CHARACTERIZATION OF PEDIATRIC HUMAN SPINE: 3-D FINITE ELEMENT STUDY

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1 Proceedings of of the the ASME International Mechanical Engineering Congress and & Exposition IMECE2011 November 11-17, 2011, Denver, Colorado, USA IMECE IMECE NONINVASIVE IN VIVO CHARACTERIZATION OF PEDIATRIC HUMAN SPINE: 3-D FINITE ELEMENT STUDY Elizabeth S. Doughty, M.S. Biomedical Engineering, University of California at Davis Davis, CA, USA Nesrin Sarigul-Klijn, Ph.D. Mechanical and Aerospace Engineering, Biomedical Engineering University of California at Davis, CA 95616, USA ABSTRACT There are no full three-dimensional computational models of the pediatric spine to study the many diseases and disorders that afflict the immature spine using finite element analysis. To fully characterize the pediatric spine, we created a pediatric specific computational model of C1-L5 using noninvasive in vivo techniques to incorporate the differences between the adult and pediatric spines: un-fused vertebrae, lax ligaments, and higher water content in the intervertebral discs. Muscle follower loads were included in the model to simulate muscle activation for five muscles involved in spine stabilization. This paper is the first pediatric three-dimensional model developed to date. Due to a lack of experimental pediatric spinal studies, this 3-D computational model has the potential to become a surgical tool to ensure that the most appropriate technique is chosen for treating pediatric spinal dysfunctions such as congenital abnormalities, idiopathic scoliosis, and vertebral fractures. Keywords: pediatric spine, high fidelity computational methods, FEM, in vivo CT, physiological loads INTRODUCTION The pediatric spine is a complex system that previously has been poorly explored. There are several disorders and diseases that affect the pediatric spine, such as congenital abnormalities, idiopathic scoliosis, and vertebral fractures [1]. These problems are important to study because of the high incidence of complications that can arise from the associated deformity. The primary complications are debilitating pain and damage to the neurological system. In addition, instability induced by these spinal disorders can result in pulmonary and respiratory complications, vascular issues, muscle spasms, gait disturbances, confounding disc degeneration, and further neurological difficulties [2-6]. It is difficult and often expensive to study these problems in vivo making it important to be able to study spinal disorders ex vivo to gain a better understanding of their etiology and determine the best treatment options. The primary elements responsible for modulating spine movement are the muscles, facet joints and ligaments; however there exists a difference between the structural system in the adult spine and the pediatric spine. The skeletally mature spine relies primarily on the intervertebral joints for stability and load bearing; however, since the pediatric spine is still undergoing skeletal development, spinal stability in children relies primarily on soft tissue structures such as ligaments, intervertebral discs, and paraspinal muscles with secondary help from the intervertebral joints, lamina, and spinous processes [3,7]. The pediatric spine also has structural differences, such as lax ligaments, facet joint orientation, and unfused vertebral structures which increase the likelihood of deformity development in an unstable spinal environment (Fig. 1) [8]. While there are several published computational models of the adult spine, there are no full three-dimensional (3-D) models of the pediatric spine. In literature, a limited number of finite element models of the pediatric spine have been published and only for the cervical and lumbar regions [9-12]. Kumaresan et al. developed a detailed cervical spine model (C4 C6) for children one, three, and six years of age [9]. Included into their scaled-down adult model were facet joint changes, ossification of vertebrae patterns, and nucleus and annulus changes within the intervertebral discs in order to make the model relevant to an immature spine. The authors chose to scale-down a validated adult model generated from CT scans of a 33-year-old male. The alternate goal of this project was to show that a scaled down adult model does not result in a representative model for the pediatric spine. In order to use a scaled-down model, one needs to include all the 1 Copyright ASME 2011

differences in anatomy in a child s spine such as bone density and canal size.

The 2-year-old has not yet finished fusion of the vertebral body to the posterior elements. Sairyo et al.

Previous work has shown that an accurate pediatric model cannot be extrapolated from adult data without taking into account the differences in tissue properties and geometries.

