A combined finite element and optimization investigation of lumbar spine mechanics with and without muscles

Vijay K. Goel*, Weizeng Kong, Jung S. Han, James Neil Weinstein, Lars G. Gilbertson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

227 Scopus citations


A combined finite element and optimization approach to study the effects of muscles on the biomechanics of the lumbar spine w as initiated. Briefly, a three-dimensional, nonlinear, finite element model of a ligamentous L3-4 motion segment was formulated (LIG model) for the predictions of stresses, etc., in the motion segment. A separate, biomechanical optimization-based force model with experimental input wa s developed to predict the forces in muscles and disc across the L3-4 segment in response to a person holding 90 N in his hands with spine flexed 30°, and knees straight. The predicted muscle forces from the optimization model were then incorporated into the L3-4 finite element mode! a s nodal forces to simulate the muscle action (M U S model). The predicted responses from the muscles active (MUS) finite element model were compared to the corresponding results from the ligamentous (LIG) finite element model subjected to an equivalent load. The biomechanical parameters compared were: translation and rotation of L3, disc bulge, intervertebral foramen gap, intradiscal pressure, facet loading, ligament tension, compressive disc load, and stresses in the vertebral body. The addition of muscular forces in the M U S model led to a decrease in the anteroposterior translation and flexion rotation (displacements in the sagittal plane) of the segment compared to the corresponding LIG model predictions. Thus, the muscles imparted stability to the ligamentous segment. The presence of muscles also led to a decrease in stresses in the vertebral body, the intradiscal pressure and other mechanical parameters of importance. However, the load bearing of the facets increased compared to the ligamentous model. Thus, facets play a significant role in transmitting loads in a normal intact spine. These results, for the first time, provide quantitative data on the stabilizing effects of muscles on the mechanics of a ligamentous spine. The results also provide a scientific explanation in support o f the "degenerative cascade" concept proposed in the literature. The model predictions, in conjunction with the degenerative cascade concept, also support the observation that the osteoarthritis of facets may follow disc degeneration. Future research directions based on the current model are presented.

Original languageEnglish (US)
Pages (from-to)1531-1541
Number of pages11
Issue number11
StatePublished - Sep 1993


  • Biomechanics
  • Degenerationage related changes
  • Finite element model
  • Instability
  • Muscles
  • Optimization-based force model

ASJC Scopus subject areas

  • Orthopedics and Sports Medicine
  • Clinical Neurology

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