0
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Delp, S. L. , Anderson, F. C. , Arnold, A. S. , Loan, P. , Habib, A. , John, C. T. , Guendelman, E. , and Thelen, D. G. , 2007, “ OpenSim: Open-Source Software to Create and Analyze Dynamic Simulations of Movement,” IEEE Trans. Biomed. Eng., 54(11), pp. 1940–1950. [CrossRef] [PubMed]
Hoy, D. , Bain, C. , Williams, G. , March, L. , Brooks, P. , Blyth, F. , Woolf, A. , Vos, T. , and Buchbinder, R. , 2012, “ A Systematic Review of the Global Prevalence of Low Back Pain,” Arthritis Rheum., 64(6), pp. 2028–2037. [CrossRef] [PubMed]
Martin, B. I. , Deyo, R. A. , Mirza, S. K. , Turner, J. A. , Comstock, B. A. , Hollingworth, W. , and Sullivan, S. D. , 2008, “ Expenditures and Health Status Among Adults With Back and Neck Problems,” JAMA, 299(6), pp. 656–664. [CrossRef] [PubMed]
Huynh, K. T. , Gibson, I. , Jagdish, B. N. , and Lu, W. F. , 2015, “ Development and Validation of a Discretised Multi-Body Spine Model in LifeMOD for Biodynamic Behaviour Simulation,” Comput. Methods Biomech. Biomed. Eng., 18(2), pp. 175–184. [CrossRef]
Stokes, I. A. , and Gardner-Morse, M. , 1995, “ Lumbar Spine Maximum Efforts and Muscle Recruitment Patterns Predicted by a Model With Multijoint Muscles and Joints With Stiffness,” J. Biomech., 28(2), pp. 173–186. [CrossRef] [PubMed]
Christophy, M. , Faruk Senan, N. A. , Lotz, J. C. , and O'Reilly, O. M. , 2012, “ A Musculoskeletal Model for the Lumbar Spine,” Biomech. Model. Mechanobiol., 11(1–2), pp. 19–34. [CrossRef] [PubMed]
de Zee, M. , Hansen, L. , Wong, C. , Rasmussen, J. , and Simonsen, E. B. , 2007, “ A Generic Detailed Rigid-Body Lumbar Spine Model,” J. Biomech., 40(6), pp. 1219–1227. [CrossRef] [PubMed]
Fujii, R. , Sakaura, H. , Mukai, Y. , Hosono, N. , Ishii, T. , Iwasaki, M. , Yoshikawa, H. , and Sugamoto, K. , 2007, “ Kinematics of the Lumbar Spine in Trunk Rotation: In Vivo Three-Dimensional Analysis Using Magnetic Resonance Imaging,” Eur. Spine J., 16(11), pp. 1867–1874. [CrossRef] [PubMed]
Neuschwander, T. B. , Cutrone, J. , Macias, B. R. , Cutrone, S. , Murthy, G. , Chambers, H. , and Hargens, A. R. , 2010, “ The Effect of Backpacks on the Lumbar Spine in Children: A Standing Magnetic Resonance Imaging Study,” Spine, 35(1), pp. 83–88. [CrossRef] [PubMed]
Li, G. , Wang, S. , Passias, P. , Xia, Q. , and Wood, K. , 2009, “ Segmental In Vivo Vertebral Motion During Functional Human Lumbar Spine Activities,” Eur. Spine J., 18(7), pp. 1013–1021. [CrossRef] [PubMed]
Wang, S. , Xia, Q. , Passias, P. , Wood, K. , and Li, G. , 2009, “ Measurement of Geometric Deformation of Lumbar Intervertebral Discs Under In-Vivo Weightbearing Condition,” J. Biomech., 42(6), pp. 705–711. [CrossRef] [PubMed]
Wu, M. , Wang, S. , Driscoll, S. J. , Cha, T. D. , Wood, K. B. , and Li, G. , 2014, “ Dynamic Motion Characteristics of the Lower Lumbar Spine: Implication to Lumbar Pathology and Surgical Treatment,” Eur. Spine J., 23(11), pp. 2350–2358. [CrossRef] [PubMed]
Adams, M. A. , and Dolan, P. , 1991, “ A Technique for Quantifying the Bending Moment Acting on the Lumbar Spine In Vivo,” J. Biomech., 24(2), pp. 117–126. [CrossRef] [PubMed]
Han, K. S. , Zander, T. , Taylor, W. R. , and Rohlmann, A. , 2012, “ An Enhanced and Validated Generic Thoraco-Lumbar Spine Model for Prediction of Muscle Forces,” Med. Eng. Phys., 34(6), pp. 709–716. [CrossRef] [PubMed]
Andersen, M. S. , and Rasmussen, J. , 2011, “ Total Knee Replacement Musculoskeletal Model Using a Novel Simulation Method for Non-Conforming Joints,” International Society of Biomechanics Conference (ISB 2011), Brussels, Belgium, July 3–7, Paper No. 343.
Marra, M. A. , Vanheule, V. , Fluit, R. , Koopman, B. H. , Rasmussen, J. , Verdonschot, N. , and Andersen, M. S. , 2015, “ A Subject-Specific Musculoskeletal Modeling Framework to Predict In Vivo Mechanics of Total Knee Arthroplasty,” ASME J. Biomech. Eng., 137(2), p. 020904. [CrossRef]
