STROKE IS THE THIRD leading cause of death and one of

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1 129 ORIGINAL ARTICLE The Influence of Applying Additional Weight to the Affected Leg on Gait Patterns During Aquatic Treadmill Walking in People Poststroke Taeyou Jung, PhD, ATC, DoKyeong Lee, MS, Charalambos Charalambous, MS, Konstantinos Vrongistinos, PhD ABSTRACT. Jung T, Lee D, Charalambous C, Vrongistinos K. The influence of applying additional weight to the affected leg on gait patterns during aquatic treadmill walking in people poststroke. Arch Phys Med Rehabil 2010;91: Objective: To investigate how the application of additional weights to the affected leg influences gait patterns of people poststroke during aquatic treadmill walking. Design: Comparative gait analysis. Setting: University-based aquatic therapy center. Participants: Community-dwelling volunteers (n 22) with chronic hemiparesis caused by stroke. Interventions: Not applicable. Main Outcome Measures: Spatiotemporal and kinematic gait parameters. Results: The use of an ankle weight showed an increase in the stance phase percentage of gait cycle (3%, P.015) when compared with no weight. However, the difference was not significant after a Bonferroni adjustment was applied for a more stringent statistical analysis. No significant differences were found in cadence and stride length. The use of an ankle weight showed a significant decrease of the peak hip flexion (7.9%, P.001) of the affected limb as compared with no weight condition. This decrease was marked as the reduction of unwanted limb flotation because people poststroke typically show excessive hip flexion of the paretic leg in the late swing phase followed by fluctuating hip movements during aquatic treadmill walking. The frontal and transverse plane hip motions did not show any significant differences but displayed a trend of a decrease in the peak hip abduction during the swing phase with additional weights. The use of additional weight did not alter sagittal plane kinematics of the knee and ankle joints. Conclusions: The use of applied weight on the affected limb can reduce unwanted limb flotation on the paretic side during aquatic treadmill walking. It can also assist the stance stability by increasing the stance phase percentage closer to 60% of gait cycle. Both findings can contribute to the development of more From Center of Achievement, Department of Kinesiology, California State University, Northridge, Northridge, CA (Jung, Vrongistinos); Center for Human Motor Research, Division of Kinesiology, University of Michigan, Ann Arbor, MI (Lee); and the Motor Behavior and Neurorehabilitation Laboratory, Division of Biokinesiology and Physical Therapy, University of Southern California, Los Angeles, CA (Charalambous). Presented in part to the American College of Sports Medicine, May 29, 2008, Indianapolis, IN. Supported by the Graduate Thesis Support Grant Program, California State University, Northridge, CA (grant no. E2134). No commercial party having a direct financial interest in the results of the research supporting this article has or will confer a benefit on the authors or on any organization with which the authors are associated. Correspondence to Taeyou Jung, PhD, ATC, Dept of Kinesiology, California State University, Northridge, Nordhoff St, Redwood Hall, Northridge, CA 91330, taeyou.jung@csun.edu. Reprints are not available from the author /10/ $36.00/0 doi: /j.apmr efficient motor patterns in gait training for people poststroke. The use of a cuff weight does not seem to reduce the limb circumduction during aquatic treadmill walking. Key Words: Exercise therapy; Gait; Hemiparesis; Rehabilitation; Stroke by the American Congress of Rehabilitation Medicine STROKE IS THE THIRD leading cause of death and one of the most common medical conditions that yield long-term disabilities among adults in the United States. 1 Stroke survivors show various neurologic deficits including motor, sensory, cognitive, perceptual, emotional, and speech-language impairments. The primary motor impairments involve paresis, altered muscle tone, lack of selective motor control, abnormal reflexes, and poor balance. 2 A combination of these motor characteristics often compromises gait. The majority of people poststroke (50% 80%) typically recover their ability to walk, whereas approximately 20% of stroke survivors remain primarily wheelchair users. 3 Even though they may recover mobility, many encounter various difficulties with their gait, such as slow walking speed, inefficient energy expenditure, altered gait kinematics, limited gait endurance, and poor gait stability, when compared with healthy adults. 4-8 The most common gait pattern found after a stroke is hemiparetic gait, which is associated with asymmetric spatiotemporal and kinematic gait characteristics. The paretic limb of people poststroke shows altered step length, decreased single-limb support time, reduced hip and knee joint angles, and increased ankle plantarflexion angle. 