A periodontal ligament driven remodeling algorithm for orthodontic tooth movement

A Soft-Tissue Driven Bone Remodeling Algorithm for Mandibular Residual Ridge Resorption Based on Patient CT Image Data

The role of the biomechanical stimulation generated from soft tissue has not been well quantified or separated from the self-regulated hard tissue remodeling governed by Wolff's Law. Prosthodontic overdentures, commonly used to restore masticatory functions, can cause localized ischemia and inflammation as they often compress patients' oral mucosa and impede local circulation. This biomechanical stimulus in mucosa is found to accelerate the self-regulated residual ridge resorption (RRR), posing ongoing clinical challenges. Based on the dedicated long-term clinical datasets, this work develops an in-silico framework with a combination of techniques, including advanced image post-processing, patient-specific finite element models and unsupervised machine learning Self-Organizing map algorithm, to identify the soft tissue induced RRR and quantitatively elucidate the governing relationship between the RRR and hydrostatic pressure in mucosa. The proposed governing equation has not only enabled a predictive simulation for RRR as showcased in this study, providing a biomechanical basis for optimizing prosthodontic treatments, but also extended the understanding of the mechanobiological responses in the soft-hard tissue interfaces and the role in bone remodeling.

Dynamic tensile viscoelastic properties of porcine periodontal ligament

The periodontal ligament plays a significant role in orthodontic and masticatory processes. To explicitly investigate the effects of dynamic force amplitude and frequency on the dynamic tensile properties of the periodontal ligament, in vitro tensile experiments were conducted using a dynamic mechanical analysis at various dynamic force amplitudes across a wide frequency range. Storage modulus, loss modulus, and loss factor values were measured. A Maxwell constitutive model based on modulus was established to describe the dynamic mechanical properties of the periodontal ligament. The results showed that the storage modulus ranged from 29.53 MPa to 158.24 MPa, the loss modulus ranged from 3.26 MPa to 76.16 MPa, and the loss factor values all increased with higher frequencies and higher dynamic force amplitudes. Based on the parameters obtained from the fitting results, it is evident that the short-term response has a more pronounced impact on the elastic response of the periodontal ligament than the long-term response. Increasing the dynamic force amplitude and its frequency amplified the viscous effects of the periodontal ligament and enhanced energy dissipation. The proposed constitutive model further demonstrated that the periodontal ligament acts as a viscoelastic biomaterial. These findings have implications for future research on the periodontal ligament.

The crucial role of periodontal ligament's Poisson's ratio and tension-compression asymmetric moduli on the evaluation of tooth displacement and stress state of periodontal ligament

The hydrostatic stress in the periodontal ligament (PDL) evaluated by finite element analysis is considered an important indicator for determining an appropriate orthodontic force. The computed result of the hydrostatic stress strongly depends on the PDL material model used in the orthodontic simulation. This study aims to investigate the effects of PDL Poisson's ratio and tension-compression asymmetric moduli on both the simulated tooth displacement and the PDL hydrostatic stress. Three tension-compression symmetric and two asymmetric PDL constitutive models were selected to simulate the tensile and compressive behavior of a PDL specimen under uniaxial loading, and the resulting numerical results were compared with the in-vitro PDL experimental results reported in the literature. Subsequently, a tooth model was established, and the selected constitutive models and parameters were employed to assess the hydrostatic stress state in the PDL under two distinct loading conditions. The simulated results indicate that PDL Poisson's ratio and tension-compression asymmetry exert substantial influences on the simulated PDL hydrostatic stress. Conversely, the elastic modulus exhibits minimal impact on the PDL stress state under the identical loading conditions. Furthermore, the PDL models with tension-compression asymmetric moduli and appropriate Poisson's ratio yield more realistic hydrostatic stress. Hence, it is imperative to employ suitable Poisson's ratio and tension-compression asymmetric moduli for the purpose of characterizing the biomechanical response of the PDL in orthodontic simulations.

Functional non-uniformity of periodontal ligaments tunes mechanobiological stimuli across soft- and hard-tissue interfaces

The bone-periodontal ligament-tooth (BPT) complex is a unique mechanosensing soft-/hard-tissue interface, which governs the most rapid bony homeostasis in the body responding to external loadings. While the correlation between such loading and alveolar bone remodelling has been widely recognised, it has remained challenging to investigate the transmitted mechanobiological stimuli across such embedded soft-/hard-tissue interfaces of the BPT complex. Here, we propose a framework combining three distinct bioengineering techniques (i, ii, and iii below) to elucidate the innate functional non-uniformity of the PDL in tuning mechanical stimuli to the surrounding alveolar bone. The biphasic PDL mechanical properties measured via nanoindentation, namely the elastic moduli of fibres and ground substance at the sub-tissue level (i), were used as the input parameters in an image-based constitutive modelling framework for finite element simulation (ii). In tandem with U-net deep learning, the Gaussian mixture method enabled the comparison of 5195 possible pseudo-microstructures versus the innate non-uniformity of the PDL (iii). We found that the balance between hydrostatic pressure in PDL and the strain energy in the alveolar bone was maintained within a specific physiological range. The innate PDL microstructure ensures the transduction of favourable mechanobiological stimuli, thereby governing alveolar bone homeostasis. Our outcomes expand current knowledge of the PDL's mechanobiological roles and the proposed framework can be adopted to a broad range of similar soft-/hard- tissue interfaces, which may impact future tissue engineering, regenerative medicine, and evaluating therapeutic strategies. STATEMENT OF SIGNIFICANCE: A combination of cutting-edge technologies, including dynamic nanomechanical testing, high-resolution image-based modelling and machine learning facilitated computing, was used to elucidate the association between the microstructural non-uniformity and biomechanical competence of periodontal ligaments (PDLs). The innate PDL fibre network regulates mechanobiological stimuli, which govern alveolar bone remodelling, in different tissues across the bone-PDL-tooth (BPT) interfaces. These mechanobiological stimuli within the BPT are tuned within a physiological range by the non-uniform microstructure of PDLs, ensuring functional tissue homeostasis. The proposed framework in this study is also applicable for investigating the structure-function relationship in broader types of fibrous soft-/hard- tissue interfaces.

Effect of temperature on dynamic compressive behavior of periodontal ligament

Periodontal ligament (PDL) attaches tooth root to the surrounding bone. Its existence between tooth and jaw bone is of utmost importance due to its significant role in absorbing and distributing physiological and para-physiological loading. According to the previous studies, various mechanical tests have been performed to characterize the mechanical properties of the PDL; however, all of them have been done at room temperature. To the best of our knowledge, this is the first study in which the testing was performed at body temperature. The present research was planned to measure the dependency of PDL's viscoelastic behavior on temperature and frequency. Three different temperatures, including body and room temperature, were opted to perform the dynamic compressive tests of the bovine PDL. In addition, a Generalized Maxwell model (GMM) was presented based on empirical outcomes. At 37 °C, amounts of loss factor were found to be greater than those in 25 °C, which demonstrates that the viscous phase of the PDL in higher temperatures plays a critical role. Likewise, by raising the temperature from 25 °C to 37 °C, the model parameters show an enlargement in the viscous part and lessening in the elastic part. It was concluded that the PDL's viscosity in body temperature is much higher than that in room temperature. This model would be functional for a more accurate computational analysis of the PDL at the body temperature (37 °C) in various loading conditions such as orthodontic simulations, mastication, and impact.

