The non-linear stress-strain behavior of the human periodontal ligament and its effect on finite element models of dental structures

Abstract

Fresh and fixed mandibular block sections were acquired from cadavers. The block sections were then sectioned to create small (1 x 1 x 4mm) uniaxial tests specimens containing tooth, PDL, and bone. Specimens were then tested in a mechanical test system to acquire load-displacement and stress-strain data. Samples were also prepared for scanning electron microscope (SEM) evaluation and PDL space variability measurements. Stress-strain data was then incorporated into FE models for analysis of model effects. Stress-strain curves of fixed and unfixed tissue indicate the PDL is highly non-linear and inelastic in its behavior. The curves are described by power functions, exhibit greater hysteresis in compression than tension, and the zero stress-strain state is shifted towards the compressive side of the curve. SEM evaluations show the PDL to be very complex three-dimensionally, with a highly branching and interweaving fiber bundle structure. The PDL space was found to vary widely in its thickness, with standard deviations as high as 53% of the mean value for a given tooth level. FE models with non-linear PDL data show vastly different stress distribution patterns when compared to linear PDL models. Stress-strain curves, as well as FE models that incorporate the measured materials behavior, suggest that the primary load carrying ability of the PDL is in compression. The non-linear nature of the PDL also results in higher compressive stresses being generated, for both lateral and axial loading, than a comparable linear model. SEM evaluation suggests that PDL fibers may function in compression by layering on top of each other. Using non-linear analysis of the PDL, the location of the center of resistance (CR) of a tooth was found to vary horizontally and vertically depending on the applied loading and PDL geometry. The shifting of CR away from the midline indicates that orthodontic tipping about a root apex may actually be impossible. The PDL was also found to be subjected to compression over the entire PDL when intrusive loading was applied to the tooth. This may explain how occlusal trauma can widen the entire PDL.