## 1 Introduction  
Gait disorder is a common complication after stroke, affecting over 80% of survivors [1]. Even after acute stroke rehabilitation, 18% are still unable to walk, 11% require assistance to walk, and only 50% are able to walk independently [2]. Particularly, reduced gait speed is an important indicator of dysfunction and is strongly associated with impaired mobility, restricted community participation, and lower quality of life [3, 4]. Therefore, gait speed is generally used as a sensitive indicator of the level of gait function recovery in patients post-stroke [5, 6].  
Stroke survivors generally walk at a speed of 0.3-0.8 m/s, significantly slower than the average 1.4 m/s observed in healthy older adults [7]. A gait speed of 0.8-1.0 m/s is generally needed for safe daily ambulation, including crossing a street [6, 8]. Furthermore, a gait speed greater than 0.83-1.0 m/s is recommended to optimize energy expenditure during walking [9].  
Gait speed, an indicator of gait performance in patients who have had a stroke, is associated with many temporospatial gait parameters, including cadence, stride length,double support duration, paretic and nonparetic stance duration, and stride period [1]. Reports of previous studies show that progressive speed-dependent treadmill training improves cadence, step length, and stride length in patients post-stroke [10,11]. Recently, the attention given to the relationship between motor recovery and gait speed in stroke rehabilitation has increased. Furthermore, there has been emphasis on qualitative and quantitative analyses of gait patterns to better understand this correlation [9,12,13]. [PERSON] et al. found that training focused on maximal gait speed was a crucial determinant of long-distance walking ability in stroke survivors [13]. Similarly, other research has shown that walking fast can significantly reduce energy expenditure during ambulation [14].  
Many studies have explored the relationship between gait speed and motor recovery in patients post-stroke; however, most have focused on difference analysis for spatiotemporal parameters, joint angles, or other kinematic parameters between fast and comfortable walking speeds on a treadmill [14, 15, 16]. Biomechanical involvement of lower limb muscles, including the rectus femoris, biceps femoris, and gastrocnemius, is important in determining gait speed after stroke [15,17,18]. However, studies investigating how lower limb muscle activation varies with gait speed on over-ground surfaces are limited [19]. Particularly, studies on kinematics and lower limb muscle activation during slow gait in patients who have had a stroke are limited [20]. A more definitive investigation into the biomechanical involvement of lower limb muscles during slow walking is needed, as slowing down below a comfortable walking speed requires more complex motor control strategies [21].  
Therefore, the aim of this study is to investigate how the over-ground walking speed variation (slow, preferred, and maximum) affects lower limb muscle activity and gait in patients post-stroke. We hypothesized that changes in walking speed would significantly influence lower limb muscle activity and gait parameters in patients post-stroke.