In silico approach towards neuro-occlusal rehabilitation for the early correction of asymmetrical development in a unilateral crossbite patient

Neuro-occlusal rehabilitation (N.O.R.) is a discipline of the stomatognathic medicine that defends early treatments of functional malocclusions, such as unilateral crossbite, for the correction of craniofacial development, avoiding surgical procedures later in life. Nevertheless, N.O.R.'s advances have not been proved analytically yet due to the difficulties of evaluate the mechanical response after the treatment. This study aims to evaluate computationally the effect of N.O.R.'s treatments during childhood. Therefore, bilateral chewing and maximum intercuspation occlusion were modelled through a detailed finite element model of a paediatric craniofacial complex, before and after different selective grinding-alternatives. This model was subjected to the muscular forces derived from a musculoskeletal model and was validated by the occlusal contacts recorded experimentally. This approach yielded errors below 2% and reproduced successfully the occlusal, muscular, functional and mechanical imbalance before the therapies. Treatment strategies balanced the occlusal plane and reduced the periodontal overpressure (>4.7 kPa) and the mandibular over deformation (>0.002 ε) on the crossed side. Based on the principles of the mechanostat theory of bone remodelling and the pressure-tension theory of tooth movement, these findings could also demonstrate how N.O.R.'s treatments correct the malocclusion and the asymmetrical development of the craniofacial complex. Besides, N.O.R.'s treatments slightly modified the stress state and functions of the temporomandibular joints, facilitating the chewing by the unaccustomed side. These findings provide important biomechanical insights into the use of N.O.R.'s treatments for the correction of unilateral crossbite, but also encourage the application of computing methods in biomedical research and clinical practise.

Biomechanical factors in the open gingival embrasure region during the intrusion of mandibular incisors: A new model through finite element analysis

Introduction: Open gingival embrasure (OGE) is a common complication in adults following clear aligner therapy and the influence of gingival or alveolar bone biotype on OGE is of great concern. Unfortunately, due to the limited number of patients with clearaligner therapy and the clinical methods to distinguish the gingival biotype of patients being invasive, it is difficult to carry out clinical studies on the gingival or alveolar bone biotype of the OGE. In the meanwhile, the detailed biomechanics of the occurrence of OGE remains unknown. The goal of this study was to establish a new model to simulate the virtual space region, namely, the OGE region, to investigate the relationship between alveolar bone biotype and the occurrence of OGE, and explore potential biomechanical factors related to OGE.

Methods: The OGE region in the interproximal space was established using a filler with a very low modulus of elasticity (1 × 10−6 MPa). To illustrate the biomechanics of OGE more exhaustively, a line was created at the top of the alveolar crest along the proximal tooth root. FEA was then used to analyze the biomechanics of the surrounding tissues, the OGE region and the line at the top of the alveolar crest along the proximal tooth root of the central incisor under two different labial bone thicknesses (thick and thin) with an axial inclination of 80°, 90° and 100°.

Results: During intrusion of the incisors in clear aligner therapy, as inclination increased or bone tissue became thinner, the stress in the surrounding tissues [tooth root, alveolar crest, and periodontal ligament (PDL)] was greater. In the OGE region and interproximal alveolar crest, the strain increased with increasing inclination and labial bone thinning. The results from the line at the top of the alveolar crest along the proximal tooth root showed more detailed biomechanics: In all groups, stress and strain were focused on the mesial-labial alveolar crest. Interestingly, our results also demonstrated that when OGE occurs, other complications may arise, including root resorption and bone dehiscence.

Efficacy of a four-curvature auxiliary arch at preventing maxillary central incisor linguoclination during orthodontic treatment: a finite element analysis

BACKGROUND

Correct torque of the incisors is beneficial in the assessment of the effects of orthodontic treatment. However, evaluating this process effectively remains a challenge. Improper anterior teeth torque angle can cause bone fenestrations and exposure of the root surface.

METHODS

A three-dimensional finite element model of the maxillary incisor torque controlled by a homemade four-curvature auxiliary arch was established. The four-curvature auxiliary arch placed on the maxillary incisors was divided into four different state groups, among which 2 groups had tooth extraction space retracted traction force set to 1.15 N. Initial displacements and pressure stresses of the periodontal tissue in the maxillary incisors and molars were calculated after torque forces (0.5, 1, 1.5, and 2 N) were applied to the teeth at different stable states.

RESULTS

The effect of using the four-curvature auxiliary arch on the incisors was significant but did not affect the position of the molars. Given the absence of tooth extraction space, when the four-curvature auxiliary arch was used in conjunction with absolute anchorage, the recommended force value was < 1.5 N. In the other 3 groups (i.e., molar ligation, molar retraction, and microimplant retraction groups), the recommended force value was < 1 N. The application of a four-curvature auxiliary arch did not influence the molar periodontal and displacement.

CONCLUSION

A four-curvature auxiliary arch may treat severely upright anterior teeth and correct cortical fenestrations of the bone and root surface exposure.

Anchorage effects of ligation and direct occlusion in orthodontics: A finite element analysis

BACKGROUND AND OBJECTIVE

During orthodontic treatment, the figure-of-eight ligature and the physiological occlusion play an important role in providing anchorage effects. However, their effects on reaction forces of tooth and stress state in periodontal ligament (PDL) have not been quantitatively evaluated yet. In this study, we presented a finite element analysis process for simulating posterior molar ligature and direct occlusion during orthodontics in order to quantitatively assess their anchorage effects.

METHODS

A high precision 3D biomechanical model containing upper and lower teeth, PDL, brackets and archwire was generated from the images of computed tomographic scan and sophisticated modelling procedures. The orthodontic treatment of closing the extraction gap was simulated via the finite element method to evaluate the biomechanical response of the molars under the conditions with or without ligation. The simulations were divided into experimental and control groups. In the experimental group, orthodontic force of 1 N was first applied, then direct occlusal forces of 3 and 10 N were applied on each opposite tooth. While in the control group, occlusal forces were applied without orthodontic treatment. The tooth displacement, the stress state in the PDL and the directions of the resultant forces on each tooth were evaluated.

RESULTS

In the case of molars ligated, the maximum hydrostatic stress in the molars' PDL decreases by 60%. When an initial tooth displacement of several microns occurs in response to an orthodontic force, the direction of the occlusal force changes simultaneously. Even a moderate occlusal force (3 N per tooth) can almost completely offset the mesial forces on the maxillary teeth, thus to provide effective anchorage effect for the orthodontics.

CONCLUSIONS

The proposed method is effective for simulating ligation and direct occlusion. Figure-of-eight ligature can effectively disperse orthodontic forces on the posterior teeth, while a good original occlusal relationship provides considerable anchorage effects in orthodontics.

Finite Element Study of Periodontal Ligament Properties for a Maxillary Central Incisor and a Mandibular Second Molar Under Percussion Conditions

Purpose

The quantitative percussion diagnostics (QPD) response of a mandibular second molar and a maxillary central incisor including their supporting ligament/bone structure was simulated using dynamic 3D finite element analysis (FEA). The focus of the work was on the role of the periodontal ligament (PDL) which acts as a damper in the dental structure and dissipates occlusal forces transmitted from the tooth surface to the surrounding bone.

Methods

Several FEA models were developed to examine the effects of mechanical characteristics that have been reported for the PDL. Specifically, the effects of changing the PDL’s quasi-static elastic modulus and Rayleigh damping properties were predicted.

