Influence of different modeling strategies for the periodontal ligament on finite element simulation results.

INTRODUCTION: The finite element method is a promising tool to investigate the material properties and the structural response of the periodontal ligament (PDL). To obtain realistic and reproducible results during finite element simulations of the PDL, suitable bio-fidelic finite element meshes of the geometry are essential. METHODS: In this study, 4 independent coworkers generated altogether 17 volume meshes (3-dimensional) based on the same high-resolution computed-tomography image data set of a tooth obtained in vivo to compare the influence of the different model generation techniques on the predicted response to loading for low orthodontic forces. RESULTS: It was shown that the thickness of the PDL has a significant effect on initial tooth mobility but only a remarkably moderate effect on the observed stress distribution in the PDL. Both the tooth and the bone can be considered effectively rigid when exploring the response of the PDL under low loads. The effect of geometric nonlinearities could be neglected for the applied force system. CONCLUSIONS: Most importantly, this study highlights the sensitivity of the finite element simulation results for accurate geometric reconstruction of the PDL.

A visco-hyperelastic-damage constitutive model for the analysis of the biomechanical response of the periodontal ligament.

The periodontal ligament (PDL), as other soft biological tissues, shows a strongly non-linear and time-dependent mechanical response and can undergo large strains under physiological loads. Therefore, the characterization of the mechanical behavior of soft tissues entails the definition of constitutive models capable of accounting for geometric and material non-linearity. The microstructural arrangement determines specific anisotropic properties. A hyperelastic anisotropic formulation is adopted as the basis for the development of constitutive models for the PDL and properly arranged for investigating the viscous and damage phenomena as well to interpret significant aspects pertaining to ordinary and degenerative conditions. Visco-hyperelastic models are used to analyze the time-dependent mechanical response, while elasto-damage models account for the stiffness and strength decrease that can develop under significant loading or degenerative conditions. Experimental testing points out that damage response is affected by the strain rate associated with loading, showing a decrease in the damage limits as the strain rate increases. These phenomena can be investigated by means of a model capable of accounting for damage phenomena in relation to viscous effects. The visco-hyperelastic-damage model developed is defined on the basis of a Helmholtz free energy function depending on the strain-damage history. In particular, a specific damage criterion is formulated in order to evaluate the influence of the strain rate on damage. The model can be implemented in a general purpose finite element code. The accuracy of the formulation is evaluated by using results of experimental tests performed on animal model, accounting for different strain rates and for strain states capable of inducing damage phenomena. The comparison shows a good agreement between numerical results and experimental data.

Articular cartilage thickness of the humeral head: an anatomic study.

This study determined the thickness of normal humeral head articular cartilage by anatomic cross section using computer-aided image analysis software. Sixteen adult cadaveric humeral heads were analyzed. Our findings reveal that the thickness of humeral articular cartilage is substantially thinner than articular cartilage found in the knee. The cartilage is thickest in the central portion of the head and becomes progressively thinner towards the periphery. Surgical techniques used to treat pathology in the glenohumeral joint, specifically thermal energy or mechanical debridement, may have deleterious effects on the relatively thin humeral articular cartilage.

Development of a model for the simulation of orthodontic load on lower first premolars using the finite element method.

AIM: This study was undertaken to calculate the stress in the tooth, surrounding periodontal ligament, and in the alveolar bone when a lower first premolar is subjected to intrusion or torque movement using a constant moment. Root resorptions occur even when very low forces and moments are used in orthodontic therapy. It is therefore of great interest to determine and measure the stress that occurs under particular treatment conditions in the periodontal ligament. MATERIAL AND METHODS: In this study, three finite element calculations were carried out with a realistic 3D model developed by CT data that consisted of a lower premolar, the surrounding periodontal ligament and alveolar bone. In close reference to the in-vivo experiments carried out by Faltin et al. in São Paulo, Brazil, our model was subjected to an intrusive force on the premolar of 0.5 N and a lingual root torque of 3 Nmm. RESULTS: The three main stress directions and hydrostatic stress were quantified in all the surrounding tissues, revealing that the hydrostatic stress profile in the periodontal ligament correlated closely with resorption findings in Faltin et al.'s patients. Resorption occurred in the experimental study in Brazil when the hydrostatic stress exceeded capillary blood pressure in the periodontal ligament. CONCLUSION: We maintain that hydrostatic stress represents a suitable indicator for potential root resorptions caused by higher forces and moments, making it a helpful tool in the development of new orthodontic appliances. We must of course mention that there are many factors other than forces that are responsible for resorptions. But at the moment, only the force can be influenced by the orthodontist.

Determination of the mechanical properties of the periodontal ligament in a uniaxial tensional experiment.

BACKGROUND: The periodontal ligament is a soft connective tissue which joins the tooth root to the alveolus and thus provides for anchorage of the tooth in the alveolar bone. Due to its composition of elastic and viscous components, this tissue displays viscoelastic material properties. In a previous study [4], in vitro experiments revealed typical viscoelastic material properties of the periodontal ligament in samples from pig mandibles. These properties included force relaxation, hysteresis, and dependence on loading history. MATERIAL AND METHODS: Based on those experiments, a dependence of tooth displacement on loading velocity was registered in the present study and the stress-strain behavior of the periodontal ligament was examined until the tissue ruptured. For this purpose, segments of the periodontal ligament taken from anterior teeth from the pig mandible were tested in a purpose-developed clamping fixture in a uniaxial tensional experiment. RESULT: It was found that the initial phase of the stress-strain curve in particular was dependent on loading velocity and that the shape of the hysteresis curve was subject to a variation in loading velocity. The stress-strain behavior of the periodontal ligament was characterized, divided into several phases, and the elastic modulus of the initial and the linear phase of the curve was determined at different loading velocities. CONCLUSION: Knowledge of the material properties of the periodontal ligament is fundamental to an understanding of orthodontic tooth movement and thus to selection of an optimal force system for orthodontic treatment.

Experiments to determine the material properties of the periodontal ligament.

PHYSIOLOGY OF THE PERIODONTAL LIGAMENT: The periodontal ligament is a soft biological tissue that controls tooth movement under physiological loads by joining tooth and alveolar bone. Its various components differ in their material properties. Their spatial configuration and interaction are responsible for the reaction of the tissue in a loading situation. Due to the combination of fluid and elastic elements the periodontal ligament shows a viscoelastic behavior typical of soft biological tissues. It is characterized by non-linearity and time dependency, and additionally depends on loading history. BEHAVIOR UNDER EXTERNAL LOADS: In orthodontics, external loads are applied to the tooth crowns using orthodontic appliances. Since stresses and strains in the periodontal tissue, caused by the initial tooth movement, stimulate alveolar bone remodeling and thus orthodontic tooth movement, knowledge of the material properties of the periodontal ligament is fundamental to selection of an optimal force system for targeted tooth movement. OWN EXPERIMENTS: For this reason, typical properties of the viscoelastic material behavior of the periodontal ligament were tested experimentally in the present study, using samples from pig mandibles. This enabled the properties of force relaxation and hysteresis of this tissue, both of which depend on loading history, to be verified. CONCLUSION: The experimental results allow characterization of the tissue and thus contribute to an understanding of the biomechanics of tooth displacement under externally applied loads.