An Electromyographically Driven Cervical Spine Model in OpenSim

in Journal of Applied Biomechanics
View More View Less
  • 1 University of Waterloo
  • | 2 MyAbilities Technologies Inc

Relatively few biomechanical models exist aimed at quantifying the mechanical risk factors associated with neck pain. In addition, there is a need to validate spinal-rhythm techniques for inverse dynamics spine models. Therefore, the present investigation was 3-fold: (1) the development of a cervical spine model in OpenSim, (2) a test of a novel spinal-rhythm technique based on minimizing the potential energy in the passive tissues, and (3) comparison of an electromyographically driven approach to estimating compression and shear to other cervical spine models. The authors developed ligament force–deflection and intervertebral joint moment–angle curves from published data. The 218 Hill-type muscle elements, representing 58 muscles, were included and their passive forces validated against in vivo data. Our novel spinal-rhythm technique, based on minimizing the potential energy in the passive tissues, disproportionately assigned motion to the upper cervical spine that was not physiological. Finally, using kinematics and electromyography collected from 8 healthy male volunteers, the authors calculated the compression at C7–T1 as a function of the head–trunk Euler angles. Differences from other models varied from 25.5 to 368.1 N. These differences in forces may result in differences in model geometry, passive components, number of degrees of freedom, or objective functions.

As employment shifts from manufacturing to office work, there has been a coincident increase in both the incidence and prevalence of chronic neck pain.1 This represents a substantial public health burden as those who suffer neck pain report considerable disability, and rarely experience a complete remission from their symptoms.2,3 Further, with the broad adoption of mobile devices, there has been attention to prolonged neck flexion, with 68% of mobile device users reporting neck pain.4 Neck postures associated with these devices have been shown to result in moderate-extensor muscle activity levels (∼15% Maximum Voluntary Contraction), with most users adopting postures at neck flexion angles smaller than those required to elicit a flexion-relaxation response.5 Despite these alarming statistics, there are few biomechanical models focused on studying the physical risk factors that might contribute to chronic neck pain.68

Biomechanical cervical spine models have typically used forward dynamics to study the head–neck response to dynamic impacts.916 However, since these models were focused on characterizing whiplash events, they have generally overlooked neck pain arising from prolonged voluntary exposures. In addition, relatively few cervical spine models have used electromyography (EMG) and inverse dynamics to estimate joint kinetics.7,1720 One problem common to all these models is the assumption of the cervical spinal rhythm: how the total head–trunk angle is partitioned among the intervertebral joints. Typically, the total angle is partitioned among intervertebral joints in proportion to the in vitro ranges of motion of the isolated intervertebral joints.2123

Therefore, the investigation was 3-fold. First, to develop, calibrate, and validate the passive structures in a biomechanical cervical spine model, designed with the intention of evaluating the physical risk factors for chronic neck pain. The second objective was to evaluate whether spinal rhythm can be predicted and explained entirely by the passive structures in the cervical spine. The third objective was to outfit the model with the capability of estimating muscle forces from measured EMG profiles, specifically using EMG-assisted static optimization.24,25

Methods

Model Description

Development of the model proceeded hierarchically, beginning from tissue force–deflection curves and progressing toward the full cervical spine model (Figure 1). After obtaining constitutive expressions for the ligaments, models of individual functional spinal units (FSUs), consisting of 2 vertebrae and the intervertebral disk, were constructed for each joint from C2–C3 to C7–T1 (6 in total). Two additional 3 degree-of-freedom gimbal joints for C0–C1 and C1–C2 were also included in this step. Finally, the entire cervical spine model was assembled from the FSU models and outfitted with muscle elements.

Figure 1
Figure 1

—Overview of model development, specifically for the validation of its passive elements. The panel underneath each phase of development elucidates how those components were validated—in most cases, against a moment–angle or force–deflection curve. Starting on the leftmost panel, each individual ligament (here the ALL is shown as an example) in the model had force–deflection characteristics that were obtained from published literature. These included the usual toe, heel, and linear regions of the ligament force–deflection curve. The next phase of validation involved assembling FSU models for all 8 spinal levels included in the whole cervical spine model. These moment–angle curves were compared to multiple in vitro studies to ensure that the model’s response was generally within 1 SD of published data (bottom second panel). The model was then fully assembled into a ligamentous model whose moment–angle curve was, once again, compared to in vitro data. Finally, once outfitted with muscle elements, the whole model had its passive moment–angle curves validated against published in vivo curves loading human volunteers in the 3 directions of movement. The final, whole model. ALL indicates anterior longitudinal ligament; FSU, functional spinal unit.

Citation: Journal of Applied Biomechanics 37, 5; 10.1123/jab.2020-0384

Anatomical Data

The anatomical data for this model were obtained from the BodyParts3D project32 from manual digitization of anatomical landmarks using MeshLab (version 2016.12; Visual Computing Lab, Italian National Research Council, Rome, Italy).33 As an initial base model, the geometry was scaled to a 50th-percentile human male using vertebral quantitative anatomy and craniometry reported in the literature (Supplementary Tables S1–S4 [available online]).3441 The inertial properties of the skull and vertebrae were taken from de Jager13 (Supplementary Table S5 [available online]). The centers of rotation for the vertebrae were calculated from the flexion–extension sagittal fluoroscopy study of Dvorak et al42 and were assumed to be the same for lateral bending and axial rotation.

Ligaments

Ligaments were modeled as nonlinear springs with force–elongation curves obtained from Mattucci26 and fit to a constitutive expression obtained from the simplification of a mechanistic model43 (Equation 1; with an example in Figure 1).
F(x)=kσ2πexp[(xμ)22σ2]+k(xμ)2[erf(xμ2σ)+1],
where k is the ligament stiffness in the linear region (N/mm), x is the ligament’s deflection (mm), and μ and σ are the average and SD of slack length in the initial distribution of collagen fibers (both in mm). Mattucci26 also provides dimensionless scaling factors for each ligament’s force (aforce) and deflection (adisp) depending on whether it is in the upper, middle, or lower cervical spine. Finally, the force calculation is normalized by the number of elements (n) constituting the ligament in the model as the reported force–deflection curves for whole ligament specimens.26 Parameters and specifics on how force–displacement curves were scaled and summarized in Supplementary Table S6 (available online).

Intervertebral Forces

Nonlinear bushing elements were used to describe intervertebral disk and facet joint interactions, lumped together as exponential functions (Supplementary Table S7 [available online]). Half the moment–angle curve in flexion can be attributed to the ligaments of the posterior elements,44 therefore the exponential curves from Camacho et al27 were halved for flexion. The slack lengths of the ligaments were chosen to match the remaining half of the curve in flexion by least-squares parameter estimation with SciPy.45 The passive tissues of the middle and lower cervical spine were calibrated to match Camacho et al27 and Yoganandan et al,46,47 whereas the upper cervical spine was calibrated to Panjabi et al.29

Muscle Elements

The whole cervical spine model was assembled and outfitted with 218 muscle elements representing 29 muscles in the cervical spine.48 The physiological cross-sectional areas were specified for each muscle according to literature values,4951 and assumed a muscle specific tension of 35 N/cm2. The passive contributions of these muscle elements to the external moment were validated by comparing whole cervical spine lumped passive stiffness curves to in vivo volunteers reported in the literature for flexion–extension, lateral bending, and axial rotation.31,52

Spinal Rhythm

The model’s kinematics are driven by experimentally measured head–trunk Euler Angles. The authors tested partitioning the intervertebral angles as the set of angles which minimized the total elastic potential energy in each FSU while still maintaining the measured whole head–neck angle. This involves solving the optimization problem:
Minimize:V(θ,φ,ψ)=i=07Vi(θi,φi,ψi)Subject to:Θ=i=07θi,Φ=i=07φi,Ψ=i=07ψi,
where θ, φ, and ψ are the flexion–extension, lateral bending, and axial twist angles of the joint between segments i and i + 1 (starting from 0 representing C0–C1); Vi is the potential energy function for that joint; and Θ, Φ, and Ψ are the overall head–trunk angles from kinematics. Spinal-rhythm values obtained from this method in flexion–extension (−45° to 30°), axial rotation (±45°), and lateral bending (±20°) were compared against pooled average in vitro and in vivo values5355 as an attempt to validate this approach.

Model Validation Overview

Validation of the model was assessed on 3 different measures. First, passive tissue validity was assessed by comparing each FSU model’s moment–angle curves against previously reported in vitro data.28,30,44,46,47,5659 Second, the cervical spine’s passive moment–angle curve, with muscle elements, was compared to in vivo reports.31,52 The spinal rhythm used in the model was compared to both in vitro and in vivo studies to ensure that the model partitions intervertebral angles in a biofidelic way. Third, since it is not possible to measure muscle or intervertebral joint forces in vivo, model predicted compression and shear forces were compared to previously published models.6,8,19,60,61

Passive Components Validation

Individual moment–angle curves for all 8 FSU models (from C0–C1 to C7–T1) were compared to those measured in vitro in flexion–extension, axial rotation, and lateral bending.27,29,30,59,62,63 This was done by slowly loading each FSU to ±1.5 N·m over 8 seconds and recording the corresponding angle as a function of applied moment. Second, once the whole cervical spine model was assembled, its lumped passive moment–angle curves for flexion–extension, axial rotation, and lateral bending were obtained by applying a slowly varying sinusoidal pure moment to the skull and measuring the assumed total head–trunk angle from forward dynamic simulations (frequency: 1/16 Hz; amplitude: 10.3, 2.2, and 4.2 N·m for flexion–extension, axial rotation, and lateral bend, respectively). For these simulations, the degrees of freedom not being loaded were locked to isolate each degree of freedom. The moment–angle curves derived this way was then compared to in vivo lumped passive curves of the cervical spine.31,52

Spinal Rhythm and Ranges of Motion

Flexion–extension joint ranges of motion were quantified by applying a 1.5 N·m pure moment to the skull segment, measuring the intervertebral angles that the passive elements of the cervical spine assume. This was the technique used for establishing the range of motion for a multitude of in vitro studies,28,29,44,57 so it was deemed as a fair comparison for model components.

Comparisons were made between experimentally measured in vivo spinal rhythms,53,54,64 in vitro rhythms,28 and the in silico spinal rhythm obtained from calculating the passive moment–angle curve of the whole spine described earlier. Specifically, this involved documenting whether the in silico rhythm was within 1 SD of the in vivo or in vitro data. The spinal rhythm is defined here as the percentage contributions of whole head–trunk angles undertaken by each intervertebral level. In cases, where the C0–C1 angle was not reported, that angle was removed from this analysis to preserve a fair comparison to experimental data.

Participants

Eight healthy males (mean age: 21.3 ± 1.7 y; height: 177.9 ±6.8 cm; body mass: 79.7 ± 11.5 kg) with no previous history of neck, shoulder, or upper back pain participated in the study to obtain normal head–neck kinematics and EMG activity during flexion–extension activity.

