −0.11, p = 1.0; Non-Paretic: 0.013 ± 0.005 J/kg vs. 0.013 ± 0.006 J/kg, Cohen’s d = −0.02, p = 1.0).
Positive work performed by individual muscle groups during stance phase showed no statistically significant changes following the 12-week strength training intervention. All muscle groups on both the paretic and non-paretic sides demonstrated non-significant changes after FDR correction. The largest effect sizes were observed for non-paretic knee extensors (Cohen’s d = 0.71, p = 0.643), paretic knee flexors (Cohen’s d = −0.52, p = 1.0), and paretic ankle dorsiflexors (Cohen’s d = −0.51, p = 1.0), though none reached statistical significance. Ankle plantar flexors, the primary contributors to positive work during push-off, showed minimal changes on both limbs with negligible effect sizes (Paretic: 0.018 ± 0.013 J/kg vs. 0.019 ± 0.013 J/kg, Cohen’s d = 0.07, p = 1.0; Non-Paretic: 0.040 ± 0.041 J/kg vs. 0.041 ± 0.045 J/kg, Cohen’s d = 0.14, p = 1.0). Hip flexors also remained unchanged on both limbs (Paretic: 0.005 ± 0.004 J/kg vs. 0.004 ± 0.004 J/kg, Cohen’s d = −0.27, p = 1.0; Non-Paretic: 0.006 ± 0.008 J/kg vs. 0.008 ± 0.004 J/kg, Cohen’s d = 0.26, p = 1.0).

