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A Numerical Investigation of Risk Factors Affecting Lumbar Spine Injuries Using a Detailed Lumbar Model

A Numerical Investigation of Risk Factors Affecting Lumbar Spine Injuries Using a Detailed Lumbar... Hindawi Applied Bionics and Biomechanics Volume 2018, Article ID 8626102, 8 pages https://doi.org/10.1155/2018/8626102 Research Article A Numerical Investigation of Risk Factors Affecting Lumbar Spine Injuries Using a Detailed Lumbar Model 1 1 2 Jiajia Zheng , Liang Tang , and Jingwen Hu School of Technology, Beijing Forestry University, Beijing 100083, China University of Michigan Transportation Research Institute, Ann Arbor, MI 48109, USA Correspondence should be addressed to Liang Tang; tang-l04@mails.tsinghua.edu.cn and Jingwen Hu; jwhu@umich.edu Received 9 December 2017; Accepted 5 March 2018; Published 17 April 2018 Academic Editor: Kiros Karamanidis Copyright © 2018 Jiajia Zheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Recent field data showed that lumbar spine fractures occurred more frequently in late model vehicles than early ones in frontal crashes. However, the lumbar spine designs of the current crash test dummies are not accurate in human anatomy and have not been validated against any human/cadaver impact responses. In addition, the lumbar spines of finite element (FE) human models, including GHBMC and THUMS, have never been validated previously against cadaver tests. Therefore, this study developed a detailed FE lumbar spine model and validated it against cadaveric tests. To investigate the mechanism of lumbar spine injury in frontal crashes, effects of changing the coefficient of friction (COF), impact velocity, cushion thickness and stiffness, and cushion angle on the risk of lumbar spine injuries were analyzed based on a Taguchi array of design of experiments. The results showed that impact velocity is the most important factor in determining the risk of lumbar spine fracture (P =0 009). After controlling the impact velocity, increases in the cushion thickness can effectively reduce the risk of lumbar spine fracture (P =0 039). 1. Introduction lumbar spines of the available FE human models, such as GHBMC (Global Human Body Model Consortium) model and THUMS (Total Human Model for Safety) model, have Safety designs in newer cars generally provided better protec- tions to occupants than those in older cars. However, several never been validated previously against cadaver tests. More recent field data analyses have shown that lumbar spine frac- recently, Arun et al. [3] applied the stiffness values obtained tures occurred more frequently in late model vehicles than from cadaver tests directly to the lumbar spine of the the early ones in frontal crashes [1, 2]. GHBMC simplified model. However, it is a rigid body- based lumbar spine model. It is lacking of detailed anatomi- This increasing trend of lumbar spine fractures in frontal crashes is extremely concerning, because none of the current cal structures of the lumbar spine and cannot estimate strain crash test programs, including FMVSS 208, US-NCAP, and and stress in the vertebrae. IIHS, considered lumbar spine injury in their safety evalua- Factors affecting the lumbar spine fracture have been dis- tion process. This is partially due to the fact that none of cussed extensively in the literature. Results indicated that the current crash test dummies can accurately estimate lum- older occupants (65+ years) were five times more likely to bar spine fracture risks. Current crash test dummies were sustain spinal injury compared to younger occupants [4], designed to focus on estimating injury risks to the head, neck, women had more lumbar spine fractures than men [5], and chest, and lower extremities, and their lumbar spine designs lower bone quality is associated with an increased number were not based on real human anatomy and were not vali- of lumbar spine fractures within the CIREN cases analyzed dated against any human/cadaver impact responses. As a [6]. Lumbar spine posture was also found to be an important result, although lumbar spine loadings could be measured factor affecting lumbar spine injuries. It was reported that in a crash test, they may not necessarily reflect the real injury slouched posture may cause an increase in stress on the lum- mechanism or injury risk in frontal crashes. In addition, bar vertebrae [7] and more reclined postures are associated 2 Applied Bionics and Biomechanics Nucleus ALL: anterior longitudinal ligament PLL Cancellous bone PLL: posterior longitudinal ligament SSL LF: flavum ligament Cortical bone CL: facet joint capsule ligament Disc fiber ISL ITL: interspinous ligament Intervertebral disc Annulus ITL SSL: supraspinous ligament Cortical bone ISL: intertransverse ligament Cancellous bone ALL CL LF (a) Original GHBMC model (b) Modified model Figure 1: Comparison between original and modified lumbar spine models. Shell elements Annulus Nucleus Collagenous fibers (a) Disc in GHBMC (shell elements) (b) Disc in current model (three parts) Figure 2: Comparison of the discs between GHBMC and modified lumbar models. with a higher lumbar vertebrae fracture risk by reconstruct- Table 1: Stiffness of ligaments used in the current study (unit: N/ ing real-world motor vehicle crashes [8]. Crash pulse magni- mm). tude and shape are also crucial for determining lumbar spine injury risk. For example, cadaver tests under axial loading Ligaments T12-L1 L1-L2 L2-L3 L3-L4 L4-L5 L5-S1 showed that triangular pulses produced pelvic fractures with ALL 32.9 32.4 20.8 39.5 40.5 32.9 no lumbar spine fractures, while a sigmoid-shaped pulse PLL 10 17.1 36.6 10.6 25.8 10 produced no pelvic fractures but did produce an L1 burst LF 24.2 23 25.1 34.5 27.2 24.2 fracture [9]. In addition, more severe crash pulses may lead CL 31.7 42.5 33.9 32.3 30.6 31.7 to higher lumbar spine injury risks [10]. ISL 12.1 10 9.6 18.1 8.7 12.1 The objectives of the present study were to develop a detailed FE lumbar spine model, validate it against cadaveric SSL 15.1 23 24.8 34.8 18 15.1 tests, and use it to investigate the effects of changing the coef- ITL 15.1 23 24.8 34.8 18 15.1 ficient of friction (COF), impact velocity, cushion thickness and stiffness, and cushion angle on the risk of lumbar spine nucleus, annulus, and collagenous fibers (Figure 2(b)). A injuries. This study could provide better understanding of 0.5 mm layer of shell element was added to the outside of how to design countermeasures to reduce occupant lumbar the original vertebrae, representing the cortical bone. spine injuries in the new generation of vehicle models. Detailed ligaments modeled by beam elements were added between the vertebrae. Nucleus, annulus, and cancellous bones were modeled by solid elements. Collagenous fibers 2. Lumbar Spine Model Development and ligaments were modeled by beam elements. The facet and Validation joint articulations were simulated as the tiebreak contact 2.1. Model Development. In this study, the GHBMC model between adjacent endplates. Note that muscles were ignored was selected as the baseline model to be modified due to its in the current study. accurate geometrical representation. In the original GHBMC The modified lumbar model (Figure 1(b)) was composed lumbar spine model (Figure 1(a)), vertebrae (T12-L5) were of 64,338 elements and 12,295 nodes. The cancellous bones and cortical bones were modeled by MAT_SIMPLIFIED_- represented by a rigid material, intervertebral discs were modeled by shell elements (Figure 2(a)), and no ligaments JOHNSON_COOK in LS_DYNA [11, 12] with 1.3% and were modeled. In the modified model (Figure 1(b)), the 0.94% effective plastic failure strains, respectively. The end- intervertebral disc was separated into three parts including plates of the discs were modeled by an elastic material, and Lower fixture Applied Bionics and Biomechanics 3 Table 2: Material properties used in the current study. ∗ ∗ Segments MAT R0 (t/mm ) E (MPa)/K (N/mm) Poisson ratio A (MPa) B (MPa) NC PSFAIL SIGMAX (MPa) Cortical bone 98 1.83E − 09 11,740 0.3 106.7 100 0.1 1 9.40E − 03 150 Cancellous bone 98 1.80E − 10 259 0.25 1.71 20 1 1 1.30E − 02 1.985 Endplate vertebra 98 1.06E − 09 9450 0.3 5.67 100 1 3 1.89E − 02 7.1 Endplate disc 1 1.20E − 09 200 0.3 Disc annulus 27 1.20E − 09 0.49 0.24 −0.06 Disc nucleus 27 1.00E − 09 0.495 0.64 −0.16 Fiber 71 1.20E − 09 Curves Ligaments 74 1.00E − 09 In LS_DYNA material keywords, the strain energy density of MAT_MOONEY-RIVLIN_RUBBER is defined as a function of constant A, constant B, and Poisson ratio [16]. before validation [18]. Therefore, a presimulation was con- ducted to adjust the spine curvature to match the specimen pretest condition, as shown in Figure 3. Impact simulations Upper fixture were performed at different loading modes corresponding to the testing conditions. As a result, six simulations under compression, anterior shear, posterior shear, lateral shear, extension, and lateral bending were performed with the modified lumbar spine model. Each simulation was run at a displacement rate of 100 mm/sec. The maximum dis- placements were set to be the same as those in the tests. During these simulations, T12 was fixed to the fixture on the top, and L5 was attached to the fixture at the bottom. In the compression and shear conditions, load was applied from the lower fixture with the upper fixture rigidly con- strained. In the bending condition, displacement was applied (a) Initial lumbar spine (b) Initial lumbar spine from the lower fixture, and a bending moment was applied to the superior end of the lumbar spine by a cable. Force, posture in experiment posture in simulation moment, and angular displacement were measured at the Figure 3: Initial posture of the lumbar spine of cadaver experiment upper fixture. and simulation. Figure 4 shows load-displacement curves in each loading condition for the modified lumbar spine model. In compres- the endplates of vertebrae were modeled by MAT_SIMPLI- sion, posterior shear, lateral shear, extension and lateral FIED_JOHNSON_COOK. The nucleus and annulus were bending, simulation results shown in red