2 differences in anatomy in a child s spine such as bone density and canal size. 2 year old patient Adult patient Figure 1: A comparison between the bony structure of L3 of a 2-year-old and an adult spine. The 2-year-old has not yet finished fusion of the vertebral body to the posterior elements. Sairyo et al. created their model of the L3-L5 section of a 14-year old by scaling down an adult model [10-11]. Previous work has shown that an accurate pediatric model cannot be extrapolated from adult data without taking into account the differences in tissue properties and geometries. In order to make their model child relevant, growth plates and apophyseal rings, two major anatomical elements of the adolescent spine that are absent in the adult spine, were included. Sylvestre et al. created a detailed model of the pediatric lumbar spine and surrounding connective tissues [12]. The emphasis of their model was placed on the growth plate which is divided into three zones: reserve, proliferative, and hypertrophic. The growth plate is sensitive to excessive loading and has a large influence on skeletal deformities. This model was reconstructed from CT scans of adolescents. The ligaments in this model were used from adult data; however, the biomechanical properties of soft tissue in a child differ from those in an adult. It is important to use appropriate values for soft tissue modeling since soft tissues have the greatest control over the mechanical behavior of the spine and the relative stress distribution in the pediatric spine. There are many weaknesses of the existing pediatric finite element models for providing an accurate simulation of the pediatric spine. Two models of pediatric spine segments for subjects under 14 years of age have been found in literature. Only one of these models was generated from pediatric scans and this model only includes lumbar spinal segments [13]. The other existing pediatric spine model did not use pediatric images to construct the geometry for their cervical model, but instead scaled down an adult model created from a 33-year-old patient. A better structural representation of the pediatric geometry can be constructed from pediatric magnetic resonance images (MRI) and CT scans which also allow for appropriate bone density calculations. Only one of the reviewed models, Villemure et al., included musculature effects into the model; however, instead of adding multidirectional loads to integrate the effects of muscle into the model they incorporated the muscle forces along with the gravitational forces [14]. The applied musculature forces can affect the stability and structure making it an appropriate addition to scoliosis and deformity models. There are many ways to improve on the existing spine models in order to create the best representation of the in vivo conditions that occur in the pediatric spine. The goal of this project was to fully characterize the pediatric spine by creating a pediatric specific finite element model using noninvasive in vivo techniques to incorporate the differences between the adult and pediatric spines: unfused vertebrae, lax ligaments, and higher water content in the intervertebral discs. METHODS a. Lumbar Spine Model A three-dimensional high fidelity model of the pediatric spine containing the first cervical vertebra to the fifth lumbar vertebra (C1-L5) was generated from computed tomography (CT) scans of a 2-year-old male patient with a normal spine (Fig. 2). The model is composed of 4-noded tetrahedral elements with 6 degrees of freedom. Bone density assignment was formulated using the dimensionless Hounsfield unit (HU) in the CT scans. The Hounsfield scale for radiodensity is used to aid in the delineation of different elements such as cancellous and cortical bone. The bony elements were divided into ten equally sized intervals of 180 HU ranging from 65 to 1700 HU. The measured HU for each region of the vertebra was used to calculate the apparent bone density, ρ, using equation (1) developed by Rho et al., resulting in density values ranging from x 10-6 kg/mm 3 [15]. ρ = (1.12 x 10-3 )*HU (1) Material properties were assigned within Abaqus/CAE Software v6.8-3 (Simulia, Providence, RI), the finite element analysis software used for this study and can be found in Table 1. The cortical and cancellous bone properties for the vertebral body were defined as transversely isotropic while the posterior bony elements were defined as isotropic. To obtain the pediatric values for these properties, ratios between the posterior element material properties for Kumaresan et al. s adult and 3-year-old model were applied to the transversely isotropic cortical bone values for our existing adult model [9]. A similar ratio was found between the cancellous core and centrum properties of Kumaresan et al. s models in order to appropriately translate the cancellous bone properties to pediatric values. 2 Copyright ASME 2011

