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Research Papers

Incorporating Six Degree-of-Freedom Intervertebral Joint Stiffness in a Lumbar Spine Musculoskeletal Model—Method and Performance in Flexed Postures

[+] Author and Article Information
Xiangjie Meng

State Key Laboratory of Automotive Safety and Energy,
Department of Automotive Engineering,
Tsinghua University,
Beijing 100084, China;
Center for Advanced Orthopaedic Studies,
Beth Israel Deaconess Medical Center,
330 Brookline Avenue, RN115,
Boston, MA 02215
e-mail: mengxjchina@gmail.com

Alexander G. Bruno

Harvard-MIT Health Sciences and Technology Program,
Cambridge, MA 02139;
Center for Advanced Orthopaedic Studies,
Beth Israel Deaconess Medical Center,
330 Brookline Avenue, RN115,
Boston, MA 02215
e-mail: agbruno@mit.edu

Bo Cheng

State Key Laboratory of Automotive Safety and Energy,
Department of Automotive Engineering,
Tsinghua University,
Beijing 100084 China
e-mail: chengbo@tsinghua.edu.cn

Wenjun Wang

State Key Laboratory of Automotive Safety and Energy,
Department of Automotive Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: wangxiaowenjun@tsinghua.edu.cn

Mary L. Bouxsein

Center for Advanced Orthopaedic Studies,
Beth Israel Deaconess Medical Center,
330 Brookline Avenue, RN115,
Boston, MA 02215;
Department of Orthopedic Surgery,
Harvard Medical School,
Boston, MA 02115
e-mail: mbouxsei@bidmc.harvard.edu

Dennis E. Anderson

Mem. ASME
Center for Advanced Orthopaedic Studies,
Beth Israel Deaconess Medical Center,
330 Brookline Avenue, RN115,
Boston, MA 02215;
Department of Orthopedic Surgery,
Harvard Medical School,
Boston, MA 02115
e-mail: danders7@bidmc.harvard.edu

1Corresponding author.

Manuscript received January 7, 2015; final manuscript received July 29, 2015; published online September 3, 2015. Assoc. Editor: Brian D. Stemper.

J Biomech Eng 137(10), 101008 (Sep 03, 2015) (9 pages) Paper No: BIO-15-1004; doi: 10.1115/1.4031417 History: Received January 07, 2015; Revised July 29, 2015

Intervertebral translations and rotations are likely dependent on intervertebral stiffness properties. The objective of this study was to incorporate realistic intervertebral stiffnesses in a musculoskeletal model of the lumbar spine using a novel force-dependent kinematics approach, and examine the effects on vertebral compressive loading and intervertebral motions. Predicted vertebral loading and intervertebral motions were compared to previously reported in vivo measurements. Intervertebral joint reaction forces and motions were strongly affected by flexion stiffness, as well as force–motion coupling of the intervertebral stiffness. Better understanding of intervertebral stiffness and force–motion coupling could improve musculoskeletal modeling, implant design, and surgical planning.

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References

Figures

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Fig. 2

Flowcharts of the algorithms for determining intervertebral rotations (left) and translations (right) in opensim and matlab. When the simulation begins, the desired overall angle is entered, and initial intervertebral translations set to 0. New values for individual intervertebral angles, RatioT, and intervertebral translations are adjusted until the value of RatioT is constant at all levels and intervertebral actuator forces are < 0.01 N.

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Fig. 4

Effects of flexion stiffness (a), anterior–posterior (A-P) translational stiffness (b), and superior–inferior (S-I) translational stiffness (c) on compressive joint reaction force at level L4–L5 during 22 deg of flexion. The symbols indicate mean measured stiffness values, while lines indicate realistic ranges of stiffness based on measurements. The dotted line indicates expected compressive joint reaction force of 500 N estimated based on measured disk pressure reported by Wilke et al. [34].

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Fig. 1

Musculoskeletal model in opensim (left), based on the lumbar spine model of Christophy et al. [6]. Each of the five lumbar intervertebral joints (L1–L2 to L5-S1, center) was implemented with 6DOFs (three translational and three rotational), with joint stiffness defined by a 6 × 6 stiffness matrix (right).

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Fig. 3

Convergence of intervertebral translation determination algorithm for a simulation of 22 deg of flexion, showing ActuatorForce (solid line) and bushing force (dashed line) in the axial direction. Simulation starts with zero translation input, producing large errors (ActuatorForce), but these errors rapidly converge to < 0.01 N in nine cycles.

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Fig. 5

Effects of flexion stiffness (a), anterior–posterior (A-P) translational stiffness (b), and superior–inferior (S-I) translational stiffness (c) on A-P (left) and S-I (right) intervertebral translations at level L4–L5 during 45 deg of flexion. The symbols indicate mean measured stiffness values, while lines indicate realistic ranges of stiffness based on measurements. Dotted lines and shaded regions are the mean ± 1SD of in vivo intervertebral translations at level L4–L5 measured by Wu et al. [12].

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Fig. 6

Effects of flexion stiffness (a), anterior–posterior (A-P) translational stiffness (b), and superior–inferior (S-I) translational stiffness (c) on intervertebral flexion angle at level L4-L5 during 45 deg of flexion. The symbols indicate mean measured stiffness values, while lines indicate realistic ranges of stiffness based on measurements.

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Fig. 7

Intervertebral flexion angles by level estimated using coupled and uncoupled stiffness and measured by Wu et al. [12]. Error bar for measured values is + 1 SD, while error bars for model estimates show ranges found with parametric variations of L4–L5 stiffness during 45 deg of flexion.

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