Influence of spinal disc translational stiffness on the lumbar spinal loads, ligament forces and trunk muscle forces during upper body inclination

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Influence of spinal disc translational stiffness on the lumbar spinal loads, ligament forces and trunk muscle forces during upper body inclination Rizwan Arshad, Thomas Zander, Maxim Bashkuev, Hendrik Schmidt∗ Julius Wolff Institute, Charité – Universitätsmedizin Berlin, Augustenburger Platz 1, 13353 Berlin, Germany

a r t i c l e

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Article history: Received 10 April 2016 Revised 4 May 2017 Accepted 27 May 2017 Available online xxx Keywords: Inverse statics Musculoskeletal modeling Spinal loads Spinal disc stiffness Muscle forces

a b s t r a c t Inverse dynamic musculoskeletal human body models are commonly used to predict the spinal loads and trunk muscle forces. These models include rigid body segments, mechanical joints, active and passive structural components such as muscles, tendons and ligaments. Several studies used simple definition of lumbar spinal discs idealized as spherical joints with infinite translational stiffness. The aim of the current sensitivity study was to investigate the influence of disc translational stiffness (shear and compressive stiffness) on the joint kinematics and forces in intervertebral discs (L1−L5), trunk muscles and ligaments for an intermediately flexed position (55°). Based on in vitro data, a range of disc shear stiffness (10 0−20 0 N/mm) and compressive stiffness (190 0−270 0 N/mm) was considered in the model using the technique of force dependent kinematics (FDK). Range of variation in spinal loads, trunk muscle forces and ligaments forces were calculated (with & without load in hands) and compared with the results of reference model (RM) having infinite translational stiffness. The discs’ centers of rotation (CoR) were computed for L3−L4 and L4−L5 motion segments. Between RM and FDK models, maximum differences in compressive forces were 7% (L1−L2 & L2−L3), 8% (L3−L4) and 6% (L4−L5) whereas in shear forces 35% (L1−L2), 47% (L2−L3), 45% (L3−L4) and more than 100% in L4−L5. Maximum differences in the sum of global and local muscle forces were approximately 10%, whereas in ligament forces were 27% (supraspinous), 40% (interspinous), 56% (intertransverse), 58% (lig. flavum) and 100% (lig. posterior). The CoRs were predicted posteriorly, below (L3−L4) and in the disc (L4−L5). FDK model predicted lower spinal loads, ligament forces and varied distribution of global and local muscle forces. Consideration of translational stiffnesses influenced the model results and showed increased differences with lower stiffness values. © 2017 IPEM. Published by Elsevier Ltd. All rights reserved.

1. Introduction Inverse dynamic musculoskeletal models are frequently used to predict the joints reactions, bending moments and trunk muscle forces for different body movements and postures [1,2]. These findings are helpful in many areas such as work place safety design, ergonomics, injury prevention, performance enhancement, implant design and rehabilitation management. Due to large scale of musculoskeletal multibody models, involving several rigid body segments connected by mechanical joints, including muscle tendon complexes and ligaments, many of the modeling aspects are sim∗ Corresponding author. Julius Wolff Institute, Charité – Universitätsmedizin Berlin, Augustenburger Platz 1, 13353 Berlin, Germany E-mail address: [email protected] (H. Schmidt).

plified. One such simplification is the idealization of the intervertebral discs as spherical joints having 3 rotational degrees of freedom (DoF) and infinite translational stiffness (zero translations). In reality, intervertebral discs have complex structure [3] which makes it flexible in all directions with a high load bearing capacity and provide ability to deform against the internal and external loads [4]. During large movements such as upper body flexion, lumbar spinal discs deform and allow relative translations of the vertebral bodies such as in anterior – posterior direction ranging from 1 to 4 mm and axial direction up to 2 mm [5]. Recently, Ghezelbash et al. showed that ignoring translational flexibilities influences the prediction of spinal loads and muscle forces up to moderate level for larger inclinations [6]. The study was based on the comparison between a specific nonlinear finite element model with a single set of model properties and other two models (stiffened finite element

http://dx.doi.org/10.1016/j.medengphy.2017.05.006 1350-4533/© 2017 IPEM. Published by Elsevier Ltd. All rights reserved.