3 Table 1: Material properties for each structure included in the C1-L5 2-year-old spine model [9, 16-19]. Structure Element Type Young's and Shear Modulii (MPa) Poisson's Ratio Density (kg/mm 3 ) Reference Cortical Bone Transversely Isotropic E xx = 650 G xy = 220 υ xy = Lu et al., 1996 E yy = 650 G yx = 300 υ yz = Kumaresan et al E zz = 1,250 G xz = 300 υ xz = Cancellous Bone Transversely Isotropic E xx = 100 G = 35 υ xy = 0.45 Lu et al., 1996 E yy = 100 υ yz = Kumaresan et al E zz = 150 υ xz = Endplate Isotropic E = 25 υ = 0.4 Kumaresan et al Neuralcentral Isotropic E = 25 υ = 0.4 Kumaresan et al Synchondrosis Posterior Elements Isotropic E = 200 υ = 0.25 Kumaresan et al Annulus Fibrosis Mooney-Rivlin C 10 = 0.18 C 01 = D = Schmidt et al., 2007 υ = 0.49 Nucleus Pulposus Mooney-Rivlin C 10 = 0.12 C 01 = 0.03 D = 1.33e-3 Schmidt et al., 2007 υ = Ligaments Axial Connections Non-linear properties below: Eberlein et al., 2004 Kumaresan et al., 2000 Pintar et al., 1992 Ligament Fiber Force (N) Displacement (mm) SSL ISL (T12/L1) ISL (L1/L5) ISL (L1/S1) ALL Ligament Fiber Force (N) Displacement (mm) ITL LF PLL FCL Copyright ASME 2011

respectively. The ISL was constructed from 4, 5, and 3 fibers for the T12/L1, L1-L5, and L5/S1 joints.

Loading Conditions The boundary conditions for the model were set such that the inferior surface of L5 was fixed in the x- and y- directions but free to move in the z- direction to simulate contact

The point of reference for the center of mass was defined as the most anterior point of the C1 vertebra. The center of mass of the pediatric head was determined to be 0.6 cm posterior and 2.

The pure moments were generated with a 250 mm loading bar placed on the superior surface of C1.

Figure 2: Three-dimensional high fidelity virtual model of the bo

4 respectively. The ISL was constructed from 4, 5, and 3 fibers for the T12/L1, L1-L5, and L5/S1 joints. In order to replicate ligament damage, the specified ligaments were removed from the model one at a time. c. Loading Conditions The boundary conditions for the model were set such that the inferior surface of L5 was fixed in the x- and y- directions but free to move in the z- direction to simulate contact with the sacrum. The initial loading condition applied to all of the study cases was the moment and load induced by the 3.19 kg head of an average 2-year-old male [20]. The point of reference for the center of mass was defined as the most anterior point of the C1 vertebra. The center of mass of the pediatric head was determined to be 0.6 cm posterior and 2.3 cm above C1 [21] (Fig. 3). The center of mass location is illustrated in Figure 3. Static loads were applied as 0 10 Nm moments in flexion/extension, lateral bending, and axial rotation. The pure moments were generated with a 250 mm loading bar placed on the superior surface of C1. Motion segment range of motion and range of motion by region (cervical, thoracic, and lumbar), were calculated as angular displacement and compared to our novel spinal instability metric (SIM). Figure 2: Three-dimensional high fidelity virtual model of the bony anatomy of a 2-year-old spine with cross sectional views of the cervical, thoracic, and lumbar vertebrae, from top to bottom. b. Soft Tissue: Intervertebral Discs and Ligaments Soft tissue structures are not easily identified in CT scans, therefore the soft tissue structures were constructed using computer aided design (CAD). The intervertebral discs (IVD) are composed of two regions: the outer region consisting of the annulus fibrosus (AF) and the inner region consisting of the nucleus pulposus (NP). The NP and AF were simulated as hyperelastic materials. These assigned Mooney-Rivlin material properties are shown in Table 1. A Mooney-Rivlin material is an incompressible, isotropic material that experiences high strains and deformations. The unfused areas of bone are filled with cartilaginous growth plates known as neurocentral synchondroses. These areas were also constructed with CAD. The material properties for these regions are defined in Table 1. Ligaments were modeled as axial cables loaded only in tension. The ligament stiffness properties were derived from non-linear adult force displacement curves and then scaled down to pediatric values [9, 18-19]. The following seven ligaments were included in the model: anterior longitudinal ligament (ALL), posterior longitudinal ligament (PLL), intertransverse ligament (ITL), ligamentum flavum (LF), facet capsular ligament (FCL), interspinous ligament (ISL), and supraspinous ligament (SSL). The ALL, PLL, ITL, LF, FCL, and SSL were constructed from 7, 2, 5, 7, 1, and 1 fibers, Figure 3: The location of the center of mass (COM) for the average 2-year-old male head. The center of mass of the pediatric head was determined to be 0.6 cm posterior and 2.3 cm with respect to the top of the spine. d. Model Verification: Instability Metric This model can be validated against cadaveric data due to the difficulty in acquiring pediatric tissues for scientific research [9]. The spinal instability metric (SIM), a quantitative 4 Copyright ASME 2011