Results

The present FEA simulations indicate that the PDL can significantly reduce forces for both the incisor and the molar compared to when there is no PDL (i.e. ankylosed tooth) as long as the quasi-static elastic modulus of the PDL is among the lowest reported (~ 0.1 MPa). In addition, the FEA simulations for both the incisor and molar with this lower value of the PDL quasi-static elastic modulus are also in reasonably good agreement with experimental percussion data. A simple approximation for partitioning Rayleigh damping properties between the hard and soft tissues was also found to provide reasonable values of overall damping that are consistent with experimental data.

Conclusion

The overall findings indicate that using a quasi-static elastic modulus of approximately 0.1 MPa for the PDL in combination with Rayleigh damping gives realistic predictions of the mechanical response of a tooth under QPD loading conditions.

Strain Measurement within an Intact Swine Periodontal Ligament

The periodontal ligament (PDL) provides support, proprioception, nutrition, and protection within the tooth–PDL–bone complex (TPBC). While understanding the mechanical behavior of the PDL is critical, current research has inferred PDL mechanics from finite element models, from experimental measures on complete TPBCs, or through direct measurement of isolated PDL sections. Here, transducers are used in an attempt to quantify ex vivo PDL strain. In-fiber Bragg grating (FBG) sensors are small flexible sensors that can be placed within an intact TPBC and yield repeatable strain measurements from within the PDL space. The objective of this study was to determine: 1) if the FBG strain measured from the PDL space of intact swine premolars ex vivo was equivalent to physical PDL strains estimated through finite element analysis and 2) if a change in FBG strain could be linearly related to a change in finite element strain under variable tooth displacement, applied to an intact swine TPBC. Experimentally, individual TPBCs were subjected to 2 displacements (n = 14). The location of the FBG was determined from representative micro–computed tomography images. From a linear elastic finite element model of a TPBC, the strain magnitudes at the sensor locations were recorded. An experimental ratio (i.e., FBG strain at the first displacement divided by the FBG strain at the second displacement) and a finite element ratio (i.e., finite element strain at the first displacement divided by the finite element strain at the second displacement) were calculated. A linear regression model indicated a statistically significant relationship between the experimental and finite element ratio (P = 0.017) with a correlation coefficient (R²) of 0.448. It was concluded that the FBG sensor could be used as a measure for a change in strain and thus could be implemented in applications where the mechanical properties of an intact PDL are monitored over time.

Obesity affects the proteome profile of periodontal ligament submitted to mechanical forces induced by orthodontic tooth movement in rats

The prevalence of obesity has increased significantly worldwide. Therefore, this study aimed to evaluate the influence of obesity on the proteomic profile of periodontal ligament (PDL) tissues of rat first maxillary molars (1 M) submitted to orthodontic tooth movement (OTM). Ten Holtzman rats were distributed into two groups (n = 5): the M group (OTM), and the OM group (obesity induction plus OTM). Obesity was induced by a high-fat diet for the entire experimental periods After that period, the animals were euthanized and the hemimaxillae removed and processed for laser capture microdissection of the PDL tissues of the 1 M. Peptide extracts were obtained and analyzed by LC-MS/MS. Data are available via ProteomeXchange with identifier PXD033647. Out of the 109 proteins with differential abundance, 49 were identified in the OM group, including Vinculin, Cathepsin D, and Osteopontin, which were selected for in situ localization by immunohistochemistry analysis (IHC). Overall, Gene Ontology (GO) analysis indicated that enriched proteins were related to the GO component cellular category. IHC validated the trends for selected proteins. Our study highlights the differences in the PDL proteome profiling of healthy and obese subjects undergoing OTM. These findings may provide valuable information needed to better understand the mechanisms involved in tissue remodeling in obese patients submitted to orthodontic treatment. SIGNIFICANCE: The prevalence of obesity is increasing worldwide. Emerging findings in the field of dentistry suggest that obesity influences the tissues around the teeth, especially those in the periodontal ligament. Therefore, evaluation of the effect of obesity on periodontal tissues remodeling during orthodontic tooth movement is a relevant research topic. To our knowledge, this is the first study to evaluate proteomic changes in periodontal ligament tissue in response to the association between orthodontic tooth movement and obesity. Our study identified a novel protein profile associated with obesity by using laser microdissection and proteomic analysis, providing new information to increase understanding of the mechanisms involved in obese patients undergoing orthodontic treatment which can lead to a more personalized orthodontic treatment approach.

Biomechanical evaluation of the unilateral crossbite on the asymmetrical development of the craniofacial complex. A mechano-morphological approach

BACKGROUND AND OBJECTIVE

The occlusion effect on the craniofacial development is a controversial topic that has attracted the interest of many researchers but that remains unclear, mainly due to the difficulties on measure its mechanical response experimentally. This mechano-morphological relationship of the craniofacial growth is often explained by the periosteal and capsular matrices of the functional matrix hypothesis (FMH); however, its outcomes have not been analytically demonstrated yet. This computational study aims, therefore, to analytically demonstrate the mechano-morphological relationship in the craniofacial development of children with unilateral crossbite (UXB) using the finite element (FE) method.

METHODS

The craniofacial complex asymmetry of ten children, five of whom exhibit UXB, was 3D-analysed and compared with the biomechanical response computed from a FE analysis of each patient's occlusion. Due to the complexity of the geometry and the multitude of contacts involved, the inherent limitations of the model were evaluated by comparing computed occlusal patterns with those recorded by an occlusal analysis on 3D printed copies.

RESULTS

Comparison's outcomes proved the reliability of our models with just a deviation error below 6% between both approaches. Out of validation process, computational results showed that the significant elongation of mandibular branch in the contralateral side could be related to the mandibular shift and increase of thickness on the crossed side, and particularly of the posterior region. These morphological changes could be associated with periodontal overpressure (>4.7 kPa) and mandibular over deformation (0.002 ε) in that side, in agreement with the periosteal matrix's principles. Furthermore, the maxilla's transversal narrowing and the elevation of the maxillary and zygomatic regions on the crossed side were statistically demonstrated and seem to be related with their respective micro displacements at occlusion, as accounted by their specific capsule matrices. Our results were consistent with those reported clinically and demonstrated analytically the mechano-morphological relationship of children's craniofacial development based on the FMH's functional matrices.

CONCLUSIONS

This study is a first step in the understanding of the occlusion's effect on the craniofacial development by computational methods. Our approach could help future engineers, researchers and clinicians to understand better the aetiology of some dental malocclusions and functional disorders improve the diagnosis or even predict the craniofacial development.

Efficacy of various multi-layers of orthodontic clear aligners: a simulated study

BACKGROUND

In the invisible orthodontic treatment, composite thermoforming film materials have become the focus of orthodontic clear aligners. The orthodontic efficacy of clear aligners which consisted of multi-layers materials remains unclear. This study aims to evaluate the biomechanical effects of various multi-layers of clear aligners on en-mass retraction of maxillary anterior teeth.

METHODS

A patient-specific 3D non-linear finite element model numerical analysis was constructed to simulate the en-mass retraction of maxillary anterior teeth with clear aligner after extraction of the first premolars. Four kinds of multi-layers clear aligners with different proportion of film materials were simulated. The biomechanical responses of four different clear aligners on invisible orthodontics were calculated. The tooth displacement in all directions, the hydrostatic pressure of periodontal ligament, the orthodontic deformation of clear aligner, and the stress distribution of alveolar bone were compared and investigated.

