## 1 Introduction  
Spondylosis refers to the chronic degenerative changes, such as bony osteophytes and excessences [1] within the region of the vertebral bodies, and the associated abnormalities, including segmental motion deviations, loss of vertebral disc height, and arthrosis of the facet joints [2]. Spondylosis is frequently found in middle-aged and older adults, with approximately 50% of individuals over forty years old and 85% of individuals over sixty years old being diagnosed with some degree of spondylosis [3; 4]. Depending on the level of the lesion, spondylosis may result in different alterations in the gait patterns and posture control [5; 6]. Compared to the other parts of the spine, the lumbar spine transmits the largest forces which are several times body weight during gait; thus, there is a higher risk of developing spondylosis [7; 8] in this region of the spine. Lumbar spondylosis (LS), mostly at L4-L5, may change not only the mechanics of the motion segment, but may also compress the cauda equina and lumbosacral nerve roots [9]. Both would lead to severe radicular pain of the lower back and/or down to one or both lower extremities [10] with restricted mobility, absent reflex, sensory changes, and muscle weakness [9; 11]. As the disease progresses, patients with LS may develop motor disturbances [12; 13], altered gait patterns, loss of balance [14], and increased risks of falling [15; 16]. Therefore, quantitative measurement of the static postural balance and dynamic gait balance in patients with LS will be useful for a more complete assessment of the progression of the disease and the risk of falls in this population. Balance control has been defined as the control of the body's position in space for the purpose of balance and orientation [17; 18]. The effectiveness of the ability of an individual in maintaining standing balance is usually assessed using variables derived from trajectories of the center of pressure (COP) of the ground reaction forces (GRF) [19; 20]. Those COP variables provide critical information which is helpful for understanding how the human body controls and maintains standing balance [21; 22; 23; 24]. Typically, the COP sway during quiet standing has been well accepted as an index to evaluate balance: the greater the COP sway, the worse the balance ability. The COP total distance is also frequently used to quantify the standing balance control [25; 26]. However, these variables are not directly applicable to the dynamic balance during walking as the COP moves along in the direction of the progression of gait. Dynamic balance control during motion is best evaluated through the description of the motion of the body's center of mass (COM) relative to the COP. During dynamic conditions, the COM can be much further away from the COP without loss of balance, as long as the COM is controlled at an appropriate velocity relative to the COP [27]. The velocity of the COM relative to the COP, as well as the influence of the body height or leg length, should be considered [28; 29]. This can be evaluated by the inclination angles (IA) of the line connecting the COM and the COP in both sagittal and frontal planes [30], and the rate of change of IA (RCIA), enabling a more complete description of the control of the body's posture [31]. Generally, the further the COM diverges from the COP (i.e., greater IA) the more difficult it becomes, and more effort (e.g., joint moments) is needed to achieve an RCIA appropriate for dynamic balance [32]. A previous study has shown that the IA and RCIA of patients with scoliosis were associated with the severity of the spinal deformity [33]. Therefore, COM-COP IA and RCIA are now becoming the typical parameters for evaluating balance control in patients with impaired motor or balance control diseases during locomotion [34].