Biomechanical Analysis of Posterior Ligaments of Cervical Spine and Laminoplasty

applied sciences

Article Biomechanical Analysis of Posterior Ligaments of Cervical Spine and Laminoplasty

Norihiro Nishida 1 , Muzammil Mumtaz 2, Sudharshan Tripathi 2, Amey Kelkar 2, Takashi Sakai 1 and Vijay K. Goel 2,*

1 Department of Orthopedic Surgery, Yamaguchi University Graduate School of Medicine, 1-1-1 Minami-Kogushi, Ube, Yamaguchi Prefecture 755-8505, Japan; [email protected] (N.N.); [email protected] (T.S.) 2 Engineering Center for Orthopaedic Research Excellence (E-CORE), Departments of Bioengineering and Orthopaedics, The University of Toledo, Toledo, OH 43606, USA; [email protected] (M.M.); [email protected] (S.T.); [email protected] (A.K.) * Correspondence: [email protected]; Tel.: +1-(419)-530-8035

Abstract: Cervical laminoplasty is a valuable procedure for myelopathy but it is associated with complications such as increased kyphosis. The effect of ligament damage during cervical laminoplasty on biomechanics is not well understood. We developed the C2–C7 cervical spine finite element model and simulated C3–C6 double-door laminoplasty. Three models were created (a) intact, (b) laminoplasty-pre (model assuming that the ligamentum flavum (LF) between C3–C6 was preserved during surgery), and (c) laminoplasty-res (model assuming that the LF between C3–C6 was resected during surgery). The models were subjected to physiological loading, and the range of motion (ROM), intervertebral nucleus stress, and facet contact forces were analyzed under flexion/extension, lateral bending, and axial rotation. The maximum change in ROM was observed Citation: Nishida, N.; Mumtaz, M.; under flexion motion. Under flexion, ROM in the laminoplasty-pre model increased by 100.2%, Tripathi, S.; Kelkar, A.; Sakai, T.; Goel, 111.8%, and 98.6% compared to the intact model at C3–C4, C4–C5, and C5–C6, respectively. The V.K. Biomechanical Analysis of ROM in laminoplasty-res further increased by 105.2%, 116.8%, and 101.8% compared to the intact Posterior Ligaments of Cervical Spine and Laminoplasty. Appl. Sci. 2021, 11, model at C3–C4, C4–C5, and C5–C6, respectively. The maximum stress in the annulus/nucleus was 7645. https://doi.org/10.3390/ observed under left bending at the C4–C5 segment where an increase of 139.5% and 229.6% compared app11167645 to the intact model was observed for laminoplasty-pre and laminoplasty-res model, respectively. The highest facet contact forces were observed at C4–C5 under axial rotation, where an increase of 500.7% Academic Editor: Mark King and 500.7% was observed compared to the intact model for laminoplasty-pre and laminoplasty-res, respectively. The posterior ligaments of the cervical spine play a vital role in restoring/stabilizing the Received: 21 July 2021 cervical spine. When laminoplasty is performed, the surgeon needs to be careful not to injure the Accepted: 17 August 2021 posterior soft tissue, including ligaments such as LF. Published: 20 August 2021 Keywords: laminoplasty; finite element method; ligamentum flavum Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. 1. Introduction Cervical laminoplasty is a decompression procedure of the lamina for asymptomatic patients of cervical spondylotic myelopathy (CSM), cervical disc herniation (CDH), and cervical ossification of the posterior longitudinal ligament (C-OPLL) [1–4]. The primary Copyright: © 2021 by the authors. purpose of laminoplasty is to decompress the cervical spinal cord by widening the spinal Licensee MDPI, Basel, Switzerland. canal, preserving the posterior anatomical structures as much as possible, and preserving This article is an open access article distributed under the terms and the widened space stability [1]. It is a technique with excellent clinical and mechanical conditions of the Creative Commons results [1,5,6]. Laminoplasty is divided into two types based on osteotomy: (1) Double- Attribution (CC BY) license (https:// door laminoplasty and (2) open-door laminoplasty [1]. In double-door laminoplasty, the creativecommons.org/licenses/by/ osteotomy is performed at the central lamina. In open-door laminoplasty, the osteotomy 4.0/).

Appl. Sci. 2021, 11, 7645. https://doi.org/10.3390/app11167645 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 7645 2 of 14

is performed at one side of the lamina. Both techniques are associated with reasonable clinical outcomes [7]. However, some authors have reported increased kyphosis and axial pain postopera- tively [8–10] due to the damage to the posterior cervical muscles and ligaments during the surgical procedure [8–11]. Concerning these papers, few reports have examined the extent of biomechanical changes when laminoplasty with/without LF is performed on the cervical spine [12–14]. The LF was reported to restrain flexion equally in a porcine model [15]. In the biomechanical study, none of the studies reported the effect of preserving/resecting the LF. In a clinical study, Duetzmann reported postoperative axial pain as prevalent in up to 30% of the patients by injured LF [11]. The development of techniques to preserve the posterior ligaments has been reported [16–19]. We hypothesize that when laminoplasty is conducted on the cervical spine model, the range of motion (ROM) and stress concentrations on the cervical spine may change with/without the LF, and the importance of posterior ligament for restoring/stabilizing the cervical spine will become evident. For this purpose, the C2–C7 three-dimension (3D) finite element (FE) model of the cervical spine was developed using CT scans of a healthy subject. The 3D FE model of the cervical spine was validated for ROM, intervertebral nucleus stress, and facet contact forces by comparing data with in vitro experiments. Later, the validated model was modified to simulate laminoplasty with and without LF.