4,9-14 In addition, compensatory motor patterns are often observed during the hemiparetic gait, such as circumduction, vaulting, and pelvic hike. 2,15,16 Overground, treadmill, and treadmill with BWS are commonly used modes for stroke gait rehabilitation. Although a treadmill is traditionally used for an exercise mode among healthy individuals, it is clinically used for locomotor rehabilitation in individuals with mobility impairment. Researchers found that people poststroke decreased step length and increased cadence, stance phase percentage, single-limb support phase, and stance/swing ratio on the affected limb while walking on a treadmill as compared with overground. The changes in their gait patterns during treadmill ambulation are often associated with the improvement of gait symmetry. 18 The effects of treadmill-based gait training have been well List of Abbreviations ANOVA analysis of variance BWS body weight support CI confidence interval 3-D 3-dimensional

2 130 GAIT IN PEOPLE POSTSTROKE, Jung documented and include increases in lower-limb strength, walking speed, gait endurance, and cardiovascular function When people poststroke cannot bear their full body weight or maintain balance during treadmill walking, a BWS system can be used over the treadmill to accommodate their special needs for gait training. A comparison study between BWS treadmill and overground walking reported that people poststroke on a BWS treadmill showed increases of single-limb support phase, swing phase percentage, and swing symmetry as well as decreases of double-limb support phase on the affected limb. 26 Additional comparative studies found that people poststroke showed decreased spasticity in the plantarflexor muscles, vertical ground reaction force, and energy expenditure while improving muscle activation patterns in the shank during BWS treadmill walking. 26,27 Several studies reported the effectiveness of BWS treadmill gait training for stroke rehabilitation, including increases in overground walking velocity, gait endurance, functional balance, motor recovery, muscle strength, and oxygen consumption. Recently, aquatic exercise has gained more attention for stroke rehabilitation. The effects of aquatic exercise have been well documented in both healthy and elderly populations as well as people poststroke Chu et al 44 found an increase of gait speed after an 8-week aquatic exercise program for participants poststroke. In addition to the use of aquatic exercise for gait improvement, aquatic treadmill walking can be used for a task-specific training for individuals poststroke. The buoyancy of water can help them practice walking while bearing less body weight, which creates a similar environment to BWS treadmill gait training. 41 As with a conventional treadmill walking on land, an aquatic treadmill belt can assist people poststroke in performing aquatic walking with enhanced step response and rhythmic gait patterns. Aquatic treadmill gait training can also benefit from the water properties, such as temperature, viscosity, hydrostatic pressure, turbulence, and drag force. 45 The warm temperature of water can help people poststroke reduce hypertonicity, whereas the viscosity and hydrostatic pressure can provide postural support for impaired balance with less fear of falling. 41 The slow-moving environment in water caused by viscosity and drag force can also help people reduce the velocity-dependent spastic response. In addition to physiologic benefits, exercise in water can offer various psychologic advantages, such as motivating and supporting participants. These benefits can make it possible for patients poststroke to initiate early gait rehabilitation. In aquatic gait training, additional weight is frequently applied to the affected leg in the form of cuff weights. The use of cuff weights is based on an assumption that they may help stabilize the paretic leg and allow people poststroke to train walking efficiently in water. A lower percentage of muscle mass and a higher percentage of fat mass in the affected limb can create uncontrolled limb flotation while walking in water. 45 Aquatic specialists often use cuff weights for people with hemiparesis to minimize the unwanted limb flotation and compensatory gait patterns. Several studies 46,47 have documented that additional loads can increase stance phase duration and plantarflexor electromyographic activities during treadmill walking on land. Similar changes were observed during aquatic walking in healthy adults, and additional loads resulted in increased electromyographic activation of the plantarflexor muscles. 