2020, Number 2
Finite element analysis of the biomechanical effects of micro-osteoperforations of cortical bone under expansive forces
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ABSTRACT
Introduction: Micro-osteoperforations (MOPs) are a procedure in which perforations are created in the bone around the teeth to accelerate tooth movement during orthodontic treatment. Objective: To determine the biomechanical effects of MOPs on the vestibular cortical bone when an expansive orthodontic force is applied in a finite element model. Material and methods: Nine 3D models of a right upper premolar were constructed: one control model; four models to evaluate the effect of the number of perforations, two models to evaluate the effect of the depth of the perforation and two models to evaluate the effect of the width of the perforation. To establish a comparison between the models, a simulated load of 2.6 Newton was applied to impose an expansive movement (0.20 mm) in the vestibular direction, taking into account the stress and unit strain patterns in the alveolar bone. Results: The finite element model showed that the simulations with 4 and 9 MOPs showed an increasing trend in the increase of micro-deformations as the diameter and depth of the MOPs increased to 1 mm in 7 of the 8 models. The 4 MOPs model with diameter of 0.5 mm and depth of 1 mm a decrease in microdeformations was observed. Conclusions: The construction of a basic finite element model of an upper second premolar evidenced that the use of MOPs produces an increase in bone microdeformations that promote the bone remodelling process in the areas of microtrauma.INTRODUCTION
The performance of orthodontic expansion poses challenges such as undesirable effects (fenestrations and dehiscence), biomechanical incompetence, and inappropriate force levels. To address these problems and in order to facilitate orthodontic movement, surgical techniques have been used such as osteotomy, distraction osteogenesis, corticotomy and micro-osteoperforations (MOPs).
MOPs are a procedure in orthodontics in which holes are created in the bone around the teeth to accelerate tooth movement during orthodontic treatment. It is a method that generates less surgical injury and has a technical simplicity that facilitates its use. MOPs produce a rupture in the cortical continuity, which generates a reduction in bone density. At the cellular level, there is an increase in microdeformations, which generates a phenomenon called mechanotransduction where mechanical signals trigger and increase biological responses. This induces the release of cytokines and chemokines that regulate the processes of bone remodelling and apposition leading to tooth movement. Therefore, microdeformation becomes the most important mechanical stimulus to increase the cellular response.
The creation of MOPs can be used in many different clinical scenarios by activating osteoclasts and temporarily reducing bone density. For example, in cases where cortical bone density is high and orthodontic treatment would not be able to produce optimal results. The procedure can be used as a complement to any orthodontic appliance, including fixed appliances, plastic aligners or removable appliances (such as expanders and distalizers).1
For the same reason, MOPs can facilitate some difficult orthodontic movements and are an excellent adjunctive technique during protraction or retraction of a single tooth or group of teeth. It is especially useful when a tooth is moved in an edentulous space where the alveolar bone is dense and had a narrow ridge.2
MATERIAL AND METHODS
The geometric modelling phase aims to represent the premolar in terms of points, lines and surfaces. The tooth model was obtained from 3D scanning of an upper right premolar.3
To evaluate the effect of the number, depth and diameter of the perforations, nine models were constructed, taking into account that all perforations would be 1 mm apart (Table 1).
- 1. One control model without MOPs.
- 2. Eight models with 4 and 9 MOPs (Figure 1).
A simulated load of 2.644 N and a counter moment of 21.34 N/mm was applied to each model, which allowed 1o of dental inclination and an expansive movement of 0.20 mm was applied in the vestibular direction, which induced a displacement in the palatal-vestibular direction (X of the model). The force was imposed on the crown of the tooth in order to achieve a movement closer to clinical reality and from this data to simulate the models with MOPs.
The comparison between models was established, taking into account the stress and unit strain patterns in cortical bone.
For the simulation, each structure was assigned the mechanical properties reported in the literature for the specific material. The structures taken into account were the tooth, periodontal ligament (PDL),4 cortical and trabecular bone. The properties of the materials used in this study were taken from previous finite element studies (Table 2).5
Modelling- 1. Tooth (upper right premolar): it was modelled with a material of isotropic and homogeneous linear elastic behaviour, differentiating enamel and dentine. The mechanical properties were obtained from previous studies.6
- 2. PDL: it was defined as a homogeneous, isotropic, non-linear elastic material with a unit stress-strain function calculated from data reported in Toms and Eberhardt.4
- 3. Cortical and trabecular bone: these were determined as a homogeneous material with isotropic linear elastic behaviour. Differences in stiffness between different bone types were taken into account, as they were considered relevant to the objectives of the study.
Bone properties were individually assigned according to the true bone morphology as obtained from CT scans by Cattaneo et al.7 So the bone structure, including trabecular structures, was modelled at a different tissue level.
In the simulation, the tooth root was surrounded by a uniform 0.3 mm thick layer representing the PDL, which in turn was surrounded by another layer with an average thickness of 0.8 mm representing the lamina dura.8
The model was constructed with all the supporting tissues, the trabecular bone, cortical bone (the lamina dura and the cortical plates were combined into a single solid with the same properties), the PDL and the tooth.
The geometry of the alveolar bone, both trabecular and cortical, and the PDL were constructed in a top-down assembly from the computer-aided design (CAD) model of the tooth using SolidWorks® 2018.
Subsequently, the geometry of the CAD model was imported into the finite element program ANSYS 19 R1®.
MeshingThe meshing of the model in these biomechanical studies used ten-node quadratic tetrahedral elements (SOLID187 ANSYS®). The models required mesh refinement in the hole areas in order to give the most accurate results. The number of nodes and elements is shown in Table 3.