Surface EMG (Ag/AgCl) electrodes were placed over 10 muscles (5 bilaterally): splenius capitis, sternocleidomastoid, levator scapulae, the cervical erectors, and upper trapezius (Figure 2). Upper trapezius was palpated against light resistance to shrugging, and sternocleidomastoid to axial rotation. These 2 muscles form the borders to the neck’s posterior triangle situated on the lateral aspect of the neck where the superficial portions of splenius capitis and levator scapulae are accessible for surface EMG. Finally, cervical erector electrodes were placed roughly 2 cm on either side of the midline at approximately the C2 level. More detail on the palpation of these muscles is available elsewhere.65,66 A 16-channel Noraxon Telemyo 2400T G2 Telemetry EMG system (Noraxon USA Inc, Scottsdale, AZ) amplified the signal, which was collected at 1500 Hz using a 16-bit analog-to-digital converter. Participants performed maximal voluntary isometric exertions while secured to a chair with Velcro™ straps with a helmet (standard issue Bell CH-146 Griffon Helicopter Helmet) secured to a robotic arm (HP50 with NX100 Controller (Yaskawa Motoman Robotics, Mississauga, ON). Exertions were performed against the resistance of the robot in forward (flexion), backward (extension), axial rotation to their right (axial rotation), or lateral bending to their right (lateral bending). Details about the maximal voluntary isometric exertion protocol are reported elsewhere.67 The maximum activation recorded from these trials were used to normalize the recorded EMG during movement trials.

Figure 2
Figure 2

—Placement of reflective markers and electrodes for the in vivo component of the validation analysis from anterior (A) and posterior (B) views. Anatomical landmarks are: posterior head marker, anterior head marker, lateral head marker, C7 spinous process, acromion process, supra-sternal notch, and xiphoid process. Muscles collected from electromyography were splenius capitis, upper neck extensors, upper trapezius, levator scapula, and sternocleidomastoid.

Citation: Journal of Applied Biomechanics 37, 5; 10.1123/jab.2020-0384

Normalized, linear-enveloped EMG amplitudes were used to estimate active muscle forces using a Hill-type approach.48,68,69 EMG is full-wave rectified and low-pass filtered with a single-pass critically damped filter at a cutoff frequency chosen to induce an electromechanical delay that mimics the muscle.70 Electromechanical delays range from 32.2 to 70.3 ms,71 yielding cutoff frequencies between 2.3 and 4.9 Hz. For those muscles where no electromechanical delay data was available, a cutoff of 4.0 Hz was used based on previous EMG studies with cervical spine musculature.72 These EMG data were used as inputs into a Hill-type element in OpenSim,48 then adjusted with EMG-assisted optimization (EMGAO),24,25 which was implemented in the Python programming language using the CVXPY package.73

Motion Capture

A passive Vicon motion capture system (Vicon MX; Vicon Motion Systems Ltd, Los Angeles, CA) was used to collect kinematic data from 9 markers, each sampled at 50 Hz. Markers from the head, placed on a rigid circlet on the posterior, anterior and lateral sides, and trunk (acromion processes, C7 spinous process, manubrium, and xiphoid process) were used to make local coordinate systems conforming to International Society of Biomechanics (ISB) standards74 (Figure 2). Participants started in a self-selected neutral posture, and moved to one of 4 deviated postures (45° of flexion, 30° of extension, 20° of lateral bending, or 45° of axial rotation), holding the deviated posture for 15 seconds, then returning to a neutral posture. The Euler Angles derived from kinematics were partitioned among the intervertebral joint postures in accordance with the in silico spinal rhythm.

Model Outputs

Compression and shear joint reaction forces at each spinal level were the outputs from the model, although to facilitate comparison with other models, the compression at C7–T1 was the primary outcome variable of interest. The model reported the joint reaction forces from the inferior vertebra onto the superior one, expressed in the inferior vertebra’s coordinate system, so that a positive anteroposterior shear force indicates anterior shear of the superior vertebra relative to the inferior one.

Assessment

Since it is currently not possible to measure joint compression and shear forces in vivo, the resulting compression and shear forces were compared to previous studies. The inputs to the model were the 3 Euler angles for inverse kinematics and linear-enveloped EMG for static optimization. The model’s geometry was kept constant as a 50th-percentile human male, with no scaling between participants. A recent model by Bayoglu et al60 in the biomechanical software AnyBody (Aalborg, Denmark), using static optimization, provided some comparison of compression and shear values in a neutral posture. They reported compression and shear values normalized to bodyweight which we extrapolated to a 67-kg male in order to keep head-masses consistent between the 2 models.75 Conversely, predicted compression at the C7–T1 joint as a function of neck flexion–extension, axial rotation, and lateral bending angle was compared to other models.6,8,19,61 This was done both qualitatively by directly comparing the plots of these functions, as well as quantitatively by evaluating the root mean squared error (RMSE) between each curve and that predicted by the model.

Results

Each FSUs passive moment–angle curve compares well against the experiment it was calibrated against (Figure 3). These curves, in aggregate, are generally within 1 SD of those measured in other experiments. With the added muscle elements, the whole cervical spine was able to produce passive curves for flexion–extension which compared well with those measured in vivo (Figure 4).

Figure 3
Figure 3

—Comparison of the model against experimental results. Positive magnitudes indicate extension, leftward axial rotation, and rightward lateral bending. The model has good agreement in flexion–extension where the moment–angle curves are all within 1 SD. To some extent, the same is true of axial rotation, although these curves do not appear to have the same consensus seen in flexion–extension. Lateral bending at C0–C1 had some difficulty and the model does not explicitly handle the bony contact between the C0–C1 or C1–C2 joints, which are primarily the structures responsible for resisting lateral bending.

Citation: Journal of Applied Biomechanics 37, 5; 10.1123/jab.2020-0384

Figure 4
Figure 4

—Comparison of the passive moment–angle curve generated by the cervical spine model compared to the average in vivo flexion–extension (A), axial rotation (B), and lateral bending (C) passive curves. Studies used were McClure et al52 (blue dashed-dot lines with error margins) and McGill et al31 (solid red line with error margin). Like before, negative values indicate flexion, right axial twist and left lateral bend. The model’s response is generally within 1 SD of the reported moment–angle relations collected from in vivo human volunteers, with some exceptions for lateral bending and extension. The model curves were obtained by applying a slowly varying pure moment to the skull (1/16 Hz), and measuring the corresponding angular displacement.

Citation: Journal of Applied Biomechanics 37, 5; 10.1123/jab.2020-0384

Spinal rhythms and ranges of motion were generally within the range of published values. The ranges of motion of each joint compared well against experimental results, generally falling within 1 SD of literature values (Tables 13). Caution is required when comparing this study’s whole model predicted ranges of motion to the pooled in vivo data, since the internal moment borne by the passive tissues during in vivo data collections is generally not reported. By contrast, it was prescribed to be exactly ± 1.5 N·m for this study’s simulations, a magnitude of moment more directly comparable to in vitro data collections. That said, the passive spinal rhythms assumed by the model resembled the in vitro pooled averages more than the in vivo ones (Figure 5). In general, the relative contributions of flexion–extension range of motion were highest in the upper cervical spine, and gradually decreased at lower levels. The C1–C2 joint contributed most to the range of motion in axial rotation (∼60%), with the other spinal levels roughly evenly contributing the remainder. Lateral bending ranges of motion were also evenly distributed among all spinal levels, with C7–T1 contributing the least.

Table 1

Comparison of Flexion–Extension Range of Motion Values From the Literature (Both in vivo and in vitro) to the Current Model Both With (Whole Model) and Without (Osteoligamentous Model) the Muscles

C0–C1C1–C2C2–C3C3–C4C4–C5C5–C6C6–C7C7–T1
In vivo
 Penning (1978)7630.030.012.018.020.020.015.0
 Dvorak (1988)7712.010.015.019.020.019.0
 Dvorak et al (1993)7814.112.017.221.122.621.4
 Ordway et al5325.412.413.016.619.018.616.6
 Wu et al6413.117.522.419.216.6
 Anderst et al54,5515.612.717.119.519.715.88.3
In vivo pooled average (SD)27.7 (11.6)16.3 (6.5)12.1 (4.1)16.9 (5.1)20.2 (5.1)20.1 (5.5)17.6 (8.2)8.3 (3.5)
In vitro
 Panjabi et al589.99.99.99.99.9
 Panjabi et al5724.522.4
 Moroney et al449.19.19.19.19.19.1
 Panjabi et al2927.424.46.27.710.19.97.1
 Nightingale et al5930.422.6
 Ivancic2818.612.06.47.98.19.98.85.3
In vitro pooled average (SD)25.1 (5.7)20.1 (5.7)7.2 (2.9)8.2 (3.6)9.4 (2.9)9.8 (3.6)8.4 (2.6)5.7 (1.3)
Current model
Osteoligamentous model (±1.5 N·m)27.323.89.79.29.510.17.74.3
Whole model (±1.5 N·m)18.814.59.47.95.05.96.13.9

Note: The bolded rows indicate the pooled averages and SDs across all studies accounting for the relative sample sizes of each study. All units are in degrees.

Table 2

Comparison of Total (Left and Right, Combined) Axial Rotation Range of Motion Values From the Literature (Both in vivo and in vitro) to the Current Model Both With (Whole Model) and Without (Osteoligamentous Model) the Muscles

C0–C1C1–C2C2–C3C3–C4C4–C5C5–C6C6–C7C7–T1
In vivo
 Penning and Wilmink792.081.06.013.013.613.810.84.2
 Dvorak et al808.086.1
 Mimura et ala8175.27.25.84.25.46.4
 Ishii et al823.470.8
 Ishii et al834.49.04.68.03.23.0
 Zhao et al844.877.06.28.010.79.24.63.2
 Salem et al855.075.03.010.011.010.08.0
 Lin et al868.49.26.02.6
 Anderst et al5511.811.39.36.53.8
In vivo pooled average (SD)4.1 (2.2)77.2 (8.1)5.5 (3.8)9.9 (2.9)9.9 (3.1)9.3 (2.9)6.8 (2.2)3.0 (1.8)
In vitro
 Panjabi et al5714.677.8
 Moroney et al443.73.73.73.73.7
 Panjabi et al299.956.73.25.16.85.12.9
 Yoganandan et al463.66.56.56.95.14.7
 Ivancic2810.262.95.87.47.57.26.16.6
In vitro pooled average (SD)11.7 (3.4)66.5 (8.7)4.1 (2.3)5.9 (3.3)6.4 (1.7)6.1 (1.6)4.6 (1.8)5.6 (2.6)
Current model
Osteoligamentous model (±1.5 N·m)13.473.06.08.07.86.65.62.6
Whole model (±1.5 N·m)4.430.65.87.67.25.84.62.2

Note: All units are in degrees.

aMimura et al81 only measured angulation between C0–C2, and for pooled averaging this was assumed to only occur at C1–C2.

