Calculation of Natural Frequencies of Teeth Supported with the Periodontal Ligament

Finite element investigation of human maxillary incisor under traumatic loading: Static vs dynamic analysis

BACKGROUND AND OBJECTIVE

Traumatic loading is the main form of injury sustained in dental injuries. In spite of the prevalence of dental trauma, little information is available on traumatic dental damage and the evaluation of tooth behavior under traumatic loading. Due to the short period of traumatic loading, at first sight, a dynamic analysis needs to be performed to investigate the dental trauma. However, it was hypothesized that dental traumatic loading could be regarded as quasi-static loading. Thus, the aim of the present study was to examine this hypothesis.

METHODS

Static and dynamic analyses of the human maxillary incisor were carried out under traumatic loading using a 3D finite element method. Also, modal analysis of the tooth model was performed in order to evaluate the assumption of the dental traumatic loading as a quasi-static one.

RESULTS

It was revealed that the static analysis of dental trauma is preferred to the dynamic analysis when investigating dental trauma, mainly due to its lower computational cost. In fact, it was shown that including the inertia of the tooth structure does not influence the results of the dental trauma simulation. Furthermore, according to the modal analysis of the tooth structure, it was found that the mechanical properties and geometry of the periodontal ligament play significant roles in the classification of dental traumatic loading as a quasi-static one, in addition to the time duration of the applied load.

CONCLUSIONS

This paper provides important biomechanical insights into the classification of dental loading as quasi-static, transient or impact loading in future dental studies.

Damping ratio analysis of tooth stability under various simulated degrees of vertical alveolar bone loss and different root types

Background

The purpose of this study was to evaluate the feasibility of using damping ratio (DR) analysis combined with resonance frequency (RF) and periotest (PTV) analyses to provide additional information about natural tooth stability under various simulated degrees of alveolar vertical bone loss and various root types.

Methods

Three experimental tooth models, including upper central incisor, upper first premolar, and upper first molar were fabricated using Ti6Al4V alloy. In the tooth models, the periodontal ligament and alveolar bone were simulated using a soft lining material and gypsum, respectively. Various degrees of vertical bone loss were simulated by decreasing the surrounding bone level apically from the cementoenamel junction in 2-mm steps incrementally downward for 10 mm. A commercially available RF analyzer was used to measure the RF and DR of impulse-forced vibrations on the tooth models.

Results

The results showed that DRs increased as alveolar vertical bone height decreased and had high coefficients of determination in the linear regression analysis. The damping ratio of the central incisor model without a simulated periodontal ligament were 11.95 ± 1.92 and 27.50 ± 0.67% respectively when their bone levels were set at 2 and 10 mm apically from the cementoenamel junction. These values significantly changed to 28.85 ± 2.54% (p = 0.000) and 51.25 ± 4.78% (p = 0.003) when the tooth model was covered with simulated periodontal ligament. Moreover, teeth with different root types showed different DR and RF patterns. Teeth with multiple roots had lower DRs than teeth with single roots.

Conclusion

Damping ratio analysis combined with PTV and RF analysis provides more useful information on the assessment of changes in vertical alveolar bone loss than PTV or RF analysis alone.

Use of a laser displacement sensor with a non-contact electromagnetic vibration device for assessment of simulated periodontal tissue conditions

A non-contact electromagnetic vibration device (NEVD) was previously developed to monitor the condition of periodontal tissues by assessing mechanical parameters. This system requires placement of an accelerometer on the target tooth, to detect vibration. Using experimental tooth models, we evaluated the performance of an NEVD system with a laser displacement sensor (LDS), which does not need an accelerometer. Simulated teeth (polyacetal rods) were submerged at various depths in simulated bone (polyurethane or polyurethane foam) containing simulated periodontal ligament (tissue conditioner). Then, mechanical parameters (resonant frequency, elastic modulus, and viscosity coefficient) were assessed using the NEVD with the following detection methods: Group 1, measurement with an accelerometer; Group 2, measurement with an LDS in the presence of the accelerometer; and Group 3, measurement with an LDS in the absence of the accelerometer. Statistical analyses were performed using nonparametric methods (n = 5) (P < 0.05). The three mechanical parameters significantly increased with increasing depth. In addition, the mechanical parameters significantly differed between the polyurethane and polyurethane foam models. Although Groups 1 and 2 did not significantly differ, most all mechanical parameters in Group 3 were significantly larger and more distinguishable than those in Groups 1 and 2. The LDS was more accurate in measuring mechanical parameters and better able to differentiate periodontal tissue conditions. (J Oral Sci 58, 93-99, 2016).

