Image-based multiscale mechanical modeling shows the importance of structural heterogeneity in the human lumbar facet capsular ligament

Vahhab Zarei, Chao J. Liu, Amy A. Claeson, Taner Akkin, Victor H. Barocas

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16 Scopus citations


The lumbar facet capsular ligament (FCL) primarily consists of aligned type I collagen fibers that are mainly oriented across the joint. The aim of this study was to characterize and incorporate in-plane local fiber structure into a multiscale finite element model to predict the mechanical response of the FCL during in vitro mechanical tests, accounting for the heterogeneity in different scales. Characterization was accomplished by using entire-domain polarization-sensitive optical coherence tomography to measure the fiber structure of cadaveric lumbar FCLs (n= 6). Our imaging results showed that fibers in the lumbar FCL have a highly heterogeneous distribution and are neither isotropic nor completely aligned. The averaged fiber orientation was + 9. 3 (+ 29. 9 in the inferior region and + 5. 1 in the middle and superior regions), with respect to lateral–medial direction (superior–medial to inferior–lateral). These imaging data were used to construct heterogeneous structural models, which were then used to predict experimental gross force–strain behavior and the strain distribution during equibiaxial and strip biaxial tests. For equibiaxial loading, the structural model fit the experimental data well but underestimated the lateral–medial forces by ∼ 16% on average. We also observed pronounced heterogeneity in the strain field, with stretch ratios for different elements along the lateral–medial axis of sample typically ranging from about 0.95 to 1.25 during a 12% strip biaxial stretch in the lateral–medial direction. This work highlights the multiscale structural and mechanical heterogeneity of the lumbar FCL, which is significant both in terms of injury prediction and microstructural constituents’ (e.g., neurons) behavior.

Original languageEnglish (US)
Pages (from-to)1425-1438
Number of pages14
JournalBiomechanics and Modeling in Mechanobiology
Issue number4
StatePublished - Aug 1 2017

Bibliographical note

Funding Information:
This work was supported by the National Institutes of Health (U01EB016638). We acknowledge the Minnesota Supercomputing Institute (MSI) at the University of Minnesota for providing resources used for our computational methods. SEM images were taken at the Characterization Facility at the University of Minnesota, which receives partial support from NSF (MRSEC program).

Publisher Copyright:
© 2017, Springer-Verlag Berlin Heidelberg.


  • Collagen fibers
  • Facet capsular ligament
  • Fiber imaging
  • Fiber structure
  • Multiscale modeling
  • Spine
  • Structural heterogeneity


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