Experimental validation of a novel spine model demonstrates the large contribution of passive muscle to the flexion relaxation phenomenon

Journal of Biomechanics xxx (xxxx) xxx

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Experimental validation of a novel spine model demonstrates the large contribution of passive muscle to the flexion relaxation phenomenon Derek P. Zwambag a, Stephen H.M. Brown b,⇑ a b

Department of Kinesiology & Physical Education, Wilfrid Laurier University, Waterloo ON, Canada Department of Human Health and Nutritional Sciences, University of Guelph, Guelph ON, Canada

a r t i c l e

i n f o

Article history: Accepted 13 October 2019 Available online xxxx Keywords: EMG Erector spinae Force-length Lumbar Mechanics Multifidus Trunk

a b s t r a c t When an individual enters a maximally flexed spine position, their largest extensor muscles become electrically inactive despite a substantial extensor moment demand being placed on the low back; this is termed flexion relaxation. Stresses within intervertebral discs, ligaments, and passive muscles are thought to support this moment thereby allowing the extensor muscles to ‘turn off’. While the mechanical behaviour of the intervertebral disc and ligaments have been studied extensively, less is known regarding the moment supported by passive muscle tissue during spine flexion. Here we estimated the L4/L5 moment supported by the passive musculature during spine flexion based on experimentally derived architectural and material properties. We then tested the validity of the passive muscle prediction by determining whether the cumulative passive tissue moment (including passive muscle, intervertebral discs, and ligaments) would support the extensor moment demand—calculated with inverse dynamics—near maximum spine flexion. The model predicted that the passive tissues were able to support the entire extensor moment demand, indicating that muscle activity was not required to support the weight of the upper body, consistent with the mechanism of flexion relaxation. The model further demonstrated that despite being inactive, spine muscles still greatly contribute to flexion relaxation by passively supporting ~47% of the extensor moment demand on the spine. Finally, there was strong agreement between the predicted active muscle moments and the recorded spine muscle activity (EMG); this strong agreement persisted when the external moment was manipulated using a pulley-system. These findings provide additional confidence that the estimated passive muscle moments are reasonably accurate throughout spine flexion. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction When individuals flex their spine forward in standing or sitting postures, extensor muscles actively generate force to counteract the weight of the upper body (Callaghan and Dunk, 2002; Donisch and Basmajian, 1972; Schinkel-Ivy et al., 2014). However, near full spine flexion, the lumbar erector spinae and multifidus— both strong spine extensor muscles—suddenly stop actively producing force. This inactivation is referred to as the flexion relaxation phenomenon (Allen, 1948; Floyd and Silver, 1955, 1951; Morris et al., 1962). While other extensor muscles, including the thoracic erector spinae, latissimus dorsi, and quadratus lumborum, do not show complete inactivation, their activity also decreases

⇑ Corresponding author at: Department of Human Health and Nutritional Sciences, University of Guelph, Guelph, ON N1G 2W1, Canada. E-mail address: [email protected] (S.H.M. Brown).

near full flexion (Andersson et al., 1996; McGill and Kippers, 1994; Zwambag et al., 2016). Flexion relaxation is believed to occur when spine structures— intervertebral discs, ligaments, and muscles—are sufficiently strained so that stresses within these tissues resist the entire moment caused by the weight of the upper body (Pauly, 1966; Wolf et al., 1979). In this position near full spine flexion, multifidus and lumbar erector spinae muscles are no longer required to actively generate an extensor moment. This mechanism is supported in the literature by studies that found that muscle inactivation occurred at greater spine flexion angles when the upper body weight was increased (Donisch and Basmajian, 1972; Howarth and Mastragostino, 2013; McGill and Kippers, 1994; Schultz et al., 1985) and lesser spine flexion angles when the upper body weight was decreased (Schultz et al., 1985; Zwambag et al., 2016). Prolonged and repeated spine flexion, which decrease the ability of viscoelastic tissues to generate passive tension at a given magnitude of strain, have also been shown to delay the flexion relaxation

https://doi.org/10.1016/j.jbiomech.2019.109431 0021-9290/Ó 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: D. P. Zwambag and S. H. M. Brown, Experimental validation of a novel spine model demonstrates the large contribution of passive muscle to the flexion relaxation phenomenon, Journal of Biomechanics, https://doi.org/10.1016/j.jbiomech.2019.109431

