After

Flexion-distraction injuries frequently causes traumatic cervical spinal cord injury (SCI). Post-traumatic instability can cause aggravation of the secondary SCI during patient’s care . However, there is little information on how the pattern of disco-ligamentous injury affects the SCI severity and mechanism. This study objective was to analyze how different flexion-distraction disco-ligamentous injuries affect the SCI mechanisms during post-traumatic flexion and extension. A cervical spine finite element model including the spinal cord was used and different combinations of partial or complete intervertebral disc (IVD) rupture and disruption of various posterior ligaments were modeled at C4-C5, C5-C6 or C6-C7. In flexion, complete IVD rupture combined with posterior ligamentous complex rupture was the most severe injury leading to the most important von Mises stress (47 to 66 kPa), principal strains p1 (0.32 to 0.41 in white matter) and p3 (-0.78 to -0.96 in white matter) in the spinal cord and to the most important spinal cord compression (35 to 48 %). The main post-trauma SCI mechanism was identified as compression of the anterior white matter at the injured level combined with distraction of the posterior spinal cord during flexion. There was also a concentration of the maximum stresses in the gray matter after injury. Finally, in extension, the injuries tested had little impact on the spinal cord. The capsular ligament was the most important struc ture in protecting the spinal cord. Its status should be carefully examined during patient’s management.


INTRODUCTION
Spinal cord injury (SCI) occurs in 34 to 45 % of cervical spine trauma [1][2][3].SCI at the cervical level is particularly damageable considering the risk of death and paralysis linked to the position of the segment in the central nervous system.SCI involves two types of mechanism: primary and secondary.Primary SCI is the direct consequence of traumatic vertebral fracture or dislocation leading to spinal canal disruption and excessive deformation or compression of the spinal cord [4].Secondary SCI is the subsequent aggravation of the neurological impairment and is caused by many different biochemical mechanisms including inflammation [5] and by mechanical instability leading to additional spinal cord disruption during pre-hospital care and early treatment [6].Following the injury, the spinal cord may remain compressed due to the disrupted spinal canal, translation between vertebrae or damaged structures like a herniated intervertebral disc (IVD) which increase the damage to the spinal cord.Clinical instability is defined as "the loss of the ability of the spine under physiologic loads to maintain relationships between vertebrae in such a way that there is neither damage nor subsequent irritation to the spinal cord or nerve roots, and, in addition, there is no development of incapacitating deformity or pain due to structural changes" [7].The integrity of the IVD and ligaments has been recognized as an important component of stability assessment [8,9].Retrospective clinical studies of hyper-extension have also correlated the integrity of the ligaments and IVD with neurological deficits [10,11].
Flexion-distraction injuries are common at the subaxial cervical spine [12] and especially at C4-C5, C5-C6 and C6-C7 levels [13][14][15].They comprise unilateral or bilateral facet subluxations or dislocations, flexion teardrop fractures, chance-type fractures and purely ligamentous injuries [8] and are frequently linked to SCI [16].Facet dislocation and bilateral facet injury in particular have been identified as significant predictors of SCI in cervical spine trauma [15].Flexion-distraction injuries present a variety of discoligamentous disruption patterns.The injured structures reported for unilateral and bilateral dislocations are the capsular ligaments (CL), the interspinous ligament (ISL), the supraspinous ligament (SSL), the ligamentum flavum (LF), the anterior longitudinal ligament (ALL), the posterior longitudinal ligament (PLL) and the IVD.However, different combinations of disco-ligamentous injuries are observed in different cases.Clinical studies reported that only 40 to 56.5 % of cervical spine dislocation cases had a complete PLL disruption [17,18].IVD disruption is also variable since different extent of horizontal tear has been observed: complete rupture accompanied with ALL tear or partial rupture [19].However, little is known about the link between the injured discoligamentous structures and the SCI severity.
Many studies have investigated mechanical instability at the cervical spine based on the integrity of disco-ligamentous structures [20][21][22][23], but without studying the biomechanical impact on the spinal cord.Liao et al. [24] produced atlanto-occipital dislocation or atlanto-axial instability on cadaver specimens and then analyzed the compression of the dural sac and the cervical spine mobility during the application of a cervical collar.They observed that important motion of the cervical spine and important dural sac compression occurred during cervical collar application.Canal occlusion has also been measured post-trauma in the context of in vitro [25,26] or clinical studies [15,27,28] but with the spine in neutral position only.
Finite element (FE) modeling is a promising solution to study the post-traumatic mechanical damages of the spinal cord since it is possible to test various discoligamentous disruption and mechanical loadings without risk of spinal cord degeneration as with in vitro tests.A few FE models of the cervical spine including the spinal cord have been developed.However, they have been exploited under traumatic conditions [29][30][31] or to study the effect of pathologies or surgical procedures on the spinal cord [32][33][34][35][36][37].To our knowledge, no FE study has analyzed the effect of discoligamentous injuries on the post-traumatic mechanical integrity of the spinal cord.
The objective of this study was to evaluate how patterns of flexion-distraction disco-ligamentous injuries affect the spinal cord damage in flexion and extension after trauma.A detailed FE model of the cervical spine was used to measure the von Mises stresses and the principal strains in the white and gray matter.The spinal cord compression was also reported.