Please cite this article as: R. Arshad et al., Influence of spinal disc translational stiffness on the lumbar spinal loads, ligament forces and trunk muscle forces during upper body inclination, Medical Engineering and Physics (2017), http://dx.doi.org/10.1016/j.medengphy.2017.05.006

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model & hinge joint model) with no translational flexibilities. However, the sensitivity of the predicted forces in lumbar joints, individual trunk muscles groups and ligaments to the normal range of translational stiffnesses was not investigated. Several in vitro studies measured shear stiffness of healthy spinal discs with and without preload [7–10]. These studies reported significant differences among the measured stiffness values due to age, sex or different spinal levels. Reported average values of the shear stiffness were 100−460 N/mm. Also, the compressive stiffness of the lumbar discs were reported in earlier investigations showed a wide range from 70 0−250 0 N/mm [11–13]. These variations exist due to large inter-subject variability, leading to numerous possible values that could be used in the inverse dynamic models. During upper body inclination, the influence of disc compressive stiffness (CS) and shear stiffness (SS) on the prediction of forces in spinal discs, trunk muscles and ligaments as well as the joint kinematics requires quantitative assessment to better understand the inter-individual differences. Therefore, the aim of the present sensitivity study was to show how spinal disc translational stiffnesses influence joint translations, discs’ center of rotation, lumbar spinal loads, trunk muscle forces and ligament forces [9,11,12,14–19] for an intermediately flexed position. 2. Methods 2.1. Reference model A commercially available musculoskeletal standing human body model (AnyBody, ver. 1.6) was used (Fig. 1). The reference model was validated previously for several activities [1,20–22]. The body height (180 cm) and body weight (75 kg) were adapted to the 50th percentile of a normal European male. The model comprised of rigid segments for the skull, arms, spine, pelvis, and legs. The trunk composed of rigid vertebral bodies for the cervical region, lumped thorax (T1−T12) assumed as one rigid body due to limited range of motion [23], five lumbar vertebrae (L1−L5) and sacrum. The biomechanical properties of lumbar ligaments (level dependent linear ligament stiffnesses, length of ligaments, crosssectional area etc.) for supraspinous (SSL), interspinous (ISL), intertransverse ligament (ITL), ligamentum flavum (LF), posterior longitudinal (PLL) and anterior longitudinal (ALL) were included in the default model [24,25]. Here, the lumbar ligaments slack lengths were pre-calibrated for the standard AnyBody model. The ligament forces at the initial position of standing were zero and generate a tensile force when stretched beyond the slack length. Trunk, arms and legs muscles were included in the model. These muscles were modeled to exert tensile forces only. The values for specific muscle tension vary in reported literature [26,27], however a default value of 90 N/cm2 was used. A total of 188 muscle fascicles of the lumbar spine were included in the model [28]. The trunk musculatures were grouped as global i.e. 1 rectus abdominis (RA), 12 internal oblique (IO), 12 external oblique (EO), 16 iliocostalis lumborum pars thoracic (ILPT), 24 longisimus thoracis pars thoracic (LTPT) and local muscles, i.e. 8 iliocostalis lumborum pars lumborum (ILPL), 10 longisimus thoracis pars lumborum (LTPL), 22 psoas major (PM), 18 iliacus (IL), 38 multifidus (MF) and 10 quadratus lumborum muscle fascicles (QL). The load distribution among the muscles groups comes in the form of muscle recruitment criterion that should satisfy the basic notions of neuromuscular control [29] as well as the underlying principles of musculoskeletal biomechanics [30]. In previous studies, several muscle recruitment criterions had been proposed and discussed [31–34]. Here, a default third degree polynomial muscle recruitment criterion (Eq. (1)) was used that insures high synerPlease

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Fig. 1. A musculoskeletal model at intermediately flexed position (55°).

gism among the muscles [31].

Minimize G =

N 

σ3

(1)

i=1

Here, G is the objective function, σ is the muscle activity, i is the muscle number and N is the total number of muscles. The IAP in a human body varies with different body postures, movements and loading conditions [35–38]. Several studies reported that the intra-abdominal pressure (IAP) increases stiffness of the spine and relieves the spinal loads during upper body flexion [39–42]. In vivo measurements showed that the IAP generated of

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during the flexed posture was up to 4.4 kPa (flexed 30°, 80 N in hands) [43]. Here, in the inverse static model, the IAP was generated by an artificial muscle that acted on the abdominal volume (idealized as a cylinder). As the abdominal volume changes for the given posture or the body movement, the changes in the volume measure lead to the change in IAP which also influenced the predicted forces in abdominal muscles, therefore becoming a part of an overall muscle recruitment problem. For the given posture, the IAP generated within the model was in the range of 3.5−3.7 kPa (no load) and 5.4−5.9 kPa (180 N in hands), found to be consistent with findings in literature [43]. The maximum IAP that could be generated within the model for any activity was limited to a value of 26.6 kPa [44].