2. Material and Methods 2.1. Model Development A 3D FE model of the cervical spine (C2–C7) was created based on the computed tomography (CT) of a 22-year-old healthy adult subject. The ethics committee approved the use of these images at the Center for Clinical Research of the corresponding author’s hospital, and written informed consent was obtained. The geometry of the vertebrae was reconstructed using the CT scans which were used for reconstructing the geometry of intervertebral discs. The 3D reconstruction of cervical spine geometry from CT scans was carried out using the image segmentation software MIMICS 15. 0 (Materialise, Leuven, Belgium). The reconstructed geometry of hard and soft tissues was meshed with the hexahedral elements using the IA-FE MESH software (Iowa, United States). The meshed vertebrae/discs were exported to the ABAQUS software 6. 14 (Dassault Systèmes, Simulia Inc., Providence, RI, USA) to assemble the C2–C7 cervical spine. The following ligaments were added to the model, anterior longitudinal ligament (ALL), posterior longitudinal ligament (PLL), interspinous ligament (ISL), supraspinous ligament (SSL), capsular ligament (CL), and LF using connector elements in ABAQUS. The outer 0.5 mm layer of the vertebrae represented a cortical shell, and the inside represented a cancellous bone. The intervertebral discs were composed of annulus ﬁbrosus (50%) and nucleus pulposus (50%). The annulus consisted of a ground substance along with embedded ﬁbers oriented at ±25◦ [20]. The facet joints in the model were represented using the surface-surface sliding contact, whereas the Lushka’s joints in the lower cervical intervertebral discs were modeled using GAPUNI elements [21]. The material properties for all the structures in the FE model were taken from the literature summarized in Table1[22,23]. Figure1 represents the intact model having 213,165 elements and 173,215 nodes. Appl. Sci. 2021, 11, 7645 3 of 14

Table 1. Material properties assigned to the ﬁnite element model [21–25].

Appl. Sci.Component 2021, 11, x FOR PEER REVIEW Material Properties Constitute Relation Element Type3 of 15 Area (mm2)

Bone [25] E = 10,000 MPa Vertebral cortical bone Table 1. Material properties assigned to the finiteIsotropic, element Elasticmodel [21–25]. C3D8 - v = 0.3 Component Material Properties Constitute Relation Element Type Area (mm2) E = 450 MPa Vertebral cancellous bone Isotropic, Elastic C3D8 - v = 0.25 Bone [25] E = 10,000 MPa Vertebral cortical bone E = 3500 MPa Isotropic, Elastic C3D8 - Vertebrae-Posterior v = 0.3 Isotropic, Elastic C3D10 - v = 0.25 E = 450 MPa Vertebral cancellous bone Isotropic, Elastic C3D8 - E =v 10,000= 0.25 MPa Artiﬁcial bone Isotropic, Elastic C3D8 - E = 3500v = MPa 0.3 Vertebrae-Posterior Isotropic, Elastic C3D10 - v = 0.25 Intervertebral Disc [24] E = 10,000 MPa GroundArtificial substance bone of C10 = 0.7 Isotropic, Elastic C3D8 - v = 0.3 Hyper-elastic, Mooney-Rivlin C3D8 - annulus ﬁbrosis C01 = 0.2 Intervertebral Disc [24] C10 = 0.12 Ground substance of an- C10 = 0.7 Hyper-elastic,Incompressible Mooney- Hyper-elastic, Nucleus pulposus C01 = 0.03 C3D8 C3D8 - - nulus fibrosis C01 = 0.2 RivlinMooney-Rivlin D1 = 0 C10 = 0.12 Incompressible Nucleus pulposus C01 = 0.03 LigamentsHyper-elastic, [23] Mooney- C3D8 - Anterior Longitudinal 15.0 (<12%),D1 = 0 30.0 (>12%) Rivlin Non-linear, Hypo-elastic T3D2 6.1 Ligament v = 0.3 Ligaments [23] Anterior Longitudinal 15.0 (<12%), 30.0 (>12%) Posterior Longitudinal 10.0 (<12%), 20.0 (>12%) Non-linear, Hypo-elastic T3D2 6.1 Non-linear, Hypo-elastic T3D3 5.4 LigamentLigament v v= 0.3 = 0.3 Posterior Longitudinal 10.0 (<12%), 20.0 (>12%) 7.0 (<30%), 30 (>12%) Non-linear, Hypo-elastic T3D3 5.4 CapsularLigament Ligament v = 0.3 Non-linear, Hypo-elastic T3D4 46.6 v = 0.3 7.0 (<30%), 30 (>12%) Capsular Ligament Non-linear, Hypo-elastic T3D4 46.6 5.0 (<25%),v = 0.3 10.0 (>25%) Ligamentum Flavum Non-linear, Hypo-elastic T3D5 50.1 5.0 (<25%),v 10.0 = 0.3 (>25%) Ligamentum Flavum Non-linear, Hypo-elastic T3D5 50.1 4.0 (20–40%),v = 0.3 8.0 (>40%) Interspinous Ligament 4.0 (20–40%), 8.0 (>40%) Non-linear, Hypo-elastic T3D6 13.1 Interspinous Ligament v = 0.3 Non-linear, Hypo-elastic T3D6 13.1 v = 0.3 Facet Joints [21] Facet Joints [21] Apophyseal JointsNon-linear Non-linear Apophyseal Joints SoftSoft contact, contact, ------

GAPPUNIGAPPUNI elements elements

FigureFigure 1. 1.TheThe intact intact (C2–C7) (C2–C7) finite ﬁniteelement element model. model. 2.2. Model Validation The intact C2–C7 model was validated using the in vitro loading protocol documented by Finn et al. [25]. A pure moment of 1.5 Nm was applied to the odontoid process of the Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 15