line fell within test modeled by MAT_MOONEY-RIVLIN_RUBBER [11, 12]. corridors reasonably well. Accordingly, the shear modulus constant A of the nucleus and annulus were 0.64 MPa and 0.24 MPa, and the constant 2.3. Validation against Failure Tests. Cadaver tests with B of nucleus and annulus were −0.16 MPa and −0.06 MPa, tissue failure conducted by Duma et al. [19] were used respectively [12]. A linear elastic material was used for liga- to validate the modified lumbar model. The validation simu- ments. Selections of stiffness of ligaments (Table 1) were lations were set up under the same configurations as those based on a previous study [13]. The collagenous fibers were in the dynamic compression tests (Figure 5). The first sim- represented by a nonlinear load-displacement curve obtained ulation used a lumbar spine motion segment (Figure 5(a)), from the literature [14]. Because external lamellae are stiffer and the second simulation used the entire lumbar spine than internal lamellae, the fibers in different layers were (Figure 5(b)). During the simulations, the superior end of weighted according to a previous research [15]. To tune the the lumbar spine was attached to the upper plate, and the model responses, the material properties of the bones and lig- inferior end was attached to the lower plate. A prescribed aments were adjusted slightly to match the test results during motion was applied on the upper plate while the lower plate model validations. The material properties of all the parts in was fixed. All the failure simulations were loaded at 1.0 m/s. the modified lumbar model are listed in Table 2. Force and moment were calculated in these simulations under different loadings. 2.2. Validation against Nonfailure Tests. Cadaveric tests from As shown in Figure 6, the model-predicted force- Demetropoulos et al. [17] were used to validate the modified displacement curve for the motion segment configuration fell lumbar model. It is important to adjust the initial posture of within the experimental corridor. Good correlations between the simulation and the test for the entire lumbar spine the lumbar spine to be consistent with the experimental data 4 Applied Bionics and Biomechanics 5000 1500 Compression Anterior shear 4000 1200 3000 900 2000 600 0 0 0 24 6 0 10 20 30 40 Displacement (mm) Displacement (mm) (a) Compression (b) Anterior shear 3500 250 Posterior shear Lateral shear 0 0 010 20 30 40 0 5 10 15 Displacement (mm) Displacement (mm) (c) Posterior shear (d) Lateral shear 400 150 Extension Lateral bending 0 0 0 5 10 15 0 5 10 15 Angle (°) Angle (°) (e) Extension (f) Lateral bending Figure 4: Response comparisons between tests and simulations (red: simulation results, grey: test corridors). Upper plate Upper plate Whole lumbar spine Lumbar disc segment Six-axis load cell Lower plate Six-axis load cell Lower plate (a) Lumbar spine motion segment (b) Whole lumbar spine Figure 5: Test configurations for dynamic compression with failure. compression were also achieved, as shown in Figure 7. In 3. Design of Experiment Analysis addition, the locations of fractures in the simulation were consistent with those in the test (underneath the T12 and A DoE analysis based on Taguchi Array was used to study the L3), as shown in Figures 7(c) and 7(d). effects of multiple factors on the risk of lumbar spine injuries. Force (N) Force (N) Moment (N m) . Force (N) Moment (N m) Force (N) Applied Bionics and Biomechanics 5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Displacement (mm) (b) Fracture location in Current simulation simulation (underneath the (a) Force-displacement curve upper vertebra) Figure 6: Lumbar spine motion segment test and simulation results under compression. 0 5 10 15 0 5 10 15 Displacement (mm) Displacement (mm) Female test Female test Male test Male test Simulation Simulation (a) Force-displacement curve (b) Moment-displacement curve (c) Fracture location in (d) Fracture location in simulation (T12) simulation (L3) Figure 7: Test and simulation results of whole lumbar spines. Table 3: Magnitude of different levels for the five factors selected for Upper mass DOE analysis. Upper platform Impact cylinder Cushion Cushion Cushion Velocity Coefficient Upper fixture Level angle thickness density (m/s) of friction Impact velocity (degrees) (mm) (kg/m ) 1 0.1 0 20 20 0 Lower fixture 2 0.3 10 60 30 0.3 Lower platform 3 0.5 20 100 40 0.6 4 0.7 30 140 50 0.9 Seat cushion foam Fixed plate Figure 8: Setup used in Taguchi design of experiment analysis. Force (N) Force (N) Moment (N m) 6 Applied Bionics and Biomechanics Table 4: Maximum principal strain of 16 simulations in DOE analysis. Cushion Maximum Velocity Cushion Coefficient Cushion density Number thickness principal (mm/ms) angle ( ) of friction (kg/m ) (mm) strain (E-3) 1 0.5 10 0.9 140 20 4.08 2 0.5 20 0.6 20 40 5.17 3 0.7 20 0.3 60 20 4.6 4 0.1 20 0.9 100 30 2.97 5 0.5 30 0 60 30 2.72 6 0.5 0 0.3 100 50 3.43 7 0.3 20 0 140 50 3.22 8 0.1 30 0.3 140 40 2.51 9 0.7 0 0.6 140 30 5.14 10 0.1 0 0 20 20 3.82 11 0.1 10 0.6 60 50 3.99 12 0.7 30 0.9 20 50 6.08 