the position of both arms was kept vertical to the ground level with or without load in hands. Spinal loads were presented for the lumbar discs L1−L2, L2−L3, L3−L4 and L4−L5 motion segments. The shear forces were computed in anterior (+) – posterior (–) direction parallel to the surface of the upper endplate of the lower vertebra and compressive forces in perpendicular direction. In FDK model, the shear and axial translations were calculated from the default CoR of the lumbar discs i.e. at the location of spherical joint in the RM. Here, the rigid bodies of upper and lower vertebrae were connected by the definition of two local reference frames defined at the spherical joint. The joint motion (rotation & translation) of the local reference frame of the upper vertebra was calculated with respect to the local reference frame of the lower vertebra. The global and local muscles forces were computed by summation of forces in respective muscles group fascicles. In addition, the distribution of forces in global and local muscles were presented as percentage of the sum of global and local muscle forces and were compared for the differences between RM and FDK model. Also, the percentage difference in ligament forces between RM and FDK models were computed in lumbar ligaments (SSL, ISL, ITL, LF, PLL, ALL) for each lumbar segment. The CoRs were predicted for L3−L4 and L4−L5 motion segments and compared qualitatively with results from the previous literature [18,19,50–52]. The CoRs were computed by Reuleaux method [53] between the adjacent vertebrae and between the initial and final position.

2.2. Remodeling lumbar joints The lumbar spinal discs in the reference model were assumed to be spherical joints (ball-and-socket-joint) having 3 rotational DoF and 3 translational constraints. The lumbar joints rotational stiffness in flexion was 1.8 Nm/° [45] and the rotational disc stiffness of 0.54 Nm/° was included in the model [46]. In general, the spherical joints have 3 translational constraints. A feature known as force dependent kinematics (FDK) was used that allows translations in all three anatomical directions [47]. This allowed the modeling of small translations in the lumbar discs by softening the constraints and setting up the translational stiffness with an elastic element that provided the reaction forces. In FDK model, the translational constraints in axial and shear directions for lumbar joints (L1−L5) were made force dependent. During inverse analysis, the FDK solver numerically solves the equilibrium equations and finds the static equilibrium (velocity and accelerations assumed zero for force dependent DoF) in axial and anterior-posterior directions. As a result, translations were computed against the translational stiffness provided within the model and the spinal loads, trunk muscle forces and ligament forces were computed to attain the equilibrium condition. To insure the compliance with equilibrium requirements in all the force dependent DoF, the residuals of the numerical computations (force dependent kinematic error) were kept within the default tolerance range.

3. Results The results from RM and FDK models showed differences in the compressive (Fig. 2a and b) and shear forces (Fig. 2e and f) between the two models and the variation for the range of translational stiffnesses in the FDK model (Table 1). For flexed posture, the axial translations showed compression in all the lumbar discs (Fig. 2c and d) that were within the range of −0.6–(−1.2) mm whereas anterior – posterior shear translations (Fig. 2g and h) were computed in the range of −0.79−1.24 mm (Table. 1). The compressive and shear forces predicted with the RM (FRM ) were comparatively higher than the FDK model (FFDK ). The maximum difference (|FRM −FFDK | / max (|FRM |, |FFDK |)) for compressive loads between RM and FDK models were 7% (L1−L2 & L2−L3), 8% (L3−L4) and 6% (L4−L5) whereas for shear forces differences were 35% (L1−L2), 47% N (L2−L3), 45% (L3−L4) and greater than 100% in L4−L5. The percentage variation (|FFDK, max – FFDK, min | / |FFDK, max |) in shear and compressive forces for the given range of translational stiffnesses were 18−51% and 1−3% for all the lumbar segments. In FDK model, the global muscle groups, ILPT and LTPT showed an increase in forces with translational flexibilities (Fig. 3a and b) whereas EO and IO muscles forces decrease (Table 2). During flexed position, almost no activity was predicted in RA muscles. The forces in local muscle groups were decreased in ILPL, LTPL and IP muscles and predicted an increase in MF and QL muscle forces (Fig 3c and d). For global muscle groups the maximum difference between RM and FDK model results were 23% (ILPT), 28% (LTPT), 22% (EO) and 19% (IO) and for local muscles were 15% (ILPL), 23% (IP), 15% (LTPL), 3% (MF) and 37% (QL), respectively. The maximum difference in the sum of global and local muscle forces computed between the RM and FDK models were about 10%. The distribution of the sum of global and local muscle forces among the respective muscles groups was computed (Fig. 4a and b) and compared for difference between RM and FDK model with lowest stiffness values (SS:10 0 N/mm, CS:190 0 N/mm). LTPT and ILPT muscle forces showed an increase (max. 10% and 4%) in the