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D.P. Zwambag, S.H.M. Brown / Journal of Biomechanics xxx (xxxx) xxx

phenomenon (Dickey et al., 2003; Solomonow et al., 2003). Because flexion relaxation is believed to occur when the external demand on the spine is equilibrated by passive structures, flexion relaxation provides an opportunity for validating estimates of passive tissue loads. Validating predictions of spine loads are generally difficult to perform in vivo yet are important to ensure accuracy of computational models. The passive spine structures responsible for supporting the weight of the upper body in flexion are the intervertebral discs, ligaments, and the passive elasticity of muscles. Various musculoskeletal (Cholewicki and McGill, 1996; Christophy et al., 2012; McGill and Norman, 1986; Stokes and Gardner-Morse, 1995) and finite element (Arjmand and Shirazi-Adl, 2006; Azari et al., 2018; Dreischarf et al., 2014) models have been developed to estimate loads within spine tissues, load sharing amongst spine structures, and spine stability. The strengths of these models are dependent on the extensive mechanical testing of human and animal cadaveric spines (Adams et al., 1980; Myklebust et al., 1988; Oxland et al., 1992; Parkinson and Callaghan, 2009; Wilke et al., 2001; Yamamoto et al., 1989) necessary to accurately model the mechanical and material properties of spine tissues. These experimental and modelling studies have consistently revealed the importance of spine muscles for actively and passively supporting and stabilizing the spine (Adams et al., 1980; Arjmand et al., 2010; Bazrgari et al., 2008; Cholewicki and McGill, 1996; McGill and Kippers, 1994). However, unlike the ligaments and intervertebral discs, considerably less is known regarding the passive mechanical properties of spine muscles. This is partially because of difficulties in testing the mechanical properties of whole spine muscles due to their complex multi-segmented architecture. Because of this lack of experimental data, spine models have had to make assumptions regarding the shape of the passive force-length curve, slack and optimal lengths (slack length is the muscle length where passive tension begins to develop; optimal length is the muscle length where maximally activated isometric forces are greatest), and the initial strain within muscles in a neutral posture. Recent work from our lab has focused on addressing these limitations by experimentally testing the material properties (Zwambag et al., 2019) and architectural parameters (Zwambag et al., 2014) of spine muscles. The primary purpose of this study was to estimate the moment at the L4/L5 intervertebral joint supported by passive musculature through the entire range of spine flexion based on experimental testing of human and animal spine muscles. The secondary objective was to determine whether the predicted passive muscle moment was physiologically reasonable. To do this, existing intervertebral disc and ligament models were included to estimate the moment supported by the cumulative passive tissues; we hypothesized that the cumulative passive tissue moment would be able to support the external demand on the spine near full spine flexion, consistent with the flexion relaxation phenomenon.