4. Discussion

The present study provides mechanistic insights into muscle-level adaptations following strength training in chronic stroke survivors using comprehensive musculoskeletal modeling analysis. Our 12-week moderate-to-high-intensity intervention produced a significant increase in non-paretic hip flexor negative work capacity, driven by enhanced rectus femoris power absorption during late stance. Moreover, we observed trends toward bilateral adaptations in key locomotor muscles—particularly knee extensor force generation during loading response and ankle plantar flexor force during push-off—though these changes did not reach statistical significance and ankle plantar flexor adaptations were not accompanied by corresponding power or work increases. While the absence of a control group and limited sample size (n = 10) preclude definitive causal conclusions, the observed biomechanical patterns suggest potential mechanisms through which strength training may contribute to the previously reported bilateral improvements in walking speed and stride length [12].
The primary finding of this study was a significant increase in non-paretic hip flexor negative work capacity (0.033 to 0.042 J/kg, Δ = +27.3%, 95% CI [0.004, 0.018], d = 0.47, p = 0.033), representing a mechanistically important adaptation for gait speed enhancement. Individual muscle analysis revealed that rectus femoris was the main contributor to this adaptation, demonstrating enhanced force generation and significantly higher power absorption post-intervention during late stance (see Figure A1 and Figure A2). The predominance of non-paretic hip flexor adaptations supports the bilateral compensation hypothesis, whereby the less-affected limb assumes greater responsibility for locomotor function to overcome paretic limb limitations [40]. While increased hip flexor energy absorption correlating with higher walking speeds has been documented [41,42,43], the underlying mechanism has remained counterintuitive and poorly explained. Neptune et al. [44] elucidated this phenomenon through forward dynamics simulations, demonstrating that during late stance (60–80% of stance phase), as the hip extends and the leg rotates posteriorly, the bi-articular rectus femoris undergoes eccentric contraction while generating force across both hip and knee joints. This eccentric action serves a dual biomechanical function: it absorbs kinetic energy from the extending leg (manifested as negative work at the muscle level), while reactive forces generated through its proximal attachment accelerate the trunk anteriorly through multi-joint force redistribution. Essentially, rectus femoris acts as an energy transfer mechanism, converting the leg’s rearward momentum into forward trunk propulsion without requiring additional energy generation. Our observed 27% increase in non-paretic hip flexor negative work capacity indicates enhanced ability to execute this energy transfer strategy post-training, providing an alternative pathway for speed augmentation.
Exploratory analysis revealed trends toward enhanced knee extensor force generation in both limbs during the loading response phase (0–20% stance), though these changes did not reach statistical significance. Individual muscle analysis suggested increased activation in all three vastii muscles during weight acceptance (Figure A1), potentially contributing to improved knee extension control and trunk stability during this critical phase [45]. Non-paretic vastii positive work showed a moderate effect size (d = 0.71, p = 0.643), while concurrent reductions in hip extensor (primarily gluteus maximus) force and power generation may reflect compensatory redistribution of lower-limb extensor function. However, given the absence of statistical significance and the exploratory nature of these observations, these apparent adaptations in knee extensor–hip extensor coordination should be interpreted cautiously and warrant investigation in larger, controlled studies.
Ankle plantar flexor force generation during the push-off phase (60–85% stance) demonstrated trends toward bilateral improvements in individual muscle analysis, though SPM analysis revealed no statistically significant changes in force time-series or work capacity (Table 3, all p > 0.64). Individual muscle patterns suggested increased soleus force in the paretic limb (Figure A1), consistent with its known role in forward progression [45,46], though positive work remained unchanged (0.018 ± 0.014 J/kg pre vs. 0.019 ± 0.016 J/kg post, d = 0.07, p = 1.0). The discrepancy between observed force trends and unchanged power output prompted investigation of contractile velocities. Fiber velocity analysis during push-off confirmed decreased shortening velocities in plantar flexors with negligible pre–post changes (soleus paretic: Δ = −0.002 mm/s, d = −0.056, p = 0.862; non-paretic: Δ = −0.014 mm/s, p = 0.375; gastrocnemius medialis paretic: Δ = −0.002 mm/s, p = 0.846; non-paretic: Δ = −0.005 mm/s, p = 0.770; gastrocnemius lateralis paretic: Δ = −0.004 mm/s, p = 0.770; non-paretic: Δ = −0.009 mm/s, d = −0.160, p = 0.624). These small changes could suggest that velocity-dependent muscular deficits characteristic of aging and stroke [47,48] remained the limiting factor for plantar flexor power generation in this cohort. This pattern differs from some studies showing increased ankle plantar flexor power correlating with speed improvements in stroke populations [26,41,42], but aligns with other reports where speed increases occurred without substantial plantar flexor power changes [49,50,51], emphasizing alternative mechanisms such as hip flexor adaptations [19]. Paretic ankle dorsiflexor patterns showed trends toward reduced force and power absorption during late stance (50–100%), with moderate effect sizes for negative work reduction (d = −0.51, p = 1.0), potentially reflecting improved ankle control coordination, though these exploratory observations require confirmation in larger controlled studies.
The current study has several limitations that should be considered when interpreting the results. First, the absence of a control group limits our ability to determine whether the observed improvements were specific to the strength training intervention or could be partially explained by time-related recovery effects, although the chronic nature of the participant population (≥6 months post-stroke) makes spontaneous recovery unlikely. Also, familiarization or learning effects from repeated testing cannot be fully excluded. Second, the relatively small sample size (n = 10) may limit statistical power to detect significant changes, although this sample size is consistent with similar musculoskeletal modeling studies in stroke populations where recruitment challenges and intensive data collection protocols limit feasibility. The reported effect sizes (Cohen’s d) and confidence intervals provide context for interpreting the clinical meaningfulness of our findings beyond statistical significance, whereas the SPM approach accounts for the temporal nature of gait data and controls for multiple comparisons across the gait cycle. Third, the small although significant speed increase as a result of the training program could also be insufficient to be elicited by significant changes in the muscle function. Fourth, the musculoskeletal modeling approach relied on static optimization algorithms that assume instantaneous muscle activation changes and minimize co-contraction, which may not accurately represent the complex neural control strategies employed by stroke survivors during walking. Finally, individual muscle forces were estimated rather than directly measured, however preliminary data on validation against electromyographic data have been performed in subgroup of the same group used in this study [52] and supported by the supplemental figures we provide showing the acceptable agreement between collected and estimated muscle activation signals of key muscles, enhancing our confidence in the profile of estimated muscle forces.