Contact conditionsIn ANSYS 19 R1® the rigid bond condition was established without relative displacement (bonded) at the following interfaces: 1) The tooth-periodontal ligament interface: presented a bond type without relative displacement. 2) The periodontal ligament-cortical bone interface: it presented a bond type without relative displacement. 3) The cortical bone-trabecular bone interface: presented a type of junction without relative displacement.
Coordinate systemA coordinate system setting the X-axis in the vestibular direction, the Y-axis in the coronal direction and the Z-axis in the distal direction was chosen.
Simulation of tooth movementA force of 2.644 N and a counter moment of 21.34 N/mm was imposed which induced a displacement of 0.20 mm in the palatal-vestibular direction. The force was imposed on the crown of the tooth in order to achieve a movement closer to clinical reality and based on these data, the simulation of the models with MOPs was performed. The displacement patterns of the premolar, showing the change of location at the maximum and minimum displacements in each case, and the distribution of stresses and deformations were obtained.
Ethical considerationsIn accordance with resolution No. 008430 of 1993 of the Ministry of Health of the Republic of Colombia, this research project is classified as non-risk, as it was not carried out on humans, therefore, there are no ethical implications.
RESULTS
The Universidad Autónoma de Manizales acquired a full-scale point cloud from TurboSquid® of the entire permanent human dentition. Anthropometric measurements of cortical bone and lamina dura were taken in order to make the different CAD solids and to be able to define each tissue in detail.
In order to evaluate the effect of MOPs on the vestibular cortical bone when applying an expansive orthodontic load, a comparison of models with 4 and 9 MOPs with depths of 1 and 0.5 mm, and diameters of 1 and 0.5 mm was carried out in relation to the control model without MOPs (Figure 2). The levels of principal unit microstrain in the zone and its effects around the MOPs were analysed and the results of the principal deformations described in Table 4 were obtained.
A fixed support condition was established at the base of the cortical bone towards the apical end, and the lateral zone had the frictionless support condition as shown in Figure 3. From this, the micro-strain in the cortical bone of all models was evaluated. The boundary and edge conditions were applied to all models in order to compare them with each other. The percentage deviation between the number of nodes of one model and another was less than 5%.
DISCUSSION
According to the numerical model developed in the present study, the performance of MOPs always amplifies and concentrates the resulting microdeformations in cortical bone.
Studies by Alikhani et al. suggest that MOPs stimulate the expression of inflammatory markers triggering a series of events. According to their proposal, a catabolic phase occurs in which osteoclasts resorb bone on both the tension and compression sides. Subsequently, an anabolic phase occurs to restore the alveolar bone to its pre-treatment levels.9
The present study shows that there is a mechanical phenomenon of increased levels of bone deformation associated with treatment with MOPs. The relationship of this phenomenon with the biological effect of increased localised bone activity could be causal or collaborative.
It was shown that disturbances occur in the area surrounding the MOPs, causing an increase in microdeformations, which generates mechanotransduction and triggers the cellular response.10
Models with deeper MOPs have higher levels of microdeformation, associated with a decrease in bone density, resulting in lower stiffness and higher elasticity in cortical bone. Alikhani11 indicates that vestibular bone remodelling processes in an expansive movement are beneficial because there is a biological response to the decrease in bone density. This facilitates the reduction of fenestrations and bone dehiscence and root resorption.
The microtrauma caused by MOPs activates the biological mechanisms of bone remodelling during dental movements,12 making MOPs a useful tool in orthodontic treatment.
The maximum microdeformations found at the level of the vestibular alveolar ridge edge are associated with the clinical impossibility of generating sufficient "counter momentum" to counteract tooth inclination in the vestibular direction. This is consistent with the findings of Houle et al,13 who conclude that expansive movement with plastic aligners is achieved between 60 and 80% of predicted translational movement, regardless of the mechanical restriction of bone tissue on movement.
Zhao et al. in 201714 evaluated the efficiency of maxillary expansion with plastic aligners and determined that expansion was achieved by movement in the vestibular direction of the posterior teeth with their respective inclination. In other words, increasing the planned intermolar width of expansion has a significant influence on the efficiency of expansion at the premolar level.
Carvalho Trojan et al.15 referred to maxillary expansion with the use of traditional expanders and concluded that tooth-borne expanders require more activation to achieve the same effect as bone-borne expanders.
When it comes to finite element modelling, both cortical and trabecular bone types should be modelled whenever deformation quantification is desired.16 This finding helps the Orthodontist to create strategies to improve treatment plan outcomes and validates the construction of our model with its respective tissues to get closer to a real clinical setting.
CONCLUSIONS
- 1. The use of MOPs amplifies and concentrates local bony microdeformations in the vestibular cortical bone during maxillary expansion. The number of MOPs does not necessarily increase the maximum principal deformation, but it does generate larger gradients.
- 2. With typical clinical loads the maximum micro-deformations are at the level of the vestibular alveolar ridge edge. Deeper MOPs generate higher levels of microdeformation.
- 3. The principal deformation increases very little with 0.5 mm depth. The combined effect of diameter and depth of the MOPs amplifies the effect of increased maximum principal deformation.
REFERENCES
AFFILIATIONS
1 Profesor asociado de Biomecánica Ortodóncica, Departamento de Salud Oral. Universidad Autónoma de Manizales, Caldas, Colombia.
2 Profesor asociado, Departamento de Mecánica y Producción. Universidad Autónoma de Manizales, Caldas, Colombia.
3 Residentes de Especialización en Ortodoncia, Departamento de Salud Oral. Universidad Autónoma de Manizales, Caldas, Colombia.
CORRESPONDENCE
Juan Pablo Gómez Arango. E-mail: jgomez@autonoma.edu.coReceived: Febrero 2020. Accepted: Mayo 2020.