5 guideline of parameters showing the range of instability in different regions of the spine, was developed for evaluating spine models and is shown in Table 2. This metric is applicable for clinical evaluation of unstable motion as well as experimental evaluation for in vitro and computational models. The instability metric was developed from existing range of motion data collected from individuals of both sexes at different ages. Flexion, extension, lateral bending, axial rotation, and vertebral translation information was used to determine typical range of motion for individuals with healthy spines. The American Medical Association (AMA) guidelines for instability aided in deciding the deviation from healthy range of motion to unstable motion [22]. Functions predicting the unstable motion for the different regions of the spine for different ages were generated so that the instability metric is applicable for all ages. Table 2: Instability metric of a 2-year-old male spine [22-27]. Region Flexion- Extension ( s) Lateral Bending ( s) Axial Rotation ( s) Translation (mm) Cervical Thoracic Lumbar CONCLUSIONS The objective of this study is to create a physiologically accurate 2-year-old pediatric spine computational model. This work will result in a noninvasive in vivo technique to monitor potential outcomes of treatment for pediatric spinal dysfunctions. Noninvasive studies using finite element modeling reduce the need for in vitro studies which are expensive, have low sample size, and are performed in nonphysiological environments often lacking several soft tissue features which produce an inaccurate representation of the in vivo environment during loading. This 3-D computational model has the potential to become a surgical tool to ensure that the most appropriate technique is chosen for treating pediatric spinal dysfunctions such as congenital abnormalities, idiopathic scoliosis, and vertebral fractures. ACKNOWLEDGEMENTS The first author, Elizabeth Doughty would like to acknowledge the HHMI-IMBS translational research training grant received during this study. REFERENCES [1] Fesmire FM and Luten RC (1989). The pediatric cervical spine: developmental anatomy and clinical aspects. J Emerg Med 7: [2] Ghanem I, El Hage S, Rachkidi R, Kharrat K, Dagher F, Kreichati G (2008). Pediatric cervical spine instability. J Child Orthop 2: [3] Lunardi P, Licastro G, Missori P, Ferrante L, Fortuna A (1993). Management of intramedullary tumours in children. Acta Neurochir (Wien), 120: [4] Ruberte LM, Natarajan RN, Andersson GB (2009). Influence of single-level lumbar degenerative disc disease on the behavior of the adjacent segments--a finite element model study. J Biomech 42: [5] Simon SL, Auerbach JD, Garg S, Sutton LN, Telfeian AE, Dormans JP (2008). Efficacy of spinal instrumentation and fusion in the prevention of postlaminectomy spinal deformity in children with intramedullary spinal cord tumors. J Pediatr Orthop 28: [6] Smith JT (2007). The use of growth-sparing instrumentation in pediatric spinal deformity. Orthop Clin North Am 38: , vii. [7] Yoganandan N, Kumaresan S, Pintar FA (2001). Biomechanics of the cervical spine Part 2. Cervical spine soft tissue responses and biomechanical modeling. Clin Biomech (Bristol, Avon) 16: [8] McGirt MJ, Chaichana KL, Atiba A, Bydon A, Witham TF, Yao KC et al (2008). Incidence of spinal deformity after resection of intramedullary spinal cord tumors in children who underwent laminectomy compared with laminoplasty. J Neurosurg Pediatr 1: [9] Kumaresan S, Yoganandan N, Pintar FA, Maiman DJ, Kuppa S (2000). Biomechanical study of pediatric human cervical spine: a finite element approach. J Biomech Eng 122: [10] Sairyo K, Goel VK, Masuda A, Vishnubhotla S, Faizan A, Biyani A, Ebraheim N, et al (2006). Three-dimensional finite element analysis of the pediatric lumbar spine. Part I: pathomechanism of apophyseal bony ring fracture. Eur Spine J 15: [11] Sairyo K, Goel VK, Masuda A, Vishnubhotla S, Faizan A, Biyani A, Ebraheim N, et al (2006). Three dimensional finite element analysis of the pediatric lumbar spine. Part II: biomechanical change as the initiating factor for pediatric isthmic spondylolisthesis at the growth plate. Eur Spine J 15: [12] Sylvestre PL, Villemure I, Aubin CE (2007). Finite element modeling of the growth plate in a detailed spine model. Med Biol Eng Comput 45: [13] Jebaseelan D, Jabaraj C, Yoganandan N, Rajasekaran S (2010). Validation effects and flexibilities of an eight-year-old human juvenile lumbar spine using a three-dimensional finite element model. Med Biol Eng Comput 48: [14] Villemure I, Aubin CE, Dansereau J, Labelle H (2002). Simulation of progressive deformities in adolescent idiopathic scoliosis using a biomechanical model integrating vertebral growth modulation. J Biomech Eng 124: [15] Rho J, Hobatho M, Ashman R (1995) Relations of mechanical properties to density and CT numbers in human bone. Med Eng Phys 17: [16] Lu Y, Hutton W, Gharpuray V (1996). Do Bending, Twisting, and Diurnal Fluid Changes in the Disc Affect the Propensity to Prolapse? A Viscoelastic Finite Element Model. Spine 21: [17] Schmidt H, Heuer F, Drumm J, Klezl Z, Claes L, Wilke HJ (2007). Application of a Calibration Method Provides 5 Copyright ASME 2011