2.2. Model Validation [24–27] The intact C2–C7 model was validated using the in vitro loading protocol documented by Finn et al. [25]. A pure moment of 1.5 Nm was applied to the odontoid process of the C2 vertebra in flexion/extension, lateral bendings, and axial rotations [25]. Further- more, the caudal endplate of the C7 vertebra was fixed by suppressing all six degrees of Appl. Sci. 2021, 11, 7645 freedom. The effects of muscular contractions and the weight of the skull were replicated4 of 14 using the follower load method by applying a connector force of 100 N. The ROM, intervertebral nucleus stress, and facet contact forces were computed for each level in flexion/extension,C2 vertebra inlateral flexion/extension, bendings, and lateral axial bendings,rotations and and were axial rotationscompared [25 with]. Furthermore, the pub- lishedthe caudalin vitro endplate data in ofthe the literature C7 vertebra by Finn was fixedet al. by[25], suppressing Pospiech et all al. six [24], degrees Kretzer of freedom. et al. [26],The and effects Patel of et muscular al. [27]. contractions and the weight of the skull were replicated using the follower load method by applying a connector force of 100 N. The ROM, intervertebral 2.3.nucleus Cervical stress, Laminoplasty and facet contact forces were computed for each level in flexion/extension, lateralClinically, bendings, both and laminoplasty axial rotations (double-door and were compared and open-door) with the publishedmethods havein vitro showndata in similarthe literature results [7]. by FinnHowever, et al. [authors25], Pospiech practice et al. double-door [24], Kretzer laminoplasty et al. [26], and clinically, Patel et al.thus [27 ]. they opted to simulate it. Double-door laminoplasty was simulated by performing osteot- omy2.3. at Cervical the central Laminoplasty spinous process and lamina. First, the ISL and SS were resected. After- wards, Clinically,the spinous both process laminoplasty was partially (double-door resected, about and open-door)4 mm of bone methods from the have center shown of thesimilar lamina results was cut, [7]. the However, medial authors side of practiceboth the double-door facet joints was laminoplasty shaved so clinically, that the lamina thus they couldopted be toopened. simulate The it. LF Double-door of C2–C3 and laminoplasty C6–C7 was was resected simulated since by these performing interfered osteotomy with the at openingthe central of the spinous lamina. process However, and lamina. the LF First,of C3–C6 the ISL segment and SS werewas preserved. resected. Afterwards, The lamina the wasspinous opened process to the right was partiallyand left sides. resected, Moreover, about 4 it mm widened of bone the from narrow the centercanal and of the decom- lamina pressedwas cut, the thespinal medial cord side region of bothposteriorly. the facet joints was shaved so that the lamina could be opened.The artificial The LF ofbone C2–C3 with and 4 mm C6–C7 height was and resected 8 mm since depth these was interfered then placed with theto fit opening the openedof the lamina lamina. (Figure However, 2). The the LFmaterial of C3–C6 properti segmentes of was the preserved.artificial bone The were lamina the was same opened as theto cortical the right bone. and The left sides.artificial Moreover, bone was it widenedconnected the to narrow the lamina canal using and decompressed the “TIE” con- the straintspinal in cordAbaqus region software. posteriorly. ThisThe model, artificial in which bone the with LF 4 of mm C3-C6 height segment and 8 was mm preserved, depth was was then used placed as the to lami- fit the noplasty-preopened lamina model (Figure (C3-C62). laminoplasty The material with properties LF preserved). of the artificial The model, bone werein which the samethe LF as of theC3–C6 cortical segment bone. of The laminoplasty-pre artificial bone was model connected was resected, to the lamina was then using created the “TIE” as the constraint laminoplasty-resin Abaqus model. software.

(a) (b)

FigureFigure 2. 2.(a) (aAxial) Axial view view of ofdouble-door double-door laminoplasty laminoplasty at atC4, C4, (b) ( bC2–C7) C2–C7 model model with with laminoplasty laminoplasty fromfrom C3–C6. C3–C6.

2.4. LoadsThis and model, Boundary in whichConditions the LF of C3-C6 segment was preserved, was used as the laminoplasty-preThe pure moment model of 1.5 (C3-C6 Nm was laminoplasty applied to the with C2 LF odontoid preserved). process The to model, simulate in flex- which ion/extension,the LF of C3–C6 lateral segment (left and of laminoplasty-preright) bendings, and model axial was (left resected, and right) was thenrotations. created Addi- as the tionally,laminoplasty-res the inferior model. endplate of the C7 was fixed. The model was subjected to the compressive follower load of 100 N to represent the weight of the head and cervical muscle 2.4. Loads and Boundary Conditions contractions. The pure moment of 1.5 Nm was applied to the C2 odontoid process to simulate ﬂexion/extension, lateral (left and right) bendings, and axial (left and right) rotations. Additionally, the inferior endplate of the C7 was ﬁxed. The model was subjected to the compressive follower load of 100 N to represent the weight of the head and cervical muscle contractions.

2.5. Data Analyses The ROM, intervertebral nucleus stress, and facet contact forces were calculated for the intact, laminoplasty-pre, and laminoplasty-res models. The ROM for each functional Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 of 15

Appl. Sci. 2021, 11, 7645 2.5. Data Analyses 5 of 14 The ROM, intervertebral nucleus stress, and facet contact forces were calculated for the intact, laminoplasty-pre, and laminoplasty-res models. The ROM for each functional spinal unit (FSU) was quantified by subtracting the absolute rotation of the upper vertebra spinal unit (FSU) was quantiﬁed by subtracting the absolute rotation of the upper vertebra from the lower vertebra. For nucleus stress, the highest value for maximum von Mises from the lower vertebra. For nucleus stress, the highest value for maximum von Mises stress was observed on the nucleus to analyze the effect of surgery on the nucleus of the stress was observed on the nucleus to analyze the effect of surgery on the nucleus of the intervertebral disc as done by Tsuang et al. [28]. For the facet joint contact force, the data intervertebral disc as done by Tsuang et al. [28]. For the facet joint contact force, the data for forfacet facet forces forces were were averaged averaged for for the the left/right left/right facets. facets.