Finite Element Model
For this study, a cervical spine (C2-T1) FE model integrating the spinal cord was used [31,38].In summary, the geometry of the vertebrae was reconstructed from CT images (0.6 mm contiguous slides) of a healthy 50th percentile male volunteer.In this specific study, the vertebrae were set as rigid bodies.The model had 22.7 degrees of lordosis at C2-C7.The IVD were created between the vertebral endplates and meshed using hexahedral solid elements.They were divided into nucleus pulposus and annulus fibrosus ground substance.IVD mechanical behavior was defined by first-order Mooney-Rivlin hyper-elastic material law representative of non-pathological quasi-static properties [39] (table 1).Collagen fibers were modeled as tension-only springs in the annulus fibrosus ground substance.The springs were organized in concentric lamella with a crosswise pattern of ± 35 degrees.The annulus was divided into three sections (anterior, posterior and lateral) and the collagen fibers force-displacement curves [40] were scaled by a different factor depending on the section [39].The nucleus properties were calibrated in a previous study [9] to adjust the intradiscal pressure in comparison to in vitro results [41].The cervical spine ligaments were created between each functional spinal unit (FSU).The geometry and attachment point of the ligaments were based on anatomical data from the literature [42,43].Each ligament was meshed with 4nodes shell elements except for the CL (3-nodes shell elements were used) (figure 1).
The ligaments behaviors were defined by tabulated non-linear stress-strain curves derived from experimental studies [44,45].The toe-regions of the curves were calibrated against the intervertebral rotation of each FSU under quasi-static flexion and extension of ± 2 Nm [9].Facet joints were represented by frictionless contact interfaces.
The spinal cord was meshed using pentahedral solid elements [31].The geometry of the white and gray matter were based on histological cadaveric spinal cord cross-sections taken from the literature [46].Tabulated non-linear and strain-rate dependent engineering stress-strain curves were assigned to the white and gray matters [47].The pia mater was modeled as the external contour of the white matter and the dura mater as the contour of the spinal canal with a 1 mm offset.Both structures were meshed as 4-nodes shell elements.Denticulate ligaments were modeled by 4-nodes shell elements and attached to dura mater lateral sides through coincident nodes (figure 2).The mechanical properties of the dura mater, pia mater and dentate ligaments were represented by linear elastic material properties (table 1).The cerebrospinal fluid was not included into this study.Total number of elements and nodes for this FE model are 506 984 and 154 915 respectively.
Nerve roots were modeled by springs (stiffness of 20 N/mm) attached to the dura matter though a rigid body at the level of the intervertebral foramen (figure 2) and cinematically linked to the superior vertebra at each spinal level.This attachment position was selected since nerve roots are disposed cranially to each spinal level [48] and are attached to the dura mater [49].
Prior to model exploitation, the spinal cord behavior in flexion and extension was validated against values of maximum and minimum principal strain of the spinal cord and relative antero-posterior and superior-inferior displacements of the spinal cord in relation to the vertebrae in healthy subjects at all spinal levels from C3 to C7 and at ± 20 degrees of C2-T1 rotation in flexion-extension [50].