2.3. Sensitivity analysis A musculoskeletal model with compressive stiffness (1900, 240 0, 270 0 N/mm) and shear stiffness (100, 150, 200 N/mm) were considered in the FDK model for all lumbar discs. In combination of the discrete values provided, a total of 18 simulations (9: no load in hands, 9: with 180 N in both hands) were performed and compared with the results of a reference model (RM) which comprised conventional spherical joints having infinite translational stiffness. 2.4. Simulated posture and data analysis The standing model was inclined at 55° (Fig. 1) with thoracic flexion (4°), lumbar flexion (35°) and pelvis rotation (16°). The relative distributions of the lumbar flexion (lumbar spine rhythm) at different lumbar levels was defined in accordance with previous literature [48]. The selected lumbo-pelvic ratio (35°/16°) at intermediately flexed position was based on the calculated median values of the normalized lumbar flexion and pelvis rotation relative to their peak values [49]. The current model consists of a lumped thoracic spine and thoracic flexion was assumed as a rotation at T12−L1 joint. The rotation at T12−L1 joint was calculated by using a linear regression model fitted to the data between (T5−L1) thoracic flexion and total lumbar flexion [49]. For the flexed posture, Please

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Fig. 2. Predicted compressive (a and b) & shear (e and f) forces, axial (c and d) and shear (g and h) translations from reference model (RM: ) and FDK (force dependent kinematics) model. Lumbar discs (L1−L2, L2−L3, L3−L4, L4−L5), CS/SS (compressive stiffness/shear stiffness) in N/mm.

Table 1 Spinal loads and lumbar joints translations at 55° inclination with and without loads in hands. Fc : compressive force, Fs : anterior (+) – posterior (−) shear force, RM: Reference model, FDK: Force dependent kinematics model. Spinal loads (N) L1−L2

Level Models

L2−L3

L3−L4

L4−L5

Fc

Fs

Fc

Fs

Fc

Fs

Fc

Fs

1724 1608−1644 2315 2213−2227

−17 −16−(−23) −28 −27−(−43)

1699 1584−1620 2286 2163−2187

−132 −76−(−96) −123 −65−(−83)

1820 1681−1724 2424 2272−2302

169 103−126 226 124−158

1723 1626−1658 2355 2241−2264

−75 −14−(−29) −10 20−41

−0.61−(−0.85) −0.82−(−1.17)

−0.09−(−0.18) −0.17−(−0.36)

−0.60−(−0.84) −0.81−(−1.14)

−0.64−(−0.89) −0.85−(−1.20)

0.63−1.03 0.79−1.24

−0.61−(−0.86) −0.84−(−1.18)

−0.08−(−0.23) 0.14−0.22

RM FDK RM 180 N FDK 180 N

Translations (mm) FDK FDK

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Fig. 3. Predicted global muscles forces (ILPT: iliocostalis lumborum pars thoracic, LTPT: longisimus thoracis par thoracic, IO: internal oblique, EO: external oblique) and local muscles forces (ILPL: iliocostalis lumborum pars lumborum, LTPL: longisimus thoracis pars lumborum, IP: Iliopsoas (PM: psoas major + IL: iliacus), MF: multifidus, QL: quadratus lumborum), RM:  (reference model), CS/SS (compressive stiffness/shear stiffness) in N/mm. Table 2 Global and local trunk muscles forces at 55° inclination. Global muscles (ILPT: iliocostalis lumborum pars thoracic, LTPT: longisimus thoracis par thoracic, IO: internal oblique, EO: external oblique) and local muscles (ILPL: iliocostalis lumborum pars lumborum, IP: iliopsoas, LTPL: longisimus thoracis pars lumborum, MF: multifidus, QL: quadratus lumborum). Global muscles (N) Models

