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Background: The lumbopelvic region plays a pivotal role in enabling various functional activities. This study quantified and compared the kinematic changes between healthy individuals and patients with recurrent low back pain (LBP) in both rested and fatigued states to gain insight into the kinematic adaptation and mechanisms underlying kinematic variations that occur in the presence of these factors. Methods: Participants were divided into two groups: the LBP (n = 23) and healthy control groups (n = 19). Dynamic lumbopelvic measurements were taken using a biplane radiography image system while the participants performed weight-bearing forward-backward bending before and after fatigue. All lumbopelvic kinematics were described as the three-dimensional motion of the vertebra relative to the pelvis and were measured at normalized time intervals from maximum extension to approximately 45° of flexion. Results: Repetitive lifting- and lowering-induced fatigue significantly affected lumbopelvic kinematics in the anterior/posterior translation (mm) and rotation around the z-axis in both healthy individuals and patients with LBP (p < 0.05). In healthy individuals, significant differences occurred in approximately 13–83% of the forward-backward bending cycle (0–100%), whereas, in patients with LBP, significant differences mainly occurred in 61–93% of the cycle (p < 0.01). Conclusions: The lumbopelvic kinematic changes observed in both LBP patients and healthy individuals after fatigue may indicate protective compensation or vulnerability and could play a role in LBP dysfunction.

Traditional optical motion capture (OMC) with retroreflective markers is commonly used to measure joint kinematics but was also reported with unavoidable soft tissue artifacts (STAs) when quantifying the motion of the spine. Additionally, the patterns of the STA on the lumbar spine remain unclear. This study aimed to 1) quantify the in vivo STAs of the human lower back in three-dimensional directions during weight-bearing forward–backward bending and 2) determine the effects of the STAs on the calculated flexion angles between the upper and lower lumbar spines and adjacent vertebrae by comparing the skin marker (SM)- and virtual bone marker (VM)-based measurements. Six healthy volunteers were imaged using a biplanar radiographic system, and thirteen skin markers were mounted on every volunteer’s lower back while performing weight-bearing forward–backward bending. The STAs in the anterior/posterior (AP), medial/lateral (ML), and proximal/distal (PD) directions were investigated. The flexion angles between the upper and lower lumbar segments and adjacent intervertebral segments (L2–L5) throughout the cycle were calculated. For all the participants, STAs continuously increased in the AP direction and exhibited a reciprocal trend in the PD direction. During flexion, the STA at the lower lumbar region (L4–L5: 13.5 ± 6.5 mm) was significantly higher than that at the upper lumbar (L1–L3: 4.0 ± 1.5 mm) in the PD direction ( p < 0.01). During extension, the lower lumbar (L4–L5: 2.7 ± 0.7 mm) exhibited significantly less STAs than that exhibited by the upper lumbar region (L1–L3: 6.1 ± 3.3 mm) ( p < 0.05). The STA at the spinous process was significantly lower than that on both sides in the AP direction ( p < 0.05). The present results on STAs, based on dual fluoroscopic measurements in healthy adult subjects, presented an anatomical direction, marker location, and anatomic segment dependency, which might help describe and quantify STAs for the lumbar spine kinematics and thus help develop location- and direction-specific weighting factors for use in global optimization algorithms aimed at minimizing the effects of STAs on the calculation of lumbar joint kinematics in the future.

Alterations in the lumbo-pelvic coordination denote changes in neuromuscular control of trunk motion as well as load sharing between passive and active tissues in the lower back. Differences in timing and magnitude aspects of lumbo-pelvic coordination between patients with chronic low back pain (LBP) and asymptomatic individuals have been reported; yet, the literature on lumbo-pelvic coordination in patients with acute LBP is scant. A case-control study was conducted to explore the differences in timing and magnitude aspects of lumbo-pelvic coordination between females with (n=19) and without (n=19) acute LBP. Participants in each group completed one experimental session wherein they performed trunk forward bending and backward return at preferred and fast paces. The amount of lumbar contribution to trunk motion (as the magnitude aspect) as well as the mean absolute relative phase (MARP) and deviation phase (DP) between thoracic and pelvic rotations (as the timing aspect) of lumbo-pelvic coordination were calculated. The lumbar contribution to trunk motion in the 2nd and the 3rd quarters of both forward bending and backward return phases was significantly smaller in the patient than the control group. The MARP and the DP were smaller in the patient vs. the control group during entire motion. The reduced lumbar contribution to trunk motion as well as the more in-phase and less variable lumbo-pelvic coordination in patients with acute LBP compared to the asymptomatic controls is likely the result of a neuromuscular adaptation to reduce painful deformation and to protect injured lower back tissues.

Electromyography (EMG)-based measures of the trunk muscles behavior have been used for objective assessment of biomechanical impairments in patients with low back pain (LBP); yet the literature on normal age-related differences in such measures is scant. A cross-sectional study was designed to assess age-related differences in activity of trunk extensors during forward bending and backward return. Sixty asymptomatic individuals were recruited to form five gender-balanced age groups between 20 and 70 years old. Participants completed two sets of trunk forward bending and backward return task using self-selected and fast motion paces. For bending and return phases of each task, the normalized lumbar flexion angles corresponding to different event times of erector spinae activity along with the peak normalized and non-normalized EMG activities of erector spinae were calculated. The mean normalized and non-normalized EMG activities of erector spinae during the entire task also were calculated. There was no age-related difference in normalized lumbar flexion angles corresponding to different event times of erector spinae activity. However, the peak normalized EMG activity during forward bending and backward return as well as the mean normalized EMG activity during the entire task were found to be larger in older vs. younger individuals. Given the suggested unreliability of normalized EMG in elders and considering that we did not find any age-related differences in non-normalized EMG activity of erector spinae, our results do not strongly support the existence of normal age-related differences in EMG profile of erector spinae during forward bending and backward return. Therefore, when interpreting EMG-based measures of trunk muscles behavior for identification of biomechanical impairment in patients with LBP, potential abnormalities in EMG activity of trunk muscles may not be attributed to patient’s age.

We introduce a new Euler-type scheme and its iterative algorithm for solving weakly coupled forward-backward stochastic differential equations (FBSDEs). Although the schemes share some common features with the ones proposed by C. Bender and J. Zhang [Ann. Appl. Probab., 2008, 18: 143-177], less computational work is needed for our method. For both our schemes and the ones proposed by Bender and Zhang, we rigorously obtain first-order error estimates, which improve the half-order error estimates of Bender and Zhang. Moreover, numerical tests are given to demonstrate the first-order accuracy of the schemes.