Table 3

Comparison of Lateral Bending Range of Motion Values From the Literature (Both in vivo and in vitro) to the Current Model Both With (Whole Model) and Without (Osteoligamentous Model) the Muscles

C0–C1C1–C2C2–C3C3–C4C4–C5C5–C6C6–C7C7–T1
In vivo
 Penning7610.012.012.012.012.012.0
 Ishii et al873.83.27.47.06.68.611.48.2
 Lin et al8612.810.412.212.2
 Anderst et al5514.313.112.314.55.6
In vivo pooled average (SD)4.6 (1.3)3.2 (1.8)10.3 (2.8)12.2 (2.5)11.3 (3.9)11.6 (2.6)12.9 (3.2)8.2 (3.2)
In vitro
 Panjabi et al5711.013.4
 Moroney et al449.49.49.49.49.4
 Panjabi et al299.16.59.59.19.36.55.4
 Yoganandan et al477.96.96.05.35.34.2
 Ivancic286.86.24.64.04.53.94.04.5
In vitro pooled average (SD)9.0 (1.6)8.9 (3.0)7.7 (3.3)7.0 (3.0)7.0 (2.4)5.7 (2.3)5.7 (2.5)4.4 (1.9)
Current model
Osteoligamentous model (±1.5 N·m)16.87.612.013.211.29.810.07.6
Whole model (±1.5 N·m)9.86.210.110.210.28.08.03.4

Note: All units are in degrees.

Figure 5
Figure 5

—The spinal rhythm obtained from minimizing the potential energy in the functional spinal units while constraining the external posture. The relative contributions for the model are within 1 SD of the in vitro pooled average, which itself is dissimilar from the in vivo average spinal rhythm, especially for the upper cervical spine in flexion–extension and lateral bending. In flexion–extension, the dissimilarity between in vivo and in vitro spinal rhythms implies that human volunteers use active musculature to constrain motion in the upper cervical spine.

Citation: Journal of Applied Biomechanics 37, 5; 10.1123/jab.2020-0384

The current model predicted less compression throughout the cervical spine in a neutral posture compared to the Bayoglu et al60 model (Figure 6). The difference between the 2 models was at most 39 N at C7–T1. In addition, the 2 models generally agree on the order of magnitude of compression, between 100 and 150 N, with more compression occurring at the caudal spinal levels. The models predicted different anterior shear patterns, which differed by at most 62 N at C7–T1. Over a range of flexion–extension, axial rotation, and lateral bending angles, the current model generally predicted more compression than previous models (Figure 7). This generally followed a U-shaped curve, where more angular deviation from neutral resulted in a nonlinear increase in compression. By contrast, earlier models predict a V-shaped curve centered around the neutral posture, where flexion or extension resulted in a proportionate increase in compression.6,8,61 These responses were similar with lateral bending, where previous models report a V-shaped curve in contrast to the U-shaped one of the current model. The predicted curve in axial rotation was also U-shaped, which differed from threshold nonlinear responses reported from other models (Figure 7). The RMSEs between these curves and the current model ranged between 25.5 and 368.1 N, with an average of 103.3 N.

Figure 6
Figure 6

—Comparison of model predicted compression (A) and AP shear (B) values against the Bayoglu et al60 model for a neutral standing posture held against gravity. The model predicts slightly less compression than Bayoglu et al60 on average, and much less shear (B). These differences may be attributable to differences in musculoskeletal geometry or the properties of passive tissues. AP indicates anteroposterior.

Citation: Journal of Applied Biomechanics 37, 5; 10.1123/jab.2020-0384

Figure 7
Figure 7

—Current model predicted compression at C7–T1 as a function of neck flexion angle. As before, positive values indicate extension, left axial rotation, and rightward lateral bend. The average response of the model is depicted with the solid black line, the SD shaded around it in gray. The other model responses are included for comparison. The Hoek van Dijke et al61 and Snijders et al6 models are from similar investigations on the same model, whereas the Mathys and Ferguson8 model is an investigation using the geometry in the Vasavada et al88 models. Bayoglu et al60 model was a whole spine model developed from a cadaveric specimen with both an articulated cervical and lumbar spine. Both the current model and that of Cheng et al19 are electromyographically driven models, which tend to predict more compression through the range of motion. EMGAO, EMG assisted optimization.

Citation: Journal of Applied Biomechanics 37, 5; 10.1123/jab.2020-0384

Discussion

We developed an anatomically detailed cervical spine model alongside the capability of predicting muscle forces from EMG using static optimization. Development began with models characterizing the force–deflection behavior of cervical spine ligaments.89 Following this, FSU models were calibrated to match published experimental curves27,29,46,47 prior to assembly into the whole cervical spine level.28 Finally, once muscle elements were added, their passive contributions were validated against in vivo lumped passive flexion–extension curves.31,52 The passive tissues of the model generally lie within a corridor acceptable for biomechanical analysis—within 1 SD of published data sources.90 The model facilitated an investigation into spinal rhythms based on in vitro passive ranges of motion and elastic energy minimization.

Inverse kinematics is a technique used throughout robotics to determine intermediate joint angles when knowing the position and orientation of an end effector. To keep model analysis relatively simple, the inverse kinematics used in this investigation assumed that the passive tissues settle into an equilibrium position instantaneously. The intervertebral angles chosen by the model tend to match in vitro experiments more-so than in vivo data (Figure 5). However, it appears that living human volunteers do not adhere to this principle. In particular, minimizing elastic potential energy disproportionately attributed motion to C0–C1 and C1–C2, compared to in vivo studies.53,91,92 Ordway et al53 used fluoroscopic imaging in vivo to quantify the cervical spinal rhythm of their participants. They observed that while the C0–C1 joint had the greatest range of motion—an observation also true of the current cervical spine model—participants tend to rely more heavily on the middle and lower cervical spine to accomplish simple flexion and extension. For instance, at maximum voluntary flexion, Ordway et al53 found that the joints of the middle and lower cervical spine were close to their end ranges of motion, whereas the C0–C1 joint was only halfway to its maximum flexion angle. This implies that living volunteers use muscle activity to limit the motion at C0–C1 rather than rely exclusively on the passive tissues. This is a property of cervical spine motion not captured by partitioning intervertebral angles based on minimizing the elastic energy in the passive structures. In addition, the observation that in vivo volunteers actively control the motion in the upper cervical spine raises concerns around using spinal rhythms determined from in vitro studies, as the active muscle contributions would also be absent from those investigations. Initially, the authors hypothesized that the spinal rhythm may be fully explained in terms of passive tissue contributions; however, this notion does not seem to be supported by evidence. Therefore, we used an angle partitioning method derived from in vivo studies for all subsequent human data processing.53,55,64 Since assumptions about spinal rhythm can substantially alter biomechanical model predictions in the cervical spine,23 more work needs to be done in order to estimate it noninvasively.

The predicted forces from the current model are within the same order of magnitude as other models, but with substantial RMSE magnitudes ranging from 25.5 to 368.1 N (Table 4). This, of course, is not equivalent to direct comparison to experimental results; it does give some indication that the model is providing force estimates which are in the range of what is expected based on the current literature. Currently, there are no measured in vivo forces or pressures to compare model predictions against. Nevertheless, the predicted model compressions are generally comparable in magnitude to other models (Figures 6 and 7). The compression values estimated here are at most 39 N less than those predicted by the AnyBody biomechanical modeling software for a neutral posture. Similarly, for anteroposterior shear, the 2 models show good agreement for the middle and upper cervical spine. However, the model of Bayoglu et al60 predicted substantially greater shear magnitudes in the spinal levels caudal of C5–C6, well outside 2SDs of our EMG-driven model data. In addition, both models predicted a shear force direction reversal between C3–C4 and C5–C6, although the exact level of this reversal is inconsistent. These differences may be attributed to differences in model geometry, like origin and insertion points of the cervical musculature or the inclusion of the thoracic spine. To that point, the Bayoglu et al60 model geometry was based on a 79-year-old cadaver and used established static optimization techniques to estimate muscle forces. By contrast, the current model is based on a 50th-percentile human male, with activation profiles informed by measured EMG. The response of the current model to changes in posture differed from previous models. For example, magnitudes of compression predicted here are generally larger than those previous, even in a neutral posture. This may be attributable to passive tissue models, driving muscle activations with EMG, differences in the reference frames that joint reaction forces are reported in, or differences in model geometry (most notably the number of degrees of freedom in the models). Driving muscle activations with EMG leads to antagonistic muscle co-activity that is difficult to capture with other static optimization approaches.6,8,61 However, in this study’s comparison with standard static optimization,93 the effect is only substantial outside of ±30° of neck flexion/extension (Supplementary Figure S1 [available online]). The models of Snijders et al,6 Hoek van Dijke et al,61 and Mathys and Ferguson8 all have 6 degrees of freedom, and it is perhaps not surprising that their predicted compression magnitudes are in good agreement. By comparison, both our model, Bayoglu et al,60 and Cheng et al19 have many more total degrees of freedom. Intuitively, the optimization solver may require additional muscle contributions to balance the added equilibrium relations, especially considering most of the muscles span many joint levels. Another key difference is the shape of the compression versus neck flexion curve. Models based on static optimization predicted this to be a V-shaped curve, with compression increasing linearly with angular deviations from a neutral posture; by contrast, the present model estimated that this curve is U-shaped, with deviated postures resulting in nonlinear increases in compression (Figure 7). Generally, there is a trend for compression to increase more in flexion than in extension. Similarly, the current model predicted the same U-shape compression versus angular displacement curves for axial rotation and lateral bending. The axial rotation curve differed markedly from previous models, which portray a threshold nonlinear response. In lateral bending, similar V-shape curves were reported by Bayoglu et al60 and Snijders et al,6 whereas the current model predicted a threshold nonlinear curve. Because the discrepancies between our model and other published models is quite large—around 100 N RMSE—it would be helpful to compare these results to other published EMG-driven cervical spine models17,18,20; however, these models have not published the same data for direct comparison. Across all models, there is a trend for joint compression to increase with angular deviation in flexion–extension, axial rotation, or lateral bending. The exact nature of the relationship is conflicting.

Table 4

RMSE Between Model Compression Predictions for Flexion–Extension, Axial Rotation, and Lateral Bending Postures

ModelFlexion–extension RMSE, NAxial rotation RMSE, NLateral bending RMSE, N
Snijders et al681.553.225.5
Hoek Van Dijke et al6177.278.941.4
Mathys and Ferguson875.684.790.2
Cheng et al19368.1331.5
Bayoglu et al6078.029.831.8

Abbreviation: RMSE, root mean squared error.

It should be noted that the current model is not the first cervical spine model to be implemented in the OpenSim environment.18,88,94 Vasavada et al88 first developed a kinematic cervical spine model which evaluated how the muscle moment arms change with posture; that model was therefore able to quantify the moment generating capacity of the 26 muscles included in their investigation. The model has since been retrofitted to include the hyoid group, and allows for kinetic analyses as well.95,96 By comparison, the current model includes more passive structures, including 511 ligament elements, and more muscle elements (218 vs 72). The Vasavada model has been used extensively for kinematic analyses and for the prediction of the moment of generating capacity of the cervical musculature for a variety of tasks,94,97,98 and was included in this investigation from a study on F-16 fighter pilots.8 The compressive forces were generally lower than the current model by an average of 75.6 N in flexion–extension, 84.7 N in axial rotation, and 90.2 N in lateral bending (Table 4). This, again, may be attributable to differences in model geometry, treatment of passive structures, and objective functions used to resolve the indeterminacy problem.