5. Conclusions

This study provides mechanistic insights into muscle-level adaptations following strength training in chronic stroke survivors through comprehensive musculoskeletal modeling analysis. The primary finding was a significant 27% increase in non-paretic hip flexor negative work capacity following the 12-week moderate-to-high-intensity intervention, driven by significantly enhanced rectus femoris power absorption during late stance. This adaptation represents a mechanistically important pathway for gait speed enhancement, as increased hip flexor energy absorption facilitates energy transfer from the extending leg to forward trunk propulsion. Beyond this primary finding, exploratory analyses revealed trends toward bilateral adaptations in knee extensors during loading response and ankle plantar flexors during push-off, though these changes did not reach statistical significance. Notably, ankle plantar flexor force trends were not accompanied by corresponding power or work increases, with fiber velocity analysis suggesting that velocity-dependent deficits remained the limiting factor for power generation in this cohort. These findings support the integration of progressive strengthening training into comprehensive stroke rehabilitation protocols, demonstrating that meaningful muscle-level adaptations can occur without task-specific gait training.

Author Contributions

Conceptualization, N.A., K.V., A.T. and G.G.; methodology, G.G., A.T., E.G. and I.K.; software, G.G. and F.C.; validation, G.G., P.M., I.K. and N.A.; formal analysis, G.G. and P.M.; investigation, E.G. and E.M.; resources, N.A., P.M. and K.V.; data curation, G.G. and E.G.; writing—original draft preparation, G.G. and A.T.; writing—review and editing, G.G., N.A. and E.G.; visualization, G.G. and E.M.; supervision, N.A., F.C. and K.V.; project administration, P.M. and I.K.; funding acquisition, N.A. and K.V. All authors have read and agreed to the published version of the manuscript.

Funding

We acknowledge the support of the work at hand by the project “Study of the interrelationships between neuroimaging, neurophysiological and biomechanical biomarkers in stroke rehabilitation (NEURO-BIO-MECH in stroke rehab)” (MIS 5047286), which is implemented under the Action “Support for Regional Excellence”-Operational Program “Competitiveness, Entrepreneurship and Innovation” (NSRFm2014-2020), under the auspices of Greece and the European Union (European Regional Development Fund).

Institutional Review Board Statement

The study was conducted in accordance with the Declaration of Helsinki and approved by the Institutional Ethics Committee of Democritus University of Thrace.

Informed Consent Statement

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

Data Availability Statement

The data and results are available upon request to interested researchers.

