A finite element study to determine the occurrence of abfraction and displacement due to various occlusal forces and with different alveolar bone height.

BACKGROUND: Noncarious cervical lesions (NCCLs) are rarely described in the periodontal literature, perhaps because no direct link between NCCLs and periodontal lesions has been demonstrated. AIM: The aim of this study is to determine the stress and displacement produced in the tooth at different bone levels under different occlusal load using finite element model (FEM) study.
MATERIALS AND METHODS: Four FEMs of maxillary incisor were designed consisting of the tooth, pulp, periodontal ligament, and alveolar bone at the various level of bone height (25%, 50%, and 75%). Different occlusal load (5 kg, 15 kg, 24 kg, and 29 kg) at an angle of 50° to the long axis of the tooth was applied on the palatal surface at the level of middle third of the crown. All the models were assumed to be isotropic, linear and elastic, and the analysis was performed on a Pentium IV processor computer using the ANSYS software.
RESULTS: The maximum stress in the tooth was seen in the cervical region and to a greater extent at the apex for all models. The maximum tooth displacement for all the occlusal loads applied in this study was at the incisal edge with the minimum tooth displacement at the cervical third of the root which shifted apically with the reduction of alveolar bone support.
CONCLUSION: The cumulative effect of increased stress and displacement at the cervical region of the tooth would result in abfraction as the age advances along with other wasting diseases.

INTRODUCTION

oncarious cervical lesions (NCCLs) are rarely described in the periodontal literature, perhaps because no direct link between NCCLs and periodontal lesions has been demonstrated. Traditionally NCCL, also called abfraction, was thought to be produced by toothbrushing.[1] Various explanations include the effect of hard bristles, soft bristles, and toothpaste.[2] Other etiologic factors have been brought forward such as consumption of acid-containing foods or regurgitations.[3] Miller and Penaud reviewed these putative factors and concluded that none were very convincing.[4] Toubol had suggested a year before that occlusal factors might be implied.[5] That same year Lee and Eagle published a paper affirming that tooth flexure caused by occlusal loading could produce NCCL, which they termed abfractions. They demonstrated that when a tooth receives an occlusal force, a large quantity of stress is concentrated in the cervical area.[6] Should a slightly oblique force be applied, a fulcrum is created near the cementoenamel junction. This in turn will cause a release of the mineral crystals contained in the enamel and then in the dentine.[7] Orientation of the forces and the position of the supporting alveolar bone determine the form and situation of the abfractions.[8] Although this new theory eliminates objections concerning the former hypothesis, many advocates of the toothbrushing explanation remain.[12] The subject could seem principally academic if it were not for the fact that NCCL, or abfractions, can be found on teeth presenting periodontitis. In such cases, informing patients that their brushing is “excessive” could be counterproductive, hindering periodontal treatment instead of enhancing it. However, data supporting this as a discrete clinical entity is not yet available.[9] Presently, the term “noncarious cervical lesion” has been advocated because of a multifactorial event.[10] The theory of abfraction is based on computer-generated models and investigations generally with data consisting of case reports, case series, and case studies.[11121314] The lacunae of studies conducted are that they have taken forces which are not relevant to normal function, hypofunction, and hyperfunction. In this study, four different forces 5 kg (hypofunction), 15 kg (normal), 24 kg, and 29 kg (hyperfunction) were considered with four different bone heights. The medline search with keywords such as hyperfunction, hypofunction, and different bone height showed only limited studies. The purpose of this study was to determine the stress and displacement in the cervical region of a maxillary central incisor considering different occlusal forces from normal to abnormal that is normofunction, hypofunction, hyperfunction, and to correlate it with different bone heights depicting periodontal bone loss at different points on the tooth.