activities (Fig. 1). To further probe the validity of model predictions, the sagittal moment demand on the spine was manipulated using a pulley system to create multiple testing conditions. 2.2. Model input data The kinematic and inverse dynamic input data for the model were taken from a previous study (Zwambag et al., 2016). Briefly, ten healthy male participants (mean ± SD: 25 ± 2.5 years; 181 ± 5.8 cm; 82 ± 11.2 kg) performed three repeated trunk flexion movements to maximum spine flexion at a self-selected pace for each of four conditions. Different unloading conditions were created by attaching zero (Control), 2.3, 4.5, or 6.8 kg of mass to a pulley which applied an upward force to the participant’s torso at approximately the T5 spine level. Kinetic force plate data and kinematic data from the lower limb and spine were input to a bottomup, rigid linked-segment, inverse dynamic model to predict the sagittal L4/L5 resultant moment; demand was defined as equal magnitude and opposite direction to the resultant moment. Physiological cross-sectional areas and geometric coordinates of 48 muscle fascicles and 14 ligaments crossing the L4/L5 intervertebral joint, representing a 50th percentile male, were taken from previous studies (Cholewicki and McGill, 1996; McGill and Kippers, 1994; McGill and Norman, 1986). To predict the geometry of the modelled spine through the flexion motion, the T12/S1 angle was proportionally distributed amongst spine levels (T12/L1: 13%; L1/L2: 14%; L2/L3: 16%; L3/L4: 20%; L4/L5 22%; L5/S1: 15% (White and Panjabi, 1978)) and sequential rotations were applied to each rigid body representing the lumbar vertebrae and the thorax. Muscles and ligaments were modelled as straight vectors from origin to insertion and nodal points were included for large muscles to account for curvature of muscle fascicles (Cholewicki and McGill, 1996). Moment arms were calculated as the cross product between the vectors representing the direction of force and the position of the origin, nodal point, or insertion coordinate relative to the L4/L5 intervertebral joint centre. 2.3. Passive muscle moment The anatomical model defines muscle fascicle lengths in physical units (i.e. cm). Because skeletal muscles are composed of highly regulated repeating units—the sarcomeres—the relative lengths of different muscles can be accounted for using sarcomere lengths, rather than strain. This is beneficial because sarcomere lengths can be experimentally measured in specific postures, and therefore the nominal length used to calculate strain doesn’t have to be assumed. Additionally, sarcomere lengths are physiologically relevant parameters for both active and passive force production. Muscle lengths (L in cm) were converted to average sarcomere length (l in mm)

l¼L 2. Methods 2.1. Overview of model For this study, inverse dynamics were used to predict the external moment demand on the L4/L5 intervertebral joint. The combined passive moment was calculated by adding moment outputs from a novel passive muscle model to existing intervertebral disc and ligament models; each predicted a passive tissue moment as a function of spine angle (Fig. 1). The net active muscle moment was predicted as the difference between the demand and the combined passive tissue moment, as required to meet dynamic equilibrium constraints. The predicted net active muscle moments were compared to recorded extensor and abdominal muscle

lN LN

ð1Þ

for each muscle fascicle based on the measured sarcomere lengths of human cadavers (Brown et al., 2011a; Gerling and Brown, 2013; Zwambag et al., 2014). The shape of the passive muscle force-length curve was defined using the logistic integral model

r¼

 34:59
ln 1 þ e5:78ðl2:76Þ þ 5:44l þ 11:01 5:78

ð2Þ

reported in (Zwambag et al., 2019) based on the best fit stresssarcomere length data of bundles of rabbit multifidus fibres. Finally, the passive muscle moment at L4/L5 (MPM in Nm) was calculated

MPM ¼

48 X Ai ri  di 10 i¼1

ð3Þ

Please cite this article as: D. P. Zwambag and S. H. M. Brown, Experimental validation of a novel spine model demonstrates the large contribution of passive muscle to the flexion relaxation phenomenon, Journal of Biomechanics, https://doi.org/10.1016/j.jbiomech.2019.109431

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D.P. Zwambag, S.H.M. Brown / Journal of Biomechanics xxx (xxxx) xxx

Zwambag et al 2016

Model Components

Moment Output (Nm)

L4/L5 Resultant Moment (Nm)

Demand

Max Flexion Angle T12/S1 Spine Angle (°) (° )

Muscle Acvaon (% MVC)

Cholewicki & McGill 1996

Adams & Dolan 1991

Ligament Length (n=14)

McGill & Norman 1986 Myklebust et al 1988 Potvin et al 1991

- ( Disc +

Ligament

+

Waveform Comparison

from

Resultant + Demand = 0

Model Inputs

Muscle Length (n=48)

Zwambag et al 2014 Zwambag et al 2019

Passive Muscle

) =

Acve Muscle

Fig. 1. Overview of the components of the model for testing predictions of spine flexion relaxation. (See above-mentioned references for further information.)

