FINITE ELEMENT ANALYSIS OF HUMAN FACET JOINT CAPSULE DURING PHYSIOLOGICAL MOTIONS FOR TWO LUMBAR MOTION SEGMENTS Anita C. Saldanha1, Yi-Xian Qin1, Vijay K. Goel2, Partap S. Khalsa1 1
Biomedical Engineering Department, Stony Brook University, Stony Brook, NY, 11794 USA Email:
[email protected] 2
Bioengineering Department, University of Toledo, Toledo, OH, 43606 USA
INTRODUCTION Eighty percent of Americans will experience low back pain (LBP) in their lifetime [Cassidy, 1998]; for the majority of LBP patients, the etiology continues to be poorly understood. A known cause of LBP is the activation of mechano-nociceptors innervating lumbar facet joint capsules. In isolated, but intact, nerve – capsule (as well as nerve – skin & nerve – muscle) mechanoreceptors and nociceptors appear to encode the local stress rather than the local strain during loading [Khalsa 1997]. In-vivo, it is virtually impossible to directly measure capsule stress; however, robust estimates of capsule stress are possible using the finite element method (FEM). Previous FEM models of the lumbar spine have not included accurate representations (geometry or material properties) of the facet joint (FJ) and its posterior capsule. The purpose of this study was to create a geometrically correct FEM model of the lumbar FJ, incorporate it into an existing lumbar spine model [Goel, 1995], and subject it to normal physiological loading conditions. METHODS Model Geometry: 13 1-mm high-resolution computed tomography (CT) images of the left L3-4 FJ from a lumbar spine were used to define the non-linear geometry of the FJ in the model. Custom software was written in PVWAVE (Visual Numerics Inc.) to perform pre-processing for FEM mesh development. The perimeter nodal points for both
the superior and inferior facet processes served as a framework to build a surface mesh in ABAQUS (v. 6.3, HKS, Inc.). ABAQUS’s automatic mesh generating algorithm was used to build slices consisting of linear elastic elements (continuum 3D, 8noded, brick elements). In MATLAB (ver. 6.5; The MathWorks Inc.), the articular cartilage and capsular ligament perimeter geometry was developed based on the superior and inferior process geometry, and subsequently modeled as linear elastic and 3-D hybrid elastic elements in ABAQUS. The 3D mesh of the facet joint was then incorporated into the L3-4 and the L4-5 joint levels of a previously validated L3-5 spine model [Goel, 1995]. Material Properties: Linear isotropic material properties were assigned to the vertebrae, intervertebral disks, FJ (3.5GPa, ν=0.25), including articular cartilage and FJ capsule (6MPa, ν=0.3). All other ligaments were modeled as hypoelastic materials. Boundary and loading conditions: The nodes along the symmetry line on the L5 inferior surface (X-axis for flexion/extension and Y-axis for bending) were fixed in all directions. Displacements of 7, 14, 20 and 28 mm, which correspond to 10, 20, 30 and 40 mm at the T12 vertebra, were applied along the line of symmetry nodes on the top surface of the L3 vertebra to simulate flexion, extension, left and right lateral bending.
RESULTS AND DISCUSSION
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Principal Strain
A 3D FEM mesh of the superior and inferior processes, articular cartilage, and capsule ligament, consisting of 2988 elements and 3882 nodes was constructed (Fig. 1). This geometry was then incorporated into an existing lumbar spine model (Fig. 2).
Extension/ Flexion (Left Capsule L3-4)
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Fig. 3: During extension/flexion, left L3-4 facet joint capsule strain magnitudes computed by the model were similar to those that occurred experimentally.
Fig. 1: FEM of facet joint capsule consisting of bony facets (gray), capsule ligament (black) and cartilage (white).
The 3D FEM model of the facet joint capsule within the lumbar spine provides a foundation to simulate and determine the mechanical states of this joint. Future work includes incorporating the relation between mechanically sensitive neurons and stress states during physiological motions. SUMMARY
Fig. 2: Lumbar spine model (white) with new facet geometry (gray) at the L3-4, and L4-5 joint levels.
The FE model representing the intact lumbar spinal unit was validated using FJ capsule strain data from a prior study in cadaveric lumbar spines (Ianuzzi, 2004). During all motion types, the facet joint capsule strains computed by the model were within the 95% confidence intervals of the capsule strains that occurred experimentally (Fig. 3, extension/flexion shown).
A 3D FEM of the human FJ capsule was created and incorporated into an existing lumbar spine model. It was then used to simulate normal physiological loading conditions on the FJ capsule. Simulated strain results in the FJ was validated and highly correlated with previously published in-situ capsule strains. REFERENCES Cassidy, J.D., et al. (1998) Spine, 23,1860-6. Khalsa, P.S., et al. (1997) J Neurophysiology vol. 77(7) 492-505. Goel, V.K., et al. (1995) Trans.of ASME 117:266-271. Ianuzzi, A., et al. (2004). Spine J, 4(2), 141-152.
ACKNOWLEDGEMENTS Funded by NIH/CCCR and the Whitaker Foundation (RG-99-24).
