Effects of Knee Flexion Angles on the Joint Force and Muscle Force during Bridging Exercise: A Musculoskeletal Model Simulation

Bridging exercise is commonly used to increase the strength of the hip extensor and trunk muscles in physical therapy practice. However, the effect of lower limb positioning on the joint and muscle forces during the bridging exercise has not been analyzed. The purpose of this study was to use a musculoskeletal model simulation to examine joint and muscle forces during bridging at three different knee joint angle positions. Fifteen healthy young males (average age: 23.5 ± 2.2 years) participated in this study. Muscle and joint forces of the lumbar spine and hip joint during the bridging exercise were estimated at knee flexion angles of 60°, 90°, and 120° utilizing motion capture data. The lumbar joint force and erector spinae muscle force decreased significantly as the angle of the knee joint increased. The resultant joint forces were 200.0 ± 23.2% of body weight (%BW), 174.6 ± 18.6% BW, and 150.5 ± 15.8% BW at 60°, 90°, and 120° knee flexion angles, respectively. On the other hand, the hip joint force, muscle force of the gluteus maxims, and adductor magnus tended to increase as the angle of the knee joint increased. The resultant joint forces were 274.4 ± 63.7% BW, 303.9 ± 85.8% BW, and 341.1 ± 85.7% BW at a knee flexion angle of 60°, 90°, and 120°, respectively. The muscle force of the biceps femoris decreased significantly with increased knee flexion during the bridging exercise. In conclusion, the knee flexion position during bridging exercise has different effects on the joint and muscle forces around the hip joint and lumbar spine. These findings would help clinicians prescribe an effective bridging exercise that includes optimal lower limb positioning for patients who require training of back and hip extensor muscles.


Introduction
Optimal hip extensor and trunk muscle strength have been associated with injury prevention, pain reduction, and an enhancement of athletic performance [1][2][3][4]. Bridging exercise is an accepted component of physical therapy programs that assist in strengthening these muscle groups of the back. Muscle activity during the bridging exercise has been analyzed with electromyography (EMG) [5][6][7][8]. Tese studies revealed that the activities of the biceps femoris and erector spinae are greater during bridging than during walking. However, muscle activity during the bridging exercise changes depending on the knee fexion position due to the alteration of the relative position of the joint center and the foor reaction force acting on the feet. Previous studies have focused on the muscle activity induced during various bridging exercises; however, studies examining the joint forces during bridging exercises are scarce. An increase in muscle activity during exercise is associated with increased muscle force. Previously, it has been shown that approximately 80% of the joint force depends on the tensile force generated by the muscles crossing the joint and that the contribution of muscle force towards joint force is greater than that of the ground reaction force [9]. Consequently, the knee fexion angle during bridging might afect both muscle and joint forces [10][11][12][13]. Mechanical loading has been identifed as an important risk factor in the development of joint pain [14,15]. Terefore, an understanding of joint forces during the bridging exercise could be an important factor for consideration when prescribing an appropriate physical therapy program.
Numerous studies have investigated the joint and muscle forces during static standing, gait, squatting, forward lunging, and lifting [16][17][18]. Joint and muscle forces were typically estimated using musculoskeletal model simulation from the kinematic and kinetic data measured by a motion capture system and a force platform. Conversely, few studies have analyzed the joint and muscle forces during supine exercise due to the difculties of measuring the foor reaction force and analyzing the subsequent kinetic data. However, an optimization method has recently been used for estimating the foor reaction force. Tis method enables the estimation of the external force acting on humans so as to the external force is balanced with the gravity and the acceleration of the center of mass. Tis allows the kinetic analysis using a musculoskeletal model simulation in various exercises, including supine exercise, without requiring the measurement of the foor reaction force [19][20][21].
Despite the frequent utilization of the bridging exercise in physical therapy practice, the efect of lower limb position on the joint and muscle forces during bridging has largely been overlooked. Te purpose of this study was to use a musculoskeletal model simulation to examine the joint and muscle forces around the hip joint and the lumbar spine during the bridging exercise performed at three knee joint angle positions. We hypothesized that the joint force in the lumbar spine and the hip decreases during bridging exercise with an increased knee fexion angle due to an decrease in the moment arm of a foor reaction force acting on the feet and around the lumbar spine and hip joint.

Exercise and Motion
Capture. Te bridging exercise with knee fexion angles of 60°, 90°, and 120°was evaluated using a motion capture system and surface EMG. Te knee fexion angles were measured using a goniometer to standardize the foot positions for the bridging exercises ( Figure 1). To maximize stability, participants performed all the bridging exercises with bare feet while arms and other body parts rested on the foor. Each participant steadily raised his pelvis to his maximum hip extension angle for two seconds, held this position for one second, and lowered it for two seconds. Bridging exercises with three lower limb positions were randomly performed fve times.
Motion capture was performed using an 8-camera OptiTrack Flex13 system (NaturalPoint, Corvallis, OR, USA) with a sampling frequency of 100 Hz. Te validity of this system has been confrmed in previous studies [22][23][24]. Each subject wore 40 refective markers based on a plug-in-gait marker set [18]. Posterior markers could not be captured in the supine posture; therefore, they were attached anteriorly to the same segment to enable capturing and defning of the local coordinate system of the segment.