ILPT

LTPT

EO

IO

SUM

RM FDK RM 180 N FDK 180 N

74 82−85 196 218−254

190 243−265 544 584−600

97 76−82 95 92−94

184 158−167 229 186−199

545 559−600 1064 1080−1147

Local muscles (N)

RM FDK RM 180 N FDK 180 N

ILPL

IP

LTPL

MF

QL

SUM

434 369−389 543 463−487

208 170−180 180 139−141

288 246−259 348 302−314

392 397−404 449 448−460

22 32−35 56 63−65

1344 1214−1267 1576 1415−1467

FDK model and a decrease in EO (max. 5%) and IO (max. 7%) muscles, respectively. However, the distribution of the sum of local muscle forces showed a marginal decrease in LTPL (1%), ILPL (2%) and IP (1%) and an increase in QL (1%) and MF (5%) muscles groups. Ligament forces were predicted in the lumbar ligaments (Table 3) except ALL in which forces predicted were zero. The percentage difference in the ligament forces between RM and FDK models were computed (Fig. 5). Results showed that the translational flexibilities significantly reduced the ligament forces in all lumbar Please

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Table 3 Predicted ligament forces with reference model at 55° trunk inclination. PLL: posterior longitudinal ligament, SSL: supraspinous ligament, ISL: interspinous ligament, ITL: intertransverse ligament and FL: flavum ligament.

of

Lumbar level

FPLL (N)

FSSL (N)

FISL (N)

FITL (N)

FFL (N)

L1−L2 L2−L3 L3−L4 L4−L5

39 63 60 11

220 165 160 152

71 45 48 51

121 93 74 54

47 45 33 26

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Fig. 4. Distribution of the sum of global muscle forces (a), (ILPT: iliocostalis lumborum pars thoracic, LTPT: longisimus thoracis par thoracic, IO: internal oblique, EO: external oblique) and local muscles forces (b), (ILPL: iliocostalis lumborum pars lumborum, LTPL: longisimus thoracis pars lumborum, IP: Iliopsoas (PM: psoas major + IL: iliacus), MF: multifidus, QL: quadratus lumborum), RM (reference model), FDK (force dependent kinematics based model with SS: 100 N/mm, CS: 1900 N/mm).

Fig. 5. Percentage difference of ligament forces between RM and FDK model (SS: 100 N/mm, CS: 1900 N/mm), SSL (supraspinous ligament), ISL (interspinous ligament), ITL (inter transverse ligament), LF (ligamentum flavum), PLL (posterior longitudinal ligament).

ligaments. The percentage decrease for all lumbar levels ranged from 9−27% (SSL), 12−40% (ISL), 18−56% (ITL), 19−58% (LF) and 34−100% (PLL), respectively. In FDK model, the CoRs were predicted for the flexed position with no load in hands (Fig. 6a and b). For L3−L4 segment, CoRs were located posterior (−2.5−(−5) mm) and below (−3−(−4) mm) to the default CoR. For L4−L5 segment, the location of CoRs were posterior (−6−(−8) mm) and above (1−3 mm) the default CoR. Please

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4. Discussion This study showed the influence of spinal disc translational stiffnesses on the prediction of spinal loads, trunk muscle forces, ligament forces and spinal discs’ center of rotation. The technique of force dependent kinematics was applied to modify the lumbar spherical joints and introduced joint translations in an inverse static musculoskeletal model. Results were compared between a standard model with ball-and-socket joints and a modified model of