RESULTS

In all experimental models, the maximum equivalent deformation of alveolar bone, the vector displacement of tooth and the compressive/tensile stress of periodontal ligament decreased with the increase of soft layer thickness. The elastic strain of clear aligners also decreased with the increase of the ratio of soft/hard layers.

CONCLUSIONS

The multi-layers clear aligner is better than the single-layer clear aligner in tooth movement, stress distribution of periodontal ligament and mechanical loading of alveolar bone, especially when the ratio of soft layer to hard layer is more than 50%. Moreover, the side effects of the multi-layers clear aligner are significantly less than those of the single-layer one.

An analysis of the optimal intrusion force of the maxillary central incisor with root horizontal resorption using the finite element method and curve fitting

There are no studies on the optimal intrusion force in orthodontic patients with the existing root resorption (RR). The study aimed to analyze the optimal intrusion force for central incisors with existing horizontal root resorption using the finite element method (FEM). We calculated the optimal intrusion force using the finite element method and curve fitting. We found that with the increase of the maxillary central incisor's root horizontal resorption length, the optimal intrusion force interval's median gradually increases. If the resorption length is more significant than 1/2 of the root length, it is not recommended to use intrusion force theoretically.

A new protocol to accurately track long-term orthodontic tooth movement and support patient-specific numerical modeling

Numerical simulation of long-term orthodontic tooth movement based on Finite Element Analysis (FEA) could help clinicians to plan more efficient and mechanically sound treatments. However, most of FEA studies assume idealized loading conditions and lack experimental calibration or validation. The goal of this paper is to propose a novel clinical protocol to accurately track orthodontic tooth displacement in three-dimensions (3D) and provide 3D models that may support FEA. Our protocol uses an initial cone beam computed tomography (CBCT) scan and several intra-oral scans (IOS) to generate 3D models of the maxillary bone and teeth ready for use in FEA. The protocol was applied to monitor the canine retraction of a patient during seven months. A second CBCT scan was performed at the end of the study for validation purposes. In order to ease FEA, a frictionless and statically determinate lingual device for maxillary canine retraction was designed. Numerical simulations were set up using the 3D models provided by our protocol to show the relevance of our proposal. Comparison of numerical and clinical results highlights the suitability of this protocol to support patient-specific FEA.

The optimal activation of plastic aligner for canine distal movement: a three-dimensional finite element analysis

This study aimed to investigate the optimal activation of plastic aligner for the canine distal movement by combining the stress and strain of periodontal ligament. Computer-aided design models of the upper canine, periodontal ligament, alveolar bone, and plastic aligner were constructed. The stresses and strains of periodontal ligament were acquired by fitting plastic aligner on the canine, which will cause the canine distal-direction movement. The activation of plastic aligner was set into 12 groups, including 0.050, 0.100, 0.125, 0.150, 0.175, 0.200, 0.225, 0.250, 0.275, 0.300, 0.350, and 0.400 mm. Assuming the volume-averaged hydrostatic stress (VAHS) ranging from 4.7 to 16 kPa to be the optimal stress, and an average strain no less than 0.3 to be the optimal strain. The optimal activation of plastic aligner was acquired based on the optimal stress and average strain. As the activation increased, the stress and strain of periodontal ligament increased visibly. The degree of activation of plastic aligner was nonlinearly and positively related to VAHS and average strain. According to the fitted curves, the activation corresponding to the optimal stress was 0.07-0.24 mm and the activation was not less than 0.21 mm based on the optimal strain. The optimal activation of plastic aligner for the canine distal movement was 0.21-0.24 mm in this study. The degree of activation affects the force system of orthodontic tooth movement, and it should be taken into consideration to obtain healthy and efficient tooth movement. The activation with 0.21-0.24 mm seems optimal for orthodontic tooth movement in the plastic aligner system in this study.

An in-silico approach to modeling orthodontic tooth movement using stimulus-induced external bone adaptation

Bone remodeling process has been used in orthodontics to treat malposition of teeth in patients by applying stimuli outside of usual everyday loads to promote tooth movement by affecting equilibrium state of the surrounding bone tissue. Accurate modeling of long term orthodontic tooth movement (OTM) is crucial in the field of dental biomechanical research since it allows to predict the behavior and interaction of bone-tooth environment in a non-destructive way, and helps to gain more insight on how exactly tooth motion progresses over time. Existence of such predictive tools might help to avoid the adverse effects of OTM on teeth and the surrounding tissues during this clinical procedure. In this study a new numerical approach to simulating long-term OTM is proposed, that involves external bone adaptation with strain energy density of the bone taken as the stimulus parameter and bone adaptation modeled by nodal movements at the bone-tooth interface using Abaqus UMESHMOTION subroutine. Contrary to conventional re-meshing algorithms, where the mesh of resorbed-apposed bone region is constantly updated and element deletion/creation is performed for each increment, the proposed method only moves nodes without changing the initial mesh topology. For this study, a 3D model of right central maxillary incisor tooth and its surrounding maxillary bone was used for the modeling of OTM for a duration of 1 week. Two test cases were performed and the results from induced tooth motion were investigated. Results indicate tooth movement values that were quite close to clinical values provided in the literature and this method is easily applicable to validate various postulates of OTM via adapting the stimulus-adaption rate relation and patient-specific planning of orthodontic patients as well.

Modelling and evaluating periodontal ligament mechanical behaviour and properties: A scoping review of current approaches and limitations

This scoping review is intended to synthesize the techniques proposed to model the tooth-periodontal ligament-bone complex (TPBC), while also evaluating the suggested periodontal ligament (PDL) material properties. It is concentrated on the recent advancements on the PDL and TPBC models, while identifying the advantages and limitations of the proposed approaches. Systematic searches were conducted up to December 2020 for articles that proposed PDL models to assess orthodontic tooth movement in Compendex, Web of Science, EMBASE, MEDLINE, PubMed, ScienceDirect, Google Scholar and Scopus databases. Although there have been many studies focused on the evaluation of PDL material properties through numerous modelling approaches, only a handful of approaches have been identified to investigate the interface properties of the PDL as a complete dynamical system (TPBC models). Past reviews on the analytical and experimental determination of the PDL properties already show a concerning range in reported output values-some nearly six orders of magnitude in difference-that strongly suggested the need for further investigation. Surprisingly, it has not yet been possible to determine a narrower range of values for the PDL material properties. Moreover, very few scientific approaches address the TPBC as an integrated complex system model. In consequence, current methods for capturing the PDL material behaviour in a clinical setting are limited and inconclusive. This synthesis encourages more systematic, pragmatic and phenomenological research in this area.

Tensile creep mechanical behavior of periodontal ligament: A hyper-viscoelastic constitutive model

OBJECTIVE

In orthodontic treatment, the biomechanical response of periodontal ligament (PDL) induces tooth movement. Coupling modeling of PDL can effectively reflect its biomechanical response. The nonlinear creep mechanical behavior of PDL was studied by uniaxial tensile creep test and a new hyper-viscoelastic constitutive model. Two coupling modeling methods with limitations were excluded.

