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Influence of Alveolar Support on Stress in Periodontal Structures
1 Removable Partial Prosthodontics, Masticatory Function Rehabilitation, Division of Oral Health Sciences, Graduate School, Tokyo Medical and Dental University, 1-5-45 Yushima, Bunkyo, Tokyo 113-8549, Japan; and Correspondence: * corresponding author, wakabayashi.rpro{at}tmd.ac.jp
The influence of alveolar bone support on the functional capability of a tooth remains unclear. It was hypothesized that a reduction in alveolar support causes an increase of maximum stress in the periodontal structures. Mathematical models of the maxillary incisor to simulate in vivo tooth movement were constructed with periodontium of normal or reduced bone height, and normal or widened periodontal ligament (PDL) space. Under simulated bite force, the maximum tensile stress at the lingual cervical region in the PDL increased with bone height reduction, but decreased with PDL widening. The compressive stress at the cervical region in the cortical bone was no more than 22% of the yield strength of bone, and did not increase by the height reduction with widened PDL. The result suggests that the height reduction potentially causes mechanical damage to the PDL, but, of itself, is not likely to have a negative effect on the bone.
Key Words: periodontal ligament • alveolar bone • stress • finite analysis • bite force
Aperiodontally compromised tooth can be diagnosed from probing depth, mobility, supporting bone volume, crown-to-root ratio, and root form (Johnson et al., 1986; McGuire and Nunn, 1996; Grossmann and Sadan, 2005). It is generally accepted that a reduction of periodontal support worsens the prognosis of a tooth. Thus, the radiographic appearance of periodontal bone loss greatly influences prosthodontic decision-making (Moser et al., 2002). However, the morphology of the periodontium with reduced structural support has not been well-understood in relation to clinical functions, such as load-bearing capability. To determine the interaction of reduced periodontal support with mechanical function, one must determine the stress and strain created in the periodontium in accordance with the morphologic alteration of the structures. The stress in the periodontium also predicts the potential pain and damage that occur under functional bite force (Kawarizadeh et al., 2004). The three-dimensional finite element (FE) method has been used to estimate the stress distribution within soft and hard tissues (Song et al., 2004). Recent progress in the application of non-linear material properties of the periodontal ligament (PDL) to simulate tooth movement has allowed for the accurate prediction of stress in periodontal tissues (Kawarizadeh et al., 2003; Muraki et al., 2004; Cattaneo et al., 2005). However, the change of stress distribution in the periodontium has not been fully assessed under simulated bite force as a function of the alveolar bone support of a periodontally compromised tooth. In this study, we created three-dimensional FE models to reproduce the load-displacement relation of a maxillary incisor. Using these models, we analyzed tooth movement and principal stress distribution in the periodontal tissues under simulated occlusal bite force. The purpose of the study was to assess the influence of progressive reduction of alveolar support on changes of stress distribution in periodontal structures. It was hypothesized that the reduction of alveolar bone height and the widening of the PDL space caused an increase of the maximum principal stress in these periodontal tissues.
Finite Element Models Each three-dimensional finite element model consisted of the maxillary right central incisor, PDL, and anterior part of the maxillary cortical and cancellous bone (I, P, Co, and Ca in Fig. 1A  ). The average anatomical dimensions of the incisor and bone in adults (Dental Anatomy & Interactive 3-D Tooth Atlas, Brown & Herbranson, Portola Valley, CA, USA) were traced and reconstructed as geometric records in the models. The distance from the incisal edge to the root apex was 24.7 mm, and that from the edge to the cementoenamel junction on the labial surface was 10.9 mm. The mesiodistal width at the incisal edge was 10.4 mm. A 0.2-mm- or 0.4-mm-thick layer of PDL was attached to the root surface to simulate normal and widened PDL spaces, respectively.
