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Journal of Biomechanical Engineering | Volume 127 | Issue 1 | TECHNICAL PAPERS
TECHNICAL PAPERS: Bone/Orthopedic

Material Properties of the Human Lumbar Facet Joint Capsule

[+] Author and Article Information
Jesse S. Little, Partap S. Khalsa

Department of Biomedical Engineering, Stony Brook University, T18-Rm 030, Stony Brook, NY 11794-8181

J Biomech Eng 127(1), 15-24 (Mar 08, 2005) (10 pages) doi:10.1115/1.1835348 History: Received March 03, 2004; Revised September 03, 2004; Online March 08, 2005
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Copyright © 2005 by ASME
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References

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(A) The load relaxation rate parallel to the collagen fibers was dependent upon strain magnitude during ramp-hold trials. The relaxation rate was determined by normalizing relaxation curves to the peak load, then finding the slope of the log (load)-log (time) plot. The relaxation rate significantly decreased with increasing strain magnitude (p<0.05 for rate at 10%, 20%, and 30% strain vs rate at 40% and 50% strain, repeated measures ANOVA with Tukey). A strain-dependent relaxation function was defined for mean rate-strain data with coefficients B(ε)=0.1110ε−0.0733,R2=0.87. (B) The load relaxation rate perpendicular to the collagen fibers was independent of strain magnitude during ramp-hold trials. A strain-dependent relaxation function was defined for mean rate-strain data with coefficients. B(ε)=−0.04ε−0.06,R2=0.34.
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The phase lag (δ) was not affected by increases in cycling amplitude, but did significantly increase with increases in cyclic frequency from 0.2 Hz to 2 Hz (p<0.001, two-factor ANOVA with Tukey). Error bars are standard deviations. * -Statistically different from 2 Hz at all strain amplitudes (p<0.05).
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(A) The storage modulus significantly increased as the cycling amplitude increased, but was not affected by changes in cyclic frequency (p<0.001 and p=0.43, two-factor ANOVA with Tukey). (B) The loss modulus significantly increased with haversine amplitude, but was unaffected by cycling frequency (p<0.001 and p=0.184, respectively, two-factor ANOVA with Tukey). (C) The complex modulus significantly increased with haversine amplitude, but was unaffected by cycling frequency (p<0.001 and p=0.294, respectively, two-factor ANOVA with Tukey). Error bars are standard deviations. ∧-Statistically significant (p<0.05) from all frequencies at 40% strain;* -Statistically significant (p<0.05) from all frequencies at 50% strain.
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The load relaxation rate parallel to the collagen fibers was dependent upon strain magnitude during dynamic loading trials, but was independent of cyclic frequency (p<0.001 and p=0.744, respectively, two-factor ANOVA with Tukey). The relaxation rate was determined from the load and time values at each peak of twenty cycles, normalized to the maximum load (which was always during the first cycle), then finding the slope of the log (load)-log (time) plot. The relaxation rate significantly increased with increasing strain magnitude (10% vs 30%–50%: p<0.001; 20% vs 40%–50%: p<0.001; 30% vs 50%: p<0.001; 30% vs 40%: p=0.001). Data for all frequencies were combined and a strain-dependent relaxation function was defined for mean rate-strain data with coefficients: B(ε)=−0.1249ε+0.0190,R2=0.92.
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(A) Sketch of two lumbar vertebrae and their left and right facet joints. On the right joint, the posterior aspect of the facet capsule has been drawn. The two dotted lines indicate the locations of the cuts through the laminae of the inferior and superior facet processes of the respective vertebrae to enable producing bone-capsule-bone specimens suitable for testing parallel to the collagen fibers. (B) Side-view drawing of the materials testing apparatus (Tytron 250, MTS, Inc.) fitted with a tissue bath. Actuator (A) is fitted with over-the-bath extension arms (B and C) in series with a force transducer (D). The facet capsule (E) is coupled to the extension arms by custom made pin-clamps (F) that attach to the respective trimmed facet processes of the joint. A CCD camera (G) is mounted above the specimen to facilitate optical measurements of strain. (C) Capsules tested perpendicular to the orientation of the collagen fibers were cut free from the facets and mounted acrylic plates glued to both the superficial and deep surfaces. The acrylic mounting plates attached to the locking pin in the pin clamps.
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Eulerian plane strain was calculated from a sequence of images in the following manner: User defined a ROI in the first frame of the sequence taken at neutral position (A) ROI was subdivided into (m×n) array, typically 4×4, of elements (B). In custom software utilizing the image correlation function in MATLAB v 6.5 (MathWorks, Inc), each element of the ROI is cross-correlated (X-Corr.) with the subsequent frame (C). The element’s new position is the location of the highest normalized correlation coefficient (D). In this manner, each element’s u AND v DISPLACEMENT VECTORS, IN THE x AND y DIRECTIONS RESPECTIVELY, WERE CALCULATED THROUGHOUT THE SEQUENCE (1 TO n) of images (E). Eulerian plane strain was calculated from the displacement vectors.
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(A) Representative force and displacement data for a single displacement controlled ramp-hold trial to 50% ramp strain. The capsule was preloaded (FP) to eliminate slack. The capsule was stretched, and the “viscous” uniaxial engineering stress was calculated as (FV−FP)/A, where A was the measured cross-sectional area. The “elastic” stress ((FE−FP)/A) was calculated as the average from the last 5 s of a 300 s hold at peak displacement. (B) Representative force and displacement data for a single displacement controlled dynamic trial at 0.2 Hz to 50% strain. Specimens were dynamically loaded using twenty haversine cycles to 10%–50% strain in 10% increments at 0.2, 1, and 2 Hz. Uniaxial engineering stress was calculated from the mean load from the peaks of the last ten cycles.
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(A) Parallel to the primary axis of the collagen fibers, the mean viscous stress-strain relationship for all joint levels (L1–2–L5-S1) was exponential in form (regression line shown). The viscous stress was computed as the peak load value that occurred during a ramp-hold trial to a specified uniaxial strain. The peak load always occurred at the end of the ramp up. (B) Parallel to the primary axis of the collagen fibers, the mean elastic stress-strain relationship for all joint levels (L1–2–L5-S1) was exponential in form (regression line shown). The elastic stress was computed from the average load during the last 5 s of a 300 s hold at incremental ramp strains. Error bars are standard deviations.
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Viscous and elastic stress-strain relationships perpendicular to the collagen fibers were linear in form. Error bars are standard deviations. Mean viscous and elastic data were linearly regressed and fit with coefficients σV=2.02ε1−0.1732,R2=0.97 and σE=1.04ε1−0.097,R2=0.99, respectively.
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