Conflicts of Interest

The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

Appendix A

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Figure A1. Individual muscle force profiles during stance phase before and after 12-week strength training intervention in chronic stroke patients. Each panel represents normalized muscle force (N/BW) across stance phase (0–100%) for paretic (solid lines) and non-paretic (dashed lines) limbs at pre-intervention (blue/teal) and post-intervention (pink/amber). Shaded regions represent standard deviation. Gait phase markers indicate initial contact (0%), loading response (~20%), mid-stance (~50%), terminal stance (~80%), and pre-swing (100%).
Figure A1. Individual muscle force profiles during stance phase before and after 12-week strength training intervention in chronic stroke patients. Each panel represents normalized muscle force (N/BW) across stance phase (0–100%) for paretic (solid lines) and non-paretic (dashed lines) limbs at pre-intervention (blue/teal) and post-intervention (pink/amber). Shaded regions represent standard deviation. Gait phase markers indicate initial contact (0%), loading response (~20%), mid-stance (~50%), terminal stance (~80%), and pre-swing (100%).
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Figure A2. Individual muscle power profiles during stance phase before and after 12-week strength training intervention in chronic stroke patients. Each panel represents normalized muscle power (W/kg) across stance phase (0–100%) for paretic (solid lines) and non-paretic (dashed lines) limbs at pre-intervention (blue/teal) and post-intervention (pink/amber). Shaded regions represent standard deviation. Gait phase markers indicate initial contact (0%), loading response (~20%), mid-stance (~50%), terminal stance (~80%), and pre-swing (100%).
Figure A2. Individual muscle power profiles during stance phase before and after 12-week strength training intervention in chronic stroke patients. Each panel represents normalized muscle power (W/kg) across stance phase (0–100%) for paretic (solid lines) and non-paretic (dashed lines) limbs at pre-intervention (blue/teal) and post-intervention (pink/amber). Shaded regions represent standard deviation. Gait phase markers indicate initial contact (0%), loading response (~20%), mid-stance (~50%), terminal stance (~80%), and pre-swing (100%).
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Figure A3. Bar plots display mean ± standard deviation of negative work (J/kg) for all muscle groups across paretic and non-paretic limbs. Individual subject trajectories are shown as connected lines (red for paretic and blue for non-paretic) between pre-intervention (Pre) and post-intervention (Post) timepoints.
Figure A3. Bar plots display mean ± standard deviation of negative work (J/kg) for all muscle groups across paretic and non-paretic limbs. Individual subject trajectories are shown as connected lines (red for paretic and blue for non-paretic) between pre-intervention (Pre) and post-intervention (Post) timepoints.
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Figure A4. Bar plots display mean ± standard deviation of positive work (J/kg) for all muscle groups across paretic and non-paretic limbs. Individual subject trajectories are shown as connected lines (red for paretic and blue for non-paretic) between pre-intervention (Pre) and post-intervention (Post) timepoints.
Figure A4. Bar plots display mean ± standard deviation of positive work (J/kg) for all muscle groups across paretic and non-paretic limbs. Individual subject trajectories are shown as connected lines (red for paretic and blue for non-paretic) between pre-intervention (Pre) and post-intervention (Post) timepoints.
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Figure 1. Kinematics and kinetics analysis of gait patterns during stance phase following 12-week strength training intervention. Joint angle trajectories (top panels) and joint moment profiles (bottom panels) are shown for hip, knee, and ankle joints across the stance phase (0–100%, where 0% represents initial foot contact and 100% represents toe-off). Solid and dashed lines represent group means with shaded areas indicating ±1 standard deviation. SPM analysis did not reveal significant bilateral adaptations, for both paretic (stroke-affected limb; blue/red) and non-paretic (unaffected limb; dashed) sides.
Figure 1. Kinematics and kinetics analysis of gait patterns during stance phase following 12-week strength training intervention. Joint angle trajectories (top panels) and joint moment profiles (bottom panels) are shown for hip, knee, and ankle joints across the stance phase (0–100%, where 0% represents initial foot contact and 100% represents toe-off). Solid and dashed lines represent group means with shaded areas indicating ±1 standard deviation. SPM analysis did not reveal significant bilateral adaptations, for both paretic (stroke-affected limb; blue/red) and non-paretic (unaffected limb; dashed) sides.
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Figure 2. Muscle group force analysis during stance phase following 12-week strength training intervention. Force profiles are shown for ten major lower-extremity muscle groups across the stance phase (0–100%, where 0% represents initial foot contact and 100% represents toe-off). Solid and dashed lines represent group means with shaded areas indicating ±1 standard deviation. SPM analysis did not reveal significant adaptations for both sides.