as the sum of the moments generated by each muscle fascicle, where A is the physiologic cross-sectional area (cm2), r is the passive muscle stress (kPa), and d is the moment arm (m) at a specific instance of the flexion movement. Detailed descriptions of the intervertebral disc moment model and the ligament moment model can be found in the Supplementary Material. 3. Results The passive muscle model predicted that in a neutral spine (upright standing) posture, passive tension in the muscles generated a net flexor moment at L4/L5 of 8 Nm (Fig. 2). In a maximally flexed posture, the L4/L5 moment due to passive muscle was on average 46 Nm and ranged between 30 and 56 Nm for the two participants with the least and greatest T12/S1 ranges of motion. Despite each muscle fascicle having a non-linear passive forcelength curve, the predicted passive spine moment at L4/L5 was approximately linear throughout spine flexion (Fig. 2B). The intervertebral disc and ligament models were tuned to each participant based on their maximum range of lumbar spine motion. In maxi-

mally flexed postures, the average intervertebral disc and ligament L4/L5 moments were predicted to be 18 and 54 Nm, respectively (Fig. 3). When the passive tissue models were combined with inverse dynamic estimates of the moment demand on the L4/L5 joint, the net active muscle moment that must be generated to meet dynamic equilibrium constraints could be estimated. Consistent with experimental findings, the model predicted that flexion relaxation would occur near full spine flexion in the control (0 kg attached to pulley) condition, as the predicted active muscle moment approached zero (Fig. 4). Further, the active muscle moment predictions across all four loading conditions strongly agreed with the recorded muscle activation patterns for spine extensor (erector spinae) and flexor (external oblique) muscles. The model predicted that when participants were unloaded by the pulley, less extensor muscle activity would be required during trunk flexion and greater abdominal muscle activity would be required to reach the fully flexed spine posture. The agreement between model predictions and recorded muscle activity patterns for all loading conditions supports the validity of model estimates for passive spine tissues.

Fig. 2. Left panel: Passive tensile forces within muscles crossing the L4/L5 intervertebral joint throughout spine flexion. Right panel: The predicted moment supported by passive muscles for each participant (grey lines) and the average participant (black lines). The x-axis is expressed as a percentage of range of motion to show differences between participants. Negative and positive moments indicate flexor and extensor moments. PM: psoas major; EO: external oblique; RA: rectus abdominus; IO: internal oblique; QL: quadratus lumborum; LD: latissimus dorsi; MU: multifidus; LES: lumbar erector spinae; TES: thoracic erector spinae.

Please cite this article as: D. P. Zwambag and S. H. M. Brown, Experimental validation of a novel spine model demonstrates the large contribution of passive muscle to the flexion relaxation phenomenon, Journal of Biomechanics, https://doi.org/10.1016/j.jbiomech.2019.109431

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Fig. 3. The predicted moments in the intervertebral disc and ligaments at L4/L5 for each participant (grey lines) and for the group average (black line).

B

Acve Muscle (Nm)

Demand (Nm)

-

E

=

Disc (Nm)

A

Movement Cycle

Ligament (Nm)

C

Predicted

4.5 kg 6.8 kg

Passive Muscle (Nm)

2.3 kg

Muscle Acvity (% MVC)

D Control

Recorded

F

Movement Cycle

Lumbar Erector Spinae

External Oblique

Movement Cycle

Fig. 4. 95% confidence intervals in the mean (grey lines) for each condition. The difference between (A) the L4/L5 extensor moment demand and (B–D) the moments generated by passive structures was used to predict (E) the active muscle moment. This was compared to the recorded activity of the lumbar erector spinae (extensor) and external oblique (flexor) muscles (F). Extensor moments are positive and flexor moments are negative. Muscle activity is normalized as a percent of activity during a maximal voluntary isometric contraction (MVC).

Based on the recorded muscle activity, the lumbar erector spinae muscles became inactive ~2–3° before full spine flexion in the control condition. At this instant, the extensor moment demand on the L4/L5 spine was 94 ± 3.4 Nm (mean ± SEM). The model predicted that the intervertebral disc, ligaments, and passive muscles supported 16%, 30%, and 44% of this demand (Table 1) with muscles actively supporting the remaining 11%. As the spine reached full flexion (T12/S1: 53 ± 1.38°), active muscles were predicted to generate a net moment <1 Nm and the proportions of the extensor moment supported by passive structures were: 17% intervertebral disc, 36% ligament, and 47% passive muscle. When the external moment demand on the L4/L5 joint was reduced by the pulley system, the cessation of recorded erector spinae activity occurred with less lumbar spine flexion. Flexion relaxation occurred with (mean ± SEM) 50.8 ± 1.2°, 49.7 ± 1.1°, and 48.6 ± 1.2° of lumbar spine flexion when 2.3, 4.5, and 6.8 kg of mass was attached to the pulley, respectively, compared to 51 ± 1.2° in the control condition. This caused all the modeled

Table 1 The external moment demand (Nm) on the L4/L5 joint (Mean ± SEM) and the predicted moments partitioned amongst passive structures and active muscle at the instant the lumbar erector spinae became inactive.