Assessing qualitative changes in simulated periodontal ligament and alveolar bone using a non-contact electromagnetic vibration device

The objective of this study is to investigate the ability of a non-contact electromagnetic vibration device to assess a simulated periodontal ligament and alveolar bone conditions in experimental tooth models by applying mechanical parameters (resonant frequency, elastic modulus, and coefficient of viscosity). The non-contact electromagnetic vibration device was made up of three components: vibrator, detector, and analyzer. The experimental tooth model consisted of a cylindrical rod made of polyacetal, a tissue conditioner for soft lining material, and urethane or urethane foam to simulate the tooth, periodontal ligament, and alveolar bone, respectively. The tissue conditioner was prepared by mixing various volumes of liquid with powder. Periotest values (PTVs) were also measured under the same conditions as those of the non-contact electromagnetic vibration device. All of the mechanical parameters derived from the non-contact electromagnetic vibration device significantly decreased as the proportion of liquid increased. Values for the three parameters of the urethane models were significantly larger than those of the urethane foam models. In contrast, PTVs increased significantly as the proportion of liquid increased; however, no significant difference was observed between the urethane and urethane foam models. The non-contact electromagnetic vibration device may be capable of evaluating not only periodontal ligament conditions but also bone quality. Mechanical parameters may be useful for assessing qualitative changes in the periodontal ligament and alveolar bone.

Characteristics of the tooth in the initial movement: the influence of the restraint site to the periodontal ligament and the alveolar bone

It is critical to clarify orthodontic load transfer mechanism from tooth to alveolar bone, and to determine the influence of applied orthodontic force on tooth behaviour. In this study, two dimensional (2-D) finite element (FE) models were constructed to simulate to mechanical behaviour observed during the initial movement of periodontal ligament (PDL) deformation, and to evaluate the effects of the presence of PDL and various restraint sites on tooth behaviour.

A 2-D solid FE model of the tooth-PDL-alveolar bone system was constructed and investigated into stress distribution pattern and displacement. The first analysis was carried out with combinations of FE model with and without PDL. The second analysis was compared with three different sites restraint of alveolar bone.

By incorporating PDL in FE models, excessively large stress values and deformation generated in a tooth and alveolar bone were relieved. Since restraint conditions did not affect a tooth and PDL, but had an effect on alveolar bone, orthodontic force necessary for tooth displacement was transmitted correctly. The results of this study revealed that inclusion of PDL in FE models is indispensable to transmit orthodontic force appropriately when investigating tooth behaviour for orthodontic treatment. Restrained sites affected stress distribution in alveolar bone.

Detection of the furcation involvement of a multi-rooted molar using natural frequency analysis: a numerical approach

The aim of this study was to evaluate the potential for using the natural frequency (NF) as a parameter to detect vertical bone loss at the furcation of human molars as well as to assess the role that the surrounding bone plays in maintaining molar stability. A three-dimensional finite element model of the human maxillary molar was built. The NF values of the molar modal were calculated with one-sided, two-sided, and three-sided vertical bone loss. It was found that the change in the NF was less than 25 per cent in molars with a one-sided defect when the bone level varied by 10 mm from the cementoenamel junction. However, when a three-sided bony defect was simulated, the change in the NF ranged from 40 to 60 per cent. In addition, it was found that bone loss that had reached the furcation entrance (4 mm) resulted in a sharp change in the NF value. Furthermore, it was found that bone loss involving the mesial and distal surfaces resulted in a larger decrease in the NF value compared with bone loss involving the buccal and palatal surfaces. These results demonstrated that the bone surrounding the mesial and distal sides plays a more important role in maintaining molar stability than does the bone surrounding the buccal and palatal sides.

Natural frequency analysis of tooth stability under various simulated types and degrees of alveolar vertical bone loss

The aim of this study was to test natural teeth stability under various simulated types and degrees of alveolar vertical bone loss, as well as to assess the role that the surrounding bone played for maintaining tooth stability. A three-dimensional finite element model of the human maxillary central incisor with surrounding tissue, including periodontal ligament, enamel, dentin, pulp, and alveolar bone, was established. One side and multiple vertical bone loss were simulated by means of decreasing the surrounding bone level apically from the cemento-enamel junction in 1 mm steps incrementally downward for 10 mm. Natural frequency values of the incisor model with various types and degrees of bone loss were then calculated. The results showed that, with one-sided bone resorption, the model with labial bone loss had the lowest natural frequency decreasing rates (8.2 per cent). On the other hand, in cases of multiple bone loss, vertical bone resorption at the mesial and distal sides had more negative effects on tooth stability compared to vertical bone losses on facial and lingual sides. These findings suggest that the natural frequency method may be a useful, auxiliary clinical tool for diagnosis of vertical periodontal diseases.