Injury Modeling
For this study, four different types of disco-ligamentous injury patterns were modeled to investigate the relative impact of the structures on the spinal cord protection and represent the diversity of possible flexion-distraction injuries [18,51] (table 2).These injuries were modeled at one spinal level at a time.Three different FSU levels were chosen, C4-C5, C5-C6 and C6-C7 since these levels are the most frequently affected by flexion-distraction injuries [13,14].This created a total of 12 different injury scenarios.Rupture of a ligament was modeled by removing the corresponding component from the FE model.IVD rupture was represented by a transversal anteroposterior cut into the middle of the disc.A contact interface was added at the rupture between the proximal and distal parts of the disc.

Effects of Injury on the Spinal Cord
After injury modeling, a quasi-static flexion and extension moment (± 2 Nm) was applied to C2 while T1 was kept fixed.This amplitude of moment (± 2 Nm) represents the elastic range of the cervical spine segment [52].The intact model was submitted to the same loads and used as baseline.This method has been used previously to evaluate intervertebral range of motions after an injury in numerical studies [9,53,54] and was deemed appropriate to evaluate the impact of post-traumatic instability on the spinal cord.The changes in antero-posterior and lateral diameter of the spinal cord during flexion and extension at the level of injury were also analyzed and compared to the SCI threshold of 40 % determined from traumatic cervical spine injury cases [28].Then, the extreme principal strains p1 and p3 and the von Mises stresses were extracted for five different spinal cord regions: anterior gray matter, gray matter horns, anterior white matter, posterior white matter and lateral white matter.The elements adjacent to the denticulate elements were excluded to avoid stress singularity resulting from the simplified modeling of the denticulate ligaments attachment.The reported data were taken at the maximum applied flexion or extension moment corresponding to 2 Nm or -2 Nm for most cases.For cases where the injuries created a high instability and an unrealistic flexibility, a threshold of evaluation were established at 73 degrees of C2-T1 rotation in flexion which is the maximal sagittal head-torso rotation plus one standard deviation in healthy subjects [55].C2-T1 rotation could not exceed C0-T1 rotation especially since C1-C2 is very flexible: the chin would touch the torso and no further flexion would be possible.
The strains results were compared to thresholds of neurological deficits determined by experimental studies.Bain et al. [56], in an in vivo animal study, have determined a strain injury threshold of 0.21 for traction loading on the optic nerve.
Injury determination was based on measurements of visual evoked potentials.Ouyang et al. [57] tested in compression samples of ex vivo ventral white matter from guinea pig.They measured that the compound action potential diminished starting at 50 % of compression and that this diminution was accelerated after 70 % of compression.