13 0.3 10 0.3 20 30 4.21 14 0.3 0 0.9 60 40 3.29 15 0.3 30 0.6 100 20 2.36 16 0.7 10 0 100 40 5.7 In this study, 5 factors were investigated, including cushion the risk of lumbar injuries. With impact velocity varying stiffness, cushion thickness, cushion angle, the coefficient of between 0.1 and 0.5 m/s, the maximum principal strain friction, and impact velocity. fluctuated between 0.0032 and 0.0038, but it increased The setup of the simulations in the DoE analysis is shown rapidly to 0.0053 when impact velocity rose to 0.7 m/s. in Figure 8 [20]. The upper mass was attached to the upper Except the impact velocity, no other factor was statistically platform to simulate the mass of the torso, head-neck, and significant (P >0 05). upper extremities. The interaction between the upper platform Because the impact velocity dominated the lumbar frac- and the upper fixture was in a form of a laterally oriented ture risk in the Taguchi array, a one-way ANOVA was then cylinder. The lumbar spine was fixed at cranial and caudal conducted for the remaining 4 factors by controlling the ends to the upper fixture and lower fixture, respectively impact velocity as a constant. The average values of the max- [20]. A cushion foam, of which the thickness was defined as imum principal strains of different factor categories are h, was attached to the fixed plate as shown in Figure 8, and shown in Figure 10. The cushion thickness (P =0 039) its density was varied for the DoE analysis. The fixed plate became significant for the lumbar injuries. An increase in was constrained at a cushion angle of θ. The initial impact the cushion thickness will lead to more energy absorption velocity was applied to the upper mass, upper platform, and and in turn lower lumbar spine fracture risk. Even though impact cylinder, through the upper fixture, lumbar spine other factors were not significant, some general trends have specimen, and lower fixture, and finally reached the lower also been noted. For example, with an increase in the COF, platform, cushion foam, and the fixed plate (Figure 8). the lumbar spine fracture risk generally increased. For the The initial setup conditions of the impact velocity, cushion angle, the highest injury risk occurred when the lum- cushion angle, thickness, and density were 0.1 m/s, 0 bar spine orientation was perpendicular to the cushion. degree, 20 mm, and 20 kg/m These trends are widely consistent to the findings from other , respectively. The coefficient of friction (COF) between the lower platform and the seat studies on lumbar spine injuries [22] and cervical spine inju- cushion was ranged from 0 to 0.9. Four different levels ries [23]. were assigned for each factor (Table 3). Because most lum- bar injuries were reported as vertebral fractures, the max- 4. Conclusions imum principal strain in the bony structures was selected to evaluate the risk of lumbar fracture [21]. These setups A detailed modified FE lumbar spine model based on the resulted in a total of 16 simulations based on the Taguchi GHBMC model was developed and validated against avail- Array, as shown in Table 4. One-way analysis of variance able cadaveric tests which appeared in the literature. Risk (ANOVA) and analysis of covariance (ANCONA) were factors affecting lumbar spine injuries were investigated performed using SPSS 20.0. using the modified model. Results of the DoE analysis The average values of the maximum principal strains of demonstrated that the impact velocity is a significant fac- different factor categories are shown in Figure 9. Impact tor influencing the lumbar injuries. After controlling the velocity (P =0 009) had the most significant influence on impact velocity, cushion thickness is another significant Applied Bionics and Biomechanics 7 P = 0.009 P = 0.407 P = 0.944 P = 0.659 6 P = 0.918 Velocity Seat cushion Coefficient Seat cushion Seat cushion angle of friction thickness density Level 1 Level 3 Level 2 Level 4 Figure 9: The average maximum principal strain with respect to all 5 factors simulated using the Taguchi array. P = 0.039 P = 0.216 P = 0.471 P = 0.948 Seat cushion Coefficient Seat cushion Seat cushion angle of friction thickness density Level 1 Level 3 Level 2 Level 4 Figure 10: The average maximum principal strain with respect to the left 4 factors without impact velocity (impact velocity was 0.7 m/s). factor influencing lumbar injuries. An increase of cushion Acknowledgments thickness or decrease of cushion stiffness will reduce the lum- The authors gratefully acknowledge the financial support of bar spine fracture risk. Additionally, minimizing the COF the National Science Foundation of China under Grant no. between the padding and the lumbar spine can reduce the 51605032, the National Science Foundation of Beijing under lumbar spine injury risk. Grant no. 3174052, and the Fundamental Research Funds for One of the limitations of this study is that human factors the Central Universities no. 2017ZY31. such as BMI (body mass index), sex, and age were not consid- ered. 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A Numerical Investigation of Risk Factors Affecting Lumbar Spine Injuries Using a Detailed Lumbar Model

