Elsevier

Journal of Thermal Biology

Volume 80, February 2019, Pages 45-55
Journal of Thermal Biology

A numerical-experimental study on thermal evaluation of orthodontic tooth movement during initial phase of treatment

https://doi.org/10.1016/j.jtherbio.2019.01.005Get rights and content

Highlights

  • Effect of tooth loading is studied on temperature profile at early stage of treatment.

  • Mechanical stress and temperature are correlated with thermo-mechanical coefficient.

  • The coefficient is found out by in vivo experiments on rats after 2 weeks of treatment.

  • Temperature profile can be obtained numerically by using this coefficient.

  • Treatment evaluation is based on comparing experimental and numerical temperatures.

Abstract

The most desired target of orthodontic treatment is tooth movement as a result of application of efficient force system. In this study, effect of tooth loading is studied on temperature profile around the tooth at early stages of treatment. The basis of temperature variation is increase of cell number and activities in periodontium as a result of compression and tension of this layer. Highest cellular activities occur in the beginning of loading procedure and aim to reduce mechanical stress in the periodontium which finally ends up with orthodontic tooth movement during couple of years. To find out the correlation between temperature variation and the applied force, in vivo experiments are conducted on ten rats and temperature is measured in specific time periods. It is observed that temperature is higher in direction of the net force about 0.3. Next, numerical finite element analysis is carried out on the rat tooth model. Mechanical stress results show that regions with compressive stress have rather high temperature in the experiments. Mechanical stress on periodontium-bone interface is multiplied by a coefficient to simulate cellular activities on this boundary as a heat source and thermal analysis is carried out to obtain temperature profile. The thermo-mechanical coefficient is identified for each rat by imposing the experimental temperatures on numerical outputs. For assessment of a treatment efficiency and deduction of the applied force, temperatures could be measured experimentally and compared with the corresponding numerical analysis temperature result obtained by employing the thermo-mechanical coefficient found earlier for each rat.

Introduction

Orthodontics is the skill of fixing tooth displacement which could appear as translation, rotation, extrusion or intrusion in different sides of a tooth (Li et al., 2014, Nakajima et al., 2007). Orthodontic treatment is performed practically by applying force on the tooth crown. In this procedure, four factors of magnitude, type (for bodily transformation and rotation of the tooth), direction and location of the force are adjusted based on the desirable tooth displacement. Orthodontic treatment is a time-consuming process and it cannot be evaluated in the early stages; therefore, any misapplication of each factor can lead to irreparable damages and can hamper the orthodontic procedure (Danz et al., 2016, Ammar et al., 2011, Dorow and Sander, 2005).

In order to prevent probable mistakes, several numerical studies have been conducted to investigate the influence of different loadings in order to accurately estimate the required force for an appropriate displacement. Liao et al. (2016) applied a wide range of force magnitudes on a model of the human maxillary teeth. They obtained the center of resistance and the optimal orthodontic force through hydrostatic stress measurement in the periodontal ligament (PDL) which is a connective soft tissue around the tooth. They concluded that when a major proportion of the tooth is under stress, orthodontic process would be more effective. In order to determine the proper loading, instead of using the moment to force ratio, the location of center of resistance was announced as an appropriate factor in determining the treatment process (Liao et al., 2016).

Numerical simulation can greatly improve the effectiveness of dental procedure. However, similar to the practical treatment, being time-consuming is one of the fundamental difficulties in the mechanical simulations of an orthodontic treatment. There are a number of attempts in the literature for long-term simulations. Zargham et al. Zargham et al. (2016) did a long-term simulation and studied tooth movement, rotation and bone loss in a four-week period while the tooth was under specific loading condition. In this study, elastic property was considered for all components of the tooth. At each iteration, geometry and mesh were updated from the last iteration. Rather than the numerical costs, long-time loading of the tooth has some consequences including enamel declassification, tooth decay and root resorption (Sameshima and Sinclair, 2001). These consequences affect the geometry and mechanical properties during the simulation and reduce accuracy of the results. Therefore, long-term evaluation of the orthodontic treatment has inevitable problems both numerically and practically.

The main objective of the present study is to focus on an early evaluation method based on temperature variation around the tooth structure as a result of appliance insertion. Detailed explanation of fundamentals of this method can be found in the work of Heidary et al. (2018). In this study, in vivo experiments are performed on ten Wistar rats and thermal parameters are measured in two time periods; in two weeks of load insertion on the first maxillary molar tooth and two subsequent weeks of load removal. Meanwhile, a thermo-mechanical finite element analysis (FEM) is conducted on the rat's tooth model which is constructed by a section of micro-CT scan images. For a reliable numerical simulation, the geometry and the mechanical properties of the tooth components should be defined precisely. To this end, the tooth structure is modeled by considering three components of the tooth, PDL and the alveolar bone. Material properties of the bone and the tooth are defined according their elastic behavior (Kawarizadeh et al., 2003).