Musculoskeletal Model.
Te present study utilized a 42 degrees-of-freedom full-body musculoskeletal model (AMMR v.2.1.1, AnyBody 7.1) for the analysis of joint and muscle forces. Marker trajectories were fltered using a Butterworth low-pass flter at a 6 Hz cut-of frequency [25]. Anthropometric data, including weight, height, and segment length, were used to scale the musculoskeletal model to match each study participant.
To estimate the external force exerted from the foor during exercise, 83 contact points between the body surface and the foor were defned on each body segment in the original model. In the supine model, one contact point was determined for the occiput, 42 points for the spine, six points for the bilateral upper limbs, eight points for the ischium, 14 points for the bilateral thighs, six points for the bilateral lower limbs, and six points for both soles ( Figure 2). Contact was determined by the distance between the foor and the contact point on the body [20], and contact elements provided compressive reaction forces. Te external force during bridging was estimated using an optimization algorithm to balance the motion of the human body model.
Each muscle was simulated using a three-element muscle model, consisting of a Hill-type contractile element, a parallel-elastic element, and a series-elastic element. Te contractile element included the force-length and forcevelocity relationships as well as the efects of the pennation angle. Te parallel-elastic element consisted of a nonlinear spring whose stifness was governed by the passive forcelength relationship to the muscle. Muscle forces were computed through inverse dynamic and optimization analysis by minimizing the sum of the cubes of muscle recruitment [26,27]. Te intersegmental resultant, proximal-distal, anterior-posterior, and mediolateral joint forces acting on the lumbar (L4-L5) spinal joint and hip joint were analyzed during bridging. Te joint force was calculated based on the net joint and tensile forces of the muscles crossing those joints and resolved into three components based on the reference frame of the child segment. Vertical, anterior, and medial forces were represented as positive values. Te following fve muscles were analyzed: gluteus maximus (GMAX), adductor magnus (ADDM), biceps femoris long head (BFLH), erector spinae (ES), and multifdus (MF). Joint and muscle forces were normalized to each participant's body weight (%BW).

Electromyography.
A signal acquisition system (biosignals plux, PLUX S.A., Lisbon, Portugal) was used to measure EMG [28] based on the SENIAM (surface EMG for noninvasive assessment of muscles) recommendations [29]. Te acquisition procedure followed the directives of the International Society of Electrophysiology and Kinesiology (acquisition at a sampling frequency of 1000 Hz and fltering using a band-pass flter between 10 and 500 Hz). Participants were required to undergo maximum voluntary contraction (MVC) tests for normalization. Te activation of GMAX, BFLH, ES, and MF was expressed as %MVC. Te normalization tests were performed based on Kendall's manual muscle testing [30]. Te MVC for the GMAX was measured by the hip extension with 90°knee fexion, against the resistance applied just above the popliteal fossa in the prone position. Te MVC of BFLH was measured at the 50°knee fexion, against the resistance applied just above the ankle, in the prone position. Te MVC of ES and MF was measured by the trunk extension in the prone position, against the resistance applied to the upper back.

Statistical Analysis.
Te mean joint force, muscle force, and EMG data during the one-second holding position with maximum hip extension were calculated. Te mean from the fve trials in each bridging exercise was analyzed. Te normality of distribution was tested using the Shapiro-Wilk test. If normality of distribution could be assumed, data were analyzed using the one-way repeated measures ANOVA  with Schafer's post hoc test to determine the efect of knee position during bridging exercise on joint and muscle load. If the normality of distribution could not be assumed, data were analyzed using the Friedman test with the Wilcoxon signed-rank test adjusted with the Holm post hoc test. In addition, efect sizes were expressed as η 2 (0.01 � small efect, 0.06 � medium efect, and 0.14 � large efect) [31].
All statistical tests were performed using the R software package (version 2.8.1). For all analyses, the threshold of signifcance was established at an alpha of 0.05. Te joint and muscle forces and EMG data determined in this study are presented as mean and standard deviations.

Muscle Forces and Electromyography.
Te GMAX and ADDM muscle forces increased signifcantly as the angle of knee fexion increased (Table 2). Conversely, the muscle forces of the MF, ES, and BFLH decreased signifcantly as the angle of knee fexion increased.
Te MF, ES, and BFLH muscle activity decreased signifcantly as the angle of knee fexion increased, similar to the muscle force. In contrast, the muscle activity of the GMAX was not afected by the angle of the knee joint (Table 3).