METHODS

PDL specimens were prepared from the central incisors of pig mandible. The theoretical step function was replaced by static loading with a total loading time of 1 s. The creep loading with the constant stresses of 0.05, 0.1, and 0.15 MPa was selected and kept unchanged for 1000 s. The instantaneous hyperelastic mechanical behavior and time-dependent nonlinear viscoelastic mechanical behavior of PDL were characterized by coupled instantaneous third-order Ogden hyperelastic and time-dependent nonlinear creep models.

RESULTS

The results showed that the instantaneous elastic curve of PDL increases in the form of hyperelastic index. The creep strain and creep compliance curves increase rapidly before 200s, and then increase slowly in steady state. The creep strain increased with an increase in the constant stress; conversely, the creep compliance decreased with an increase in the constant stress. The results showed that the experimental data were highly consistent with the hyper-viscoelastic constitutive model (R²>0.97).

SIGNIFICANCE

We normalize the framework of hyper-viscoelastic coupling modeling (Instantaneous hyperelastic model + time-dependent nonlinear viscoelastic model). Which can be extended to other nonlinear viscoelastic biomaterials.

Microstructural heterogeneity of the collagenous network in the loaded and unloaded periodontal ligament and its biomechanical implications

The periodontal ligament (PDL) is a highly heterogeneous fibrous connective tissue and plays a critical role in distributing occlusal forces and regulating tissue remodeling. Its mechanical properties are largely determined by the extracellular matrix, comprising a collagenous fiber network interacting with the capillary system as well as interstitial fluid containing proteoglycans. While the phase-contrast micro-CT technique has portrayed the 3D microscopic heterogeneity of PDL, the topological parameters of its network, which is crucial to understanding the multiscale constitutive behavior of this tissue, has not been characterized quantitatively. This study aimed to provide new understanding of such microscopic heterogeneity of the PDL with quantifications at both tissue and collagen network levels in a spatial manner, by combining phase-contrast micro-CT imaging and a purpose-built image processing algorithm for fiber analysis. Both variations within a PDL and among the PDL with different shapes, i.e. round-shaped and kidney-shaped PDLs, are described in terms of tissue thickness, fiber distribution, local fiber densities, and fiber orientation (namely azimuthal and elevation angles). Furthermore, the tissue and collagen fiber network responses to mechanical loading were evaluated in a similar manner. A 3D helical alignment pattern was observed in the fiber network, which appears to regulate and adapt a screw-like tooth motion under occlusion. The microstructural heterogeneity quantified here allows development of sample-specific constitutive models to characterize the PDL's functional and pathological loading responses, thereby providing a new multiscale framework for advancing our knowledge of this complex limited mobility soft-hard tissue interface.

Biomechanical analysis of reinstating buccally flared maxillary 2nd molars using 3D printing anchorage supports: a 3D finite element study

The buccally flared maxillary 2nd molar has certain consequences on oral function and health. However, existing methods have some degree of disadvantages, such as invasion, complexity and side effects. The objectives of this study were to design anchorage systems to correct buccally flared maxillary 2nd molars and analyze their biomechanical effects by 3-dimensional (3D) finite element analysis. Finite element (FE) models of the 3D tanspalatal arches (TPAs) and 3D splints with different thicknesses and force points were constructed. The stress distribution on teeth, the hydrostatic pressure on periodontal ligaments and the initial displacement of teeth were analyzed. A total of 18 FE models were constructed and analyzed. The stress concentrated on a single anchorage tooth, and the hydrostatic pressure and initial displacement of the anchorage tooth were greater than those of the malposed 2nd molar in the 3D splint anchorage system. The stress spread on all anchorage teeth and the hydrostatic pressure and initial displacement of the anchorage tooth were less than those of the malposed 2nd molar in the 3D TPA anchorage system. Theoretically, the 3D TPA was better than the 3D splint as an anchorage to correct the buccally flared 2nd molar. A combination of 0.8 mm of thickness and mesial force point provided the optimal conditions for the 3D TPA. Further clinical studies should be conducted to verify the effects of 3D appliances.

Three-dimensional coupling between orthodontic bone remodeling and superelastic behavior of a NiTi wire applied for initial alignment

PURPOSE

NiTi wires are considered as the most appropriate wires to be used during the initial phase of orthodontic treatment. This work presents a numerical method to simulate the coupling between the orthodontic appliance and bone remodeling, which are the two mechanisms responsible for the orthodontic tooth movement.

METHODS

The superelastic behavior of a NiTi wire was integrated in a three-dimensional simulation model to reproduce the long-term bone remodeling coupled with tooth alignment using the finite element method. The orthodontic load was derived by deforming the superelastic wire in order to adopt itself to the original position of irregular teeth. Root form was extracted from cone beam tomography imaging files.

RESULTS

As a result, the teeth were aligned while the wire was recovering its initial shape. The canine was intruded by 0.53 mm, while the neighboring teeth were extruded by 0.44 and 0.46 mm. When the wire was loaded, it generated a load of 4.6 N on the bracket bonded on the canine. This force was active during the first day of the treatment. Then, the force continued to decline until the end of the correction period. The decreasing load delivered from the wire affected the teeth displacements as observed in real situations.

CONCLUSION

Despite the complexity of the presented numerical simulation, this procedure allowed the analysis of the orthodontic forces that were generated in the clinical experiments and of the biomechanical response of the periodontal support elements when using this kind of wire.

A new perspective: Periodontal ligament is a viscoelastic fluid biomaterial as evidenced by dynamic shear creep experiment

Currently, Periodontal ligament (PDL) is considered as a viscoelastic solid biomaterial. However, we observed the steady-state rheological behavior of PDL through long time loading experiments, and suggested the theoretical definition of PDL as a viscoelastic fluid biomaterial. PDL specimens were prepared from the middle area of the mandibular central incisors in pigs. Dynamic force loading with frequencies of 0 (static load), 2, 5, and 10 Hz and amplitudes of 0.01, 0.02, and 0.03 MPa was adopted. The shear strain-time curve at the equilibrium position of PDL was obtained by a dynamic shear creep experiment. The results showed that the shear strain increased exponentially at first and then inclined toward an oblique line. The results showed that the PDL has viscoelastic fluid characteristics, independent of frequency and amplitude. The shear strain decreased with an increase in frequency and amplitude. To further analyze the viscoelastic characteristics of PDL, a 50000-s static shear creep experiment was re-designed. PDL exhibited viscoelastic fluid biomaterial characteristics according to the three aspects of the algebraic fitting, geometric characteristics, and physical results. For the first time, a viscoelastic fluid constitutive model was established to characterize the mechanical properties of PDL with high fitting accuracy. Furthermore, the shear viscosity coefficient of the dynamic load was larger than that of the static load, increasing with an increase in frequency and amplitude; compared with the static force, the dynamic force improved the viscosity of PDL, enhancing its function of fixing teeth, and introducing the new medical knowledge of "No tooth extraction after a meal."

Numerical simulation of optimal range of rotational moment for the mandibular lateral incisor, canine and first premolar based on biomechanical responses of periodontal ligaments: a case study

OBJECTIVES

The objective of this study was to investigate the optimal range of rotational moment for the mandibular lateral incisor, canine and first premolar to determine tooth movements during orthodontic treatment using hydrostatic stress and logarithmic strain on the periodontal ligament (PDL) as indicators by numerical simulations.