de Leva, P. , 1996, “ Adjustments to Zatsiorsky-Seluyanov's Segment Inertia Parameters,” J. Biomech., 29(9), pp. 1223–1230. [CrossRef] [PubMed]
McConville, J. T. , Churchill, T. D. , Kaleps, I. , Clauser, C. E. , and Cuzzi, J. , 1980, “ Anthropometric Relationships of Body and Body Segment Moments of Inertia,” Aerospace Medical Research Laboratory, Wright-Patterson Air Force Base, OH, Report No. AFAMRL-TR-80-119.
Millard, M. , Uchida, T. , Seth, A. , and Delp, S. L. , 2013, “ Flexing Computational Muscle: Modeling and Simulation of Musculotendon Dynamics,” ASME J. Biomech. Eng., 135(2), p. 021005. [CrossRef]
Arjmand, N. , and Shirazi-Adl, A. , 2006, “ Role of Intra-Abdominal Pressure in the Unloading and Stabilization of the Human Spine During Static Lifting Tasks,” Eur. Spine J., 15(8), pp. 1265–1275. [CrossRef] [PubMed]
Schultz, A. , Andersson, G. , Ortengren, R. , Haderspeck, K. , and Nachemson, A. , 1982, “ Loads on the Lumbar Spine. Validation of a Biomechanical Analysis by Measurements of Intradiscal Pressures and Myoelectric Signals,” J. Bone Jt. Surg., 64(5), pp. 713–720.
Marras, W. S. , and Mirka, G. A. , 1996, “ Intra-Abdominal Pressure During Trunk Extension Motions,” Clin. Biomech., 11(5), pp. 267–274. [CrossRef]
Gardner-Morse, M. G. , and Stokes, I. A. , 2004, “ Structural Behavior of Human Lumbar Spinal Motion Segments,” J. Biomech., 37(2), pp. 205–212. [CrossRef] [PubMed]
Panjabi, M. M. , Brand, R. A., Jr. , and White, A. A., III , 1976, “ Three-Dimensional Flexibility and Stiffness Properties of the Human Thoracic Spine,” J. Biomech., 9(4), pp. 185–192. [CrossRef] [PubMed]
Heuer, F. , Schmidt, H. , Klezl, Z. , Claes, L. , and Wilke, H. J. , 2007, “ Stepwise Reduction of Functional Spinal Structures Increase Range of Motion and Change Lordosis Angle,” J. Biomech., 40(2), pp. 271–280. [CrossRef] [PubMed]
Panjabi, M. M. , Oxland, T. R. , Yamamoto, I. , and Crisco, J. J. , 1994, “ Mechanical Behavior of the Human Lumbar and Lumbosacral Spine as Shown by Three-Dimensional Load-Displacement Curves,” J. Bone Jt. Surg., 76(3), pp. 413–424.
Tencer, A. F. , Ahmed, A. M. , and Burke, D. L. , 1982, “ Some Static Mechanical Properties of the Lumbar Intervertebral Joint, Intact and Injured,” ASME J. Biomech. Eng., 104(3), pp. 193–201. [CrossRef]
Yamamoto, I. , Panjabi, M. M. , Crisco, T. , and Oxland, T. , 1989, “ Three-Dimensional Movements of the Whole Lumbar Spine and Lumbosacral Joint,” Spine, 14(11), pp. 1256–1260. [CrossRef] [PubMed]
Lin, H. S. , Liu, Y. K. , and Adams, K. H. , 1978, “ Mechanical Response of the Lumbar Intervertebral Joint Under Physiological (Complex) Loading,” J. Bone Jt. Surg., Am., 60(1), pp. 41–55.
Markolf, K. L. , 1972, “ Deformation of the Thoracolumbar Intervertebral Joints in Response to External Loads: A Biomechanical Study Using Autopsy Material,” J. Bone Jt. Surg., 54(3), pp. 511–533.
El Ouaaid, Z. , Shirazi-Adl, A. , Plamondon, A. , and Lariviere, C. , 2013, “ Trunk Strength, Muscle Activity and Spinal Loads in Maximum Isometric Flexion and Extension Exertions: A Combined In Vivo-Computational Study,” J. Biomech., 46(13), pp. 2228–2235. [CrossRef] [PubMed]
Tafazzol, A. , Arjmand, N. , Shirazi-Adl, A. , and Parnianpour, M. , 2014, “ Lumbopelvic Rhythm During Forward and Backward Sagittal Trunk Rotations: Combined In Vivo Measurement With Inertial Tracking Device and Biomechanical Modeling,” Clin. Biomech., 29(1), pp. 7–13. [CrossRef]
Wong, K. W. , Luk, K. D. , Leong, J. C. , Wong, S. F. , and Wong, K. K. , 2006, “ Continuous Dynamic Spinal Motion Analysis,” Spine, 31(4), pp. 414–419. [CrossRef] [PubMed]
Wilke, H. , Neef, P. , Hinz, B. , Seidel, H. , and Claes, L. , 2001, “ Intradiscal Pressure Together With Anthropometric Data—A Data Set for the Validation of Models,” Clin. Biomech., 16(Suppl. 1), pp. S111–S126. [CrossRef]