Figure 2. Muscle group force analysis during stance phase following 12-week strength training intervention. Force profiles are shown for ten major lower-extremity muscle groups across the stance phase (0–100%, where 0% represents initial foot contact and 100% represents toe-off). Solid and dashed lines represent group means with shaded areas indicating ±1 standard deviation. SPM analysis did not reveal significant adaptations for both sides.
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Figure 3. Muscle group power analysis during stance phase following 12-week strength training intervention. Power profiles are shown for ten major lower extremity muscle groups across the stance phase (0–100%, where 0% represents initial foot contact and 100% represents toe-off). Solid and dashed lines represent group means with shaded areas indicating ±1 standard deviation. SPM analysis did not reveal significant adaptations for both sides.
Figure 3. Muscle group power analysis during stance phase following 12-week strength training intervention. Power profiles are shown for ten major lower extremity muscle groups across the stance phase (0–100%, where 0% represents initial foot contact and 100% represents toe-off). Solid and dashed lines represent group means with shaded areas indicating ±1 standard deviation. SPM analysis did not reveal significant adaptations for both sides.
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Table 1. Description of the 12-Week Progressive Pilates-Based Resistance Training Intervention for Individuals with Chronic Stroke.
Table 1. Description of the 12-Week Progressive Pilates-Based Resistance Training Intervention for Individuals with Chronic Stroke.
Description
Brief nameProgressive Pilates-based resistance training program
WhyTo improve muscular strength, balance, and functional capacity in individuals with chronic stroke. Pilates-based resistance training emphasizes controlled movement, postural alignment and breath regulation. The progressive resistance approach aligns with established neuromuscular and neuroplasticity principles, facilitating strength gains and improved motor control post-stroke.
What (materials)A range of Pilates equipment was used, including reformer towers, Wunda chairs, armchairs, barrels, Pilates rings, elastic bands, exercise balls, soft free weights, and Bosu platforms. Body weight was also used as resistance
What (procedures)Each session included three phases: (a) Warm-up (5–10 min): Breathing exercises, postural alignment training, spine and limb mobility drills. (b) Main program (35–50 min): Individualized progressive resistance exercises targeting key muscle groups with specific dosage:• Hip extensors (e.g., leg press variations): 2–3 exercises • Knee extensors (e.g., seated leg extension on chair, sit ups): 2–3 exercises • Ankle plantar flexors (e.g., calf raises on reformer): 2–3 exercises • Hip flexors (e.g., standing hip flexion with bands): 2–3 exercises • Upper-body musculature (e.g., seated rows, chest press on reformer): 2–3 exercises. (c) Cool-down (5 min): Breathing, flexibility, and stretching exercises. Exercise intensity was progressively increased throughout the program based on Rating of Perceived Exertion (RPE).
Who providedFive qualified instructors administered the intervention. Each participant was supervised by two instructors during every session, ensuring safety, proper technique, and appropriate load progression
HowDelivered face-to-face, individually, with hands-on cueing, verbal feedback, and continuous real-time monitoring
WhereConducted in a fully equipped Pilates studio suitable for resistance training and neurorehabilitation, with all necessary Pilates apparatus and safety supports
When and how muchParticipants completed a 12-week program consisting of two sessions per week, for a total of 24 sessions. Each session lasted 45–60 min
TailoringPrograms were personalized based on participants’ abilities, strength levels, balance capacity, and fatigue. Exercise selection, spring settings, resistance level, range of motion, and movement complexity were adjusted individually. Progressions were introduced when participants demonstrated safe and controlled execution
ModificationsThe training load and exercise complexity were progressively increased over the 12 weeks. Should participants experience excessive fatigue, difficulty, or pain, exercises were modified by reducing load, adjusting range of motion, or selecting alternative apparatus
How well (planned)Planned monitoring included session attendance logs, instructor documentation of exercise selection and resistance levels, and weekly tracking of perceived exertion scores to ensure progressive overload
How well (actual)Participants were supervised continuously by two instructors to maintain exercise fidelity. Perceived exertion was systematically monitored using the Borg 1–10 scale, beginning with moderate intensity (5–6) in early sessions and progressing to high intensity (7–8, “really hard”) as tolerated
Table 2. Negative work (energy absorption) performed by muscle groups during stance phase before and after 12-week strength training intervention in chronic stroke patients. Values represent mean ± standard deviation of negative work (J/kg) for paretic and non-paretic limbs at pre-intervention and post-intervention timepoints. Negative work represents energy absorption during eccentric muscle contractions throughout the stance phase of gait. Statistically significant changes are denoted with asterisk (*) after correcting for multiple comparisons according to the Benjamini–Hochberg procedure.