MATERIAL AND METHODS

Teeth, PDL and alveolar bone numerical models were constructed as analytical objects based on computed tomography (CT) images. Teeth were assumed to be rigid bodies, and rotational moments ranging from 1.0 to 4.0 Nmm were exerted on the crowns. PDL was defined as a hyperelastic-viscoelastic material with a uniform thickness of 0.25 mm. The alveolar bone model was constructed using a non-uniform material with varied mechanical properties determined based on Hounsfield unit (HU) values calculated using CT images, and its bottom was fixed completely. The optimal range values of PDL compressive and tensile stress were set as 0.47-12.8 and 18.8-51.2 kPa, respectively, whereas that of PDL logarithmic strain was set as 0.15-0.3%.

RESULTS

The rotational tendency of PDL was around the long axis of teeth when loaded. The optimal range values of rotational moment for the mandibular lateral incisor, canine and first premolar were 2.2-2.3, 3.0-3.1 and 2.8-2.9 Nmm, respectively, referring to the biomechanical responses of loaded PDL. Primarily, the optimal range of rotational moment was quadratically dependent on the area of PDL internal surface (i.e. area of PDL internal surface was used to indicate PDL size), as described by the fitting formula.

CONCLUSIONS

Biomechanical responses of PDL can be used to estimate the optimal range of rotational moment for teeth. These rotational moments were not consistent for all teeth, as demonstrated by numerical simulations.

CLINICAL RELEVANCE

The quantitative relationship between the area of PDL internal surface and the optimal orthodontic moment can help orthodontists to determine a more reasonable moment and further optimise clinical treatment.

Orthodontic force prediction model of T-loop closing spring based on dynamic resistance model

Malocclusion has been seriously endangering human oral function. The most effective and mature therapy is orthodontic treatment. But the relationship between the shape of the T-loop and the orthodontic force is unclear, and the precise mathematical model has not been established. In this article, the dynamic orthodontic force prediction model of the T-loop was established by analyzing the treatment process of the T-loop. The model was based on the dynamic resistance model of waxy dental jaw, the theory of beam deformation, and the deformation characteristics of the T-loop. In the experimental process, 11 kinds of orthodontic archwires were used as experimental samples, including 2 kinds of common archwire materials, 7 kinds of cross-sectional sizes, and 10 kinds of clearance distances. The T-loop was put into the extraction space and immersed in 75°C constant temperature water for 2 min. And the experimental data were measured and collected by the dynamic force measuring device. The experimental results show that the cross-sectional size and the clearance distance are positively correlated with the orthodontic force. The influence of the clearance distance on the orthodontic force is greater than that of the cross-section size. The deviation rates between the experimental values of orthodontic force and the theoretical values are between 1.10% and 9.09%, which verifies the accuracy of the dynamic orthodontic force prediction model. The model can predict the orthodontic force, improve the treatment effect, shorten the treatment cycle, and provide reference and guidance for orthodontists to carry out orthodontic treatment safely and effectively.

Linear Momenta Transferred to the Dental Implant-Bone and Natural Tooth-PDL-Bone Constructs Under Impact Loading: A Comparative in-vitro and in-silico Study

During dental trauma, periodontal ligament (PDL) contributes to the stability of the tooth-PDL-bone structure. When a dental implant is inserted into the bone, the dental implant-bone construct will be more prone to mechanical damage, caused by impact loading, than the tooth-PDL-bone construct. In spite of the prevalence of such traumas, the behavioral differences between these two constructs have not been well-understood yet. The main goal of this study was to compare the momentum transferred to the tooth-PDL-bone and dental implant-bone constructs under impact loading. First, mechanical impact tests were performed on six canine mandibles of intact (N = 3) and implanted (N = 3) specimens using a custom-made drop tower apparatus, from release heights of 1, 2, and 3 cm. Next, computed tomography-based finite element models were developed for both constructs, and the transferred momenta were calculated. The experimental results indicated that, for the release heights of 1, 2, and 3 cm, the linear momenta transferred to the dental implant-bone construct were 33.1, 31.0, and 27.5% greater than those of the tooth-PDL-bone construct, respectively. Moreover, results of finite element simulations were in agreement with those of the experimental tests (error <7.5%). This work tried to elucidate the effects of impact loading on the dental implant-bone and tooth-PDL-bone constructs using both in-vitro tests and validated in-silico simulations. The findings can be employed to modify design of the current generation of dental implants, based on the lessons one can take from the biomechanical behavior of a natural tooth structure.

Mandible Integrity and Material Properties of the Periodontal Ligament during Orthodontic Tooth Movement: A Finite-Element Study

We used the finite-element method (FEM) to investigate the effects of jawbone model integrity and the material properties of the periodontal ligament (PDL) on orthodontic tooth movement. Medical imaging software and computer-aided design software were used to create finite-element models of a partial and complete mandibles based on dental cone beam computed tomography images of the human skull. Additionally, we exerted an orthodontic force on the canine crown in the direction of an orthodontic miniscrew under a lower molar root to compare the von Mises strain on the canine PDL in three models: a partial mandible model under orthodontic force (Model 1), a complete mandible model under orthodontic force (Model 2), and a complete mandible model under orthodontic force with clench occlusion in the intercuspal position (ICP; Model 3). Additionally, in the complete mandible model under orthodontic force with ICP occlusion, we analyzed the effects of a PDL with a low (Model 4), moderate (Model 5), and high (Model 6) linear elastic modulus and a PDL a bilinear elastic modulus (Model 7). The simulation results for mandible integrity indicated that the maximum von Mises strains on the canine PDL for Models 1, 2, and 3 were 0.461, 0.394, and 1.811, respectively. Moreover, for the models with different PDL material properties, the maximum von Mises strains on the canine PDLs for Models 4, 5, 6, and 7 were 6.047, 2.594, 0.887, and 1.811, respectively. When the FEM was used to evaluate tooth movement caused by orthodontic force, the transformation of a complete mandible model into a partial mandible model or alteration of the elastic modulus of the PDL influenced the biomechanical responses of the PDL. Additionally, the incorporation of daily ICP occlusion resulted in a larger effect.

In silico study of cuspid' periodontal ligament damage under parafunctional and traumatic conditions of whole-mouth occlusions. A patient-specific evaluation

BACKGROUND AND OBJECTIVE

Although traumatic loading has been associated with periodontal ligament (PDL) damage and therefore with several oral disorders, the damage phenomena and the traumatic loads involved are still unclear. The complex composition and extremely thin size of the PDL make experimentation difficult, requiring computational studies that consider the macroscopic loading conditions, the microscopic composition and fine detailed geometry of the tissue. In this study, a new methodology to analyse the damage phenomena in the collagen network and the extracellular matrix of the PDL caused by parafunctional and traumatic occlusal forces was proposed.

METHODS

The entire human mandible and a portion thereof containing a full cuspid tooth were separately modelled using finite element analysis based on computed tomography and micro-computed tomography images, respectively. The first model was experimentally validated by occlusion analysis and subjected to the muscle loads produced during hard and soft chewing, traumatic cuspid occlusion, grinding, clenching, and simultaneous grinding and clenching. The occlusal forces computed by the first model were subsequently applied to the single tooth model to evaluate damage to the collagen network and the extracellular matrix of the PDL.