The maxillary bone was modeled as a cancellous core surrounded by 2.0-mm-thick cortical bone. The buccolingual and the anterior-posterior lengths of the bone models were 7.3 mm and 13 mm, respectively, at the root apex level. Each bone model had one of two alveolar heights at the mesial side of the central incisor: 21 mm for normal, and 12.5 mm for reduced height. Resultant crown-to-root ratios of the incisor were 0.7 for the normal and 2.1 for the reduced height, respectively (N and R in Fig. 1A  ). Four models—including those of normal bone height with normal and widened PDL space, and those of reduced bone height with normal and widened PDL space—were therefore constructed. Each model was meshed by structurally solid elements defined by 20 nodes having 3 degrees of freedom in tetrahedral bodies (ANSYS 8.1, ANSYS Inc., Canonsburg, PA, USA). The models consisted of approximately 25,000 elements for the normal bone height and 18,000 elements for the reduced bone height.
Material Properties
The material property of the PDL was assumed by a reverse-engineering approach of modulating the non-linear load-displacement relationship to accommodate the realistic movement of a maxillary incisor. The property was determined in the linear elastic and the non-linear elastic phases. For the linear elastic phase, we obtained the maximum elastic modulus in the preliminary analysis using the model of normal bone height with normal PDL space, and calculating backward so that the incisor displaced 170 µm under a horizontal load of 10 N from the labial to the lingual direction. This load-displacement relationship was used to fit the model to previous in vivo data (Mühlemann, 1951) (solid lines in Fig. 1B
Based on the report that the stress of PDL in the non-linear elastic phase is expressed by a cubic-function of strain in small tooth movement (Pini et al., 2002), the following approximated equation was determined for strain between –0.4 and 0.4 (dotted curve in Fig. 1C
The stress-strain curve was entered into a computer equipped with the FE software. The load-displacement relationships calculated for the 4 models under horizontal loads are shown in Fig. 1B
Loading and Boundary Conditions
The horizontal tooth displacement increased as the bone height decreased, or as the PDL space increased (Table , Fig. 2). The displacement also increased as the bite force increased; however, the increment was not proportional to the force. The horizontal displacement of 57 µm in the model of normal bone height with normal PDL space under 1 N bite force increased by a factor of approximately 4, to 202 µm under 20 N.
In the PDL space (Figs. 2 , 3A), the maximum 1st principal (tensile) stress was observed at the lingual cervical region, while the maximum 3rd principal (compressive) stress was shown at the site adjacent to the root apex. Directions of the tensile stresses at the lingual cervical region coincided with those of the tooth displacements, while the compressive stresses seen near the apex were directed to the long axis of the tooth, with a slight inclination to lingual. Under the simulated bite force of 20 N, the highest maximum tensile stress of 7.35 MPa was found in the model of reduced bone height with normal PDL space, while the lowest tensile stress of 1.64 MPa was observed in the model of normal bone height with widened PDL space.
In the labial cervical region of the cortical bone, the compressive stresses were created in the same direction as that of tooth displacement, while the tensile hoop stresses were seen perpendicular to the displacement (Fig. 3B ). Relatively higher maximum compressive stresses of approximately 13 MPa were observed in the models with widened PDL space, regardless of the alveolar bone height. The lowest maximum compressive stress of 9.95 MPa was found in the model of normal bone height with normal PDL space. The maximum tensile hoop stresses were increased by both bone height reduction and PDL widening, with a maximum value of 19.80 MPa. The damage to the lingual cervical region in the bone by tension force between the root and bone may not happen in real clinical conditions, because rupture of the ligament is more likely to occur prior to bone damage. For this reason, the stress calculated on this region was excluded from the result.