L4/L5 Demand Disc Ligament Passive Muscle Active Muscle

Control

2.3 kg

4.5 kg

6.8 kg

94 ± 3.4 15 ± 0.4 28 ± 2.0 41 ± 1.1 10 ± 5.2

79 ± 2.9 13 ± 0.5 22 ± 1.7 40 ± 1.2 3 ± 4.6

66 ± 3.2 13 ± 0.5 19 ± 1.6 39 ± 1.0 5 ± 4.8*

62 ± 3.0 12 ± 0.5 18 ± 2.6 39 ± 1.2 6 ± 5.6*

* Negative moments indicate that active muscles must generate a net flexion moment to overcome the pulley.

passive tissue moments at the instant of flexion relaxation to decrease because passive tissue moments were predicted by monotonic (non-decreasing) functions of spine angle. The ligament moment was the most sensitive to these small changes in spine flexion angle (Table 1). In these conditions, the model also predicted flexion relaxation, as demonstrated by the predicted net

Please cite this article as: D. P. Zwambag and S. H. M. Brown, Experimental validation of a novel spine model demonstrates the large contribution of passive muscle to the flexion relaxation phenomenon, Journal of Biomechanics, https://doi.org/10.1016/j.jbiomech.2019.109431

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active moments being small or even negative. The negative active moments indicate a net flexor moment was required to overcome the resistance of the pulley mass, which is supported by the recorded EMG patterns. The pulley system also had a small effect on the maximum flexion angle reached in each condition (Control: 53 ± 1.8°; 2.3 kg: 52.5 ± 1.9°; 4.5 kg: 51.5 ± 1.8°; 6.8 kg: 51.5 ± 1.9°). Because the ligaments are rotationally stiff near full flexion, these small changes in spine angle led to noticeable differences in the ligament moment between conditions (Fig. 4C) but had had a negligible effect on the passive muscle and disc moments.

4. Discussion The purpose of this study was to predict the L4/L5 moment generated by passive spine muscles throughout a flexion movement based on experimentally determined material and architectural properties. In a neutral posture, the model predicted that passive tension of spine muscles would generate a net flexor moment at L4/L5 of 8 Nm. This was because the abdominal muscles were measured to have longer sarcomere lengths (2.6–3.2) in a neutral position (Brown et al., 2011a) than the extensor muscles (Gerling and Brown, 2013; Zwambag et al., 2014), which represents an increased pre-strain. The psoas major muscle also had long sarcomere lengths (~3.4 mm); however, this muscle did not greatly contribute to the L4/L5 moment due to its short moment arm. With flexion, passive tension in the abdominal muscles decreased while tension developed in the extensor muscles. Interestingly, despite muscle fascicles each having non-linear passive force-length properties, the relationship between the L4/L5 moment and spine angle was almost linear. This means that the rotational stiffness of the passive spine muscles is approximately constant across all flexion angles. While this was not an expected finding, it may be due to the organized distribution of sarcomere lengths recorded in the neutral position (Zwambag et al., 2014). The secondary objective of this study was to determine whether the combined (muscle, intervertebral disc, ligament) passive tissue moment estimates would predict the flexion relaxation phenomenon in human participants. If so, this would provide additional confidence in the validity of these model predictions for estimating tissue loads in vivo. The model predicted L4/L5 net active muscle moments, based on kinematic and inverse dynamic inputs, that closely resembled the recorded muscle activity of spine muscles (Fig. 4). This high level of agreement was maintained when the input conditions to the model were manipulated using a pulley to unload the spine. Based on these results we believe that the computational model is able to predict tissue loads within passive spine structures with a reasonable level of accuracy. An important observation from this study is that muscles contribute substantially to the flexion relaxation phenomenon. A number of other authors have also emphasized this point (Adams et al., 1980; Arjmand et al., 2010; Bazrgari et al., 2008; McGill and Kippers, 1994); however it bears repeating as the mechanism of flexion relaxation is often described in terms of the osteoligamentous spine. Even though lumbar erector spinae and multifidus muscles are inactive near full spine flexion, they still produce large extensor moments due to their passive elasticity. Adams et al., 1980 suggested that muscles must support ~50% of the external demand at full spine flexion but these authors did not predict passive and active muscle forces directly. Our findings demonstrate that muscles passively generate extensor moments of this magnitude (47% of external demand at full flexion). McGill and Kippers (1994) predicted the total muscle (active and passive) moment and the ligament moment at L4/L5 would be 38 and 113 Nm,

