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Refinement of Elastic, Poroelastic, and Osmotic Tissue Properties of Intervertebral Disks to Analyze Behavior in Compression

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Abstract

Intervertebral disks support compressive forces because of their elastic stiffness as well as the fluid pressures resulting from poroelasticity and the osmotic (swelling) effects. Analytical methods can quantify the relative contributions, but only if correct material properties are used. To identify appropriate tissue properties, an experimental study and finite element analytical simulation of poroelastic and osmotic behavior of intervertebral disks were combined to refine published values of disk and endplate properties to optimize model fit to experimental data. Experimentally, nine human intervertebral disks with adjacent hemi-vertebrae were immersed sequentially in saline baths having concentrations of 0.015, 0.15, and 1.5 M and the loss of compressive force at constant height (force relaxation) was recorded over several hours after equilibration to a 300-N compressive force. Amplitude and time constant terms in exponential force–time curve-fits for experimental and finite element analytical simulations were compared. These experiments and finite element analyses provided data dependent on poroelastic and osmotic properties of the disk tissues. The sensitivities of the model to alterations in tissue material properties were used to obtain refined values of five key material parameters. The relaxation of the force in the three bath concentrations was exponential in form, expressed as mean compressive force loss of 48.7, 55.0, and 140 N, respectively, with time constants of 1.73, 2.78, and 3.40 h. This behavior was analytically well represented by a model having poroelastic and osmotic tissue properties with published tissue properties adjusted by multiplying factors between 0.55 and 2.6. Force relaxation and time constants from the analytical simulations were most sensitive to values of fixed charge density and endplate porosity.

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Acknowledgments

This study was funded by NIH Grant R01 AR 049370. Lumbar spines were provided by the National Disease Research Interchange (NDRI). Jacob Lubinski assisted with a preliminary study. Richard Stanley provided technical support for experimental work.

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Authors and Affiliations

  1. Department of Orthopaedics and Rehabilitation, University of Vermont, Stafford Hall, Burlington, VT, 05405-0084, USA

    Ian A. F. Stokes & Mack G. Gardner-Morse

  2. College of Engineering, University of Vermont, Burlington, VT, USA

    Jeffrey P. Laible & James C. Iatridis

  3. School of Computer Science, Engineering and Mathematics, Flinders University, Adelaide, SA, Australia

    John J. Costi

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  1. Ian A. F. Stokes
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  2. Jeffrey P. Laible
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  3. Mack G. Gardner-Morse
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Correspondence to Ian A. F. Stokes.

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Associate Editor Peter E. McHugh oversaw the review of this article.

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Stokes, I.A.F., Laible, J.P., Gardner-Morse, M.G. et al. Refinement of Elastic, Poroelastic, and Osmotic Tissue Properties of Intervertebral Disks to Analyze Behavior in Compression. Ann Biomed Eng 39, 122–131 (2011). https://doi.org/10.1007/s10439-010-0140-1

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