48 However, these previous studies involved only healthy populations, and the location of additional loading was near the center of mass or not specified. Previous research that investigated aquatic walking used physiologic and biomechanical measures, including electromyography, energy expenditure, kinetics, and 2-dimensional kinematics. Few of them used 3-D gait analysis to examine gait patterns in people poststroke. Because people poststroke exhibit various compensatory gait patterns, such as gait asymmetry, circumduction, vaulting, and pelvic hike, 15 it can be more insightful to analyze their motions in a 3-D perspective rather than 2-dimensional. Thus, the purpose of this study was to investigate how the application of additional weights to the affected leg influences gait patterns of people poststroke during aquatic treadmill walking via a 3-D underwater motion analysis system. It was hypothesized that the application of additional weights would change (1) the stance phase percentage of gait cycle, (2) the amount of unwanted limb flotation identified by the angle of peak hip flexion during the late swing phase, and (3) the amount of limb circumduction evaluated by the angle of peak hip abduction during the early swing phase of the affected limb. METHODS Participants A total of 22 participants poststroke with chronic hemiparesis (16 men, 6 women; average age, y) completed this investigation. Initially, 52 individuals poststroke were randomly recruited from local hospitals and community centers. Later, they were screened for eligibility to participate in this study. A total of 28 people were eliminated for not meeting the inclusion criteria, and 2 more persons were excluded for not being able to complete the test procedures. Inclusion criteria were (1) age over 40 years, (2) minimum 1 year poststroke, (3) ability to walk 10 minutes with or without an assistive device, and (4) ability to cooperate with the test procedures. Participants were excluded if they had (1) fear of water, (2) uncontrolled seizure, (3) cardiovascular or other medical conditions, (4) orthopedic surgery within the past 6 months, and (5) cognitive impairment that limited their ability to follow the test procedure. The study was approved by the Institutional Review Board, and informed consent was obtained from each participant. Setting/Instruments All participants walked on an aquatic treadmill a with the water level adjusted to chest depth (the xiphoid process level) via a movable-floor pool b in which the water temperature was maintained at 34 C. Before data collection, 15 waterproof reflective markers (10mm in diameter) were attached to the bony landmarks of the lower extremities by using the Helen Hayes lower-limb marker set model. 61 The 3-D trajectories of the lower-limb motions were captured via 6 waterproof under- Fig 1. Instrument setting: 3-D underwater motion analysis system and aquatic treadmill in the movable floor pool.

3 GAIT IN PEOPLE POSTSTROKE, Jung 131 Fig 2. Data collection: participant walking on the aquatic treadmill in 3 test conditions: (A) no weight, (B) knee weight, and (C) ankle weight. water lenses c (60Hz) connected to 6 digital video recorders d out of the water (fig 1). The 6 underwater lenses were positioned 1.5m away from the aquatic treadmill with approximately 60 of separation among them. A digital music player e was used to synchronize video clips from the 6 cameras with sound. Procedures The general procedure of this investigation required all participants to walk on an aquatic treadmill in 3 different test modes within a single day. The 3 test conditions were (1) no additional weight, (2) knee weight (a cuff weight placed right below the knee), and (3) ankle weight (a cuff weight placed right above the ankle) (fig 2). All test modes were compared at a consistent water depth individually adjusted to each participant s chest level, and a matched walking speed was applied across all test modes. After participants were informed about the test procedures and signed a consent form, they changed into a tight-fitting swimsuit and aqua shoes. A designated researcher measured the lower-limb anthropometric data and attached reflective markers on the bony landmarks. All participants were given a 5-minute practice trial that allowed them to get familiarized with aquatic treadmill walking. During the practice trial, participants were asked to select their comfortable walking speed and a preferred cuff weight (0.7kg or 1.1kg). Then, they walked on the aquatic treadmill in a randomized order. Each participant completed 3 test trials of 2-minute treadmill walking for each test condition. To minimize fatigue, a 2-minute rest period was provided after each test trial. All participants were instructed to hold onto the treadmill handrails for safety. Participants used an ankle foot orthotic if they had to wear it for overground walking. It took approximately 50 minutes to complete the whole test procedure. Data Process and Analysis Captured data were imported to Vicon Peak Motus software v9.2, f digitized, and reconstructed for 3-D coordinates. All raw data were low-pass filtered digitally (at 6Hz) by using a fourth-order 0-lag Butterworth filter. The spatiotemporal and lower-limb kinematic gait parameters were computed with the Vicon Peak Motus program. Gait variables from the affected limb were analyzed for this study. Spatiotemporal parameters were normalized by using the formula explained by Hof. 62 Statistical Analysis All data were examined for normality of distribution, equal variance, and independence of each observation in order to establish the statistical assumptions of ANOVA. 