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Research Papers

Validation of an In Vivo Medical Image-Based Young Human Lumbar Spine Finite Element Model

[+] Author and Article Information
Matthew J. Mills

Mechanical and Aerospace
Engineering Department,
University of California, Davis,
2132 Bainer Drive,
Davis, CA 95616
e-mail: mjmills@ucdavis.edu

Nesrin Sarigul-Klijn

Professor
Fellow ASME
Mechanical and Aerospace
Engineering Department,
University of California, Davis,
2132 Bainer Drive,
Davis, CA 95616;
Biomedical Engineering Department,
University of California, Davis,
451 E. Health Sciences Drive,
Davis, CA 95616
e-mail: nsarigulklijn@ucdavis.edu

1Corresponding author.

Manuscript received May 5, 2018; final manuscript received November 25, 2018; published online January 18, 2019. Assoc. Editor: Joel D. Stitzel.

J Biomech Eng 141(3), 031003 (Jan 18, 2019) (12 pages) Paper No: BIO-18-1216; doi: 10.1115/1.4042183 History: Received May 05, 2018; Revised November 25, 2018

Mathematical models of the human spine can be used to investigate spinal biomechanics without the difficulties, limitations, and ethical concerns associated with physical experimentation. Validation of such models is necessary to ensure that the modeled system behavior accurately represents the physics of the actual system. The goal of this work was to validate a medical image-based nonlinear lumbosacral spine finite element model of a healthy 20-yr-old female subject under physiological moments. Range of motion (ROM), facet joint forces (FJF), and intradiscal pressure (IDP) were compared with experimental values and validated finite element models from the literature. The finite element model presented in this work was in good agreement with published experimental studies and finite element models under pure moments. For applied moments of 7.5 N·m, the ROM in flexion–extension, axial rotation, and lateral bending were 39 deg, 16 deg, and 28 deg, respectively. Excellent agreement was observed between the finite element model and experimental data for IDP under pure compressive loading. The predicted FJFs were lower than those of the experimental results and validated finite element models for extension and torsion, likely due to the nondegenerate properties chosen for the intervertebral disks and morphology of the young female spine. This work is the first to validate a computational lumbar spine model of a young female subject. This model will serve as a valuable tool for predicting orthopedic spinal injuries, studying the effect of intervertebral disk replacements using advanced biomaterials, and investigating soft tissue degeneration.

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Figures

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Fig. 1

Medical image-based nonlinear finite element model of the L2-S lumbosacral spine based on a living 20-yr-old female subject with no known spinal abnormalities. X—Global coordinate system anterior direction, Y—Global coordinate system superior direction, Z—Global coordinate system transverse direction, xL3—L3 vertebra local coordinate system x-axis, yL3—L3 vertebra local coordinate system y-axis, zL3—L3 vertebra local coordinate system z-axis.

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Fig. 2

Calibrated ligament stiffness curves: ALL, PLL, ISL, SSL, intertransverse ligament, facet capsular ligament, and LF

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Fig. 3

Simplified L3–L4 vertebral motion segment model used for convergence study

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Fig. 4

Ligament calibration algorithm: θsimMi—computed ROM, θexpMi—experimental ROM, Mi—ith moment, n—number of data points, β—threshold value, Fi(x)—initial ligament load–displacement function,Fnew,i(x)—adjusted ligament load–displacement function, k—displacement scaling factor, and m—number of active ligaments

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Fig. 5

Convergence study results for applied moments of 7.5N·m in flexion and axial rotation

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Fig. 6

Calibrated ligament stiffness curves: ALL, PLL, ISL, SSL, intertransverse ligament, facet capsular ligament, and LF

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Fig. 7

Total L2-S ROM for 7.5 N·m applied moments compared with in vitro experimental studies and validated FE models. The first bar shows the results for the finite element model presented in this work. The second bar shows the results from a L2-S in vitro study of a single specimen [7]. The third bar indicates the median and range of results for the motion for ten L5–L1 specimens [52]. The fourth bar shows the median ROM values of eight validated finite element models and their range of results [1].

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Fig. 8

Flexion-extension (top), axial rotation (middle), and lateral bending (bottom) ROM for the L2-S segment compared with in vitro experimental studies [7,52]. Error bars indicate the range of the Rohlmann experimental results at an applied moment of 7.5 N·m.

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Fig. 9

Intervertebral rotations for flexion (positive) and extension (negative) compared with experimental data [54]. The experimental data points represent the mean and standard deviation of nine L1-S specimens.

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Fig. 10

Intervertebral rotations for left (positive) and right (negative) axial rotation compared with experimental data [54]. The experimental data points represent the mean and standard deviation of nine L1-S specimens.

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Fig. 11

Intervertebral rotations for right (positive) and left (negative) lateral bending compared with experimental data [54]. The experimental data points represent the mean and standard deviation of nine L1-S specimens.

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Fig. 12

IDP within the L4–L5 nucleus pulposus under compressive loading compared with experiment data [55] and a validated finite element model [22]. Data points for the experimental study represent the mean and range of results for 15 lumbar intervertebral disk specimens.

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Fig. 13

IDP within L2–L3, L3–L4, and L4–L5 nuclei pulposi for flexion compared with experimental data [25] and a validated finite element model [18]. The L2–L3 and L3–L4 values correspond to an applied moment of 3.0 N·m, whereas the L4–L5 values correspond to an applied moment of 7.5 N·m. The first bar indicates the mean hydrostatic pressure and standard deviation within the nucleus pulposus for this work. The second bar corresponds to the mean measurement and standard deviation from the in vitro experimental study by Ayturk. The third bar corresponds to the mean IDP and standard deviation within the nucleus pulposus for a validated finite element model.

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Fig. 14

Median FJFs of all spinal levels for extension, axial rotation, and lateral bending under applied moments of 7.5 N·m compared with experimental data [59] and validated finite element models [1]. The range given for this work corresponds to maximum and minimum FJFs in the model. The range indicated by the gray error bars represents the range of experimental results. The striped bar indicates the median FJF and range of results of eight validated finite element models.

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Fig. 15

FJFs at the L2–L3, L3–L4, and L4–L5 levels for extension (upper), lateral bending (middle), and axial rotation (lower) compared with validated finite element models [1]. The striped bar indicates the median FJF and range of results of eight validated finite element models.

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Fig. 16

Direction unit vectors for both fiber populations: ai—unit vector in direction of ifiber population, ϕi—inclination of ith fiber population relative to horizontal

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