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Research Papers

Quantifying Variability in Lumbar L4-L5 Soft Tissue Properties for Use in Finite-Element Analysis

[+] Author and Article Information
Dana J. Coombs

Center for Orthopaedic Biomechanics,
2135 E. Wesley Ave.,
University of Denver,
Denver, CO 80208
e-mail: cd-coombs@msn.com

Paul J. Rullkoetter, Peter J. Laz

Center for Orthopaedic Biomechanics,
2135 E. Wesley Ave.,
University of Denver,
Denver, CO 80208

1Corresponding author.

2Present address: 867 Church Road, Harleysville, PA 19438.

Manuscript received December 15, 2015; final manuscript received July 17, 2016; published online August 11, 2016. Assoc. Editor: Tina Morrison.

J. Verif. Valid. Uncert 1(3), 031007 (Aug 11, 2016) (10 pages) Paper No: VVUQ-15-1057; doi: 10.1115/1.4034322 History: Received December 15, 2015; Revised July 17, 2016

Soft tissue structures of the L4-L5 level of the human lumbar spine are represented in finite-element (FE) models, which are used to evaluate spine biomechanics and implant performance. These models typically use average properties; however, experimental testing reports variation up to 40% in ligament stiffness and even greater variability for annulus fibrosis (AF) properties. Probabilistic approaches enable consideration of the impact of intersubject variability on model outputs. However, there are challenges in directly applying the variability in measured load–displacement response of structures to a finite-element model. Accordingly, the objectives of this study were to perform a comprehensive review of the properties of the L4-L5 structures and to develop a probabilistic representation to characterize variability in the stiffness of spinal ligaments and parameters of a Holzapfel–Gasser–Ogden constitutive material model of the disk. The probabilistic representation was determined based on direct mechanical test data as found in the literature. Monte Carlo simulations were used to determine the uncertainty of the Holzapfel–Gasser–Ogden constitutive model. A single stiffness parameter was defined to characterize each ligament, with the anterior longitudinal ligament (ALL) being the stiffest, while the posterior longitudinal ligament and interspinous ligament (ISL) had the greatest variation. The posterior portion of the annulus fibrosis had the greatest stiffness and greatest variation up to 300% in circumferential loading. The resulting probabilistic representation can be utilized to include intersubject variability in biomechanics evaluations.

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Figures

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Fig. 1

Location and loading direction of annulus fibrosis specimens: (a) Holzapfel et al. [31]—posterior inner and outer and anteriolateral inner and outer single lamellar load, (b) Ebara et al. [30]—anterior outer and posteriolateral inner and outer circumferential load, (c) Wagner and Lotz [29]—anterior circumferential load, (d) Guerin and Elliott [27]—anterior circumferential load, (e) Fujita et al. [26]—anterior and posteriolateral radial load, and (f) O'Connell et al. [28]—anterior outer circumferential load, radial load, and axial load

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Fig. 2

Representative force–displacement curves based on combined literature data, ALL, PLL, LFL, and SSL

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Fig. 3

Force–displacement curves of AF specimens based on combined literature data, circumferential loading for anterior and posterior and lateral quadrants, radial loading for anterior and posterior and lateral quadrants, axial loading for anterior quadrant, and single lamellar loading for anterior and lateral and posterior quadrants

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Fig. 4

Monte Carlo results compared to combined literature curves—anterior quadrant

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Fig. 5

Monte Carlo results compared to combined literature curves—posterior quadrant

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Fig. 6

Monte Carlo results compared to combined literature curves—lateral quadrant

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