Table 2. Negative work (energy absorption) performed by muscle groups during stance phase before and after 12-week strength training intervention in chronic stroke patients. Values represent mean ± standard deviation of negative work (J/kg) for paretic and non-paretic limbs at pre-intervention and post-intervention timepoints. Negative work represents energy absorption during eccentric muscle contractions throughout the stance phase of gait. Statistically significant changes are denoted with asterisk (*) after correcting for multiple comparisons according to the Benjamini–Hochberg procedure.
Muscle GroupSidePre (Mean ± SD)Post (Mean ± SD)95% CICohen’s dp-Value (FDR)
ankle dorsiflexorsNon Paretic0.0013 ± 0.00070.0011 ± 0.0005[−0.0005, 0.0001]−0.280.645
ankle dorsiflexorsParetic0.0018 ± 0.00290.0009 ± 0.0008[−0.0032, 0.0014]−0.391
ankle plantar flexorsNon Paretic0.0131 ± 0.00460.0129 ± 0.0059[−0.0023, 0.0020]−0.021
ankle plantar flexorsParetic0.0134 ± 0.00660.0128 ± 0.0052[−0.0041, 0.0027]−0.111
hip abductorsNon Paretic0.0037 ± 0.00270.0032 ± 0.0019[−0.0022, 0.0013]−0.181
hip abductorsParetic0.0023 ± 0.00140.0022 ± 0.0013[−0.0009, 0.0007]−0.051
hip adductorsNon Paretic0.0019 ± 0.00170.0019 ± 0.0014[−0.0004, 0.0005]0.041
hip adductorsParetic0.0014 ± 0.00110.0012 ± 0.0008[−0.0012, 0.0009]−0.131
hip extensorsNon Paretic0.0029 ± 0.00350.0015 ± 0.0011[−0.0034, 0.0007]−0.50.645
hip extensorsParetic0.0013 ± 0.00100.0008 ± 0.0005[−0.0011, 0.0002]−0.560.273
hip external rotatorsNon Paretic0.0004 ± 0.00070.0003 ± 0.0005[−0.0003, 0.0001]−0.220.56
hip external rotatorsParetic0.0004 ± 0.00050.0003 ± 0.0002[−0.0006, 0.0002]−0.460.984
hip flexorsNon Paretic0.0332 ± 0.01680.0421 ± 0.0189[0.0042, 0.0135]0.470.04 *
hip flexorsParetic0.0225 ± 0.01550.0250 ± 0.0155[−0.0052, 0.0101]0.150.984
hip internal rotatorsNon Paretic0.0005 ± 0.00040.0005 ± 0.0004[−0.0003, 0.0002]−0.11
hip internal rotatorsParetic0.0003 ± 0.00020.0004 ± 0.0002[−0.0001, 0.0001]0.031
knee extensorsNon Paretic0.0130 ± 0.00400.0141 ± 0.0062[−0.0016, 0.0037]0.190.984
knee extensorsParetic0.0049 ± 0.00330.0051 ± 0.0036[−0.0007, 0.0010]0.041
knee flexorsNon Paretic0.0003 ± 0.00020.0002 ± 0.0001[−0.0001, 0.0001]−0.290.984
knee flexorsParetic0.0004 ± 0.00050.0002 ± 0.0002[−0.0004, 0.0001]−0.490.645
Table 3. Positive work (energy generation) performed by muscle groups during stance phase before and after 12-week strength training intervention in chronic stroke patients. Values represent mean ± standard deviation of negative work (J/kg) for paretic and non-paretic limbs at pre-intervention and post-intervention timepoints. Positive work represents energy generation during concentric muscle contractions throughout the stance phase of gait. No statistically significant changes were found after correcting for multiple comparisons according to the Benjamini–Hochberg procedure.
Table 3. Positive work (energy generation) performed by muscle groups during stance phase before and after 12-week strength training intervention in chronic stroke patients. Values represent mean ± standard deviation of negative work (J/kg) for paretic and non-paretic limbs at pre-intervention and post-intervention timepoints. Positive work represents energy generation during concentric muscle contractions throughout the stance phase of gait. No statistically significant changes were found after correcting for multiple comparisons according to the Benjamini–Hochberg procedure.
Muscle GroupSidePre (Mean ± SD)Post (Mean ± SD)95% CICohen’s dp-Value (FDR)
ankle dorsiflexorsNon Paretic0.0006 ± 0.00040.0006 ± 0.0003[−0.0002, 0.0002]−0.041
ankle dorsiflexorsParetic0.0021 ± 0.00290.0009 ± 0.0008[−0.0031, 0.0008]−0.511
ankle plantar flexorsNon Paretic0.0398 ± 0.01210.0414 ± 0.0097[−0.0031, 0.0063]0.141
ankle plantar flexorsParetic0.0176 ± 0.01360.0187 ± 0.0160[−0.0045, 0.0068]0.071
hip abductorsNon Paretic0.0119 ± 0.00410.0126 ± 0.0049[−0.0012, 0.0026]0.141
hip abductorsParetic0.0089 ± 0.00500.0089 ± 0.0049[−0.0014, 0.0012]−0.011
hip adductorsNon Paretic0.0009 ± 0.00030.0012 ± 0.0011[−0.0004, 0.0011]0.431
hip adductorsParetic0.0010 ± 0.00060.0009 ± 0.0008[−0.0004, 0.0003]−0.061
hip extensorsNon Paretic0.0142 ± 0.00630.0137 ± 0.0050[−0.0038, 0.0027]−0.091
hip extensorsParetic0.0101 ± 0.00790.0079 ± 0.0045[−0.0077, 0.0032]−0.331
hip external rotatorsNon Paretic0.0008 ± 0.00080.0010 ± 0.0008[−0.0004, 0.0008]0.211
hip external rotatorsParetic0.0007 ± 0.00060.0007 ± 0.0007[−0.0003, 0.0004]0.081
hip flexorsNon Paretic0.0061 ± 0.00450.0078 ± 0.0072[−0.0009, 0.0042]0.261
hip flexorsParetic0.0052 ± 0.00490.0042 ± 0.0015[−0.0042, 0.0022]−0.271
hip internal rotatorsNon Paretic0.0016 ± 0.00080.0020 ± 0.0013[−0.0001, 0.0008]0.321
hip internal rotatorsParetic0.0015 ± 0.00090.0014 ± 0.0008[−0.0005, 0.0003]−0.111
knee extensorsNon Paretic0.0084 ± 0.00350.0114 ± 0.0046[0.0003, 0.0058]0.710.643
knee extensorsParetic0.0045 ± 0.00400.0055 ± 0.0047[−0.0010, 0.0030]0.211
knee flexorsNon Paretic0.0024 ± 0.00130.0025 ± 0.0016[−0.0004, 0.0005]0.041
knee flexorsParetic0.0022 ± 0.00140.0015 ± 0.0009[−0.0016, 0.0003]−0.521
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Giarmatzis, G.; Aggelousis, N.; Giannakou, E.; Karagiannakidou, I.; Makri, E.; Tsiakiri, A.; Christidi, F.; Malliou, P.; Vadikolias, K. The Mechanistic Causes of Increased Walking Speed After a Strength Training Program in Stroke Patients: A Musculoskeletal Modeling Approach. Biomechanics 2025, 5, 97. https://doi.org/10.3390/biomechanics5040097

