Abstract
Osmotic swelling and residual stress are increasingly recognized as important factors in soft tissue biomechanics. Little attention has been given to residual stress in periodontal ligament (PDL) biomechanics despite its rapid growth and remodeling potential. Those tissues that bear compressive loads, e.g., articular cartilage, intervertebral disk, have received much attention related to their capacities for osmotic swelling. To understand residual stress and osmotic swelling in the PDL, it must be asked (1) to what extent, if any, does the PDL exhibit residual stress and osmotic swelling, and (2) if so, whether residual stress and osmotic swelling are mechanically significant to the PDL’s stress/strain behavior under external loading. Here, we incrementally built a series of computer models that were fit to uniaxial loading, osmotic swelling and residual stretch data. The models were validated with in vitro shear tests and in vivo tooth-tipping data. Residual stress and osmotic swelling models were used to analyze tension and compression stress (principal stress) effects in PDL specimens under external loads. Shear-to-failure experiments under osmotic conditions were performed and modeled to determine differences in mechanics and failure of swollen periodontal ligament. Significantly higher failure shear stresses in swollen PDL suggested that osmotic swelling reduced tension and thus had a strengthening effect. The in vivo model’s first and third principal stresses were both higher with residual stress and osmotic swelling, but smooth stress gradients prevailed throughout the three-dimensional PDL anatomy. The addition of PDL stresses from residual stress and osmotic swelling represents a unique concept in dental biomechanics.
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Abbreviations
- Lo :
-
Unloaded PDL gauge length
- Lsitu :
-
in situ PDL length
- L:
-
Swollen PDL length
- Leq :
-
Swollen PDL length at equilibrium
- t:
-
Time
- k:
-
Inverse characteristic swelling time
- γ:
-
Shear strain
- Δz :
-
Z-Direction displacement
- τ:
-
Shear stress
- Fz :
-
Z-Direction load
- h:
-
Specimen thickness
- Cinner :
-
PDL inner circumference
- Couter :
-
PDL outer circumference
- γtransition :
-
Transition shear strain
- G1 :
-
Toe-regime shear modulus
- G2 :
-
Linear-regime shear modulus
- W:
-
Strain energy density
- cp :
-
Bulk-like modulus
- c1 :
-
Shear modulus
- m:
-
Nonlinear Ogden stiffness parameter
- λ:
-
Stretch ratio
- J:
-
Jacobian
- Π:
-
Osmotic pressure
- cF :
-
Fixed charge density
- \(\overline{{\varvec{c}} }\) * :
-
PBS sodium concentration
- φο w :
-
Fluid volume fraction
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Acknowledgements
This research was supported by NIH grant RO1-EB005813 and NIH grant U54CA210190 which supports the development and maintenance of the Provenzano lab multiphoton laser-scanning microscope. We also thank the Visible Heart Lab (VHL) for providing tissue used to carry out this work.
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Specimens were derived from animals killed in an unrelated study that was compliant with the Institutional Animal Care and Use Committee (IACUC) standards. The authors have no conflicts of interest.
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10237_2021_1493_MOESM1_ESM.tif
Transition shear strains in 0X (ddH2O), 1X, and 10X PBS of 0.32, 0.30, and 0.28, respectively. Under shear, the PDL exhibited a larger transition strain (and toe regime) in ddH2O than in 10X PBS (p = 0.2) (TIF 18116 kb)
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Nedrelow, D.S., Damodaran, K.V., Thurston, T.A. et al. Residual stress and osmotic swelling of the periodontal ligament. Biomech Model Mechanobiol 20, 2047–2059 (2021). https://doi.org/10.1007/s10237-021-01493-x
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DOI: https://doi.org/10.1007/s10237-021-01493-x