Experimental and numerical investigations on the fluid contribution to the tensile-compressive mechanical behavior of the bovine periodontal ligament

Orthodontic treatments are all based on the experimental evidence that teeth can be forced to move in the dental arch by means of applied mechanical forces. Since it allows for prediction of dental mobility, the mechanical characterization of the tissues involved in this process is of paramount importance. In fact, as technologies and strategies in treating pathological situations become increasingly more advanced, better knowledge of dental mobility allows for the optimization of these tools and thus, minimization of the costs of the interventions. Among the tissues that made up the periodontium, the functional unit comprising the bone of the jaw, the periodontal ligament (PDL, a soft connective tissue which binds the teeth to the jaw) and the cementum of the teeth, the PDL is commonly considered to play the major role in dental movements. To obtain insights on its mechanical behavior, specimens of PDL, containing also bone and cementum parts, are extracted and tested with adequate loading profiles. However, due to morphology and size, the excision of such specimens is often delicate and represents one of the main challenge in the experimental characterization of the PDL. Furthermore, for the investigation to be pertinent, it is necessary to test the in-vitro specimens in an environment recreating at best physiological conditions. In this study, the characterization of the mechanical behavior of the periodontium was based on histo-morphological investigation, on mechanical testing of excised specimens containing the three tissues and on numerical modeling. Micro-structural aspects of the periodontium were assessed by morphometric analysis of histological sections. Since it plays a central role in the tooth supporting mechanism, the vascular system was characterized by assessing densities and sizes of blood vessels present in the PDL. Also, the roughness of the interfaces between PDL and bone and between PDL and cementum was quantified via their fractal dimensions. To approach as much as possible an in-vivo–like situation for the mechanical testing of in-vitro specimens, physiological conditions were reconstructed at best in a closed environment created in a custom-made pressure chamber filled with physiological solution. Cylindrical specimens, with diameter of approximately 6mm, were obtained from mandibular first molars of freshly slaughtered bovines. A thorough experimental determination of the contribution of the fluid phase, comprised in the periodontium, to the overall response of the tissues was carried out by imposing sinusoidal tensile-compressive loading profiles (simulating mastication) to specimens subjected to different environmental conditions. A numerical model was then developed to reproduce and analyze the observed phenomena. Eventually, the mechanical response to multiaxial loading was investigated by simultaneously applying axial displacement and lateral hydrostatic confinement to specimens which were wrapped in a thin rubbery membrane. The morphometrical investigation enhanced the high heterogeneity and porosity of the tissues involved. In fact, no general pattern could be established for the structural description of the periodontium. Moreover, the presence of large blood vessels in the PDL suggested that the vascular system should somehow be taken into consideration when describing the mechanical behavior of this ligament. The mechanical testing proved the response of the bone-PDL-cementum functional system to be characterized by the interactions between a porous solid skeleton, forming the structural matrix of the tissues, and a fluid content flowing through it during cyclic tensile-compressive loading profiles. In fact, the solid matrix alone (i.e., emptied of its fluid content) clearly showed an hyperelastic behavior (both for tensile and compressive loading), so that the highly time-dependent hysteric behavior shown during compressive loadings of fully fluid-saturated specimens was mainly attributed to the fluid phase. The numerical model, based on a multiphase mixture formulation, allowing thus for the description of the interactions between a porous compressible hyperelastic matrix (described by an Ogden's strain energy potential) and the fluid filling its pores, well reproduced the mechanical response of the periodontium subjected to cyclic tensile-compressive loadings. The model enhanced also the significant exchange of fluid taking place between the PDL and the bone part of the specimens, proving thus the importance of considering the fluid phase in the mechanical description of the periodontium. Loading rate dependences of the compressive response were also partially captured by such a model. The experimental response to a multiaxial loading showed eventually the dependence of the axial stress on the joined action of level of lateral confinement (hydrostatic pressure) and extent of fluid saturation of the solid matrix.

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