3. Results3. Results 3.1.3.1. Model Model Validation Validation 3.1.1.ROM ROM TheThe intact intact cervical cervical spine spine model model demonstra demonstratedted ROM ROM in inflexion/extension, ﬂexion/extension, lateral lateral bending,bending, and and axial axial rotations rotations within within the range the range of the ofin thevitroin ROM vitro dataROM published data published by Finn by et al.Finn (Figure et al. 3) (Figure [25]. 3)[25].

(a)

(b)

(c)

FigureFigure 3. ( 3.a) (Comparisona) Comparison of the of theflexion-extension ﬂexion-extension moti motionon between between the theFE FEmodel model results results and and the the results reported in the literature . (b) Comparison of the lateral bending motion between the FE results reported in the literature[25] [25]. (b) Comparison of the lateral bending motion between the FE model results and the results reported in the literature [25]. (c) Comparison of the axial rotation motion between the FE model results and the results reported in the literature [25]. Appl. Sci. 2021, 11, 7645 6 of 14

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3.2. Intervertebral Nucleus Stress model results and the results reported in the literature [25]. (c) Comparison of the axial rotation motion betweenThe intact the FE C2–C7 model results cervical and the spine results modelreported demonstratedin the literature [25] intervertebral. nucleus stress in ﬂexion/extension, lateral bending, and axial rotations within the range of the in vitro data 3.2.documented Intervertebral Nucleus by Kretzer Stress et al. and Pospiech et al. [24,26]. Unfortunately, no documented in vitroThe intactintervertebral C2–C7 cervical nucleus spine model stress demo datanstrated were intervertebral available nucleus for comparison stress in for the C4–C5 flexion/extension, lateral bending, and axial rotations within the range of the in vitro data documentedlevel in the by publishedKretzer et al. literature and Pospiech (Table et al.2 [24,26].; Figure Unfortunately,4). no documented in vitro intervertebral nucleus stress data were available for comparison for the C4–C5 Table 2. Comparison of thelevel intervertebral in the published nucleus literature stress (Table between 2; Figure the FE4). model results and the in vitro results reported in the literature [24,26]. Table 2. Comparison of the intervertebral nucleus stress between the FE model results and the in vitro results reported inIntervertebral the literature [24,26] Nucleus. Stress (MPa)—FE Model Segment Flexion ExtensionIntervertebral Left Bending Nucleus Stress Right (MPa)—FE Bending Model Left Rotation Right Rotation Segment Right Left Right Flexion Extension Left Bending C2–C3 0.26 0.35 0.23Bending 0.22 Rotation Rotation 0.27 0.26 C3–C4 0.17C2–C3 0.26 0.14 0.35 0.140.23 0.22 0.150.27 0.190.26 0.24 C4–C5 0.21C3–C4 0.17 0.16 0.14 0.110.14 0.15 0.170.19 0.220.24 0.21 C5–C6 0.17C4–C5 0.21 0.12 0.16 0.10.11 0.17 0.140.22 0.180.21 0.18 C6–C7 0.11C5–C6 0.17 0.14 0.12 0.090.1 0.14 0.110.18 0.10.18 0.13 C6–C7 0.11 Intervertebral0.14 0.09 Nucleus Stress0.11 (MPa)—In0.1 Vitro 0.13 Segment Intervertebral Nucleus Stress (MPa)—In Vitro FlexionSegment Extension Left Bending RightRight Bending Left Left RotationRight Right Rotation Flexion Extension Left Bending C2–C3 0.08–0.36 0.08–0.36 0.12–0.36Bending 0.12–0.36 Rotation Rotation - - C3–C4 0.12–0.43C2–C3 0.08–0.36 0.12–0.43 0.08–0.36 0.08–0.31 0.12–0.36 0.12–0.36 0.08–0.31 - 0.14–0.36 - 0.14–0.36 C4–C5 -C3–C4 0.12–0.43 - 0.12–0.43 0.08–0.31 - 0.08–0.31 -0.14–0.36 0.14–0.36 - - C5–C6 0.01–0.56C4–C5 0.01–0.56- - 0.01–0.38- - 0.01–0.38 - 0.04–0.49- 0.04–0.49 C6–C7 0.01–0.17C5–C6 0.01–0.56 0.01–0.17 0.01–0.56 0.01–0.110.01–0.38 0.01–0.38 0.01–0.11 0.04–0.49 0.04–0.49 - - C6–C7 0.01–0.17 0.01–0.17 0.01–0.11 0.01–0.11 - -

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(a)

(b) Figure 4. (a) Comparison of the intervertebral nucleus stress at C3–C4 between the FE model results Figure 4. (a) Comparison of the intervertebral nucleus stress at C3–C4 between the FE model results and the results reported in the literature [24]. (b) Comparison of the intervertebral nucleus stress at C5-C6and the between results the reportedFE model results in the and literature the results [24 reported]. (b) Comparisonin the literature of[24] the. intervertebral nucleus stress at C5-C6 between the FE model results and the results reported in the literature [24]. 3.3. Facet Contact Force The C2–C7 cervical spine model exhibited facet forces in extension, lateral bending, and axial rotations for those levels in the range of in vitro facet contact force data published by Patel et al. (Table 3; Figure 5). Unfortunately, no in vitro data for facet forces for C2–C3, C5–C6, and C6–C7 levels were available for comparison.

Table 3. Comparison of the facet contact forces between the FE model results and the in vitro results reported in the literature [27].