63,64 Repeatedmeasures ANOVA was used to examine any differences across 3 test modes. The significance level was adjusted with a Bonferonni correction (P.004) to reduce any possibility of creating errors by repeating ANOVA procedures for multiple gait variables. When ANOVA yielded a significant difference, post hoc analyses were conducted to identify which modes were significantly different from each other by using paired t tests with a Bonferonni correction. All statistical analyses were performed by using SPSS v software. g RESULTS A total of 22 participants completed aquatic treadmill walking trials in 3 test modes. Two participants had to wear an ankle foot orthotic during the test because they used it for functional overground walking. A summary of all participants profiles is presented in table 1. It was hypothesized that the use of an additional weight would alter gait variables on the affected limb compared with no weight condition. The results are summarized in table 2. The use of an ankle weight showed a significant increase in the stance phase percentage in the affected limb by 3% (P.015) compared with no weight condition. The stance phase percentage increased from 58.5% to 60.2% of the gait cycle (CI ). However, this change was not significant when a more stringent statistical analysis was used with a Bonferroni correction. Repeated-measures ANOVAs showed a significant difference in the peak hip flexion angle across 3 test conditions Table 1: Participants Profiles (n 22) Characteristics Descriptive Values and Frequencies Age (y) Height (m) Weight (kg) Time poststroke (mo) Type of stroke (n) Ischemia 14 Hemorrhage 8 Paretic side (n) Right 11 Left 11 Sex (n) Women 16 Men 6 NOTE. Values are mean SD or (n).

4 132 GAIT IN PEOPLE POSTSTROKE, Jung Table 2: Result Summary: Gait Parameters Comparison Across 3 Test Modes Mean SD P Variables N K A ANOVA N K K A A N Cadence (steps/min) NS NS NS NS Stride length (m) NS NS NS NS Stance phase % (cycle) NS NS NS 0.015* Hip flexion (deg) * NS Hip extension (deg) NS NS NS NS Hip abduction (deg) NS NS NS NS Hip adduction (deg) NS NS NS NS Hip internal rotation (deg) NS NS NS NS Hip external rotation (deg) NS NS NS NS Knee flexion (deg) NS NS NS NS Knee extension (deg) NS NS NS NS Ankle dorsiflexion (deg) NS NS NS NS Ankle plantarflexion (deg) NS NS NS NS Abbreviations: A, ankle weight; K, knee weight; N, no weight; NS, not significant. *Significant at P.05. Significant at P.004. (P.004). Both ankle and knee weight positions showed significant decreases in the peak hip flexion angle of the affected limb (P.003) during the late swing phase compared with no weight condition. The use of an ankle weight showed a significant reduction in the peak hip flexion by 7.9% (P.001, CI ). The peak hip flexion angle during the late swing phase decreased from 35.0 to The knee weight also decreased the peak hip flexion angle by 5.4% (P.015, CI ) from 35.0 to However, the change from the use of the knee weight was not statistically significant when a Bonferroni correction was applied. Additional weights did not change cadence, stride length, frontal or transverse plane hip motions, or sagittal plane motions of the knee and ankle joints. DISCUSSION Results Summary The main purpose of this study was to investigate gait pattern changes when a cuff weight was applied to the affected limb of people poststroke during aquatic treadmill walking. Three specific hypotheses were tested to elucidate if the use of an additional weight would change (1) stance phase stability, (2) unwanted limb flotation, and (3) circumduction of the affected limb. Stance phase stability was operationally defined as an ability to keep the stance phase for 60% of the gait cycle, and it was evaluated based on the stance phase percentage. Unwanted limb flotation on the affected side was marked by excessive hip flexion in the late swing phase during aquatic walking. Any changes in the unwanted limb flotation were assessed by the peak hip flexion angles during the swing phase. Lastly, circumduction was defined as forward-limb swing in a hemicircular pattern shown by a combination of excessive hip abduction and pelvic hike with anterior tilt. 16 We checked the peak hip abduction angle during the swing phase to determine if there was any change in circumduction. The first 2 hypotheses were supported by our results. People poststroke showed an increase of the stance phase percentage with an ankle weight. In addition, the use of a cuff weight, regardless of its position on either the knee or ankle, decreased the amount of excessive hip flexion of the swing leg on the affected side. However, our results did not support the third hypothesis on circumduction. Our analysis of the hip frontal plane kinematics did not show any statistical differences, but the kinematics graph displayed a trend of a decrease in the peak hip abduction during the swing phase with the use of an additional weight. Stance Phase Stability The results showed a trend that the use of an additional weight increased the stance phase percentage of the gait cycle (P.015). The stance phase increase from 58.5% to 60.2% would likely be meaningful even though the change was not statistically significant with a Bonferonni correction, and the percentage change (3%) was relatively small. The phase transition from stance to swing at 60% of the gait cycle is consistent with the outcomes from an aquatic gait study with healthy adults by Barela and Duarte. 