6 More Realistic Results for a Finite Element Model of a Lumbar Spinal Segment. Clinical Biomechanics 22: [18] Eberlein R, Holzapfel G, Fröhlich M (2004). Multi- Segment FEA of the Human Lumbar Spine Including the Heterogeneity of the Annulus Fibrosus. Computational Mechanics 34: [19] Pintar F, Yoganandan N, Myers T, Elhagediab A, Sances A (1992). Biomechanical Properties of Human Lumbar Spine Ligaments. Journal of Biomechanics 25: [20] Roche AF, Mukherjee D, Guo SM, et al (1987) Head circumference reference data: birth to 18 years. Pediatrics 79: [21] Clauser CE, McConville J, Young JW (1969). Weight, volume, and center of mass of segments of the human body. Wright Patterson Airforce Base, OH. [22] American Medical Association (1990). Guides to the Evaluation of Permanent Impairment 3 rd Edition, American Medical Association, Chicago, [23] Arbogast KB, Gholve PA, Friedman JE, Maltese MR, Tomasello MF, Dormans JP (2007). Normal cervical spine range of motion in children 3-12 years old. Spine 32: E [24] Feipel V, Rondelet B, Le Pallec J, Rooze M (1999). Normal global motion of the cervical spine: an electrogoniometric study. Clin Biomech (Bristol, Avon) 14: [25] Hsu CJ, Chang YW, Chou WY, Chiou CP, Chang WN, Wong CY (2008). Measurement of spinal range of motion in healthy individuals using an electromagnetic tracking device. J Neurosurg Spine 8: [26] Mellin G, Poussa M (1992). Spine Mobility and Posture in 8- to 16-Year Old Children. Journal of Orthopedic Research 10: [27] Sforza C, Grassi G, Fragnito N, Turci M, Ferrario V (2002). Three-dimensional analysis of active head and cervical spine range of motion: effect of age in healthy male subjects. Clin Biomech (Bristol, Avon) 17: Copyright ASME 2011

It consist of two components: the outer, laminar fibrous container (or annulus), and the inner, semifluid mass (the nucleus pulposus).

It consist of two components: the outer, laminar fibrous container (or annulus), and the inner, semifluid mass (the nucleus pulposus). Lumbar Spine The lumbar vertebrae are the last five vertebrae of the vertebral column. They are particularly large and heavy when compared with the vertebrae of the cervical or thoracicc spine. Their bodies