Although the passive tissues were thoroughly evaluated in this investigation, there remains areas where the model could potentially have increased biofidelity. Intervertebral disk and facet joint contributions to moment–angle curves were lumped together to determine intervertebral joint passive moments, whereas the contributions from ligaments were partitioned out. This is a limitation, seeing as a component of the resulting calculated compression values could conceivably be transferred through the facet joint surfaces. The moment arising from facet joint contact would be accounted for in the model, but the contact force would be absent. This would manifest as an underprediction of facet joint contact forces by the current model. The load sharing effect would be posture specific, as extension has been demonstrated to preferentially load the facet joints.99 Another artifact of lumped facet-intervertebral disk modeling is that the kinematic coupling of lateral bending and axial rotation, as well as changes in the position of the center of rotation between vertebrae, is not accounted for in the model.100 Effectively, due to the angle of the facet joints, each FSU has 2 rotational degrees of freedom, rather than 3: flexion–extension, and rotation about an axis normal to the facet joint surface.54,100 Conversely, in the current model, each intervertebral joint is treated as having 3 degrees of freedom, with no kinematic coupling between them. Both these limitations—load sharing in intervertebral joints and kinematic coupling—can be addressed in the future with additional terms, but these may require additional in vitro data. For the time being, there is insufficient data to incorporate these features into the cervical spine model. An additional limitation is that the passive components of the model were calibrated and validated against several different in vitro studies; the natural variability between cadaver donors, experimental protocols, and investigator idiosyncrasies likely contributes to variability between studies.101

A major limitation of the current model is the variability inherent in modeling human data. The curvature, neuromuscular control, and state of degeneration of the cervical spine vary widely from one person to another; and these changes likely alter the mechanical properties of both the passive and active structures in the cervical spine. Ultimately, a subject-specific model would overcome these limitations, but it is currently not possible to measure any of these tissue mechanical properties in vivo, nor is it feasible for laboratories which do not have access to magnetic resonance imaging to measure such properties. Scaling various aspects of the model to specified percentiles is also enticing but doing so requires stochastic methods outside of the scope of this investigation. As a first step, we opted to capture, within the large margin of variability, a 50th-percentile human male.

In conclusion, a cervical spine model was developed with thoroughly assessed passive structures, intended for use in occupational and ergonomic applications. A technique for partitioning cervical motion based on the passive range of motion of each joint was tested, with results that compared well against in vitro studies, but not with in vivo studies. In particular, the motion attributed to the upper cervical spine was disproportionately higher when based solely on passive structures; this implied that motion at these joints is constrained in vivo by active muscle contributions. Therefore, the model was updated to partition joint angles based on best established in vivo values. The results provided compression and shear values throughout the cervical spine, which compared favorably against previously published models, with a few caveats which may be explained by differences in model geometry.

Acknowledgments

The authors acknowledge funding from the Natural Science and Engineering Research Council of Canada. J.P.C. is supported as a Canada Research Chair in Spine Biomechanics and Injury Prevention. We would also like to acknowledge Madelyne Claire Holman for her Sisyphean task in digitizing all experimental curves for FSU-level validation. The authors declare no conflict of interest.

References

  • 1.

    Côté P, van der Velde G, Cassidy JD, et al. The burden and determinants of neck pain in whiplash-associated disorders after traffic collisions. Eur Spine J. 2008;17(1):5259. doi:10.1007/s00586-008-0625-x

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 2.

    Côté P, Cassidy JD, Carroll L. The saskatchewan health and back pain survey. Spine. 1998;23(15):16891698. PubMed ID: 9704377 doi:10.1097/00007632-199808010-00015

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 3.

    Côté P, Cassidy DJ, Carroll LJ, Kristman V. The annual incidence and course of neck pain in the general population: a population-based cohort study. Pain. 2004;112(3):267273. PubMed ID: 15561381 doi:10.1016/j.pain.2004.09.004

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 4.

    Berolo S, Wells RP, Amick BC. Musculoskeletal symptoms among mobile hand-held device users and their relationship to device use: a preliminary study in a Canadian university population. Appl Ergon. 2011;42(2):371378. PubMed ID: 20833387 doi:10.1016/j.apergo.2010.08.010

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 5.

    Douglas EC, Gallagher KM. Are the neck positions and muscle activity observed when reading a tablet similar to that of the cervical flexion-relaxation onset? IISE Trans Occup Ergon Hum Factors. 2018;6(1):4350. doi:10.1080/24725838.2018.1450310

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 6.

    Snijders CJ, Hoek van Dijke GA, Roosch ER. A biomechanical model for the analysis of the cervical spine in static postures. J Biomech. 1991;24(9):783792. PubMed ID: 1752862 doi:10.1016/0021-9290(91)90303-5

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 7.

    Moroney SP, Schultz AB, Miller JA. Analysis and measurement of neck loads. J Orthop Res. 1988;6(5):713720. PubMed ID: 3404328 doi:10.1002/jor.1100060514

  • 8.

    Mathys R, Ferguson SJ. Simulation of the effects of different pilot helmets on neck loading during air combat. J Biomech. 2012;45(14):23622367. PubMed ID: 22840756 doi:10.1016/j.jbiomech.2012.07.014

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 9.

    Williams JL, Belytschko TB. A three-dimensional model of the human cervical spine for impact simulation. J Biomech Eng. 1983;105(4):321331. PubMed ID: 6645440 doi:10.1115/1.3138428

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 10.

    van der Horst MJ. Human Head Neck Response in Frontal, Lateral and Rear end Impact Loading—Modelling and Validation. [Thesis]. Eindhoven, Netherlands: Eindhoven University of Technology; 2002. doi:10.6100/ir554047

    • Search Google Scholar
    • Export Citation
  • 11.

    Garcia T. A biomechanical evaluation of whiplash using a multi-body dynamic model. J Biomech Eng. 2003;125(2):254. PubMed ID: 12751288 doi:10.1115/1.1556856

  • 12.

    Stemper BD, Yoganandan N, Pintar FA. Validation of a head-neck computer model for whiplash simulation. Med Biol Eng Comput. 2004;42(3):333338. PubMed ID: 15191078 doi:10.1007/BF02344708

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 13.

    de Jager M. Mathematical Head-Neck Models for Acceleration Impacts. [Thesis]. Eindhoven University of Technology; 1996.

  • 14.

    Brolin K, Halldin P. Development of a finite element model of the upper cervical spine and a parameter study of ligament characteristics. Spine. 2004;29(4):376385. PubMed ID: 15094533 doi:10.1097/01.BRS.0000090820.99182.2D

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 15.

    DeWit JA, Cronin DS. Cervical spine segment finite element model for traumatic injury prediction. J Mech Behav Biomed Mater. 2012;10:138150. PubMed ID: 22520426 doi:10.1016/j.jmbbm.2012.02.015

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 16.

    Panzer MB, Fice JB, Cronin DS. Cervical spine response in frontal crash. Med Eng Phys. 2011;33(9):11471159. PubMed ID: 21665513 doi:10.1016/j.medengphy.2011.05.004

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 17.

    Choi H, Vanderby R. Muscle forces and spinal loads at C4/5 level during isometric voluntary efforts. Med Sci Sports Exerc. 2000;32(4):830838. PubMed ID: 10776903 doi:10.1097/00005768-200004000-00016

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 18.

    Netto KJ, Burnett AF, Green JP, Rodrigues JP. Validation of an EMG-driven, graphically based isometric musculoskeletal model of the cervical spine. J Biomech Eng. 2008;130(3):031014. doi:10.1115/1.2913234

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 19.

    Cheng CH, Chien A, Hsu WL, Chen CPC, Cheng HYK. Investigation of the differential contributions of superficial and deep muscles on cervical spinal loads with changing head postures. PLoS One. 2016;11(3):112. doi:10.1371/journal.pone.0150608

    • Search Google Scholar
    • Export Citation
  • 20.

    Alizadeh M, Aurand A, Knapik GG, et al. An electromyography-assisted biomechanical cervical spine model: model development and validation. Clin Biomech. 2020;80(January):105169. doi:10.1016/j.clinbiomech.2020.105169

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 21.

    McGill SM, Norman RW. Partitioning of the L4-L5 dynamic moment into disc, ligamentous, and muscular components during lifting. Spine. 1986;11(7):666678. PubMed ID: 3787338

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 22.

    White AA, Panjabi MM. Clinical Biomechanics of the Spine. Vol 2. Philadelphia, PA: Lippincott Company; 1990.

  • 23.

    Vasavada AN, Hughes E, Nevins DD, Monda SM, Lin DC. Effect of subject-specific vertebral position and head and neck size on calculation of spine musculoskeletal moments. Ann Biomed Eng. 2018;46(11):18441856. PubMed ID: 29987540 doi:10.1007/s10439-018-2084-9

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 24.

    Cholewicki J, McGill SM. EMG assisted optimization: a hybrid approach for estimating muscle forces in an indeterminate biomechanical model. J Biomech. 1994;27(10):12871289. PubMed ID: 7962016 doi:10.1016/0021-9290(94)90282-8

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 25.

    Gagnon D, Arjmand N, Plamondon A, Shirazi-Adl A, Larivière C. An improved multi-joint EMG-assisted optimization approach to estimate joint and muscle forces in a musculoskeletal model of the lumbar spine. J Biomech. 2011;44(8):15211529. PubMed ID: 21439569 doi:10.1016/j.jbiomech.2011.03.002

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 26.

    Mattucci SF, Moulton JA, Chandrashekar N, Cronin DS. Strain rate dependent properties of younger human cervical spine ligaments. J Mech Behav Biomed Mater. 2012;10:216226. PubMed ID: 22520433 doi:10.1016/j.jmbbm.2012.02.004

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 27.

    Camacho DL, Nightingale RW, Robinette JJ, Vanguri SK, Coates DJ, Myers BS. Experimental flexibility measurements for the development of a computational head-neck model validated for near-vertex head impact. SAE Transaction. 1997;106:39894002. doi:10.4271/973345

    • Search Google Scholar
    • Export Citation
  • 28.

    Ivancic PC. Effects of orthoses on three-dimensional load-displacement properties of the cervical spine. Eur Spine J. 2013;22(1):169177. PubMed ID: 23090094 doi:10.1007/s00586-012-2552-0

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 29.

    Panjabi MM, Crisco JJ, Vasavada A, et al. Mechanical properties of the human cervical spine as shown by three-dimensional load–displacement curves. Spine. 2001;26(24):26922700. PubMed ID: 11740357 doi:10.1097/00007632-200112150-00012

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 30.