49 It is also similar to the stance phase percentage of overground treadmill walking in healthy adults 15 as well as normal overground walking. 15,16 The stance phase increase also indicates that the ankle weight can improve stance phase stability. The additional weight on the affected limb may contribute to stabilizing the base of the stance foot, particularly in the single-limb support phase, during aquatic treadmill walking. With an ankle weight, the distal segment of the stance leg appears to have an improved anchoring effect on the base of support. The increased stability in the base of support must assist people poststroke by improving the dynamic balance required during aquatic treadmill walking. During aquatic walking in chest-depth water, the center of mass is elevated mostly because of the buoyancy of water. Approximately 75% of the body weight is supported during aquatic walking at the chest level as in our investigation. 45 The partial body weight support effects and the elevated center of mass tend to make the stance phase percentage shorter when compared with full weight-bearing walking. 65 Additional loading increases the stance phase percentage of the gait cycle in healthy adults both on land and in water. 46 Additional loading might trigger the central nervous system to exhibit different timing and intensity of muscle activation in the lower extremity. The altered muscle activations around the ankle may influence the stability of the stance limb. Also, the bracing effect from the ankle cuff weight may affect somatosensory inputs from the gastroc-soleus complex, possibly extending the stance phase percentage and enhanced stability. However, this

5 GAIT IN PEOPLE POSTSTROKE, Jung 133 walk comfortably, and most complained it was too heavy when any cuff weight heavier than 1.1kg was applied. In addition, we explored various options for developing more scientific and systematic weight-selection procedures. However, we could not establish a reliable protocol for the weight selection primarily because of large variability issues in physical profiles among our participants. We have piloted the use of paresis level, body composition, muscular strength, and limb girth in our attempt to set up a consistent system, but none of them provided any reliable basis for the weight-selection procedure. Based on our pilot trial outcomes and empiric evidence from our aquatic therapy programs, we determined that the weight options between 0.7kg and 1.1kg are most commonly used and appropriate for our investigation. Fig 3. Hip flexion/extension. Averaged kinematic graphs for sagittal plane hip motion (Flex. and Ext.) during aquatic treadmill walking in 3 test modes. Abbreviations: Ext., extension; Flex., flexion. explanation needs further investigations accompanied with electromyographic data. Conversely, it is possible that additional weights may have forced the paretic limb to delay the timing of transition from the stance to swing phase by demanding higher torque generation for pushoff in preswing. As a result, we may have observed the slightly prolonged stance phase percentage. A future study with kinetic measures could validate such explanation with more robust evidence. Unwanted Limb Flotation The sagittal plane hip kinematic findings revealed that an additional weight on the affected limb, regardless of its position, produced a significant decrease in the peak hip flexion during the late swing phase. This decrease indicates that a cuff weight can help people poststroke reduce the unwanted flotation of the paretic limb during aquatic walking. Unlike the hip kinematics of overground walking, the peak hip flexion during aquatic treadmill walking occurs much earlier in the late swing phase (fig 3). It also shows a greater degree of peak hip flexion when compared with that of the terminal swing phase or the initial stance phase. These together create the unnecessary fluctuation of hip flexion and extension in the late swing phase as displayed in figure 3. The premature and excessive peak hip flexion contributes to exhibiting unwanted flotation of the limbs and is more evident on the paretic side. The body composition of the paretic limb is different from the lessaffected side because of decreases in muscle mass and bone mineral density after a stroke. 66,67 The lower percentage of muscle mass, the higher percentage of fat mass, and the weak muscular strength in the affected limb can make the limb flotation more difficult to control during aquatic walking. 