RESULTS
The validation process for the spinal cord showed that the model response fitted generally well with the clinical data [50] (figures 3 and 4) as all the results from the FE model were within one standard deviation of the reference with a few exceptions within two standard deviations.The distribution of p1 strains between the spinal levels respected the trends from the literature, but this was not the case for p3 strains: the strain at the superior spinal levels was more important.The direction of relative displacement was also reversed at C3 for superior-inferior displacement and anteroposterior displacement in flexion.
For extension loading, the impact of the injuries was moderate.In the baseline model at -2 Nm, the maximum principal strain p1 was 0.06 in the gray matter and 0.10 in the white matter and the minimum strain p3 was -0.09 in the gray matter and -0.15 in the white matter.The most extreme principal strain p1 and p3 recorded in the injured models were 0.17 and -0.23 respectively which is under the established thresholds for injury.The spinal cord compression in the antero-posterior and lateral direction in extension was 4 % or less for the uninjured simulation and all the injury scenarios.The maximum von Mises stress was 4.4 kPa in the baseline model at -2 Nm.The difference between the baseline and the injured model was equal or under 2.3 kPa.
For flexion loading, important differences were seen for the different injury cases.The percentage of compression at 2 Nm flexion is presented in figure 5.
Percentage of antero-posterior compression in the baseline model was 2 % at C4-C5 and C5-C6 and 1 % at C6-C7.The highest compressions were measured for injury case 4 for every FSU.For injury case 1 and 2, antero-posterior compression stayed under 18 %.The maximum compression measured was 48 % for injury case 4 at C5-C6 in the anteroposterior direction.Generally, the spinal cord compression increased gradually from case 1 to case 4 at all FSU levels.Lateral diameter changes were negligible (under 4 % of difference with baseline for every case).
The extreme principal strains in the spinal cord are presented by axial sections in figures 6 and 7.The maximum p1 strain in the baseline was 0.096 in the gray matter and 0.11 in the white matter.The minimum p3 strain in the baseline was -0.051 in the gray matter and -0.075 in the white matter.For all cases, the injuries had a higher impact on the p3 strain than the p1 strain.In the uninjured model, there is minimal compressive strain and mainly a distractive strain in the posterior spinal cord caused by the flexion of the cervical spine.For the injured cases, this distraction increases up to 0.35.The absolute value of principal strain p1 and p3 increased from case 1 to case 4. The p1 and p3 principal strains were generally uniform in the gray matter, but the posterior gray matter was under more distraction due to the flexion of the spinal cord.In the gray matter, only case 4 injuries had a maximum principal p1 strain over the injury threshold of 0.21 [56].In the white matter, all case 4 injuries and case 3 at C4-C5 and C6-C7 went over 0.21 of p1 strain.For principal strain p3, only case 4 injuries lead to strains under the -0.5 threshold for compound action potentials decrease [57] in the white matter and in the anterior gray matter for injury 4 at C5-C6.The threshold of -0.7 for accelerated compound action potentials was also reached in the anterior white matter in all case 4 injuries and in the lateral white matter for injury case 4 at C5-C6.The anterior and then the lateral white matter were the sections under the most extreme principal strain p3.Points of compression and distraction are seen at the denticulate ligaments attachments which has also been observed on MRI images of healthy patients [50].The most extreme principal strains p3 are concentrated in the anterior part of the white matter.
This phenomenon was present for every injury scenario, but the amplitude of the compression increases form injury cases 1 to 4, while this area of compression is not present in the baseline model.In the baseline model, the principal strains p3 in the spinal cord were between 0 and -0.075.The same strain pattern was observed for injuries at level C5-C6 and C6-C7.
The maximum von Mises stresses in the spinal cord and their location in the axial cross-section of the spinal cord are presented in table 3. The stress was highest for the case 4 injuries and lead to an increase of 44 to 63 kPa of the maximum von Mises stresses compared to baseline.While the maximum von Mises stress was situated in the posterior white matter in the uninjured model, it moved to the gray matter in all injury cases except for case 1 at C5-C6 where it stayed in the posterior white matter.
The von Mises stress distribution in the spinal cord in flexion for baseline model and injuries cases 1 to 4 at level C4-C5 are shown in figure 9.The stress in the baseline model at 2 Nm flexion is small (under 3 kPa) and concentrated in the posterior spinal cord.In the injured cases, the maximum stress is in the gray matter and mainly in the horns at the injury level.