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respectively, at peak spine flexion when holding an 8 kg mass in the hands. Even though we used the same muscular geometries as McGill and Kippers (1994), our model predicted greater passive muscle moments because tension began to develop at shorter muscle lengths. Conversely, Arjmand and Shirazi-Adl (2006) predicted passive muscle moments using their model which were greater than those reported here. These authors had participants flex forward to trunk inclination angles of 40 and 65°, which appears to correspond in the current study with T12/S1 angles of 24 and 35°, respectively (based on Arjmand and Shirazi-Adl, 2005). Arjmand and Shirazi-Adl (2006) reported passive muscle moments of 27 and 42 Nm, whereas our model predicted 11 and 23 Nm at similar angles. At these mid-range motions, these differences could be due to our model including passive tension in the abdominal muscles near neutral spine postures. Previous muscle models have assumed that passive tension only develops when muscles are stretched beyond their optimal length and that optimal lengths correspond to a neutral spine position. Our experimental data (as well as those of others) have shown that these assumptions are often not appropriate (Brown et al., 2011; Delp et al., 2001; Gerling and Brown, 2013; Regev et al., 2011; Ward et al., 2009a, 2009b; Zwambag et al., 2019, 2014); but until recently, there were no experimental data to adjust these parameters accordingly. It should also be noted that despite generating large extensor moments, the stiffness due to passive muscle is less than the stiffness of the intervertebral disc or ligaments near full flexion (Fig. 4). Instead, passive muscles were able to generate large extensor moments because they began generating passive tension at relatively short muscle lengths (i.e. early in spine flexion) and because they have large cross-sectional areas and moment arms. It was unsurprising to find that ligaments had the greatest stiffness in flexed spine positions. This results in the ligament moment being more sensitive to small changes in flexion angle, as observed near full flexion amongst the different unloading conditions, than either the intervertebral disc or passive muscle moments (Table 1; Fig. 4B–D). This has implications for patients with chronic low back pain who are less likely to demonstrate flexion relaxation of the lumbar erector spinae muscles (Neblett et al., 2003). For the lumbar erector spinae muscles to become inactive, the ligaments must be sufficiently loaded. Flexion relaxation will not occur if pain or fear-avoidance limits the magnitude of spine flexion or if injury reduces ligament stiffness. In these cases, strengthening spine extensor muscles, leading to increased cross-sectional area and passive muscle force, may be able to ‘re-train’ flexion relaxation if that is a rehabilitative goal (Neblett et al., 2010; Wolf et al., 1979). The findings of this study also reveal that co-contraction between abdominal and extensor muscles can affect the presence or absence of flexion relaxation. Note that we assumed the model would predict flexion relaxation when the net active muscle moment approached zero; this is a simplification because not all muscles demonstrate flexion relaxation. At full spine flexion, the thoracic erector spinae, latissimus dorsi, quadratus lumborum, rectus abdominus, external oblique, and internal oblique are all active (Andersson et al., 1996; McGill and Kippers, 1994; Zwambag et al., 2016). Here, we assume that at the instant of flexion relaxation, the activity in the abdominal muscles and extensor muscles oppose each other which is why the net active moment approaches zero. Participants may be coactivating their abdominal and extensor muscles in order to ensure dynamic equilibrium at other spine levels or to increase the rotational stiffness of the spine. A notable feature of this study is that recorded muscle activity was not used to predict active muscle forces and moments, as is often done in similar type models (e.g. Cholewicki and McGill, 1996; Dolan et al., 2001; Marras and Sommerich, 1991; McGill and Norman, 1986; van Dieën and Kingma, 2005). Instead, predic-