RESULTS

Early occlusal contact on the left cuspid tooth guided the mandible to the more occluded side (16.5% greater in the right side) and absorbed most of the lateral load. The intrusive occlusal loads on the posterior teeth were 0.77-13.3% greater than those on the cuspid. According to our findings, damage to the collagen network and the extracellular matrix of the PDL could occur in traumatic and grinding conditions, mainly due to fibre overstretching (>60%) and interstitial fluid overpressure (>4.7 kPa), respectively.

CONCLUSIONS

Our findings provide important biomechanical insights into the determination of damage mechanisms which are caused by mechanical loading and the key role of the porous-fibrous behaviour of the PDL in parafunctional and traumatic loading scenarios. Besides, the 3D loading conditions computed from occlusal contacts will help future studies in the design of new orthodontics appliances and encourage the application of computing methods in medical practice.

Establishment and Experiment of Utility Archwire Dynamic Orthodontic Moment Prediction Model

OBJECTIVE

This study investigated the performance of a dynamic orthodontic moment prediction model by analyzing orthodontic treatment processes with different utility archwires.

METHOD

The prediction model was based on a wax resistance model, the combined load theory of beams and the lateral buckling theory of prisms. The experimental samples used herein comprised 12 different archwire configurations (3 different materials and 4 different diameters). The utility archwire was ligated to the 11th tooth of the wax mold, which was immersed in a constant temperature water environment at 75 °C for 2 min.

RESULT

As the archwire diameter increased, increasing the elastic modulus of the archwire produced greater increases in the change rate of the orthodontic moment with respect to the lateral arc length. A comparison of the orthodontic moment values from three common orthodontic archwire materials revealed the following trend: stainless steel wire > Australian wire > Ni-Ti wire.

CONCLUSION

The accuracy of the utility archwire dynamic orthodontic moment prediction model was verified through a comparison of the experimental measurements and theoretical calculations.

SIGNIFICANCE

The presented model can help make timely adjustments to orthodontic treatment schemes, improve the orthodontic effect, shorten the treatment cycle, and provide reference and guidance that enables orthodontists to carry out orthodontic treatment safely and efficiently.

Numerical simulation of hydro-mechanical coupling of periodontal ligament

Orthodontic tooth movement in the alveolar bone is due to the mechanical response of periodontal ligament to applied forces. Definition of a proper constitutive model of the periodontal ligament to investigate its response to orthodontic loading is required. For this purpose, a three-dimensional finite element model of incisor tooth, periodontal ligament, and bone was built utilizing the hydro-mechanical coupling theory. Tooth displacement in response to orthodontic loading was then investigated, and the effect of different mechanical behaviors assigned to the solid phase of the periodontal ligament was compared. Results showed that where the periodontal ligament was placed in tension, pore volume was filled with fluid intake from the bone, but fluid flow direction was from the periodontal ligament toward the bone where the periodontal ligament was placed in compression. Because of the existence of interaction between solid and fluid phases of the periodontal ligament, considering biphasic material formulation was capable to address its microscopic behavior as well as time-dependent and large deformation behaviors. This article provides beneficial biomechanical data for future dental studies in determination of optimal orthodontic force.

Finite element modeling of the periodontal ligament under a realistic kinetic loading of the jaw system

Purpose

The stresses and deformations in the periodontal ligament (PDL) under the realistic kinetic loading of the jaw system, i.e., chewing, are difficult to be determined numerically as the mechanical properties of the PDL is variably present in different finite element (FE) models. This study was aimed to conduct a dynamic finite element (FE) simulation to investigate the role of the PDL (PDL) material models in the induced stresses and deformations using a simplified patient-specific FE model of a human jaw system.

Methods

To do that, a realistic kinetic loading of chewing was applied to the incisor point, contralateral, and ipsilateral condyles, through the experimentally proven trajectory approach. Three different material models, including the elasto-plastic, hyperelastic, and viscoelastic, were assigned to the PDL, and the resulted stresses of the tooth FE model were computed and compared.

Results

The results revealed the highest von Mises stress of 620.14 kPa and the lowest deformation of 0.16 mm in the PDL when using the hyperelastic model. The concentration of the stress in the elastoplastic and viscoelastic models was in the mid-root and apex of the PDL, while for the hyperelastic model, it was concentrated in the cervical margin. The highest deformation in the PDL regardless of the employed material model was located in the caudal direction of the tooth. The viscoelastic PDL absorbed the transmitted energy from the dentine and led to lower stress in the cancellous bone compared to the elastoplastic and hyperelastic material models.

Conclusion

These results have implications not only for understanding the stresses and deformations in the PDL under chewing but also for providing comprehensive information for the medical and biomechanical experts in regard of the role of the material models being used to address the mechanical behavior of the PDL in other components of the tooth.

Effect of different implant configurations on biomechanical behavior of full-arch implant-supported mandibular monolithic zirconia fixed prostheses

Mechanical failure of zirconia-based full-arch implant-supported fixed dental prostheses (FAFDPs) remains a critical issue in prosthetic dentistry. The option of full-arch implant treatment and the biomechanical behaviour within a sophisticated screw-retained prosthetic structure have stimulated considerable interest in fundamental and clinical research. This study aimed to analyse the biomechanical responses of zirconia-based FAFDPs with different implant configurations (numbers and distributions), thereby predicting the possible failure sites and the optimum configuration from biomechanical aspect by using finite element method (FEM). Five 3D finite element (FE) models were constructed with patient-specific heterogeneous material properties of mandibular bone. The results were reported using volume-averaged von-Mises stresses (σ_VM^VA) to eliminate numerical singularities. It was found that wider placement of multi-unit copings was preferred as it reduces the cantilever effect on denture. Within the limited areas of implant insertion, the adoption of angled multi-unit abutments allowed the insertion of oblique implants in the bone and wider distribution of the multi-unit copings in the prosthesis, leading to lower stress concentration on both mandibular bone and prosthetic components. Increasing the number of supporting implants in a FAFDPs reduced loading on each implant, although it may not necessarily reduce the stress concentration in the most posterior locations significantly. Overall, the 6-implant configuration was a preferable configuration as it provided the most balanced mechanical performance in this patient-specific case.

An immunofluorescence study on VEGF and extracellular matrix proteins in human periodontal ligament during tooth movement

The periodontal ligament (PDL) is a highly vascularized connective tissue surrounding the root of a tooth. In particular, the PDL is continuously exposed to mechanical stresses during the phases of mastication, and it provides physical, sensory, and trophic functions. It is known that the application of orthodontic force creates a change in periodontal structures. In fact, these forces generate a pressure on the ligament that closes the vessels. The aim of this study is to observe the modifications of vascular endothelial growth factor (VEGF) in the PDL and extracellular matrix proteins after application of a pre-calibrated and constant orthodontic force at different phases of treatment. We used a 50-g NiTi coiled spring and in vivo samples of PDL of maxillary and mandibular premolars of patients subjected to orthodontic treatment. These teeth were extracted at 1, 7, 14, 21, and 30 days, respectively, by application of force. The extraction of the PDL was effectuated by scarifying the radicular surface on the pressure and tension sides. The mechanical stress induced by the application of force caused an increase in the reactive type of metabolism of extracellular matrix proteins and modulation of neoangiogenesis until restoration.