Facet Contact Forces (N)—FE Facet Contact Forces (N)—In Vitro Model Segment Lateral Axial Lateral Axial Extension Extension Bending Rotation Bending Rotation C2–C3 50.9 45.6 21.3 - - - C3–C4 42.6 34.2 36.2 12.5–62.5 29.5–81.2 34.5–88.1 C4–C5 31.4 35.8 20.7 13.9–43.9 36.2–74.8 34.7–88.2 C5–C6 32.4 34.6 34.7 - - - C6–C7 24.6 31.9 28.4 - - -

(a) Appl. Sci. 2021, 11, x FOR PEER REVIEW 7 of 15

(b) Figure 4. (a) Comparison of the intervertebral nucleus stress at C3–C4 between the FE model results and the results reported in the literature [24]. (b) Comparison of the intervertebral nucleus stress at C5-C6 between the FE model results and the results reported in the literature [24]. Appl. Sci. 2021, 11, 7645 7 of 14 3.3. Facet Contact Force The C2–C7 cervical spine model exhibited facet forces in extension, lateral bending, and axial rotations for those levels in the range of in vitro facet contact force data pub- 3.3. Facet Contact Force lished by Patel et al. (Table 3; Figure 5). Unfortunately, no in vitro data for facet forces for C2–C3, C5–C6,The C2–C7 and C6–C7 cervical levels spine were model available exhibited for comparison. facet forces in extension, lateral bending, and axial rotations for those levels in the range of in vitro facet contact force data published Tableby 3. Comparison Patel et al. (Tableof the 3facet; Figure contact5). forces Unfortunately, between the no FEin model vitro resultsdata forand facet the in forces vitro results for C2–C3, reportedC5–C6, in the and literature C6–C7 [27] levels. were available for comparison.

Table 3. Comparison of the facet contactFacet forces Contact between Forces the FE (N)—FE model results and the in vitro results reported in the Facet Contact Forces (N)—In Vitro literature [27]. Model Segment Lateral Axial Lateral Axial Facet Contact ForcesExtension (N)—FE Model FacetExtension Contact Forces (N)—In Vitro Segment Bending Rotation Bending Rotation ExtensionC2–C3 Lateral Bending50.9 Axial 45.6 Rotation 21.3 Extension - Lateral Bending - Axial - Rotation C2–C3 50.9C3–C4 45.642.6 34.2 21.3 36.2 -12.5–62.5 29.5–81.2 - 34.5–88.1 - C3–C4 42.6C4–C5 34.231.4 35.8 36.2 20.7 12.5–62.5 13.9–43.9 29.5–81.236.2–74.8 34.7–88.2 34.5–88.1 C4–C5 31.4 35.8 20.7 13.9–43.9 36.2–74.8 34.7–88.2 C5–C6 32.4C5–C6 34.632.4 34.6 34.7 34.7 ------C6–C7 24.6C6–C7 31.924.6 31.9 28.4 28.4 ------

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(a)

(b)

FigureFigure 5. ( 5.a) (Comparisona) Comparison of the of thefacet facet contact contact forces forces at C3–C4 at C3–C4 between between the the FE FEmodel model results results and and the the in vitroin vitro resultsresults reported reported in the in the literature literature [27] [27. (].b) ( bComparison) Comparison of the of the facet facet contact contact forces forces at C4–C5 at C4–C5 betweenbetween the theFE FEmodel model results results and and the the in vi intro vitro results results reported reported in the in the literature literature [27] [27. ].

3.4. Comparison of Intact and the Laminoplasty Models 3.4.1. ROM In the extension, both laminoplasty-pre and laminoplasty-res models show similar ROM results for C3–C4 and C4–C5 levels. ROMs were significantly decreased by 54.3% and 8.2%, respectively at C3–C4 and C4–C5 levels than the intact model. At the same time, for flexion motion at C3–C4 and C4–C5 levels, the laminoplasty-pre model increased ROMs by 100.2% and 111.8%, respectively than intact. While for the laminoplasty-res model, it was increased by 105.2% and 116.8%, respectively for C3–C4 and C5–C6 levels than intact. In left bending and the laminoplasty-pre and laminoplasty-res models, ROM significantly reduced at the C3–C4 and C4–C5 levels by 77.2% and 9.7%, respectively than intact. In contrast, for right bending, the ROM at the C2–C3 level increased by 135.3% and decreased at the C4–C5, C5–C6, and C6–C7 levels by 87.1%, 90.5%, and 12.4%, respectively than the intact model. For left and right rotation, the ROM of C4–C5 was decreased in laminoplasty-pre and laminoplasty models-res than in the intact model by 86.1% and 76.9%, respectively than intact (Figure 6).

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(b)

Appl. Sci. 2021, 11, 7645 Figure 5. (a) Comparison of the facet contact forces at C3–C4 between the FE model results and8 the of 14 in vitro results reported in the literature [27]. (b) Comparison of the facet contact forces at C4–C5 between the FE model results and the in vitro results reported in the literature [27].

3.4.3.4. Comparison Comparison of of Intact Intact and and the the Laminoplasty Laminoplasty Models Models 3.4.1.ROM ROM InIn the the extension, extension, both both laminoplasty-pre laminoplasty-pre and and laminoplasty-res laminoplasty-res models models show show similar similar ROMROM results results for for C3–C4 C3–C4 and and C4–C5 C4–C5 levels. levels. ROMs ROMs were were significantly significantly decreased decreased by by 54.3% 54.3% andand 8.2%, 8.2%, respectively respectively at atC3–C4 C3–C4 and and C4–C5 C4–C5 levels levels than than the intact the intact model. model. At the Atsame the time, same fortime, flexion for flexion motion motion at C3–C4 at C3–C4 and andC4–C5 C4–C5 levels, levels, the the laminoplasty-pre laminoplasty-pre model model increased increased ROMsROMs by by 100.2% 100.2% and and 111.8%, 111.8%, respectively respectively than than intact. intact. While While for for the the laminoplasty-res laminoplasty-res model,model, it it was was increased increased by by 105.2% 105.2% and and 116.8%, 116.8%, respectively respectively for for C3–C4 C3–C4 and and C5–C6 C5–C6 levels levels thanthan intact. intact. In In left left bending bending and and the the laminoplasty-pre laminoplasty-pre and and laminoplasty-res laminoplasty-res models, models, ROM ROM significantlysignificantly reduced reduced at at the the C3–C4 C3–C4 and and C4–C5 C4–C5 levels levels by by 77.2% 77.2% and and 9.7%, 9.7%, respectively respectively than than intact.intact. In In contrast, contrast, for for right right bending, bending, the the RO ROMM at at the the C2–C3 C2–C3 level level increased increased by by 135.3% 135.3% and and decreased at the C4–C5, C5–C6, and C6–C7 levels by 87.1%, 90.5%, and 12.4%, respectively decreased at the C4–C5, C5–C6, and C6–C7 levels by 87.1%, 90.5%, and 12.4%, respectively than the intact model. For left and right rotation, the ROM of C4–C5 was decreased in than the intact model. For left and right rotation, the ROM of C4–C5 was decreased in laminoplasty-pre and laminoplasty models-res than in the intact model by 86.1% and 76.9%, laminoplasty-pre and laminoplasty models-res than in the intact model by 86.1% and respectively than intact (Figure6). 76.9%, respectively than intact (Figure 6).

Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 15

(a) (b)

(e) (f)

FigureFigure 6. RangeRange of of motion. motion. (a) ( aExtension,) Extension, (b) ( flexion,b) ﬂexion, (c) left (c) leftbending, bending, (d) right (d) right bending, bending, (e) left (e rota-) left rotation,tion, and and(f) right (f) right rotation. rotation. The vertical The vertical axis is axisan angle is an (degree), angle (degree), the horizontal the horizontal axis is each axis interver- is each tebral level. intervertebral level. 3.5. Intervertebral Nucleus Stress In extension, intervertebral nucleus stress between C4–C5 was significantly increased in laminoplasty-pre and laminoplasty-res models than in the intact model by 114.2%. For flexion, intervertebral nucleus stress between C4–C5 was significantly increased in laminoplasty-pre and especially laminoplasty-res models than in the intact model by 101.8% and 105.3%, respectively. In lateral (left and right) bending and right rotation, the intervertebral nucleus stress of the nucleus between C4–C5 was significantly increased in laminoplasty-pre by 139.4%, 111.5%, and 123.3%, respectively and laminoplasty-res models by 139.5%, 111.7%, and 123.4%, respectively than in the intact model (Figure 7).

(a) (b)

(e) (f) Figure 6. Range of motion. (a) Extension, (b) flexion, (c) left bending, (d) right bending, (e) left rota- Appl. Sci. 2021, 11, 7645 tion, and (f) right rotation. The vertical axis is an angle (degree), the horizontal axis is each interver-9 of 14 tebral level.

3.5. Intervertebral Nucleus Stress 3.5. Intervertebral Nucleus Stress In extension, intervertebral nucleus stress between C4–C5 was significantly increased in laminoplasty-preIn extension, intervertebraland laminoplasty-res nucleus models stress between than in C4–C5the intact was model significantly by 114.2%. increased For flexion,in laminoplasty-pre intervertebral nucleus and laminoplasty-res stress between modelsC4–C5 was than significantly in the intact increased model byin lami- 114.2%. noplasty-preFor flexion, and intervertebral especially laminoplasty-res nucleus stress between models C4–C5than in wasthe intact significantly model increasedby 101.8% in laminoplasty-pre and especially laminoplasty-res models than in the intact model by and 105.3%, respectively. In lateral (left and right) bending and right rotation, the inter- 101.8% and 105.3%, respectively. In lateral (left and right) bending and right rotation, the vertebral nucleus stress of the nucleus between C4–C5 was significantly increased in lam- intervertebral nucleus stress of the nucleus between C4–C5 was significantly increased in inoplasty-pre by 139.4%, 111.5%, and 123.3%, respectively and laminoplasty-res models laminoplasty-pre by 139.4%, 111.5%, and 123.3%, respectively and laminoplasty-res models by 139.5%, 111.7%, and 123.4%, respectively than in the intact model (Figure 7). by 139.5%, 111.7%, and 123.4%, respectively than in the intact model (Figure7).

(a) (b)

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(e) (f)

FigureFigure 7. Intervertebral 7. Intervertebral nucleus nucleus stress stress in ( ina) (extension,a) extension, (b) (flexion,b) ﬂexion, (c) (leftc) left bending, bending, (d) (rightd) right bending, bending, (e)( lefte) left rotation, rotation, and and (f) (rightf) right rotation. rotation. The The vertical vertical axis axis is st isress stress (MPa), (MPa), the the horizontal horizontal axis axis is each is each intervertebralintervertebral level. level.

3.6.3.6. Facet Facet Contact Contact Forces Forces In Inextension, extension, facet facet contact contact forces forces of ofC3–C4 C3–C4 and and C4–C5 C4–C5 levels levels were were increased increased by by133% 133% andand 361.7%, 361.7%, respectively respectively in inlaminoplasty-pre laminoplasty-pre and and laminoplasty-res laminoplasty-res models models compared compared to to thethe intact intact model. model. In Inlateral lateral bending, bending, facet facet contact contact forces forces of ofC3–C4 C3–C4 and and C4–C5 C4–C5 levels levels were were increased increased by by 131%131% and and 256.3%, 256.3%, respectively respectively in in laminoplasty-prelaminoplasty-pre andand laminoplasty-res laminoplasty-res models models compared com- paredto the to intactthe intact model. model. In Inaxial axial rotation, rotation, facet facet contact contact forces forces of C3–C4 of C3–C4 and andC4–C5 C4–C5 levels levels were wereincreased increased by 140.7%by 140.7% and 500.7%, and 500.7%, respectively respectively in laminoplasty-pre in laminoplasty-pre and laminoplasty-res and laminoplasty-res models modelscom- paredcompared to the intact to the (Figure intact (Figure 8). 8).

(a)

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(e) (f) Figure 7. Intervertebral nucleus stress in (a) extension, (b) flexion, (c) left bending, (d) right bending, (e) left rotation, and (f) right rotation. The vertical axis is stress (MPa), the horizontal axis is each intervertebral level.