Discussion
We analyzed the efect of knee joint angles on joint and muscle forces in the lumbar spine and the hip joint during the bridging exercise. We hypothesized that the joint forces would decrease as the knee fexion increased. Our results showed that although the lumbar joint force decreased in bridging with increased knee fexion, the hip joint did not.
Te resultant lumbar joint force decreased in the bridging exercise with increased knee fexion. Similarly, the proximal, distal, and anterior lumbar forces decreased during bridging with increased knee fexion. Lumbar joint force is largely afected by ES and MF muscle forces. During bridging exercise, the external fexion moments in the lumbar and hip joints are caused by the foor reaction force acting on the bilateral feet. Tus, increasing the knee fexion angle during bridging exercise decreased the distance between the foor reaction force and the center of the lumbar and hip joints, resulting in decreased external fexion moment [9]. Te observed decrease in the muscle force in the ES and MF during the bridging exercise with increased knee fexion refects the decrease in the external lumbar fexion moment. Tese results are consistent with ES and MF muscle  Note. * P < 0.05 vs 90°; * * P < 0.01 vs 90°; †P < 0.05 vs 120°; † †P < 0.01 vs 120°. All variables were assumed to be normally distributed.
activation as measured using EMG in both the present as well as previous studies [13,32]. Terefore, an increased knee fexion angle decreased the load on the lumbar joints and musculature during bridging exercise. Lumbar joint force during bridging ranged from approximately 150%BW to 200%BW and was larger than the previously reported joint force of 100-130%BW during walking [33,34]. Tis observation suggests that although bridging is performed in a supine position, this exercise exerts a larger force on the lumbar spine than the force exerted by walking. Furthermore, these fndings suggest that the physical therapists should carefully position the lower limb during bridging in order to mitigate the load on the lumbar joints and surrounding musculature. Conversely, the resultant force of the hip joint increased during bridging with increased knee fexion. Similarly, proximal-distal, medial, and posterior forces increased during the bridging exercise with increased knee fexion. Te hip joint force was greatly afected by the muscle force of the hip extensor muscles. Te ADDM muscle force was 75.7%BW at 120°k nee fexion, which was the highest among the muscles analyzed in this study. Te hip extension moment is generated sequentially by the GMAX, hamstrings, and ADDM, as they cross the posterior hip joint. An increase in the knee fexion angle shortens the biceps femoris [35] and decreases the maximal force generated by the biceps femoris according to the length-tension curve. Te force of the ADDM, rather than that of the hamstrings, generated the hip extensor moment as noted by increased tension force during bridging with increased knee fexion. Previous studies have reported that the moment arm of the ADDM is smaller than that of the other hip extensor muscle groups, such as the hamstrings, at a neutral hip position [36,37]. Te muscle with a short moment arm with respect to the joint center requires a larger tension force when compared to a similar joint moment generated by the muscle with a larger moment arm. Tus, the recruitment of the ADDM during bridging with increased knee fexion would increase the resultant force acting on the hip joint. Considering the pathway of this muscle, increased activation of the ADDM would also contribute to the increase in both medial and posterior forces. Te largest hip joint force during bridging exercise was 341.1% BW in this study. Tis force is almost equivalent to that observed during walking (367-430%BW) [38,39]. While the bridging exercise with a 120°knee fexion position is considered a supine exercise supported bilaterally by the feet and the back, a therapist should pay attention to the hip joint force.
Increased muscle force of the GMAX would also contribute to the increase in the hip joint force during bridging with increased knee fexion. However, consistent with previous studies [8,24], GMAX activity measured using EMG during the bridging exercise was not signifcantly afected by the knee fexion position. Te EMG muscle activity measurement is impacted by the thickness of the subcutaneous fat [40,41], and this might be a potential factor responsible for the observed discrepancy between the GMAX muscle force estimated by the musculoskeletal simulation and the GMAX muscle activation measured using EMG.
Tis study had several limitations. Due to the difculty of measurement in the supine position, we analyzed muscle and joint forces using foor reaction force estimated by the optimization technique. We also used surface EMG to estimate muscle activity during the bridging exercise. Although the muscle force and muscle activity were consistent in the MF, ES, and BFLH depending on the exercise conditions, the GMAX force and activity measurements were inconsistent. Also, the ADDM was not analyzed by EMG due to crosstalk. We estimated the muscle and joint forces in healthy young males by simulation using a scaled musculoskeletal model base on average male characteristics. Terefore, these results should be cautiously adapted to females, older people, and people with pathological conditions. Additional studies are required to address these issues and to perform a comprehensive analysis of the efect of the lower limb position on the muscle and joint forces around the hip joint and lumbar spine during the bridging exercise. Further investigations will also be needed to generalize these fndings to people requiring exercise, including frail older people and people with lower back pain.

Conclusions
In conclusion, knee fexion during the bridging exercise has diferent efects on the joint forces of the lumbar spine and hip joint. Moreover, depending on the knee joint fexion position, those joint forces could be equal to or greater than those during gait. Tis study has provided the basic data to help clinicians prescribe the optimal lower limb position during the bridging exercise for patients who require training of the back and hip extensor muscles.

Data Availability
Te data used to support the fnding of the current study are available from the corresponding author upon request.

Conflicts of Interest
Te authors declare that they have no conficts of interest regarding the publication of this paper. Note. * P < 0.05 vs 90°; * * P < 0.01 vs 90°; †P < 0.05 vs 120°; † †P < 0.01 vs 120°. Multifdus and erector supine muscle activities were assumed to be normally distributed.
Journal of Healthcare Engineering 5