    Wheeldon JA, Pintar FA, Knowles S, Yoganandan N. Experimental flexion/extension data corridors for validation of finite element models of the young, normal cervical spine. J Biomech. 2006;39(2):375380. PubMed ID: 16321642 doi:10.1016/j.jbiomech.2004.11.014

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 31.

    McGill SM, Jones K, Bennett G, Bishop PJ. Passive stiffness of the human neck in flexion, extension, and lateral bending. Clin Biomech. 1994;9(3):193198. doi:10.1016/0268-0033(94)90021-3

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 32.

    Mitsuhashi N, Fujieda K, Tamura T, Kawamoto S. BodyParts3D: 3D structure database for anatomical concepts. Nucleic Acids Res. 2009;37(suppl 1):D782D785. doi:10.1093/nar/gkn613

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 33.

    Cignoni P, Corsini M, Ranzuglia G. MeshLab: an open-source 3D mesh processing system. Ercim News. 2008;73(6):4748.

  • 34.

    Panjabi MM, Oxland T, Parks E. Quantitative anatomy of cervical spine ligaments. Part II. Middle and lower cervical spine. J Spinal Disord. 1991;4(3):277285. PubMed ID: 1802158 doi:10.1097/00002517-199109000-00004

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 35.

    Panjabi MM, Oxland T, Parks E. Quantitative anatomy of cervical spine ligaments. Part I. Upper cervical spine. J Spinal Disord. 1991;4(3):270276. PubMed ID: 1802157 doi:10.1097/00002517-199109000-00003

    • PubMed
    • Search Google Scholar
    • Export Citation
  • 36.

    Nissan M, Gilad I. The cervical and lumbar vertebrae—an anthropometric model. Eng Med. 1984;13(3):111114. doi:10.1243/emed_jour_1984_013_030_02

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 37.

    Doherty BJ, Heggeness MH. The quantitative anatomy of the Atlas. Spine. 1994;19:24972500. doi:10.1097/00007632-199411001-00001

  • 38.

    Doherty BJ, Heggeness MH. Quantitative anatomy of the second cervical vertebra. Spine. 1995;20(5):513517. PubMed ID: 7604318 doi:10.1097/00007632-199503010-00002

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 39.

    Marlow EJ, Pastor RF. Sex determination using the second cervical vertebra—a test of the method. J Forensic Sci. 2011;56(1):165169. PubMed ID: 20735699 doi:10.1111/j.1556-4029.2010.01543.x

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 40.

    Heller JG, Alson MD, Schaffler MB, Garfin SR. Quantitative internal dens morphology. Spine. 1992;17(8):861866. PubMed ID: 1523487 doi:10.1097/00007632-199208000-00001

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 41.

    Benfer RA. Morphometric analysis of Cartesian coordinates of the human skull. Am J Phys Anthropol. 1975;42(3):371382. PubMed ID: 1096639 doi:10.1002/ajpa.1330420305

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 42.

    Dvorak J, Panjabi MM, Novotny JE, Antinnes JA. In vivo flexion/extension of the normal cervical spine. J Orthop Res. 1991;9(6):828834. PubMed ID: 1919845 doi:10.1002/jor.1100090608

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 43.

    Barrett JM, Callaghan JP. A mechanistic damage model for ligaments. J Biomech. 2017;61:1117. PubMed ID: 28728790 doi:10.1016/j.jbiomech.2017.06.039

  • 44.

    Moroney SP, Schultz AB, Miller JA, Andersson GB. Load-displacement properties of lower cervical spine motion segments. J Biomech. 1988;21(9):769779. PubMed ID: 3053721 doi:10.1016/0021-9290(88)90285-0

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 45.

    Virtanen P, Gommers R, Oliphant TE, et al. Der Walt SJ. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat Methods. 2007;17(3):261–272. doi:10.1038/s41592-019-0686-2

    • Search Google Scholar
    • Export Citation
  • 46.

    Yoganandan N, Stemper BD, Pintar FA, Baisden JL, Shender BS, Paskoff G. Normative segment-specific axial and coronal angulation corridors of subaxial cervical column in axial rotation. Spine. 2008;33(5):490496. PubMed ID: 18317191 doi:10.1097/BRS.0b013e3181657f67

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 47.

    Yoganandan N, Pintar FA, Stemper BD, Wolfla CE, Shender BS, Paskoff G. Level-dependent coronal and axial moment-rotation corridors of degeneration-free cervical spines in lateral flexion. J Bone Joint Surg Am. 2007;89(5):10661074. doi:10.2106/JBJS.F.00200

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 48.

    Millard M, Uchida T, Seth A, Delp SL. Flexing computational muscle: modeling and simulation of musculotendon dynamics. J Biomech Eng. 2013;135(2):021005. doi:10.1115/1.4023390

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 49.

    Kamibayashi LK, Richmond FJR. Morphometry of human neck muscles. Spine. 1998;23(12):13141323. PubMed ID: 9654620 doi:10.1097/00007632-199806150-00005

  • 50.

    Chancey VC, Nightingale RW, Van Ee CA, Knaub KE, Myers BS. Improved estimation of human neck tensile tolerance: reducing the range of reported tolerance using anthropometrically correct muscles and optimized physiologic initial conditions. Stapp Car Crash J. 2003;47(October):135153.

    • PubMed
    • Search Google Scholar
    • Export Citation
  • 51.

    Pearson WG, Langmore SE, Zumwalt AC, et al. Evaluating the structural properties of suprahyoid muscles and their potential for moving the hyoid. Dysphagia. 2010;26(4):345351. PubMed ID: 21069388 doi:10.1007/s00455-010-9315-z

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 52.

    McClure P, Siegler S, Nobilini R. Three-dimensional flexibility characteristics of the human cervical spine in vivo. Spine. 1998;23(2):216223. PubMed ID: 9474729 doi:10.1097/00007632-199801150-00013

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 53.

    Ordway N, Seymour R, Donelson R, Hojnowski L, Edwards T. Cervical flexion, extension, protrusion, and retraction: a radiographic segmental analysis. Spine. 1999;24(3):240247. PubMed ID: 10025018 doi:10.1097/00007632-199902010-00008

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 54.

    Anderst WJ, Iii WFD, Lee JY, Kang JD. Three-dimensional intervertebral kinematics in the healthy young adult cervical spine during dynamic functional loading. J Biomech. 2015;48(7):12861293. PubMed ID: 25814180 doi:10.1016/j.jbiomech.2015.02.049

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 55.

    Anderst WJ, Donaldson WF, Lee JY, Kang JD. Cervical motion segment contributions to head motion during flexion\extension, lateral bending, and axial rotation. Spine J. 2015;15(12):25382543. PubMed ID: 26334229 doi:10.1016/j.spinee.2015.08.042

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 56.

    Lysell E. Motion in the cervical spine: an experimental study on autopsy specimens. Acta Orthop. 1969;40(suppl 123):161. doi:10.3109/ort.1969.40.suppl-123.01

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 57.

    Panjabi MM, Dvorak J, Duranceau J, Yamamoto I. Three-Dimensional Movements of the Upper Cervical Spine. In: Baumann JU, Herron RE, eds. Bellingham, WA: SPIE;  1988:370377. doi:10.1117/12.950491

    • Search Google Scholar
    • Export Citation
  • 58.

    Panjabi MM, Summers DJ, Pelker RR, Videman T, Friedlaender GE, Southwick WO. Three-dimensional load-displacement curves due to froces on the cervical spine. J Orthop Res. 1986;4(2):152161. PubMed ID: 3712124

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 59.

    Nightingale RW, Carol Chancey V, Ottaviano D, et al. Flexion and extension structural properties and strengths for male cervical spine segments. J Biomech. 2007;40(3):535542. PubMed ID: 16620838 doi:10.1016/j.jbiomech.2006.02.015

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 60.

    Bayoglu R, Galibarov PE, Verdonschot N, Koopman B, Homminga J. Twente spine model: a thorough investigation of the spinal loads in a complete and coherent musculoskeletal model of the human spine. Med Eng Phys. 2019;68:3545. PubMed ID: 31010615 doi:10.1016/j.medengphy.2019.03.015

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 61.

    Hoek van Dijke GA, Snijders CJ, Roosch ER, Burgers PI. Analysis of biomechanical and ergonomic aspects of the cervical spine in F-16 flight situations. J Biomech. 1993;26(9):10171025. PubMed ID: 8408084 doi:10.1016/S0021-9290(05)80001-6

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 62.

    Goel VK, Clark CR, Gallaes K, Liu YK. Moment-rotation relationships of the ligamentous occipito-atlanto-axial complex. J Biomech. 1988;21(8):673680. PubMed ID: 3170621 doi:10.1016/0021-9290(88)90204-7

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 63.

    Wen N, Lavaste F, Santin JJ, Lassau JP. Three-dimensional biomechanical properties of the human cervical spine in vitro. Eur Spine J. 1993;2(1):211. PubMed ID: 20058441 doi:10.1007/bf00301048

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 64.

    Wu S, Kuo L, Lan HH, Tsai S. Segmental percentage contributions of cervical spine during different motion ranges of flexion and extension. J Spinal Disord Tech. 2010;23(4):278284. PubMed ID: 20068468

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 65.

    Keshner EA, Campbell D, Katz RT, Peterson BW. Neck muscle activation patterns in humans during isometric head stabilization. Exp Brain Res. 1989;75(2):335344. PubMed ID: 2721613 doi:10.1007/BF00247939

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 66.

    Schüldt K, Ekholm J, Harms-Ringdahl K, Németh G, Arborelius UP. Effects of changes in sitting work posture on static neck and shoulder muscle activity. Ergonomics. 1986;29(12):15251537. PubMed ID: 3816746 doi:10.1080/00140138608967266

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 67.

    McKinnon CD, Dickerson CR, Laing ACT, Callaghan JP. Neck muscle activity during simulated in-flight static neck postures and helmet mounted equipment. Occup Ergon. 2016;13(3–4):119130. doi:10.3233/OER-170245

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 68.

    Winter D. Biomedical model relating EMG to changing isometric tension. Presented at: 11th International Conference on Medical and Biological Engineering, Ottawa, Canada. 1976:362363.

    • Search Google Scholar
    • Export Citation
  • 69.

    Winters JM, Woo SL-Y. Multiple Muscle Systems. New York City, NY: Springer; 1990. doi:10.1007/978-1-4613-9030-5

  • 70.

    Winter D. Biomechanics and Motor Control of Human Movement. Hoboken, NJ: John Wiley & Sons Inc; 1990.

  • 71.

    Almosnino S, Pelland L, Pedlow SV, Stevenson JM. Between-day reliability of electromechanical delay of selected neck muscles during performance of maximal isometric efforts. Sports Med Arthrosc Rehabil Ther Technol. 2009;1(1):22. PubMed ID: 19775461 doi:10.1186/1758-2555-1-22

    • PubMed
    • Search Google Scholar
    • Export Citation
  • 72.

    Lu WW, Bishop PJ. Electromyographic activity of the cervical musculature during dynamic lateral bending. Spine. 1996;21(21):24432449. PubMed ID: 8923629 doi:10.1097/00007632-199611010-00007

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 73.