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In FDK model, with translational flexibilities included, non-fixed CoRs were predicted for the flexed position, an important parameter that could be used to identify the normal kinematics or pathological movements of a joint [54]. The CoRs were predicted for L3−L4 and L4−L5 motion segments (Fig. 6a and b) which differed in locations from the fixed CoRs in the RM. For L3−L4 segment, the CoRs predicted were found posteriorly and below the disc in the lower vertebra (L4), whereas for L4−L5 segment CoRs were located posteriorly within the disc. The qualitative comparison of the predicted CoRs for both segments showed good agreement with the previous studies [18,19,52]. Based on the current study, an answer to a relevant question, whether to include the translational flexibilities within the model depends upon the type of problem that needs to be investigated. For instance, if the body posture or movement under investigation have smaller inclination angle or joint rotations, simple spherical joints may be acceptable to predict the spinal loads and trunk muscle forces as suggested in the study of Ghezelbash et al. [6]. Here, intermediately flexed posture was simulated for an individual with body height and weight adapted to the 50th percentile of a normal European male. However, even to simulate a person in a flexed posture pose its challenges to replicate the physical conditions that can vary significantly. For instance, the diurnal variation in the disc height of an individual is evident from previous studies and adds to the complexity of the problem [55–57]. It has been shown that even subjects without low back pain have less range of flexion early in the morning as the disc height is increased due to rehydration of spinal discs [55]. On the contrary, later during the day, the disc height is reduced due to normal physical activities along with the ones that would involve carrying external loads [56,58,59]. These factors, could increase or decrease the slackness of ligaments and their resistance to the flexed posture [59,60]. The resulting changes in the slackness of ligaments therefore, would alter the corresponding distribution of loads in the surrounding structural components during upper body inclination and alter the joint kinematics as well. However, such effects could only be investigated with the spinal disc translational stiffnesses included in the model. This study showed the influence of translational stiffness on the predicted results. Lower translational stiffnesses can significantly alter the predicted results which could be more pronounced for larger flexion angles. In addition, considering translational flexibilities would be important when investigating certain musculoskeletal disorders. For instance, spinal instability caused by muscular imbalances, muscular weaknesses [61–67] or due to the loss of stiffness within spinal discs (e.g. due to aging, damage or degeneration), resulting in abnormal rotations and translations between the vertebrae [68–70]. In a normal person, healthy spinal discs and trunk muscles allow to perform normal body movements. However, such musculoskeletal disorders could lead to translations and rotations of vertebral structures beyond a normal range, eventually altering the load distribution among the muscle groups and spinal structures. In silico investigations for such problems with inverse dynamic musculoskeletal models would require the translational flexibilities to be included so that influence of such pathological movements on the distribution of spinal loads, ligaments and trunk muscles forces could be investigated. The inverse dynamic models use numerical optimization algorithms to calculate joint, ligaments and muscle forces, removing an artificial constraint of infinite translational stiffness would lead to a more optimal result. However, to evaluate the changes more precisely, a thorough validation with respect to the question being investigated is necessary. Here, only intermediate flexion was investigated. Due to inter-subject variability, several factors could possibly influence the results of the FDK models such as lumbar ligaments stiffness, slack lengths etc., which vary widely among

Fig. 6. Predicted CoRs for L3−L4 and L4−L5 motion segments at 55° trunk inclination, CS/SS (compressive stiffness/shear stiffness) in N/mm. Yellow box represent spinal discs and filled red circles at (0,0) coordinate are default CoRs for reference model. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

with translational flexibilities included in the lumbar joints. The computed results showed the differences between the two models for a range of spinal disc compressive and shear stiffnesses at 55° trunk inclination. The FDK model results showed increased differences with RM for lower values of the translational stiffnesses. For compressive forces, maximum difference between two models’ results was 8% (L3−L4), whereas the predicted shear forces were smaller though, the percentage difference was high (> 100% for L4−L5). Simulation results showed that reduced translational stiffnesses also lead to the differences in trunk muscle forces when compared with the reference model. As the compressive forces decreased with translational flexibility, forces in certain global muscles (ILPT and LTPT) and local muscles (QL and MF) were increased to provide more spinal stability when a decrease in other global (EO and IO) and local (ILPL, LTPL and IP) muscles forces was predicted. The translational flexibility in the lumbar joints varied the distribution of the sum of global muscles forces relatively more than the sum of local muscles forces which were marginally changed (Fig. 4a and b). Due to translational flexibilities, the relative decrease in maximum muscle activity was about 10%. Ligaments play an important role in spinal stabilization and restricting the range of motion during upper body flexion. In the reference model with infinite translational stiffness, ligaments forces were higher whereas in FDK model ligament forces were reduced significantly due to laxity provided by the translational flexibility. The axial and shear translations within the lumbar joints altered the ligaments forces by providing additional slackness, except in ligament ALL that remain unloaded during the flexed position. Please

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the reported literature. Different lumbar spine rhythms i.e. the distribution of rotations in lumbar segments and lumbo-pelvic ratio during upper body flexion could also influence the spinal loads and trunk muscles forces [22,49]. In this study, only one spine rhythm and lumbo-pelvic ratio was considered. Also, different back shapes of the lumbar spine may result in different outcome [71], however, only one morphology was considered in the study.

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of

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loads, ligament forces and trunk muscle forces during upper body inclination, Medical Engineering and Physics (2017), http://dx.doi.org/10.1016/j.medengphy.2017.05.006