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Copyright © 2018 Jiajia Zheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Hindawi Applied Bionics and Biomechanics Volume 2018, Article ID 8626102, 8 pages https://doi.org/10.1155/2018/8626102 Research Article A Numerical Investigation of Risk Factors Affecting Lumbar Spine Injuries Using a Detailed Lumbar Model 1 1 2 Jiajia Zheng , Liang Tang , and Jingwen Hu School of Technology, Beijing Forestry University, Beijing 100083, China University of Michigan Transportation Research Institute, Ann Arbor, MI 48109, USA Correspondence should be addressed to Liang Tang; tang-l04@mails.tsinghua.edu.cn and Jingwen Hu; jwhu@umich.edu Received 9 December 2017; Accepted 5 March 2018; Published 17 April 2018 Academic Editor: Kiros Karamanidis Copyright © 2018 Jiajia Zheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Recent field data showed that lumbar spine fractures occurred more frequently in late model vehicles than early ones in frontal crashes. However, the lumbar spine designs of the current crash test dummies are not accurate in human anatomy and have not been validated against any human/cadaver impact responses. In addition, the lumbar spines of finite element (FE) human models, including GHBMC and THUMS, have never been validated previously against cadaver tests. Therefore, this study developed a detailed FE lumbar spine model and validated it against cadaveric tests. To investigate the mechanism of lumbar spine injury in frontal crashes, effects of changing the coefficient of friction (COF), impact velocity, cushion thickness and stiffness, and cushion angle on the risk of lumbar spine injuries were analyzed based on a Taguchi array of design of experiments. The results showed that impact velocity is the most important factor in determining the risk of lumbar spine fracture (P =0 009). After controlling the impact velocity, increases in the cushion thickness can effectively reduce the risk of lumbar spine fracture (P =0 039). 1. Introduction lumbar spines of the available FE human models, such as GHBMC (Global Human Body Model Consortium) model and THUMS (Total Human Model for Safety) model, have Safety designs in newer cars generally provided better protec- tions to occupants than those in older cars. However, several never been validated previously against cadaver tests. More recent field data analyses have shown that lumbar spine frac- recently, Arun et al. [3] applied the stiffness values obtained tures occurred more frequently in late model vehicles than from cadaver tests directly to the lumbar spine of the the early ones in frontal crashes [1, 2]. GHBMC simplified model. However, it is a rigid body- based lumbar spine model. It is lacking of detailed anatomi- This increasing trend of lumbar spine fractures in frontal crashes is extremely concerning, because none of the current cal structures of the lumbar spine and cannot estimate strain crash test programs, including FMVSS 208, US-NCAP, and and stress in the vertebrae. IIHS, considered lumbar spine injury in their safety evalua- Factors affecting the lumbar spine fracture have been dis- tion process. This is partially due to the fact that none of cussed extensively in the literature. Results indicated that the current crash test dummies can accurately estimate lum- older occupants (65+ years) were five times more likely to bar spine fracture risks. Current crash test dummies were sustain spinal injury compared to younger occupants [4], designed to focus on estimating injury risks to the head, neck, women had more lumbar spine fractures than men [5], and chest, and lower extremities, and their lumbar spine designs lower bone quality is associated with an increased number were not based on real human anatomy and were not vali- of lumbar spine fractures within the CIREN cases analyzed dated against any human/cadaver impact responses. As a [6]. Lumbar spine posture was also found to be an important result, although lumbar spine loadings could be measured factor affecting lumbar spine injuries. It was reported that in a crash test, they may not necessarily reflect the real injury slouched posture may cause an increase in stress on the lum- mechanism or injury risk in frontal crashes. In addition, bar vertebrae [7] and more reclined postures are associated 2 Applied Bionics and Biomechanics Nucleus ALL: anterior longitudinal ligament PLL Cancellous bone PLL: posterior longitudinal ligament SSL LF: flavum ligament Cortical bone CL: facet joint capsule ligament Disc fiber ISL ITL: interspinous ligament Intervertebral disc Annulus ITL SSL: supraspinous ligament Cortical bone ISL: intertransverse ligament Cancellous bone ALL CL LF (a) Original GHBMC model (b) Modified model Figure 1: Comparison between original and modified lumbar spine models. Shell elements Annulus Nucleus Collagenous fibers (a) Disc in GHBMC (shell elements) (b) Disc in current model (three parts) Figure 2: Comparison