Busscher, I. , van Dieen, J. H. , van der Veen, A. J. , Kingma, I. , Meijer, G. J. , Verkerke, G. J. , and Veldhuizen, A. G. , 2011, “ The Effects of Creep and Recovery on the In Vitro Biomechanical Characteristics of Human Multi-Level Thoracolumbar Spinal Segments,” Clin. Biomech., 26(5), pp. 438–444. [CrossRef]
Zhao, F. , Pollintine, P. , Hole, B. D. , Dolan, P. , and Adams, M. A. , 2005, “ Discogenic Origins of Spinal Instability,” Spine, 30(23), pp. 2621–2630. [CrossRef] [PubMed]
Gardner-Morse, M. G. , and Stokes, I. A. , 1998, “ The Effects of Abdominal Muscle Coactivation on Lumbar Spine Stability,” Spine, 23(1), pp. 86–91; discussion 91–92. [CrossRef] [PubMed]
Stokes, I. A. , and Gardner-Morse, M. , 2001, “ Lumbar Spinal Muscle Activation Synergies Predicted by Multi-Criteria Cost Function,” J. Biomech., 34(6), pp. 733–740. [CrossRef] [PubMed]
Stokes, I. A. , and Gardner-Morse, M. , 2003, “ Spinal Stiffness Increases With Axial Load: Another Stabilizing Consequence of Muscle Action,” J. Electromyogr. Kinesiol., 13(4), pp. 397–402. [CrossRef] [PubMed]
Christophy, M. , Curtin, M. , Senan, N. A. F. , Lotz, J. C. , and O'Reilly, O. M. , 2013, “ On the Modeling of the Intervertebral Joint in Multibody Models for the Spine,” Multibody Syst. Dyn., 30(4), pp. 413–432. [CrossRef]
Weisse, B. , Aiyangar, A. K. , Affolter, C. , Gander, R. , Terrasi, G. P. , and Ploeg, H. , 2012, “ Determination of the Translational and Rotational Stiffnesses of an L4-L5 Functional Spinal Unit Using a Specimen-Specific Finite Element Model,” J. Mech. Behav. Biomed. Mater., 13, pp. 45–61. [CrossRef] [PubMed]
Izzo, R. , Guarnieri, G. , Guglielmi, G. , and Muto, M. , 2013, “ Biomechanics of the Spine. Part II: Spinal Instability,” Eur. J. Radiol., 82(1), pp. 127–138. [CrossRef] [PubMed]
Harris, B. M. , Hilibrand, A. S. , Savas, P. E. , Pellegrino, A. , Vaccaro, A. R. , Siegler, S. , and Albert, T. J. , 2004, “ Transforaminal Lumbar Interbody Fusion: The Effect of Various Instrumentation Techniques on the Flexibility of the Lumbar Spine,” Spine, 29(4), pp. E65–E70. [CrossRef] [PubMed]
Sim, H. B. , Murovic, J. A. , Cho, B. Y. , Lim, T. J. , and Park, J. , 2010, “ Biomechanical Comparison of Single-Level Posterior Versus Transforaminal Lumbar Interbody Fusions With Bilateral Pedicle Screw Fixation: Segmental Stability and the Effects on Adjacent Motion Segments,” J. Neurosurg. Spine, 12(6), pp. 700–708. [CrossRef] [PubMed]
Demetropoulos, C. K. , Sengupta, D. K. , Knaub, M. A. , Wiater, B. P. , Abjornson, C. , Truumees, E. , and Herkowitz, H. N. , 2010, “ Biomechanical Evaluation of the Kinematics of the Cadaver Lumbar Spine Following Disc Replacement With the ProDisc-L Prosthesis,” Spine, 35(1), pp. 26–31. [CrossRef] [PubMed]
Cripton, P. A. , Bruehlmann, S. B. , Orr, T. E. , Oxland, T. R. , and Nolte, L. P. , 2000, “ In Vitro Axial Preload Application During Spine Flexibility Testing: Towards Reduced Apparatus-Related Artefacts,” J. Biomech., 33(12), pp. 1559–1568. [CrossRef] [PubMed]
Gardner-Morse, M. G. , and Stokes, I. A. , 2003, “ Physiological axial Compressive Preloads Increase Motion Segment Stiffness, Linearity and Hysteresis in all Six Degrees of Freedom for Small Displacements About the Neutral Posture,” J. Orthop. Res., 21(3), pp. 547–552. [CrossRef] [PubMed]
Janevic, J. , Ashton-Miller, J. A. , and Schultz, A. B. , 1991, “ Large Compressive Preloads Decrease Lumbar Motion Segment Flexibility,” J. Orthop. Res., 9(2), pp. 228–236. [CrossRef] [PubMed]

Figures

Grahic Jump Location
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).

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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].

Grahic Jump Location
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].

Grahic Jump Location
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.

Grahic Jump Location
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.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In