AMA Style

Giarmatzis G, Aggelousis N, Giannakou E, Karagiannakidou I, Makri E, Tsiakiri A, Christidi F, Malliou P, Vadikolias K. The Mechanistic Causes of Increased Walking Speed After a Strength Training Program in Stroke Patients: A Musculoskeletal Modeling Approach. Biomechanics. 2025; 5(4):97. https://doi.org/10.3390/biomechanics5040097

Chicago/Turabian Style

Giarmatzis, Georgios, Nikolaos Aggelousis, Erasmia Giannakou, Ioanna Karagiannakidou, Evangelia Makri, Anna Tsiakiri, Foteini Christidi, Paraskevi Malliou, and Konstantinos Vadikolias. 2025. "The Mechanistic Causes of Increased Walking Speed After a Strength Training Program in Stroke Patients: A Musculoskeletal Modeling Approach" Biomechanics 5, no. 4: 97. https://doi.org/10.3390/biomechanics5040097

APA Style

Giarmatzis, G., Aggelousis, N., Giannakou, E., Karagiannakidou, I., Makri, E., Tsiakiri, A., Christidi, F., Malliou, P., & Vadikolias, K. (2025). The Mechanistic Causes of Increased Walking Speed After a Strength Training Program in Stroke Patients: A Musculoskeletal Modeling Approach. Biomechanics, 5(4), 97. https://doi.org/10.3390/biomechanics5040097

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