of the discs between GHBMC and modified lumbar models. with a higher lumbar vertebrae fracture risk by reconstruct- Table 1: Stiffness of ligaments used in the current study (unit: N/ ing real-world motor vehicle crashes [8]. Crash pulse magni- mm). tude and shape are also crucial for determining lumbar spine injury risk. For example, cadaver tests under axial loading Ligaments T12-L1 L1-L2 L2-L3 L3-L4 L4-L5 L5-S1 showed that triangular pulses produced pelvic fractures with ALL 32.9 32.4 20.8 39.5 40.5 32.9 no lumbar spine fractures, while a sigmoid-shaped pulse PLL 10 17.1 36.6 10.6 25.8 10 produced no pelvic fractures but did produce an L1 burst LF 24.2 23 25.1 34.5 27.2 24.2 fracture [9]. In addition, more severe crash pulses may lead CL 31.7 42.5 33.9 32.3 30.6 31.7 to higher lumbar spine injury risks [10]. ISL 12.1 10 9.6 18.1 8.7 12.1 The objectives of the present study were to develop a detailed FE lumbar spine model, validate it against cadaveric SSL 15.1 23 24.8 34.8 18 15.1 tests, and use it to investigate the effects of changing the coef- ITL 15.1 23 24.8 34.8 18 15.1 ficient of friction (COF), impact velocity, cushion thickness and stiffness, and cushion angle on the risk of lumbar spine nucleus, annulus, and collagenous fibers (Figure 2(b)). A injuries. This study could provide better understanding of 0.5 mm layer of shell element was added to the outside of how to design countermeasures to reduce occupant lumbar the original vertebrae, representing the cortical bone. spine injuries in the new generation of vehicle models. Detailed ligaments modeled by beam elements were added between the vertebrae. Nucleus, annulus, and cancellous bones were modeled by solid elements. Collagenous fibers 2. Lumbar Spine Model Development and ligaments were modeled by beam elements. The facet and Validation joint articulations were simulated as the tiebreak contact 2.1. Model Development. In this study, the GHBMC model between adjacent endplates. Note that muscles were ignored was selected as the baseline model to be modified due to its in the current study. accurate geometrical representation. In the original GHBMC The modified lumbar model (Figure 1(b)) was composed lumbar spine model (Figure 1(a)), vertebrae (T12-L5) were of 64,338 elements and 12,295 nodes. The cancellous bones and cortical bones were modeled by MAT_SIMPLIFIED_- represented by a rigid material, intervertebral discs were modeled by shell elements (Figure 2(a)), and no ligaments JOHNSON_COOK in LS_DYNA [11, 12] with 1.3% and were modeled. In the modified model (Figure 1(b)), the 0.94% effective plastic failure strains, respectively. The end- intervertebral disc was separated into three parts including plates of the discs were modeled by an elastic material, and Lower fixture Applied Bionics and Biomechanics 3 Table 2: Material properties used in the current study. ∗ ∗ Segments MAT R0 (t/mm ) E (MPa)/K (N/mm) Poisson ratio A (MPa) B (MPa) NC PSFAIL SIGMAX (MPa) Cortical bone 98 1.83E − 09 11,740 0.3 106.7 100 0.1 1 9.40E − 03 150 Cancellous bone 98 1.80E − 10 259 0.25 1.71 20 1 1 1.30E − 02 1.985 Endplate vertebra 98 1.06E − 09 9450 0.3 5.67 100 1 3 1.89E − 02 7.1 Endplate disc 1 1.20E − 09 200 0.3 Disc annulus 27 1.20E − 09 0.49 0.24 −0.06 Disc nucleus 27 1.00E − 09 0.495 0.64 −0.16 Fiber 71 1.20E − 09 Curves Ligaments 74 1.00E − 09 In LS_DYNA material keywords, the strain energy density of MAT_MOONEY-RIVLIN_RUBBER is defined as a function of constant A, constant B, and Poisson ratio [16]. before validation [18]. Therefore, a presimulation was con- ducted to adjust the spine curvature to match the specimen pretest condition, as shown in Figure 3. Impact simulations Upper fixture were performed at different loading modes corresponding to the testing conditions. As a result, six simulations under compression, anterior shear, posterior shear, lateral shear, extension, and lateral bending were performed with the modified lumbar spine model. Each simulation was run at a displacement rate of 100 mm/sec. The maximum dis- placements were set to be the same as those in the tests. During these simulations, T12 was fixed to the fixture on the top, and L5 was attached to the fixture at the bottom. In the compression and shear conditions, load was applied from the lower fixture with the upper fixture rigidly con- strained. In the bending condition, displacement was applied (a) Initial lumbar spine (b) Initial lumbar spine from the lower fixture, and a bending moment was applied to the superior end of the lumbar spine by a cable. Force, posture in experiment posture in simulation moment, and angular displacement were measured at the Figure 3: Initial posture of the lumbar spine of cadaver experiment upper fixture. and simulation. Figure 4 shows load-displacement curves in each loading condition for the modified lumbar spine model. In compres- the endplates of vertebrae were modeled by MAT_SIMPLI- sion, posterior shear, lateral shear, extension and lateral FIED_JOHNSON_COOK. The nucleus and annulus were bending, simulation results shown in red line fell