MATERIALS AND METHODS

A three-dimensional finite element model (FEM) of maxillary central incisor was designed comprising of the tooth, pulp, periodontal ligament, and alveolar bone. The cementum was considered as a too thin layer to be adequately modeled in finite element simulation.[15] The analytical model was built by scanning the pictures of the maxillary central incisor in the Wheeler's textbook. Cross-section measurements of the tooth at 2 mm distances were determined using Vernier calipers and variable periodontal width was taken from the data of Coolidge.[16] The completed model consisted of 47229 elements and 68337 nodes. The alveolar bone height was changed in increments representing 25%, 50%, and 75% loss of alveolar bone. The Poisson's ratio and young's modulus for different materials used were assigned from the data available in the literature [Table 1].[17] All the nodes at the base of the model were fixed so as not to move when subjected to force systems. The boundary condition is an important factor in the FEM reflecting the manner of movements occurring at the nodes and their relationship. Different occlusal loads of 5 kg, 15 kg, 24 kg, and 29 kg were applied in a palate – labial direction at an angle of 50° to the long axis of the tooth at the level of the middle third of the crown at varying bone height (normal, 25%, 50%, and 75% bone loss). The stresses were analyzed at the sampling points positioned on the tooth [Figures 1a and b, 2a and b, 3a and b, and 4a and b].

Table 1

Material parameters used in finite elements model

Figure 1

(a) Stress and displacement at various anatomical points considered in a maxillary central incisor with normal bone level. (b) The finite element model of the maxillary central incisor with normal bone level (stress and displacement at cervical third of the crown [DT, DD], stress and displacement at cervical third of the root [ET, ED], stress, and displacement at junction of cervical and middle third of the root [FT, F])

Figure 2

(a) Stress and displacement at various anatomical points considered in a maxillary central incisor with 25% bone level. (b) The finite element model of the maxillary central incisor with 25% bone level

Figure 3

(a) Stress and displacement at various anatomical points considered in a maxillary central incisor with 50% bone level. (b) The finite element model of the maxillary central incisor with 50% bone level

Figure 4

(a) Stress and displacement at various anatomical points considered in a maxillary central incisor with 75% bone level. (b) The finite element model of the maxillary central incisor with 75% bone level

RESULTS

Areas of high compressive stress were seen in the tooth, near the alveolar crest, and to a lesser extent in the apical one-half of the root for all the loads applied in the study. Reduction of the alveolar bone height had little effect on the degree of tooth and the supporting tissue stresses when 25% of bone support was lost, however, the stresses increased dramatically when 50% and 75% of bone support was lost and also shifted apically on the tooth coinciding with the alveolar crest for that amount of bone loss. Compressive stresses were three times more in a normal occlusal load of 15 kg than that representing hypofunction (5 kg). However, the stresses increased to approximately 1.5 to 2 times that of the normal when excessive loads of 24 or 29 kg were applied. An increase of the tooth displacements was pronounced at the cervical third with the minimum displacement shifting apically to the junction of the cervical and middle third of the 25% and 50% loss of bone support and further shifting apically to the junction of the middle and apical thirds of the 75% alveolar bone loss [Tables 2–4]

Table 2

Stress (Mpa) and displacement (mm) in the cervical region of tooth with decreasing bone height and increasing forces

Table 4

Displacement at reference points on tooth with increasing bone loss and increasing force

At point DT (cervical region of tooth) the stresses were found to increase to about 64–67% with varying bone level (25%, 50%, 75%) and varying forces applied (5 kg, 24 kg, 29 kg) when compared to stresses seen with normal bone height [Table 3].

Table 3

Various stress levels at reference points with increasing bone loss and increasing force

At point ET (junction of cervical and middle third) there is an about 83–85% increase in stresses with 25% bone loss with varying forces (5 kg, 24 kg, 29 kg) and 275–277% increase in stress with 50% and 75% bone loss [Table 3].

At point FT (junction of middle and apical third) there was about 89–92% increase in stresses with 25% bone loss which increased to 504–512% with 50% bone loss to 1741–1772% with 75% bone loss.

The above data reveals that there is an apical shift in the location of the highest stress concentration with decreasing periodontal support [Table 3].