3.6. Facet Contact Forces In extension, facet contact forces of C3–C4 and C4–C5 levels were increased by 133% and 361.7%, respectively in laminoplasty-pre and laminoplasty-res models compared to the intact model. In lateral bending, facet contact forces of C3–C4 and C4–C5 levels were increased by 131% and 256.3%, respectively in laminoplasty-pre and laminoplasty-res models compared to the intact model. Appl. Sci. 2021, 11, 7645 In axial rotation, facet contact forces of C3–C4 and C4–C5 levels were increased10 ofby 14 140.7% and 500.7%, respectively in laminoplasty-pre and laminoplasty-res models compared to the intact (Figure 8).

(a)

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(b)

(c)

FigureFigure 8. Facet 8. Facet contact contact forces. forces. (a) (Extension,a) Extension, (b) (lateralb) lateral bending, bending, (c) (axialc) axial rotation. rotation. Vertical Vertical axis axis is is forceforce (N), (N), horizontal horizontal axis axis is each is each intervertebral intervertebral level. level.

4. Discussion4. Discussion ThisThis study study aimed aimed to toinvestigate investigate the the laminoplasty laminoplasty with/without with/without LF LFof posterior of posterior liga- liga- mentsments on onthe the cervical cervical spine spine biomechanics biomechanics using using a validated a validated model model of ofC2–C7 C2–C7 spine. spine. ThereThere are are two two types types of ofspinal spinal cord cord injuri injurieses for for CSM, CSM, CDH, CDH, an andd C-OPLL: C-OPLL: Static Static and and dynamicdynamic compression. compression. The The causes causes for forstatic static damage damage include include congenital congenital spinal spinal stenosis, stenosis, cervicalcervical disc disc herniation, herniation, osteophytosis, osteophytosis, and and ligamentous ligamentous hypertrophy hypertrophy [29,30]. [29,30 The]. The causes causes forfor dynamic dynamic compression compression injury injury include include translation translation and and angulation angulation of of the the spinal spinal column or or overlapping of of the the lamina lamina (pincer (pincer mechanis mechanism)m) and and buckling buckling of ofthe the ligamentum ligamentum flavum ﬂavum (LF)(LF) [31–33]. [31–33 Laminoplasty]. Laminoplasty as asextensive extensive poster posteriorior decompression decompression is suitable is suitable for for cervical cervical spinalspinal cord cord myelopathy myelopathy resulting resulting from from static static and and dynamic dynamic compression. compression. ModificationsModiﬁcations in the in the current current procedures procedures are are being being suggested suggested by byclinicians clinicians to toaddress address thethe current current surgical surgical complications complications for for the the increased increased kyphosis kyphosis and and axial axial pain. pain. In Inrecent recent years,years, minimally minimally invasive invasive methods methods for forlaminopl laminoplasty,asty, such such as asselective selective laminoplasty, laminoplasty, skip skip laminectomy,laminectomy, and and endoscopic endoscopic laminectomy, laminectomy, have have been reported andand havehave shown shown promising prom- isingclinical clinical outcomes outcomes [17 –[17–19,34–36].19,34–36]. Hirabayashi Hirabayashi reported reported on the on developmentthe development of double-door of double-door laminoplasty. At first, a pyramidal-shaped osteotomy is made at the cranial base of the spinous process to obtain a good visual field. Next, the remaining part of the spinous process is split centrally from its surface, and the split portion is connected to the pyramidal-shaped dome [16]. Minamide conducted articular segmental decompression surgery using endoscopy (cervical microendoscopic laminotomy) for cervical spondylotic myelopathy and reported patients to have similar neurological outcomes to conventional laminoplasty, with significantly less postoperative axial pain and improved subaxial cervical lordosis [17]. Shiraishi proposed a skip laminectomy method that preserved the attachments of the semispinalis cervicis and multifidus muscles on the cervical spinous processes and limited the damage to the attachments of the interspinous and rotator muscles [18]. Kanchiku proposed performing selective laminoplasty on subjects diagnosed with CSM at a single intervertebral level or two consecutive intervertebral levels based on preoperative neurological symptoms and imaging findings. They concluded that the clinical outcomes of selective laminoplasty were similar to the C3–C7 laminoplasty with significantly less operation time and blood loss, compared with conventional C3–C7 laminoplasty [19]. The fundamental purpose of these techniques is to figure out ways on how to avoid damaging the posterior soft tissues, including ligaments. The studies of injuring the posterior ligamentous structures of the cervical spine indicated that each structure contributes to cervical stability [14,37]. The SS, IS, and LF were reported to restrain flexion equally in a porcine model [15]. However, there has been no FE model analysis of the effect of damaging the posterior ligaments on the cervical spine in laminoplasty. Studying the biomechanics of laminoplasty of the cervical spine can be divided into the FE model and cadaver analysis. However, there are few analyses of laminoplasty models in the literature. Stoner compared intact, laminectomy, and double-door laminoplasty Appl. Sci. 2021, 11, 7645 11 of 14