Unlike the bone and the tooth, the PDL has a complex structure and behavior (Jiang et al., 2016). It plays a determining role in the orthodontic procedure (Christopher et al., 2000). In spite of inaccurate and limited information about the PDL, researchers have tried to simulate mechanical behavior of this tissue in different ways. Many previous studies have simulated the PDL as a linear elastic material. Cai et al. (2015) conducted a 3D finite element modeling on canine's tooth to study stresses in the canine's PDL during canine's translation, inclination, and rotation. They considered an elastic behavior for the periodontium and observed that stresses in the PDL were exponential in transparent tooth correction treatment. Provatidis (Provatidis, 2000) studied different mechanical representations of the PDL and their effects on the tooth mobility. The PDL was considered as linear and nonlinear elastic materials while isotropic, anisotropic and orthotropic orientations were considered for the constitutive fibers. FEM was used to estimate the occlusal positions on the maxillary central incisor. Viecilli et al. Viecilli and Burstone (2015) produced a finite element model of all teeth and applied four different types of loads. They calculated the third principal stresses of different teeth in areas of most compression while the PDL was assumed as a linear elastic material. Based on the results, resistance numbers representative of the load proportions for each tooth were determined. Bouton et al. Bouton et al. (2017) developed a finite element (FE) analysis to evaluate stresses and their distribution on the level of the tooth, the elastic PDL and the alveolar bone when a force is applied. They could monitor the tooth movement by obtaining optical impressions at each stage of treatment. FE analyses were correlated with the clinically-observed displacement.

However, according to the tissue structure, elastic assumption could not properly characterize the tissue behavior (McCormack et al., 2014, Toms et al., 2002). PDL has a fibrous structure which causes a nonlinear mechanical response of the soft tissue. It also acts as a damper when it is confronted with mechanical stress which results in time-dependent responses (Heidary et al., 2018, Storey, 1973). In some studies, hyperelastic property has been considered for nonlinear variations of mechanical stress and strain in the PDL. However, viscoelastic property can best characterize the nonlinear behavior of stress and strain with regard to the time (Qian et al., 2009, Su et al., 2013, Maruo et al., 2016, Oskui and Hashemi, 2016).

The main role of the PDL is providing space for bone cells accumulation. Osteoblasts and osteoclasts are two types of cells that exist near the bone layer in the PDL tissue. These cells play a significant role in orthodontics displacement and are sensitive to the mechanical stress. By applying force to the tooth crown, osteoclast cells accumulate in the regions where the compressive stress exists and destroy the bone tissue on the common surface between the PDL and the alveolar bone (Kawarizadeh et al., 2003). Afterwards, osteoblast cells are activated in the regions with tensile stress (Kawarizadeh et al., 2003). Therefore, by analyzing the mechanical compressive stress in the PDL, erosion of the alveolar bone could be estimated and that is where orthodontics process is believed to initiate (Field et al., 2009).

Osteoblast cells generate extra heat in the periodontium during metabolic process which is referred to as metabolic heat. Amount of the metabolic heat depends on the number of osteoclast cells which has correlation with the value of compressive stress. The extra metabolic heat affects normal temperature distribution in the tooth structure and gives rise to the temperature in the regions of compressive stress which depends on the direction of the applied force to the tooth. To find out the correlation between the applied force and the corresponding temperature rise, the profile of temperature variation in the experimental study are equalized with the temperature outputs in the numerical study and the required thermal conditions are estimated. The acquired thermal condition provides the coupling between mechanical stress and temperature values.

Section snippets

Problem definition

The desired target of orthodontic treatment is tooth movement as a result of application of efficient force system. Orthodontic tooth movement takes a long time therefore the inefficiency cannot be early detected. In the present study, temperature variation is measured around the tooth structure after a few weeks of load insertion on the tooth crown. The main objective is to find a correlation between the applied force and the temperature profile.

The reason for temperature rise is increase of

Experimental results

An experimental study is carried out on 10 rats to measure the temperature of the first molar in upper jaw (maxilla). For each rat, temperature is measured in three directions of palatal, buccal and mesial. Due to small size of the maxillary molar tooth and size of the temperature sensor, for each tooth surface only one temperature is reported. Moreover, temperature measurements on the buccal and palatal surfaces are carried out in the vicinity of the mesial surface close to the common edge

Conclusions and future work

In the present study, in vivo experiments are carried out on rats to study effect of an applied force to the tooth crown on temperature variation around the tooth. In the experiments, the first maxillary left molar teeth of 10 rats are loaded by a concentrated force in the mesial direction. Temperature is measured along different directions and comparison is made between the initial values and the corresponding values after two weeks of appliance insertion. It is observed that temperature

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This study does not involve human subjects. Institutional guide for the care and use of laboratory animals was followed.

Ms. Afsaneh Mojra has obtained her BSCE degree in Mechanical Engineering from Sharif University of Technology, Tehran, Iran in 2004, her MSC in Biomedical Engineering from Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran in 2006 and her PHD in Biomedical Engineering from Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran in 2011. She has spent a sabbatical position in the Biomedical Department, Eindhoven University of Technology, Netherlands in 2010. She

References (27)

Ms. Afsaneh Mojra has obtained her BSCE degree in Mechanical Engineering from Sharif University of Technology, Tehran, Iran in 2004, her MSC in Biomedical Engineering from Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran in 2006 and her PHD in Biomedical Engineering from Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran in 2011. She has spent a sabbatical position in the Biomedical Department, Eindhoven University of Technology, Netherlands in 2010. She is now an assistant professor in K. N. Toosi University of Technology in the Mechanical Engineering Department.

Mr. Mehdi Fakhimi Bonab is now a MSC student in Mechanical Engineering in K. N. Toosi University of Technology, Tehran, Iran.

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