Please cite this article as: D. P. Zwambag and S. H. M. Brown, Experimental validation of a novel spine model demonstrates the large contribution of passive muscle to the flexion relaxation phenomenon, Journal of Biomechanics, https://doi.org/10.1016/j.jbiomech.2019.109431

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tions of the net active muscle moments were made purely based on modeled mechanical and material properties of lumbar spine passive tissues (ligaments, intervertebral discs, and muscles); these active muscle moments were then compared to recorded muscle activity waveforms (EMG). The recorded EMG and predicted net active muscle moments were only compared qualitatively, as direct comparison would involve additional assumptions regarding the EMG-force relationship and would not be able to account for differences in physiological cross-sectional areas, inertial characteristics, and moment arms amongst participants. Interestingly, even though the active muscle force predictions in this study do not directly consider the velocity dependence of muscle contraction, this effect can still be observed by comparing the magnitudes of the peak muscle activity to the peak predicted active muscle moments. During spine flexion, when the extensor muscles are eccentrically contracting, less muscle activity was required to generate the predicted active muscle moment than during the return to standing portion of the movement which involves concentric contraction of the spine extensor muscles and greater extensor muscle activity. Finally, there are several considerations that should be made in the evaluation of this model. Here we used a multibody musculoskeletal spine model as this was the simplest model for testing the passive muscle predictions. This model does not include translational degrees of freedom or account for changes in intervertebral disc height, which have a low to moderate influence on spinal loading and predicted passive muscle forces (Ghezelbash et al., 2015). The simple intervertebral disc and ligament models used in this study also do not consider the effect of compressive forces due to muscles and gravity on the rotational stiffness of motion segments. However, the rotational stiffness of our simplified ligament + intervertebral disc model was similar to the median of eight finite element (FE) models tested by Driescharf et al (2014). Applying a 7.5 Nm moment to the FE models resulted in ~ 18-25° motion (Driescharf er al. 2014), whereas the simplified model in the current study generated 7.5 Nm when rotated an average of ~25° (range 17–34°). Therefore, the simplified intervertebral disc and ligament models were deemed appropriate for our secondary objective of verifying that the combined passive muscle, intervertebral disc, and ligament moments were reasonable. Studies interested in predicting the internal loads of the disc and ligaments should use more detailed finite-element models. In order to partition the experimentally recorded T12/S1 spine angle amongst spine levels, we used a proportional distribution model. Recent work using bi-planar radiography (Dombrowski et al., 2018) and fluoroscopy (Eskandari et al., 2017) has shown that the distribution of motion amongst spine levels is complex and non-linear; however, accounting for these effects requires medical imaging technology. Finally, the passive muscle model does not currently include tendon deformations and is only represented by experimental data from some of the intramuscular connective tissues. Including tendon deformations will decrease muscle fascicle strain, whereas including the epimysium and perimysium may affect passive stiffness if the modulus of these tissues is substantially greater than the modulus of muscle fibre bundles (composed of muscle fibres, basement membrane, and endomysium). Here we demonstrated that the active muscle moment at the L4/L5 spine joint could be predicted throughout a trunk flexion movement based on inverse dynamic data and modeled passive tissue loads within the spine muscles, intervertebral disc, and ligaments. Even though the lumbar erector spinae and multifidus muscles become inactive near full spine flexion, these muscles still greatly contribute to supporting the weight of the upper body through their passive elastic properties. This study highlights that the flexion relaxation phenomenon likely requires stiff ligaments, more compliant but large extensor muscles, and minimal co-

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Please cite this article as: D. P. Zwambag and S. H. M. Brown, Experimental validation of a novel spine model demonstrates the large contribution of passive muscle to the flexion relaxation phenomenon, Journal of Biomechanics, https://doi.org/10.1016/j.jbiomech.2019.109431