DISCUSSION
While disco-ligamentous injuries are frequent at the cervical spine [51] and have been linked to instability [8], the relation between the injured structures and the mechanical damage to the spinal cord has not been thoroughly investigated.This study used a C2-T1 FE model including the spinal cord to quantify the effect of various combinations of flexion-distraction disco-ligamentous injuries on the compression of the spinal cord and the strains and stresses in the spinal cord following quasi-static flexion and extension (± 2 Nm).The FE model was validated against clinical data from healthy patients of spinal cord strains and displacements in flexion and extension [50].The results generally fitted within one standard deviation.Some differences were seen in the relative distribution of p3 strains between spinal levels since the strain at the superior levels was more important.Also, the direction of relative displacements was reversed at C3 in flexion.These differences can be explained by the fact that the upper spinal cord motion is kinematically bound to C2 in the model which could affect the behavior of the spinal cord.Since the injury cases were model at lower spinal levels, these differences seemed acceptable in the context of our study.
In extension, the four disco-ligamentous injury cases studied had little to no impact on the spinal cord.This is partly because the spinous processes acted as a physical barrier and limited the mobility of the injured segment, therefore protecting the spinal cord.Also, the posterior ligaments are mostly loaded in tension as during flexion [58].The intact ALL and, depending on the injury cases, the CL or anterior IVD also retained the stability of the cervical spine in extension.The impact on the spinal cord von Mises stresses (maximum difference of 52 % from baseline) and principal strains (maximum difference of 70 % with baseline) was small compared to flexion loading.Also, the strain injury thresholds determined for SCI were not reached.The spinal cord compression was under 4% which is small compared to the proposed clinical injury threshold of 40 % [28].
In flexion however, the injuries impacted the spinal cord stresses and strains to different degrees depending on the injury case.At all FSU levels, injury case 1, transversal injury of the IVD and posterior ligaments rupture with intact ALL and CL, had little impact on the spinal cord.While this injury case is very unlikely for subluxation or dislocation injuries, it is interesting to analyze the importance of the CL versus the IVD.
CL are important in resisting flexion, lateral bending and torsion [21,59] and facets disruption have been linked with neurological deficits [59] which support our finding that, from the disco-ligamentous structures investigated in this paper, the CL was the most important structure for keeping the stability of the segment and protecting the spinal cord.Maeda et al. [11] found that the IVD was associated with segmental instability and neurological impact, but most of their patients were suffering from hyper-extension injury while we studied flexion-type injuries.Richter et al. [23] demonstrated the significant impact of CL rupture on the range of motion in flexion and extension.Pitzen et al. [60] showed that both the CL and IVD are important in stabilizing the cervical spine in flexion and extension.The fact that injury case 4 presented more extreme levels of strains and von Mises stresses than injury case 3, where only 1/3 of the IVD is ruptured posteriorly, shows that the IVD still plays a role in maintaining clinical stability at the cervical spine.All case 4 injuries had principal strains p3 under -0.5 which was determined as a threshold for decrease of compound action potentials in the white matter.This suggests that case 4 injury leads to important aggravation of SCI during cervical spine flexion.The strains and stresses increased from case 1 to case 4 with injury case 4 being the most severe situation.The FSU level of the injury also had an impact on the solicitation of the spinal cord.Since C5-C6 is at the apex of the cervical spine model, injury case 4 caused more damage at this level due to its higher rotation: the highest spinal cord antero-posterior compression and the most extreme strains and stresses.It is also the only case where the threshold of -0.5 of compressive strain was reached in the gray matter.C6-C7 was the only FSU level where injury case 3 reached the extreme C2-T1 rotation of 73 degrees.This can be explained by the superior size of this FSU and its position in the cervical spine.Since T1 is fixed, less motion is necessary for C6-C7 to be at risk of subluxation.
In our study, antero-posterior compression of the spinal cord over 20 % lead to more important levels of stresses and strains than the other cases.Similarly, Kato et al.
[61] concluded from a numerical analysis that there may be a critical point in SCI between 20 and 40 % of antero-posterior spinal cord compression as the stress in the cord increased significantly between these two levels.The stresses and strains patterns obtained in this FE study showed that flexion-distraction injury leads to important compressive strains in the anterior spinal cord at the injured FSU level during posttraumatic flexion.The injury mechanism of the spinal cord from flexion-distraction injury has been debated in the literature.The SCI could originate from the excessive traction of the spinal cord during trauma [62] or from shear loading on the spinal cord from the relative translation of the adjacent vertebrae leading to a band of injured tissue at the shear plane [63], while the most extreme form of flexion-distraction injury, dislocation, leads to central lesion impacting principally the gray matter vasculature [64].From our analysis, the von Mises stress was more important in the gray matter at the level of injury which points toward a central spinal cord lesion.However, the von Mises stress computation is independent of volumetric deformation which should not be neglected in the investigation of potential spinal cord injury.In the baseline model, there were mostly distractive strains in the spinal cord caused by the flexion of the cervical spine.For the injured cases, the distraction in the posterior white matter increased up to 0.35 which is over the 0.21 threshold established for traction loading of optic nerves [56].This distraction increase is caused by an increase of the flexion range of motion at the injured level and was therefore located at the level of injury.In parallel, the spinal cord was pushed anteriorly onto the vertebra due to high rotation and disturbed antero-posterior motion of the injured level which causes compression of spinal cord and mainly the anterior white matter.This could explain why flexion-distraction leads to important neurological impairment since the blood vessels in the spinal cord are more susceptible to be disrupted by antero-posterior forces [58].
Therefore, at the injured level, the spinal cord is simultaneously susceptible to axons damage at the posterior white matter and disturbance of vascularisation in the gray matter and anterior white matter.However, since this is a post-traumatic study, the mechanism of injury occurring during the trauma cannot be inferred directly from our results.
Limitations of this study linked to model simplification need to be reported.First, the cervical spine was modeled in a neutral erected initial position and no representation of the cervical spine kyphosis linked to hyperflexion sprains [65] or initial subluxation or dislocation was modeled.We believe that these conditions would aggravate the levels of stresses and strains reported but would not change considerably the conclusions regarding the relative impact of the various injuries modeled.The flexion-extension moment of ± 2 Nm used may not be representative of the real-life multidirectional loads that trauma victims experienced.However, this method was necessary to evaluate the effect of a possible post-traumatic spinal instability on the spinal cord.There was no representation of the canal narrowing that can occur from the disruption of disco-ligamentous structures, however this would have probably aggravated the compression of the spinal cord.For example, the material from the IVD could leak in the spinal canal and compress the spinal cord.Muscles were also not represented in this model.While presence of active and passive muscles would have restrained the mobility of the cervical spine, an in vitro study has shown that the instability of the spine is not overestimated if normalized to the intact mobility [66].
There was no representation of the cerebrospinal fluid, however since the load was applied in quasi-static conditions the protective role of the cerebrospinal fluid is negligible.The thresholds used for traction and compression strains were taken from experimental studies of the white matter and not the gray matter, therefore it is difficult to conclude on the effect of the injuries on the gray matter.Finally, the nerve roots were represented only by simple springs.Therefore, it was impossible to determine the impact of the injuries on the stresses and strains of the nerve roots.This could be implemented in a future study.