laminoplasty. At first, a pyramidal-shaped osteotomy is made at the cranial base of the spinous process to obtain a good visual field. Next, the remaining part of the spinous process is split centrally from its surface, and the split portion is connected to the pyramidal- shaped dome [16]. Minamide conducted articular segmental decompression surgery using endoscopy (cervical microendoscopic laminotomy) for cervical spondylotic myelopathy and reported patients to have similar neurological outcomes to conventional laminoplasty, with significantly less postoperative axial pain and improved subaxial cervical lordosis [17]. Shiraishi proposed a skip laminectomy method that preserved the attachments of the semispinalis cervicis and multifidus muscles on the cervical spinous processes and limited the damage to the attachments of the interspinous and rotator muscles [18]. Kanchiku proposed performing selective laminoplasty on subjects diagnosed with CSM at a single intervertebral level or two consecutive intervertebral levels based on preoperative neurological symptoms and imaging findings. They concluded that the clinical outcomes of selective laminoplasty were similar to the C3–C7 laminoplasty with significantly less operation time and blood loss, compared with conventional C3–C7 laminoplasty [19]. The fundamental purpose of these techniques is to figure out ways on how to avoid damaging the posterior soft tissues, including ligaments. The studies of injuring the posterior ligamentous structures of the cervical spine indicated that each structure contributes to cervical stability [14,37]. The SS, IS, and LF were reported to restrain flexion equally in a porcine model [15]. However, there has been no FE model analysis of the effect of damaging the posterior ligaments on the cervical spine in laminoplasty. Studying the biomechanics of laminoplasty of the cervical spine can be divided into the FE model and cadaver analysis. However, there are few analyses of laminoplasty models in the literature. Stoner compared intact, laminectomy, and double-door laminoplasty models for spinal cord [38]. Tejapongvorachai reported that the stabilities of the hinge sides of plate-augmented open-door laminoplasties based on cutting in a curved or straight line were compared using a FE model and the potential of the proposed technique to reduce the risk of hinge fracture and displacement [39]. Khuyagbaatar analyzed biomechanical changes in the spinal cord and nerve roots following the open-door and double-door laminoplasty for OPLL [40]. However, none of the studies have reported on the effect of preserving/resecting the LF ligament. In cadaver research, there are few papers on cervical laminoplasty. Kubo reported that 3D kinematics changes after double-door cervical laminoplasty, with and without the spacer, were studied in a human cadaveric model and the use of hydroxyapatite spacer well contributes to maintaining the total stiffness of cervical spine [41]. Subramaniam reported that open-door laminoplasty leaves the spine in a significantly more stable condition than laminectomy compared with biomechanical stability during flexion and extension [42]. Kode analyzed five human cadaveric specimens with laminoplasty at C5–C6, laminoplasty at C3–C6, and laminectomy. Laminoplasty was closer to intact than laminectomy, and there was no significant difference in laminoplasty, but laminoplasty at C3–C6 was associated with greater motion in lateral bending and axial rotation [43]. However, they did not report on the role of LF in laminoplasty/laminectomy. To study the effect of preserving/resecting LF in laminoplasty, the FE model of cervical spine was developed and validated. The model was considered validated as ROM, intervertebral nucleus stress, and facet force were all within the range of the experimental results of the in vitro data. Some differences for average data of cadaver about ROM, intervertebral nucleus stress, and facet loads, and our results were considered acceptable due to the higher mean age and possible deformed cervical spine in the cadaver. It will be necessary to compare the FE model analysis with the experiments of any individual in the future. In this laminoplasty-pre and laminoplasty-res analysis, the ROM of C2–C7 was decreased except for flexion. Seichi et al. reported that mean mobility decreased from 36 to 8◦ following double-door laminoplasty [44]. Ratliff and Cooper reported that the range of motion was reduced by 46% for open-door laminoplasty and 50% for double-door Appl. Sci. 2021, 11, 7645 12 of 14

laminoplasty relative to pre-operation [45]. Thus, these suggest that the laminoplasty affects stability, and the results of this study were in agreement with the literature. On the other hand, the increased mobility in flexion suggests that posterior ligament may be one of the causes of post-operative kyphosis. The intervertebral nucleus stress and facet force stress were higher at C4–C5 and were elevated in laminoplasty-pre and laminoplasty-res than the intact model. There are no papers that have experimentally verified the stress on the disc and facet of laminoplasty. However, the clinical and radiolog- ical analysis of the ROM of the cervical vertebrae indicate that when the stability of the caudal vertebrae increases, the mobility and instability of the cranial side (C3–C4, C4–C5) also increases [46,47]. In the present analysis, the bottom of C7 was fixed, and due to the increased stability of laminoplasty, the load of the cervical vertebrae was considered to be concentrated in the cranial side (C3–C4, C4–C5). There are several limitations to our study. It does not include the trapezius or other muscles. Spine alignment was lordotic only. This model simulates an immediate postoperative scenario and does not consider conditions such as fusion and non-fusion of the lamina, and does not fully simulate the long-term condition of laminoplasty. The LF covered the interlaminar space. In the present model, it is impossible to conclude the mechanical characteristics of the partial or total resection of LF for laminoplasty [48]. Although there are several methods of laminoplasty [49], this paper only analyzes double-door laminoplasty. This study does not consider the change in material property that may be altered by osteoporosis or osteoarthritis. Despite these limitations, this study provides valuable insights on the effect of preserving/resecting the LF during laminoplasty.

5. Conclusions The FE model created from medical images was used to analyze the effects of preserving/resecting LF in the laminoplasty procedure. This study concluded that laminoplasty alters the intervertebral mobility. Moreover, the cranial cervical level load increases signiﬁ- cantly when the LF is injured, which leads to hyper ﬂexion. In light of the current study, the surgeon should be mindful of the role of LF as well as pay attention to LF resection or injury during laminoplasty.

Author Contributions: Conceptualization, N.N.; data curation, M.M., N.N., and S.T.; formal analysis, M.M., N.N., and S.T.; funding acquisition, V.K.G.; methodology, N.N. and A.K.; project administration, N.N. and M.M.; supervision, T.S.; validation, M.M. and N.N.; visualization, T.S.; writing—original draft, N.N.; writing—review and editing, M.M., N.N., A.K., S.T., and V.K.G. All authors have read and agreed to the published version of the manuscript. Funding: Work supported in part by the NSF Industry/University Cooperative Research Center at the University of California at San Francisco, University of Toledo, and Ohio State University. Award number: 206965. Institutional Review Board Statement: The study was conducted according to the guidelines of the Declaration of Helsinki, and approved by the Institutional Review Board of The University of Toledo. Informed Consent Statement: Informed consent was obtained from the subjects involved in the study. Data Availability Statement: The data presented in this study are available. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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