DISCUSSION

Any type of stress (tensile, compressive, or shearing), when sufficient in magnitude, can inflict damage on the tooth structure. Tooth flexure has been described as a lateral or axial bending under occlusal loading, tooth flexure produces tensile, or compressive strains causing a disruption of the bonds between hydroxyapatite crystals leading to the formation of cracks in the enamel, and the eventual loss of enamel and underlying dentin.[18]

In the present study, four isotopic, linear, and elastic FEMs of maxillary central incisor were designed at four levels of bone height (25%, 50%, and 75% of bone loss). Occlusal load of 5 Kg, 15 Kg, 24 Kg, and 29 Kg were applied at an angulation of 50° to the palatal surface at middle third of the crown. The finite element computer program used for this study was ANSYS 8.1 (Marketed by ANSYS Inc., USA) and analysis was performed on a Pentium IV microprocessor.

In a similar study conducted by (Reddy et al. 2012) using a three-dimensional FEM of a maxillary central incisor a occlusal load of 24 kg (hyperfunctional force) at an angle of 50° to the long axis of the tooth at various bone height (25%, 50%, and 75%) was applied. The result was analyzed using a Pentium 1V computer using the NISA II Display III software which showed that maximum stress in the tooth is seen in the cervical region as observed in the present study. However in the above study hypofunction and normofunction have not been tested using the normal occlusal load.[18]

The results of this study were similar to the findings of Allahyar Geramy who conducted a study using a 3D FEM model of maxillary central incisor applying loads of 1.5 N on the palatal side of the crown in five stages, with varying directions progressing from tipping to intrusion. Two separate approaches (displacement and stress) were considered which showed the maximum deflections were in the cementoenamel junction area and the same area undergo the maximum of von Mises stress and stress intensity. The result of this study was in complete agreement with our study.[19]

In a study conducted by Brezeanu et al. a two-dimensional mathematical finite elements analysis model was generated using intact normal extracted human mandibular canine oblique nodal force of 40° and varying magnitude (40 N, 60 N, 120 N, 160 N, and 200 N) at 8.993 mm from cervical area and vertical nodal force of increasing magnitude (40 N, 60 N, 120 N, 160 N, and 200 N) was applied at the incisal edge. Equivalent stress von Mises, stress following tooth direction Z-Z, minimum principal stress (compression effect), and the resultant displacement. It was seen that maximum values for both displacement and stress appeared in the cervical area.[20]

Clinical implications

Abfractions are less likely to occur on a tooth with diminished periodontal support, and if does occur, must be more apically located.[21] The magnitude of the occlusal force applied to periodontally compromised tooth may be, in many instances expected to be reduced.[2223] The result of this study showed that with decreasing periodontal support the location of the highest stress concentration tended to shift away from CEJ, which is supposed to be susceptible to abfraction, toward the apical dentin region[24]

Flexure produces the maximal strain in the cervical region, and the strain appears to be resolved in tension or compression within local regions, sometimes causing the loss of bonded Class V restorations in preparations with no retention grooves. Additionally, in unbonded or leaking restorations, this flexure of the dentin also may produce changes in fluid flow and microleakage, leading to sensitivity and pulpal inflammation, respectively. Barreling results from heavy centric forces that produce compressive stresses along the marginal interface with cervical restoration in entire CEJ region, resulting in lateral displacement (loss) of the restoration.[25]

CONCLUSION

Within the scope of this study, the following observations were made:

High compressive stress, under normal occlusal load, in the tooth was noted near the alveolar crest and to a lesser extent in the apical one-half of the root

Reduction of the alveolar bone height representing the weakened periodontal support or more appropriately secondary trauma from occlusion, had little effect on the degree of tooth and the supporting tissue stresses when 25% of bone support was lost, however, the stresses increased dramatically when 50% and 75% of bone support was lost and also shifted apically on the tooth coinciding with the alveolar crest for that amount of bone loss

An increase of the tooth displacements was pronounced at the cervical third with the minimum displacement shifting apically to the junction of the cervical and middle third of the 25% and 50% loss of bone support and further shifting apically to the junction of the middle and apical thirds of the 75% alveolar bone loss.

The cumulative effect of increased stress and displacement at the cervical region of the tooth would result in abfraction as the age advances along with other wasting diseases.

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.