within test modeled by MAT_MOONEY-RIVLIN_RUBBER [11, 12]. corridors reasonably well. Accordingly, the shear modulus constant A of the nucleus and annulus were 0.64 MPa and 0.24 MPa, and the constant 2.3. Validation against Failure Tests. Cadaver tests with B of nucleus and annulus were −0.16 MPa and −0.06 MPa, tissue failure conducted by Duma et al. [19] were used respectively [12]. A linear elastic material was used for liga- to validate the modified lumbar model. The validation simu- ments. Selections of stiffness of ligaments (Table 1) were lations were set up under the same configurations as those based on a previous study [13]. The collagenous fibers were in the dynamic compression tests (Figure 5). The first sim- represented by a nonlinear load-displacement curve obtained ulation used a lumbar spine motion segment (Figure 5(a)), from the literature [14]. Because external lamellae are stiffer and the second simulation used the entire lumbar spine than internal lamellae, the fibers in different layers were (Figure 5(b)). During the simulations, the superior end of weighted according to a previous research [15]. To tune the the lumbar spine was attached to the upper plate, and the model responses, the material properties of the bones and lig- inferior end was attached to the lower plate. A prescribed aments were adjusted slightly to match the test results during motion was applied on the upper plate while the lower plate model validations. The material properties of all the parts in was fixed. All the failure simulations were loaded at 1.0 m/s. the modified lumbar model are listed in Table 2. Force and moment were calculated in these simulations under different loadings. 2.2. Validation against Nonfailure Tests. Cadaveric tests from As shown in Figure 6, the model-predicted force- Demetropoulos et al. [17] were used to validate the modified displacement curve for the motion segment configuration fell lumbar model. It is important to adjust the initial posture of within the experimental corridor. Good correlations between the simulation and the test for the entire lumbar spine the lumbar spine to be consistent with the experimental data 4 Applied Bionics and Biomechanics 5000 1500 Compression Anterior shear 4000 1200 3000 900 2000 600 0 0 0 24 6 0 10 20 30 40 Displacement (mm) Displacement (mm) (a) Compression (b) Anterior shear 3500 250 Posterior shear Lateral shear 0 0 010 20 30 40 0 5 10 15 Displacement (mm) Displacement (mm) (c) Posterior shear (d) Lateral shear 400 150 Extension Lateral bending 0 0 0 5 10 15 0 5 10 15 Angle (°) Angle (°) (e) Extension (f) Lateral bending Figure 4: Response comparisons between tests and simulations (red: simulation results, grey: test corridors). Upper plate Upper plate Whole lumbar spine Lumbar disc segment Six-axis load cell Lower plate Six-axis load cell Lower plate (a) Lumbar spine motion segment (b) Whole lumbar spine Figure 5: Test configurations for dynamic compression with failure. compression were also achieved, as shown in Figure 7. In 3. Design of Experiment Analysis addition, the locations of fractures in the simulation were consistent with those in the test (underneath the T12 and A DoE analysis based on Taguchi Array was used to study the L3), as shown in Figures 7(c) and 7(d). effects of multiple factors on the risk of lumbar spine injuries. Force (N) Force (N) Moment (N m) . Force (N) Moment (N m) Force (N) Applied Bionics and Biomechanics 5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Displacement (mm) (b) Fracture location in Current simulation simulation (underneath the (a) Force-displacement curve upper vertebra) Figure 6: Lumbar spine motion segment test and simulation results under compression. 0 5 10 15 0 5 10 15 Displacement (mm) Displacement (mm) Female test Female test Male test Male test Simulation Simulation (a) Force-displacement curve (b) Moment-displacement curve (c) Fracture location in (d) Fracture location in simulation (T12) simulation (L3) Figure 7: Test and simulation results of whole lumbar spines. Table 3: Magnitude of different levels for the five factors selected for Upper mass DOE analysis. Upper platform Impact cylinder Cushion Cushion Cushion Velocity Coefficient Upper fixture Level angle thickness density (m/s) of friction Impact velocity (degrees) (mm) (kg/m ) 1 0.1 0 20 20 0 Lower fixture 2 0.3 10 60 30 0.3 Lower platform 3 0.5 20 100 40 0.6 4 0.7 30 140 50 0.9 Seat cushion foam Fixed plate Figure 8: Setup used in Taguchi design of experiment analysis. Force (N) Force (N) Moment (N m) 6 Applied Bionics and Biomechanics Table 4: Maximum principal strain of 16 simulations in DOE analysis. Cushion Maximum Velocity Cushion Coefficient Cushion density Number thickness principal (mm/ms) angle ( ) of friction (kg/m ) (mm) strain (E-3) 1 0.5 10 0.9 140 20 4.08 2 0.5 20 0.6 20 40 5.17 3 0.7 20 0.3 60 20 4.6 4 0.1 20 0.9 100 30 2.97 5 0.5 30 0 60 30 2.72 6 0.5 0 0.3 100 50 3.43 7 0.3 20 0 140 50 3.22 8 0.1 30 0.3 140 40 2.51 9 0.7 0 0.6 140 30 5.14 10 0.1 0 0 20 20 3.82 11 0.1 10 0.6 60 50 3.99 12 0.7 30 0.9 20 50 6.08 13 0.3 