The maximum tensile stress in the lingual cervical region of the PDL increased as the alveolar height reduced. As resorption of the supporting bone progresses, the root area available for support is reduced. This may cause an increase of the maximum stress within the PDL. In the models in this study, the maximum tensile stresses under the simulated bite force of 20 N were above or close to the tensile strength of 2.4 MPa reported for the PDL (Ralph, 1982). Theoretically, the colored areas on the contour graphics of the PDL indicate areas that are potentially damaged by bite force (Fig. 3A ). The result suggests that the reduction of the alveolar bone height under the maximum bite force increased the risk of mechanical damage in the PDL. Meanwhile, the potential risk of the PDL was reduced by the widening of the space. The ability of the PDL to adapt to occlusal forces has been indicated by findings such as the thicker PDL space observed histologically at the regions of stress concentration by the application of horizontal load (Biancu et al., 1995), and the atrophic changes in the PDL induced by the loss of occlusal function, including narrowing of the PDL space and disorientation of collagen fibers (Kaneko et al., 2001). While widening caused an increase in tooth mobility, the stress suppression revealed the self-defensive effect of the PDL. Although this mechanism should be further explored in relation to the association with bacterial stimulations, the results of stress and strain supported previous findings that the PDL physiologically adapts to the accumulated occlusal loading by resorption of alveolar structures and resultant increased tooth mobility, which is actually occlusal trauma and is reversible if the load is reduced (Davies et al., 2001). Influence of stress in the PDL on biting ability of the tooth has not been well-investigated. Researchers have indicated that periodontal mechano-receptors control the biting force to protect the periodontium from mechanical stimulations (Dessem et al., 1988), and that tensile stress enhances the remodeling and functional regulations of the PDL (Ozaki et al., 2005). Meanwhile, others have questioned the effect of periodontal attachment level on biting ability (Morita et al., 2003). The mechanisms involved in the control of biting ability regulated by tensile stress remain to be fully elucidated. On the labial cervical aspect of the cortical bone, the principal compressive stresses were distributed in a direction similar to that of tooth displacement, while the tensile hoop stresses were perpendicular to the displacement. The stress distribution patterns were in agreement with those reported in a recent study (Cattaneo et al., 2005). The stresses were created as the impact on root surface was transmitted through the PDL to the surrounding bone as a result of tooth displacement. The concentration of the compressive stresses on the labial cervical aspect of the alveolar bone can be one of the causative factors for bone resorption, in association with bacterial stimulations (Polson and Zander, 1983). Both the maximum compressive and tensile hoop stresses in bone were well below the reported yield stress that might cause detrimental effects on human cortical bone (60 MPa) (Biewener, 1993). However, the stresses cannot be ignored, because repetitive fatigue loadings can potentially ’accumulate’ the stress, causing resorption or degeneration of the bone (Jepsen and Davy, 1997). Further studies—such as on stress accumulation in the periodontal structures during repetitive occlusal loadings, and on estimation of their recovering behavior—might be useful in clarifying the influence of fatigue loading on risk of damage to the periodontal structures during function. The maximum compressive stress in the bone increased proportionally as the bite force increased; however, the increase in rate by the reduction of the bone height was relatively mild (12.9%) for the normal PDL, and even decreased slightly (–0.7%) for the widened PDL. The cushion effect of the soft ligament (Kuroiwa et al., 1996), as well as the tilting movement of the tooth, may have contributed to the suppression of the potential increase of stresses in bone. An increase in the tilting movement with reduction of bone height was evidenced by the horizontal displacements of the tooth. The results indicated that the progressive reduction of bone height caused considerable increase in tooth mobility; however, this did not lead to a noticeable change of stress in the cortical bone surface. It is suggested that the reduction of bone height due to resorption is not the single causative factor leading to secondary trauma in the bone. This may support the argument that tooth mobility is associated with a prognosis that is unlikely to improve, but is not associated with a worsening prognosis (McGuire, 1991). The results of this study suggest that the reduction of the alveolar height potentially causes mechanical damage to the PDL, while it is not likely, on its own, to have a negative effect on the bone. Therefore, the proposed hypothesis was not accepted. The limitations of the mathematical models used in this study, where the stresses were calculated for the initial failure of the tissues, should be indicated. Further technological progress may allow for a time-dependent analysis for further hypothesis, with the structural model updated to account for changes in supporting tissues with degeneration or necrosis. In this study, the FE method, with material non-linearity to reproduce in vivo tooth movements, was applicable in the analyses of the mechanical behavior of the tooth and the periodontal structures, under small and large occlusal loads. Prediction of internal stress distribution within the periodontium, in relation to the morphologic alteration that could not be directly measured, was possible.
This study was supported by grant No. 16591936 (N.W.), and by the High-Tech Research Project (2005–2009) from The Ministry of Education, Science, and Culture of Japan. We acknowledge Dr. Takashi Ohyama, Professor Emeritus of Tokyo Medical and Dental University, for his inspiration for our work. Received for publication November 20, 2005. Revision received July 23, 2006. Accepted for publication September 5, 2006.
Journal of Dental Research, Vol. 85, No. 12,
1087-1091 (2006)
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