    Diamond S, Boyd S. CVXPY: a python-embedded modeling language for convex optimization. J Mach Learn Res. 2016;17(83):15.

  • 74.

    Wu G, Siegler S, Allard P, et al. ISB recommendation on definitions of joint coordinate system of various joints for the reporting of human joint motion—part I: ankle, hip, and spine. J Biomech. 2002;35(4):543548. PubMed ID: 11934426 doi:10.1016/S0021-9290(01)00222-6

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 75.

    de Leva P. Adjustments to Zatsiorsky-Seluyanov’s segment inertia parameters. J Biomech. 1996;29(9):12231230. PubMed ID: 8872282 doi:10.1016/0021-9290(95)00178-6

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 76.

    Penning L. Normal movements of the cervical spine. Am J Roentgenol. 1978;130(2):317326. PubMed ID: 414586 doi:10.2214/ajr.130.2.317

  • 77.

    Dvorak J, Froehlich D, Penning L, Baumgartner H, Panjabi MM. Functional radiographic diagnosis of the cervical spine: flexion/extension. Spine (Phila Pa 1976). 1988;13(7):748755. PubMed ID: 3194782 doi:10.1097/00007632-198807000-00007

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 78.

    Dvorak J, Panjabi MM, Grob D, Novotny JE, Antinnes JA. Clinical validation of functional flexion/extension radiographs of the cervical spine. Spine (Phila Pa 1976). 1993;18(1):120127. PubMed ID: 8434312 doi:10.1097/00007632-199301000-00018

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 79.

    Penning L, Wilmink JT. Rotation of the cervical spine. A CT study in normal subjects. Spine (Phila Pa 1976). 1987;12(8):732738. PubMed ID: 3686228 doi:10.1097/00007632-198710000-00003

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 80.

    Dvorak J, Panjabi MM, Gerber M, Wichmann W. CT-functional diagnostics of the rotatory instability of upper cervical spine. Spine (Phila Pa 1976). 1987;12(3):197205. PubMed ID: 3589813 doi:10.1097/00007632-198704000-00001

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 81.

    Mimura M, Moriya H, Watanabe T, Takahashi K, Yamagata M, Tamaki T. Three-dimensional motion analysis of the cervical spine with special reference to the axial rotation. Spine (Phila Pa 1976). 1989;14(11):11351139. PubMed ID: 2603046 doi:10.1097/00007632-198911000-00001

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 82.

    Ishii T, Mukai Y, Hosono N, et al. Kinematics of the upper cervical spine in rotation: in vivo three-dimensional analysis. Spine (Phila Pa 1976). 2004;29(7):E139E144. PubMed ID: 15087810 doi:10.1097/01.brs.0000116998.55056.3c

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 83.

    Ishii T, Mukai Y, Hosono N, et al. Kinematics of the subaxial cervical spine in rotation in vivo three-dimensional analysis. Spine (Phila Pa 1976). 2004;29(24):28262831. PubMed ID: 15599286 doi:10.1097/01.brs.0000147806.31675.6b

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 84.

    Zhao X, Wu Z, Han B, Yan Y, Zhang Y, Lei W. Three-dimensional analysis of cervical spine segmental motion in rotation. Arch Med Sci AMS. 2013;9(3):515. PubMed ID: 23847675 doi:10.5114/aoms.2013.35325

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 85.

    Salem W, Lenders C, Mathieu J, Hermanus N, Klein P. In vivo three-dimensional kinematics of the cervical spine during maximal axial rotation. Man Ther. 2013;18(4):339344. PubMed ID: 23375147 doi:10.1016/j.math.2012.12.002

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 86.

    Lin C-C, Lu T-W, Wang T-M, Hsu C-Y, Hsu S-J, Shih T-F. In vivo three-dimensional intervertebral kinematics of the subaxial cervical spine during seated axial rotation and lateral bending via a fluoroscopy-to-CT registration approach. J Biomech. 2014;47(13):33103317. PubMed ID: 25218506 doi:10.1016/j.jbiomech.2014.08.014

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 87.

    Ishii T, Mukai Y, Hosono N, et al. Kinematics of the cervical spine in lateral bending: in vivo three-dimensional analysis. Spine (Phila Pa 1976). 2006;31(2):155160. PubMed ID: 16418633 doi:10.1097/01.brs.0000195173.47334.1f

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 88.

    Vasavada AN, Li S, Delp SL. Influence of muscle morphometry and moment arms on the moment-generating capacity of human neck muscles. Spine. 1998;23(4):412422. PubMed ID: 9516695 doi:10.1097/00007632-199802150-00002

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 89.

    Mattucci SFE, Moulton JA, Chandrashekar N, Cronin DS. Strain rate dependent properties of human craniovertebral ligaments. J Mech Behav Biomed Mater. 2013;23:7179. PubMed ID: 23665484 doi:10.1016/j.jmbbm.2013.04.005

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 90.

    Hicks JL, Uchida TK, Seth A, Rajagopal A, Delp S. Is my model good enough? Best practices for verification and validation of musculoskeletal models and simulations of human movement. J Biomech Eng. 2015;137(2):020905. doi:10.1115/1.4029304

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 91.

    Vasavada AN, Nevins DD, Monda SM, et al. Gravitational demand on the neck musculature during tablet computer use. Ergonomics. 2015;58(6):9901004. PubMed ID: 25643042 doi:10.1080/00140139.2015.1005166

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 92.

    Douglas EC, Gallagher KM. The influence of a semi-reclined seated posture on head and neck kinematics and muscle activity while reading a tablet computer. Appl Ergon. 2017;60:342347. PubMed ID: 28166894 doi:10.1016/j.apergo.2016.12.013

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 93.

    Crowninshield RD, Brand RA. A physiologically based criterion of muscle force prediction in locomotion. J Biomech. 1981;14(11):793801. PubMed ID: 7334039 doi:10.1016/0021-9290(81)90035-x

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 94.

    Vasavada AN, Danaraj J, Siegmund GP. Head and neck anthropometry, vertebral geometry and neck strength in height-matched men and women. J Biomech. 2008;41(1):114121. PubMed ID: 17706225 doi:10.1016/j.jbiomech.2007.07.007

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 95.

    Mortensen JD, Vasavada AN, Merryweather AS. The inclusion of hyoid muscles improve moment generating capacity and dynamic simulations in musculoskeletal models of the head and neck. PLoS One. 2018;13(6):e0199912. doi:10.1371/journal.pone.0199912

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 96.

    Roos PE, Vasavada A, Zheng L, Zhou X. Neck musculoskeletal model generation through anthropometric scaling. PLoS One. 2020;15(1):e0219954. doi:10.1371/journal.pone.0219954

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 97.

    Vasavada AN, Brault J, Siegmund G. Musculotendon and fascicle strains in anterior and posterior neck muscles during whiplash injury. Spine. 2007;32(7):756765. PubMed ID: 17414909 doi:10.1097/01.brs.0000259058.00460.69

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 98.

    Gallagher KM, Vasavada AN, Fischer L, Douglas EC. Cervical spine musculotendon lengths when reading a tablet in three seated positions. J Appl Biomech. 2021;37(2):122129. doi:10.1123/jab.2020-0062

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 99.

    Panzer MB, Cronin DS. C4-C5 segment finite element model development, validation, and load-sharing investigation. J Biomech. 2009;42(4):480490. PubMed ID: 19200548 doi:10.1016/j.jbiomech.2008.11.036

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 100.

    Bogduk N, Mercer S. Biomechanics of the cervical spine. I: normal kinematics. Clin Biomech. 2000;15(9):633648. doi:10.1016/S0268-0033(00)00034-6

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 101.

    Naserkhaki S, Arjmand N, Shirazi-Adl A, Farahmand F, El-Rich M. Effects of eight different ligament property datasets on biomechanics of a lumbar L4-L5 finite element model. J Biomech. 2018;70:3342. PubMed ID: 28549604 doi:10.1016/j.jbiomech.2017.05.003

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation

Barrett, Dickerson, and Callaghan are with the Department of Kinesiology and Health Science, Faculty of Health, University of Waterloo, Waterloo, ON, Canada. McKinnon is with MyAbilities Technologies Inc, Mississauga, ON, Canada.

Callaghan (jack.callaghan@uwaterloo.ca) is corresponding author.
  • View in gallery

    —Overview of model development, specifically for the validation of its passive elements. The panel underneath each phase of development elucidates how those components were validated—in most cases, against a moment–angle or force–deflection curve. Starting on the leftmost panel, each individual ligament (here the ALL is shown as an example) in the model had force–deflection characteristics that were obtained from published literature. These included the usual toe, heel, and linear regions of the ligament force–deflection curve. The next phase of validation involved assembling FSU models for all 8 spinal levels included in the whole cervical spine model. These moment–angle curves were compared to multiple in vitro studies to ensure that the model’s response was generally within 1 SD of published data (bottom second panel). The model was then fully assembled into a ligamentous model whose moment–angle curve was, once again, compared to in vitro data. Finally, once outfitted with muscle elements, the whole model had its passive moment–angle curves validated against published in vivo curves loading human volunteers in the 3 directions of movement. The final, whole model. ALL indicates anterior longitudinal ligament; FSU, functional spinal unit.

  • View in gallery

    —Placement of reflective markers and electrodes for the in vivo component of the validation analysis from anterior (A) and posterior (B) views. Anatomical landmarks are: posterior head marker, anterior head marker, lateral head marker, C7 spinous process, acromion process, supra-sternal notch, and xiphoid process. Muscles collected from electromyography were splenius capitis, upper neck extensors, upper trapezius, levator scapula, and sternocleidomastoid.

  • View in gallery

    —Comparison of the model against experimental results. Positive magnitudes indicate extension, leftward axial rotation, and rightward lateral bending. The model has good agreement in flexion–extension where the moment–angle curves are all within 1 SD. To some extent, the same is true of axial rotation, although these curves do not appear to have the same consensus seen in flexion–extension. Lateral bending at C0–C1 had some difficulty and the model does not explicitly handle the bony contact between the C0–C1 or C1–C2 joints, which are primarily the structures responsible for resisting lateral bending.

  • View in gallery

    —Comparison of the passive moment–angle curve generated by the cervical spine model compared to the average in vivo flexion–extension (A), axial rotation (B), and lateral bending (C) passive curves. Studies used were McClure et al52 (blue dashed-dot lines with error margins) and McGill et al31 (solid red line with error margin). Like before, negative values indicate flexion, right axial twist and left lateral bend. The model’s response is generally within 1 SD of the reported moment–angle relations collected from in vivo human volunteers, with some exceptions for lateral bending and extension. The model curves were obtained by applying a slowly varying pure moment to the skull (1/16 Hz), and measuring the corresponding angular displacement.

  • View in gallery

    —The spinal rhythm obtained from minimizing the potential energy in the functional spinal units while constraining the external posture. The relative contributions for the model are within 1 SD of the in vitro pooled average, which itself is dissimilar from the in vivo average spinal rhythm, especially for the upper cervical spine in flexion–extension and lateral bending. In flexion–extension, the dissimilarity between in vivo and in vitro spinal rhythms implies that human volunteers use active musculature to constrain motion in the upper cervical spine.