Figure 8
Figure8shows the distribution of strains (absolute maximum strain) in the spinal In conclusion, a FE model of the cervical spine was used to quantify how different combinations of disco-ligamentous injuries representative of flexion-distraction trauma impact the principal strains and von Mises stresses in the spinal cord.The analysis showed that these injuries can lead to high strains and stresses in the spinal cord and spinal cord compression of up to 48 % during post-traumatic flexion.On the opposite, extension of the cervical spine had little impact on the spinal cord.The SCI mechanism was identified as an important compression of the anterior spinal cord at the level of injury caused by the relative motion of the vertebrae during flexion following injury with the highest levels of strains in the anterior white matter.Distraction of the posterior white matter is simultaneously present at the injured level and reached the injury threshold for traction.The CL were the structures, in combination with the IVD, that limited the most the solicitation of the spinal cord.These structures should be examined carefully to assess SCI severity.FUNDINGThis research was funded by the Canada research chair in biomechanics of head and spine injuries (grant number 231815) and the Fonds de recherche du Quebec -Nature et technologies (FRQNT) (grant number 271503).
Figure Captions List

Table 2 :
Type of disco-ligamentous injury patterns Case 1 -Rupture of the interspinous ligament, ligamentum flavum, supraspinous ligament and posterior longitudinal ligament accompanied with a transversal rupture of the intervertebral disc Case 2 -Rupture of the interspinous ligament, ligamentum flavum, supraspinous ligament and posterior longitudinal ligament accompanied with rupture of the capsular ligament Case 3 -Rupture of the interspinous ligament, ligamentum flavum and supraspinous ligament accompanied with rupture of the capsular ligament and a partial transversal rupture of the intervertebral disc (1/3 of the disc length) Case 4 -Rupture of the interspinous ligament, ligamentum flavum and supraspinous ligament with rupture of the capsular ligament and transversal rupture of the intervertebral disc.The posterior longitudinal ligament is kept intact.

Figure 1 :
Figure 1: Cervical spine model.Left: lateral view of the entire finite element model with boundary conditions.Right: sagittal cross-section of a functional spinal unit

Figure 2 :
Figure 2: Central Nervous System.Left: axial cross-section.Right: lateral view of the left C6-C7 nerve root

Figure 3 :Figure 4 :
Figure 3: Maximum and minimum principal strains.Error bars represent one standard deviation

Figure 5 :
Figure 5: Percentage of spinal cord compression at the injured functional spinal unit at 2 Nm flexion.Asterisk (*) represents the C2-T1 73 degrees threshold

Table Caption List
Table 1Material properties of the finite element model structures