45 Additional weights appear to help minimize this unwanted flotation as revealed in our results. Moreover, with additional weights, the average peak hip flexion of the affected limb was similar to that of the less-affected limb, which can help promote gait kinematic symmetry. The improved kinematic symmetry can also affect spatiotemporal symmetry of gait, for which a further investigation is warranted. Initially, the application of heavier cuff weights than those used in this study was experimented. However, the majority of participants could not Circumduction We hypothesized that additional weights on the affected limb could change the degree of peak hip abduction during the swing phase. Our results did not support this hypothesis, showing no significant differences in the peak hip abduction among 3 test conditions. This suggests that the use of cuff weight may not be effective for reducing circumduction on the paretic side of the limb (fig 4). The kinematic graphs display the trend of a decrease in the peak hip abduction during the early swing phase with the use of an additional weight even though the change was not statistically significant. The circumduction in our study was defined as forward-limb swing in a hemicircular pattern with the extended knee shown by a combination of excessive hip abduction and pelvic hike with anterior tilt. 16,68 It appears that the assessment of peak hip abduction alone may not be sufficient enough to detect any changes in such a complex compensatory gait pattern. As suggested by Kerrigan s study, circumduction may need to be evaluated by comprehensive analyses of associated gait variables including pelvic tilt and obliquity as well as thigh angles. 68 The fact that our investigation focused on only the peak hip abduction during the swing phase might have limited our ability to find any changes in circumduction. In our recent preliminary study that compared kinematics of aquatic treadmill walking and conventional Fig 4. Hip adduction/abduction. Averaged kinematic graphs for frontal plane hip motion (Add. and Abd.) during aquatic treadmill walking in 3 test modes. Abbreviations: Abd., abduction; Add., adduction.

6 134 GAIT IN PEOPLE POSTSTROKE, Jung pool walking, we noticed that people poststroke walked with decreased peak hip abduction on aquatic treadmill. It is possible that the aquatic treadmill may constrain frontal plane hip motions regardless of the weight use because of its nature of stationary walking on a narrow path, whereas it may help people walk with less effort to fight against water resistance, turbulence, and drag force as compared with conventional pool walking. Other Variables Although the stance phase percentage showed a significant increase with an additional weight, other spatiotemporal parameters did not show any differences. No changes in cadence or stride length were found in this investigation. This may be related to the fact that the current study participants walked on an aquatic treadmill at a fixed belt speed. As documented, many gait parameters, particularly spatiotemporal gait variables, are dependent on gait velocity. Therefore, walking on a treadmill at a fixed speed might have limited our ability to observe any changes in spatiotemporal variables even when an additional weight was applied to the paretic limb. It may be insightful to repeat this study in a speed-matched conventional pool walking environment instead of aquatic treadmill walking. Although we found significant changes in sagittal plane hip kinematics, we did not find any alterations in the knee and ankle kinematics. This pattern of kinematic outcomes is consistent with what Miyoshi et al 48 reported. The authors documented no significant changes in the knee and ankle joint angles when an additional load was applied to healthy adults during aquatic walking, whereas they reported significant changes in the muscle activation amplitudes in the soleus and gastrocnemius. It is conceivable that the effects of additional weights on the sagittal plane of the knee and ankle kinematics might have been minimized by hydrodynamic factors, such as buoyancy and water resistance. Study Limitations All of our study participants were instructed to hold the front handrail during aquatic treadmill walking because many of them could not walk without using it. The use of the handrail could have affected our study outcomes, possibly by limiting trunk and arm movements. Second, our data-processing procedures could have imbedded limitations because we used a video-based retro-digitization technique for our 3-D underwater motion analysis protocol. Every effort was made to minimize any potential issues concerning the reliability of our data, such as designating a single researcher for all marker attachment and digitization procedures. However, this investigation took more processing steps, potentially creating more errors as compared with a real-time 3-D motion analysis system typically used for gait analysis on dry land. CONCLUSIONS The current study findings provide clinical evidence that the use of an additional weight on the affected limb can help clinicians and aquatic professionals offer more effective gait training in water for people poststroke or with similar hemiparetic conditions. The results show that the application of additional weights to the ankle of the paretic leg results in improved stability of stance phase. It also results in a decrease of unwanted flotation of the paretic leg independent of the weight placement of the leg, such as the knee or ankle. The increase of stance stability and the decrease of unwanted flotation with an additional weight can help individuals with hemiparesis to improve their gait symmetry. 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