  • View in gallery

    —Comparison of model predicted compression (A) and AP shear (B) values against the Bayoglu et al60 model for a neutral standing posture held against gravity. The model predicts slightly less compression than Bayoglu et al60 on average, and much less shear (B). These differences may be attributable to differences in musculoskeletal geometry or the properties of passive tissues. AP indicates anteroposterior.

  • View in gallery

    —Current model predicted compression at C7–T1 as a function of neck flexion angle. As before, positive values indicate extension, left axial rotation, and rightward lateral bend. The average response of the model is depicted with the solid black line, the SD shaded around it in gray. The other model responses are included for comparison. The Hoek van Dijke et al61 and Snijders et al6 models are from similar investigations on the same model, whereas the Mathys and Ferguson8 model is an investigation using the geometry in the Vasavada et al88 models. Bayoglu et al60 model was a whole spine model developed from a cadaveric specimen with both an articulated cervical and lumbar spine. Both the current model and that of Cheng et al19 are electromyographically driven models, which tend to predict more compression through the range of motion. EMGAO, EMG assisted optimization.

  • 1.

    Côté P, van der Velde G, Cassidy JD, et al. The burden and determinants of neck pain in whiplash-associated disorders after traffic collisions. Eur Spine J. 2008;17(1):5259. doi:10.1007/s00586-008-0625-x

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 2.

    Côté P, Cassidy JD, Carroll L. The saskatchewan health and back pain survey. Spine. 1998;23(15):16891698. PubMed ID: 9704377 doi:10.1097/00007632-199808010-00015

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 3.

    Côté P, Cassidy DJ, Carroll LJ, Kristman V. The annual incidence and course of neck pain in the general population: a population-based cohort study. Pain. 2004;112(3):267273. PubMed ID: 15561381 doi:10.1016/j.pain.2004.09.004

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 4.

    Berolo S, Wells RP, Amick BC. Musculoskeletal symptoms among mobile hand-held device users and their relationship to device use: a preliminary study in a Canadian university population. Appl Ergon. 2011;42(2):371378. PubMed ID: 20833387 doi:10.1016/j.apergo.2010.08.010

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 5.

    Douglas EC, Gallagher KM. Are the neck positions and muscle activity observed when reading a tablet similar to that of the cervical flexion-relaxation onset? IISE Trans Occup Ergon Hum Factors. 2018;6(1):4350. doi:10.1080/24725838.2018.1450310

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 6.

    Snijders CJ, Hoek van Dijke GA, Roosch ER. A biomechanical model for the analysis of the cervical spine in static postures. J Biomech. 1991;24(9):783792. PubMed ID: 1752862 doi:10.1016/0021-9290(91)90303-5

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 7.

    Moroney SP, Schultz AB, Miller JA. Analysis and measurement of neck loads. J Orthop Res. 1988;6(5):713720. PubMed ID: 3404328 doi:10.1002/jor.1100060514

  • 8.

    Mathys R, Ferguson SJ. Simulation of the effects of different pilot helmets on neck loading during air combat. J Biomech. 2012;45(14):23622367. PubMed ID: 22840756 doi:10.1016/j.jbiomech.2012.07.014

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 9.

    Williams JL, Belytschko TB. A three-dimensional model of the human cervical spine for impact simulation. J Biomech Eng. 1983;105(4):321331. PubMed ID: 6645440 doi:10.1115/1.3138428

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 10.

    van der Horst MJ. Human Head Neck Response in Frontal, Lateral and Rear end Impact Loading—Modelling and Validation. [Thesis]. Eindhoven, Netherlands: Eindhoven University of Technology; 2002. doi:10.6100/ir554047

    • Search Google Scholar
    • Export Citation
  • 11.

    Garcia T. A biomechanical evaluation of whiplash using a multi-body dynamic model. J Biomech Eng. 2003;125(2):254. PubMed ID: 12751288 doi:10.1115/1.1556856

  • 12.

    Stemper BD, Yoganandan N, Pintar FA. Validation of a head-neck computer model for whiplash simulation. Med Biol Eng Comput. 2004;42(3):333338. PubMed ID: 15191078 doi:10.1007/BF02344708

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 13.

    de Jager M. Mathematical Head-Neck Models for Acceleration Impacts. [Thesis]. Eindhoven University of Technology; 1996.

  • 14.

    Brolin K, Halldin P. Development of a finite element model of the upper cervical spine and a parameter study of ligament characteristics. Spine. 2004;29(4):376385. PubMed ID: 15094533 doi:10.1097/01.BRS.0000090820.99182.2D

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 15.

    DeWit JA, Cronin DS. Cervical spine segment finite element model for traumatic injury prediction. J Mech Behav Biomed Mater. 2012;10:138150. PubMed ID: 22520426 doi:10.1016/j.jmbbm.2012.02.015

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 16.

    Panzer MB, Fice JB, Cronin DS. Cervical spine response in frontal crash. Med Eng Phys. 2011;33(9):11471159. PubMed ID: 21665513 doi:10.1016/j.medengphy.2011.05.004

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 17.

    Choi H, Vanderby R. Muscle forces and spinal loads at C4/5 level during isometric voluntary efforts. Med Sci Sports Exerc. 2000;32(4):830838. PubMed ID: 10776903 doi:10.1097/00005768-200004000-00016

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 18.

    Netto KJ, Burnett AF, Green JP, Rodrigues JP. Validation of an EMG-driven, graphically based isometric musculoskeletal model of the cervical spine. J Biomech Eng. 2008;130(3):031014. doi:10.1115/1.2913234

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 19.

    Cheng CH, Chien A, Hsu WL, Chen CPC, Cheng HYK. Investigation of the differential contributions of superficial and deep muscles on cervical spinal loads with changing head postures. PLoS One. 2016;11(3):112. doi:10.1371/journal.pone.0150608

    • Search Google Scholar
    • Export Citation
  • 20.

    Alizadeh M, Aurand A, Knapik GG, et al. An electromyography-assisted biomechanical cervical spine model: model development and validation. Clin Biomech. 2020;80(January):105169. doi:10.1016/j.clinbiomech.2020.105169

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 21.

    McGill SM, Norman RW. Partitioning of the L4-L5 dynamic moment into disc, ligamentous, and muscular components during lifting. Spine. 1986;11(7):666678. PubMed ID: 3787338

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 22.

    White AA, Panjabi MM. Clinical Biomechanics of the Spine. Vol 2. Philadelphia, PA: Lippincott Company; 1990.

  • 23.

    Vasavada AN, Hughes E, Nevins DD, Monda SM, Lin DC. Effect of subject-specific vertebral position and head and neck size on calculation of spine musculoskeletal moments. Ann Biomed Eng. 2018;46(11):18441856. PubMed ID: 29987540 doi:10.1007/s10439-018-2084-9

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 24.

    Cholewicki J, McGill SM. EMG assisted optimization: a hybrid approach for estimating muscle forces in an indeterminate biomechanical model. J Biomech. 1994;27(10):12871289. PubMed ID: 7962016 doi:10.1016/0021-9290(94)90282-8

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 25.

    Gagnon D, Arjmand N, Plamondon A, Shirazi-Adl A, Larivière C. An improved multi-joint EMG-assisted optimization approach to estimate joint and muscle forces in a musculoskeletal model of the lumbar spine. J Biomech. 2011;44(8):15211529. PubMed ID: 21439569 doi:10.1016/j.jbiomech.2011.03.002

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 26.

    Mattucci SF, Moulton JA, Chandrashekar N, Cronin DS. Strain rate dependent properties of younger human cervical spine ligaments. J Mech Behav Biomed Mater. 2012;10:216226. PubMed ID: 22520433 doi:10.1016/j.jmbbm.2012.02.004

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 27.

    Camacho DL, Nightingale RW, Robinette JJ, Vanguri SK, Coates DJ, Myers BS. Experimental flexibility measurements for the development of a computational head-neck model validated for near-vertex head impact. SAE Transaction. 1997;106:39894002. doi:10.4271/973345

    • Search Google Scholar
    • Export Citation
  • 28.

    Ivancic PC. Effects of orthoses on three-dimensional load-displacement properties of the cervical spine. Eur Spine J. 2013;22(1):169177. PubMed ID: 23090094 doi:10.1007/s00586-012-2552-0

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 29.

    Panjabi MM, Crisco JJ, Vasavada A, et al. Mechanical properties of the human cervical spine as shown by three-dimensional load–displacement curves. Spine. 2001;26(24):26922700. PubMed ID: 11740357 doi:10.1097/00007632-200112150-00012

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 30.

    Wheeldon JA, Pintar FA, Knowles S, Yoganandan N. Experimental flexion/extension data corridors for validation of finite element models of the young, normal cervical spine. J Biomech. 2006;39(2):375380. PubMed ID: 16321642 doi:10.1016/j.jbiomech.2004.11.014

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 31.

    McGill SM, Jones K, Bennett G, Bishop PJ. Passive stiffness of the human neck in flexion, extension, and lateral bending. Clin Biomech. 1994;9(3):193198. doi:10.1016/0268-0033(94)90021-3

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 32.

    Mitsuhashi N, Fujieda K, Tamura T, Kawamoto S. BodyParts3D: 3D structure database for anatomical concepts. Nucleic Acids Res. 2009;37(suppl 1):D782D785. doi:10.1093/nar/gkn613

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 33.

    Cignoni P, Corsini M, Ranzuglia G. MeshLab: an open-source 3D mesh processing system. Ercim News. 2008;73(6):4748.

  • 34.

    Panjabi MM, Oxland T, Parks E. Quantitative anatomy of cervical spine ligaments. Part II. Middle and lower cervical spine. J Spinal Disord. 1991;4(3):277285. PubMed ID: 1802158 doi:10.1097/00002517-199109000-00004

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 35.

    Panjabi MM, Oxland T, Parks E. Quantitative anatomy of cervical spine ligaments. Part I. Upper cervical spine. J Spinal Disord. 1991;4(3):270276. PubMed ID: 1802157 doi:10.1097/00002517-199109000-00003

    • PubMed
    • Search Google Scholar
    • Export Citation
  • 36.

    Nissan M, Gilad I. The cervical and lumbar vertebrae—an anthropometric model. Eng Med. 1984;13(3):111114. doi:10.1243/emed_jour_1984_013_030_02

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 37.

    Doherty BJ, Heggeness MH. The quantitative anatomy of the Atlas. Spine. 1994;19:24972500. doi:10.1097/00007632-199411001-00001

  • 38.

    Doherty BJ, Heggeness MH. Quantitative anatomy of the second cervical vertebra. Spine. 1995;20(5):513517. PubMed ID: 7604318 doi:10.1097/00007632-199503010-00002

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 39.