10 0.3 20 30 4.21 14 0.3 0 0.9 60 40 3.29 15 0.3 30 0.6 100 20 2.36 16 0.7 10 0 100 40 5.7 In this study, 5 factors were investigated, including cushion the risk of lumbar injuries. With impact velocity varying stiffness, cushion thickness, cushion angle, the coefficient of between 0.1 and 0.5 m/s, the maximum principal strain friction, and impact velocity. fluctuated between 0.0032 and 0.0038, but it increased The setup of the simulations in the DoE analysis is shown rapidly to 0.0053 when impact velocity rose to 0.7 m/s. in Figure 8 [20]. The upper mass was attached to the upper Except the impact velocity, no other factor was statistically platform to simulate the mass of the torso, head-neck, and significant (P >0 05). upper extremities. The interaction between the upper platform Because the impact velocity dominated the lumbar frac- and the upper fixture was in a form of a laterally oriented ture risk in the Taguchi array, a one-way ANOVA was then cylinder. The lumbar spine was fixed at cranial and caudal conducted for the remaining 4 factors by controlling the ends to the upper fixture and lower fixture, respectively impact velocity as a constant. The average values of the max- [20]. A cushion foam, of which the thickness was defined as imum principal strains of different factor categories are h, was attached to the fixed plate as shown in Figure 8, and shown in Figure 10. The cushion thickness (P =0 039) its density was varied for the DoE analysis. The fixed plate became significant for the lumbar injuries. An increase in was constrained at a cushion angle of θ. The initial impact the cushion thickness will lead to more energy absorption velocity was applied to the upper mass, upper platform, and and in turn lower lumbar spine fracture risk. Even though impact cylinder, through the upper fixture, lumbar spine other factors were not significant, some general trends have specimen, and lower fixture, and finally reached the lower also been noted. For example, with an increase in the COF, platform, cushion foam, and the fixed plate (Figure 8). the lumbar spine fracture risk generally increased. For the The initial setup conditions of the impact velocity, cushion angle, the highest injury risk occurred when the lum- cushion angle, thickness, and density were 0.1 m/s, 0 bar spine orientation was perpendicular to the cushion. degree, 20 mm, and 20 kg/m These trends are widely consistent to the findings from other , respectively. The coefficient of friction (COF) between the lower platform and the seat studies on lumbar spine injuries [22] and cervical spine inju- cushion was ranged from 0 to 0.9. Four different levels ries [23]. were assigned for each factor (Table 3). Because most lum- bar injuries were reported as vertebral fractures, the max- 4. Conclusions imum principal strain in the bony structures was selected to evaluate the risk of lumbar fracture [21]. These setups A detailed modified FE lumbar spine model based on the resulted in a total of 16 simulations based on the Taguchi GHBMC model was developed and validated against avail- Array, as shown in Table 4. One-way analysis of variance able cadaveric tests which appeared in the literature. Risk (ANOVA) and analysis of covariance (ANCONA) were factors affecting lumbar spine injuries were investigated performed using SPSS 20.0. using the modified model. Results of the DoE analysis The average values of the maximum principal strains of demonstrated that the impact velocity is a significant fac- different factor categories are shown in Figure 9. Impact tor influencing the lumbar injuries. After controlling the velocity (P =0 009) had the most significant influence on impact velocity, cushion thickness is another significant Applied Bionics and Biomechanics 7 P = 0.009 P = 0.407 P = 0.944 P = 0.659 6 P = 0.918 Velocity Seat cushion Coefficient Seat cushion Seat cushion angle of friction thickness density Level 1 Level 3 Level 2 Level 4 Figure 9: The average maximum principal strain with respect to all 5 factors simulated using the Taguchi array. P = 0.039 P = 0.216 P = 0.471 P = 0.948 Seat cushion Coefficient Seat cushion Seat cushion angle of friction thickness density Level 1 Level 3 Level 2 Level 4 Figure 10: The average maximum principal strain with respect to the left 4 factors without impact velocity (impact velocity was 0.7 m/s). factor influencing lumbar injuries. An increase of cushion Acknowledgments thickness or decrease of cushion stiffness will reduce the lum- The authors gratefully acknowledge the financial support of bar spine fracture risk. Additionally, minimizing the COF the National Science Foundation of China under Grant no. between the padding and the lumbar spine can reduce the 51605032, the National Science Foundation of Beijing under lumbar spine injury risk. Grant no. 3174052, and the Fundamental Research Funds for One of the limitations of this study is that human factors the Central Universities no. 2017ZY31. such as BMI (body mass index), sex, and age were not consid- ered. 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