    Marlow EJ, Pastor RF. Sex determination using the second cervical vertebra—a test of the method. J Forensic Sci. 2011;56(1):165169. PubMed ID: 20735699 doi:10.1111/j.1556-4029.2010.01543.x

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 40.

    Heller JG, Alson MD, Schaffler MB, Garfin SR. Quantitative internal dens morphology. Spine. 1992;17(8):861866. PubMed ID: 1523487 doi:10.1097/00007632-199208000-00001

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 41.

    Benfer RA. Morphometric analysis of Cartesian coordinates of the human skull. Am J Phys Anthropol. 1975;42(3):371382. PubMed ID: 1096639 doi:10.1002/ajpa.1330420305

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 42.

    Dvorak J, Panjabi MM, Novotny JE, Antinnes JA. In vivo flexion/extension of the normal cervical spine. J Orthop Res. 1991;9(6):828834. PubMed ID: 1919845 doi:10.1002/jor.1100090608

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 43.

    Barrett JM, Callaghan JP. A mechanistic damage model for ligaments. J Biomech. 2017;61:1117. PubMed ID: 28728790 doi:10.1016/j.jbiomech.2017.06.039

  • 44.

    Moroney SP, Schultz AB, Miller JA, Andersson GB. Load-displacement properties of lower cervical spine motion segments. J Biomech. 1988;21(9):769779. PubMed ID: 3053721 doi:10.1016/0021-9290(88)90285-0

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 45.

    Virtanen P, Gommers R, Oliphant TE, et al. Der Walt SJ. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat Methods. 2007;17(3):261–272. doi:10.1038/s41592-019-0686-2

    • Search Google Scholar
    • Export Citation
  • 46.

    Yoganandan N, Stemper BD, Pintar FA, Baisden JL, Shender BS, Paskoff G. Normative segment-specific axial and coronal angulation corridors of subaxial cervical column in axial rotation. Spine. 2008;33(5):490496. PubMed ID: 18317191 doi:10.1097/BRS.0b013e3181657f67

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 47.

    Yoganandan N, Pintar FA, Stemper BD, Wolfla CE, Shender BS, Paskoff G. Level-dependent coronal and axial moment-rotation corridors of degeneration-free cervical spines in lateral flexion. J Bone Joint Surg Am. 2007;89(5):10661074. doi:10.2106/JBJS.F.00200

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 48.

    Millard M, Uchida T, Seth A, Delp SL. Flexing computational muscle: modeling and simulation of musculotendon dynamics. J Biomech Eng. 2013;135(2):021005. doi:10.1115/1.4023390

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 49.

    Kamibayashi LK, Richmond FJR. Morphometry of human neck muscles. Spine. 1998;23(12):13141323. PubMed ID: 9654620 doi:10.1097/00007632-199806150-00005

  • 50.

    Chancey VC, Nightingale RW, Van Ee CA, Knaub KE, Myers BS. Improved estimation of human neck tensile tolerance: reducing the range of reported tolerance using anthropometrically correct muscles and optimized physiologic initial conditions. Stapp Car Crash J. 2003;47(October):135153.

    • PubMed
    • Search Google Scholar
    • Export Citation
  • 51.

    Pearson WG, Langmore SE, Zumwalt AC, et al. Evaluating the structural properties of suprahyoid muscles and their potential for moving the hyoid. Dysphagia. 2010;26(4):345351. PubMed ID: 21069388 doi:10.1007/s00455-010-9315-z

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 52.

    McClure P, Siegler S, Nobilini R. Three-dimensional flexibility characteristics of the human cervical spine in vivo. Spine. 1998;23(2):216223. PubMed ID: 9474729 doi:10.1097/00007632-199801150-00013

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 53.

    Ordway N, Seymour R, Donelson R, Hojnowski L, Edwards T. Cervical flexion, extension, protrusion, and retraction: a radiographic segmental analysis. Spine. 1999;24(3):240247. PubMed ID: 10025018 doi:10.1097/00007632-199902010-00008

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 54.

    Anderst WJ, Iii WFD, Lee JY, Kang JD. Three-dimensional intervertebral kinematics in the healthy young adult cervical spine during dynamic functional loading. J Biomech. 2015;48(7):12861293. PubMed ID: 25814180 doi:10.1016/j.jbiomech.2015.02.049

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 55.

    Anderst WJ, Donaldson WF, Lee JY, Kang JD. Cervical motion segment contributions to head motion during flexion\extension, lateral bending, and axial rotation. Spine J. 2015;15(12):25382543. PubMed ID: 26334229 doi:10.1016/j.spinee.2015.08.042

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 56.

    Lysell E. Motion in the cervical spine: an experimental study on autopsy specimens. Acta Orthop. 1969;40(suppl 123):161. doi:10.3109/ort.1969.40.suppl-123.01

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 57.

    Panjabi MM, Dvorak J, Duranceau J, Yamamoto I. Three-Dimensional Movements of the Upper Cervical Spine. In: Baumann JU, Herron RE, eds. Bellingham, WA: SPIE;  1988:370377. doi:10.1117/12.950491

    • Search Google Scholar
    • Export Citation
  • 58.

    Panjabi MM, Summers DJ, Pelker RR, Videman T, Friedlaender GE, Southwick WO. Three-dimensional load-displacement curves due to froces on the cervical spine. J Orthop Res. 1986;4(2):152161. PubMed ID: 3712124

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 59.

    Nightingale RW, Carol Chancey V, Ottaviano D, et al. Flexion and extension structural properties and strengths for male cervical spine segments. J Biomech. 2007;40(3):535542. PubMed ID: 16620838 doi:10.1016/j.jbiomech.2006.02.015

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 60.

    Bayoglu R, Galibarov PE, Verdonschot N, Koopman B, Homminga J. Twente spine model: a thorough investigation of the spinal loads in a complete and coherent musculoskeletal model of the human spine. Med Eng Phys. 2019;68:3545. PubMed ID: 31010615 doi:10.1016/j.medengphy.2019.03.015

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 61.

    Hoek van Dijke GA, Snijders CJ, Roosch ER, Burgers PI. Analysis of biomechanical and ergonomic aspects of the cervical spine in F-16 flight situations. J Biomech. 1993;26(9):10171025. PubMed ID: 8408084 doi:10.1016/S0021-9290(05)80001-6

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 62.

    Goel VK, Clark CR, Gallaes K, Liu YK. Moment-rotation relationships of the ligamentous occipito-atlanto-axial complex. J Biomech. 1988;21(8):673680. PubMed ID: 3170621 doi:10.1016/0021-9290(88)90204-7

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 63.

    Wen N, Lavaste F, Santin JJ, Lassau JP. Three-dimensional biomechanical properties of the human cervical spine in vitro. Eur Spine J. 1993;2(1):211. PubMed ID: 20058441 doi:10.1007/bf00301048

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 64.

    Wu S, Kuo L, Lan HH, Tsai S. Segmental percentage contributions of cervical spine during different motion ranges of flexion and extension. J Spinal Disord Tech. 2010;23(4):278284. PubMed ID: 20068468

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 65.

    Keshner EA, Campbell D, Katz RT, Peterson BW. Neck muscle activation patterns in humans during isometric head stabilization. Exp Brain Res. 1989;75(2):335344. PubMed ID: 2721613 doi:10.1007/BF00247939

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 66.

    Schüldt K, Ekholm J, Harms-Ringdahl K, Németh G, Arborelius UP. Effects of changes in sitting work posture on static neck and shoulder muscle activity. Ergonomics. 1986;29(12):15251537. PubMed ID: 3816746 doi:10.1080/00140138608967266

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 67.

    McKinnon CD, Dickerson CR, Laing ACT, Callaghan JP. Neck muscle activity during simulated in-flight static neck postures and helmet mounted equipment. Occup Ergon. 2016;13(3–4):119130. doi:10.3233/OER-170245

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 68.

    Winter D. Biomedical model relating EMG to changing isometric tension. Presented at: 11th International Conference on Medical and Biological Engineering, Ottawa, Canada. 1976:362363.

    • Search Google Scholar
    • Export Citation
  • 69.

    Winters JM, Woo SL-Y. Multiple Muscle Systems. New York City, NY: Springer; 1990. doi:10.1007/978-1-4613-9030-5

  • 70.

    Winter D. Biomechanics and Motor Control of Human Movement. Hoboken, NJ: John Wiley & Sons Inc; 1990.

  • 71.

    Almosnino S, Pelland L, Pedlow SV, Stevenson JM. Between-day reliability of electromechanical delay of selected neck muscles during performance of maximal isometric efforts. Sports Med Arthrosc Rehabil Ther Technol. 2009;1(1):22. PubMed ID: 19775461 doi:10.1186/1758-2555-1-22

    • PubMed
    • Search Google Scholar
    • Export Citation
  • 72.

    Lu WW, Bishop PJ. Electromyographic activity of the cervical musculature during dynamic lateral bending. Spine. 1996;21(21):24432449. PubMed ID: 8923629 doi:10.1097/00007632-199611010-00007

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 73.

    Diamond S, Boyd S. CVXPY: a python-embedded modeling language for convex optimization. J Mach Learn Res. 2016;17(83):15.

  • 74.

    Wu G, Siegler S, Allard P, et al. ISB recommendation on definitions of joint coordinate system of various joints for the reporting of human joint motion—part I: ankle, hip, and spine. J Biomech. 2002;35(4):543548. PubMed ID: 11934426 doi:10.1016/S0021-9290(01)00222-6

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 75.

    de Leva P. Adjustments to Zatsiorsky-Seluyanov’s segment inertia parameters. J Biomech. 1996;29(9):12231230. PubMed ID: 8872282 doi:10.1016/0021-9290(95)00178-6

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 76.

    Penning L. Normal movements of the cervical spine. Am J Roentgenol. 1978;130(2):317326. PubMed ID: 414586 doi:10.2214/ajr.130.2.317

  • 77.

    Dvorak J, Froehlich D, Penning L, Baumgartner H, Panjabi MM. Functional radiographic diagnosis of the cervical spine: flexion/extension. Spine (Phila Pa 1976). 1988;13(7):748755. PubMed ID: 3194782 doi:10.1097/00007632-198807000-00007

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 78.

    Dvorak J, Panjabi MM, Grob D, Novotny JE, Antinnes JA. Clinical validation of functional flexion/extension radiographs of the cervical spine. Spine (Phila Pa 1976). 1993;18(1):120127. PubMed ID: 8434312 doi:10.1097/00007632-199301000-00018

    • Crossref
    • PubMed
    • Search Google Scholar
    • Export Citation
  • 79.

    Penning L, Wilmink JT. Rotation of the cervical spine. A CT study in normal subjects. Spine (Phila Pa 1976). 1987;12(8):732738. PubMed ID: 3686228 doi:10.1097/00007632-198710000-00003

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 80.

    Dvorak J, Panjabi MM, Gerber M, Wichmann W. CT-functional diagnostics of the rotatory instability of upper cervical spine. Spine (Phila Pa 1976). 1987;12(3):197205. PubMed ID: 3589813 doi:10.1097/00007632-198704000-00001

    • Crossref
    • PubMed