In vivo effects of different orthodontic loading on root resorption and correlation with mechanobiological stimulus in periodontal ligament

Orthodontic root resorption is a common side effect of orthodontic therapy. It has been shown that high hydrostatic pressure in the periodontal ligament (PDL) generated by orthodontic forces will trigger recruitment of odontoclasts, leaving resorption craters on root surfaces. The patterns of resorption craters are the traces of odontoclast activity. This study aimed to investigate resorptive patterns by: (i) quantifying spatial root resorption under two different levels of in vivo orthodontic loadings using microCT imaging techniques and (ii) correlating the spatial distribution pattern of resorption craters with the induced mechanobiological stimulus field in PDL through nonlinear finite-element analysis (FEA) in silico. Results indicated that the heavy force led to a larger total resorption volume than the light force, mainly by presenting greater individual crater volumes ( p < 0.001) than increasing crater numbers, suggesting that increased mechano-stimulus predominantly boosted cellular resorption activity rather than recruiting more odontoclasts. Furthermore, buccal-cervical and lingual-apical regions in both groups were found to have significantly larger resorption volumes than other regions ( p < 0.005). These clinical observations are complemented by the FEA results, suggesting that root resorption was more likely to occur when the volume average compressive hydrostatic pressure exceeded the capillary blood pressure (4.7 kPa).

A porous fibrous hyperelastic damage model for human periodontal ligament: Application of a microcomputerized tomography finite element model

The periodontal ligament (PDL) is a soft biological tissue that connects the tooth with the trabecular bone of the mandible. It plays a key role in load transmission and is primarily responsible for bone resorption and most common periodontal diseases. Although several numerical studies have analysed the biomechanical response of the PDL, most did not consider its porous fibrous structure, and only a few analysed damage to the PDL. This study presents an innovative numerical formulation of a porous fibrous hyperelastic damage material model for the PDL. The model considers two separate softening phenomena: fibre alignment during loading and fibre rupture. The parameters for the material model characterization were fitted using experimental data from the literature. Furthermore, the experimental tests used for characterization were computationally modelled to verify the material parameters. A finite element model of a portion of a human mandible, obtained by microcomputerized tomography, was developed, and the proposed constitutive model was implemented for the PDL. Our results confirm that damage to the PDL may occur mainly because of overpressure of the interstitial fluid, while large forces must be applied to damage the PDL fibrous network. Moreover, this study clarifies some aspects of the relationship between PDL damage and the bone remodelling process.

The circadian expression of osteogenic factors in periodontal tissue loading mechanical force: new concepts of the personalized orthodontic care

Objective

The need for orthodontic treatment continues to increase. Strategies that shorten the treatment course and reduce discomfort are most welcome in clinic. Circadian rhythm plays important role in various physiological processes, including bone formation. This study intended to depict a possible circadian releasing property of the osteogenic factors within the periodontal tissue during orthodontic treatment, which may direct a more efficient and satisfactory orthodontic treatment to the patient.

Methods

Primary periodontal ligament cells (PDLCs) were obtained from the Sprague-Dawley (SD) rats. An equibiaxial strain value of 12% was applied on rat PDLCs (rPDLCs). After 2 h stimuli of 10^-7 M dexamethasone (DX), the osteogenic genes' expressions were detected by real-time polymerase chain reaction (RT-PCR) at Zeitgeber times 0, 4, 8, 12, 16, 20, and 24. An orthodontic appliance was placed on 45 SD rats. Animals were maintained under 12-h light/dark periods and euthanized at 9 time points over the diurnal cycle. The orthodontic sensitive tissues of the mesial root of the maxillary first molar were collected for RT-PCR and immunohistological assay.

Results

The rPDLCs displayed typical fibroblastic spindle shape, and subcultured steadily in vitro. Induced by DX, the mRNA expression of Col-1, OPN, and IBSP within the loaded/unloaded rPDLCs oscillated as that of the main clock gene Per-1. The osteogenic genes' expressions as well as the protein releases sustained a circadian oscillation trend in vivo.

Conclusions

This study indicates the existence of a circadian rhythm of the osteogenic factors within the orthodontic sensitive tissues, which highlights the importance of precise timing of force loading in further orthodontic treatment. Thus, a periodicity pattern of orthodontic traction at night may prove a more efficient tooth movement while minimizing the treatment window and discomfort complains.

A biomechanical case study on the optimal orthodontic force on the maxillary canine tooth based on finite element analysis

Excessive forces may cause root resorption and insufficient forces would introduce no effect in orthodontics. The objective of this study was to investigate the optimal orthodontic forces on a maxillary canine, using hydrostatic stress and logarithmic strain of the periodontal ligament (PDL) as indicators. Finite element models of a maxillary canine and surrounding tissues were developed. Distal translation/tipping forces, labial translation/tipping forces, and extrusion forces ranging from 0 to 300 g (100 g=0.98 N) were applied to the canine, as well as the force moment around the canine long axis ranging from 0 to 300 g·mm. The stress/strain of the PDL was quantified by nonlinear finite element analysis, and an absolute stress range between 0.47 kPa (capillary pressure) and 12.8 kPa (80% of human systolic blood pressure) was considered to be optimal, whereas an absolute strain exceeding 0.24% (80% of peak strain during canine maximal moving velocity) was considered optimal strain. The stress/strain distributions within the PDL were acquired for various canine movements, and the optimal orthodontic forces were calculated. As a result the optimal tipping forces (40-44 g for distal-direction and 28-32 g for labial-direction) were smaller than the translation forces (130-137 g for distal-direction and 110-124 g for labial-direction). In addition, the optimal forces for labial-direction motion (110-124 g for translation and 28-32 g for tipping) were smaller than those for distal-direction motion (130-137 g for translation and 40-44 g for tipping). Compared with previous results, the force interval was smaller than before and was therefore more conducive to the guidance of clinical treatment. The finite element analysis results provide new insights into orthodontic biomechanics and could help to optimize orthodontic treatment plans.

A novel approach for early evaluation of orthodontic process by a numerical thermomechanical analysis

The main objective of this paper is to propose a novel method that provides an opportunity to evaluate an orthodontic process at early phase of the treatment. This was accomplished by finding out a correlation between the applied orthodontic force and thermal variations in the tooth structure. To this end, geometry of the human tooth surrounded by the connective soft tissue called the periodontal ligament and the bone was constructed by employing dental CT scan images of a specific case. The periodontal ligament was modeled by finite strain viscoelastic model through a nonlinear stress-strain relation (hyperelasticity) and nonlinear stress-time relation (viscoelasticity). The tooth structure was loaded by a lateral force with 15 different quantities applied to 20 different locations, along the midedge of the tooth crown. The resultant compressive stress in the periodontal ligament was considered as the cause of elevated cell activity that was modeled by a transient heat flux in the thermal analysis. The heat flux value was estimated by conducting an experiment on a pair of rats. The numerical results showed that by applying an orthodontic force to the tooth structure, a significant temperature rise was observed. By measuring the temperature rise, the orthodontic process can be evaluated.

Identification of dynamic load for prosthetic structures

Dynamic load exists in numerous biomechanical systems, and its identification signifies a critical issue for characterizing dynamic behaviors and studying biomechanical consequence of the systems. This study aims to identify dynamic load in the dental prosthetic structures, namely, 3-unit implant-supported fixed partial denture (I-FPD) and teeth-supported fixed partial denture. The 3-dimensional finite element models were constructed through specific patient's computerized tomography images. A forward algorithm and regularization technique were developed for identifying dynamic load. To verify the effectiveness of the identification method proposed, the I-FPD and teeth-supported fixed partial denture structures were investigated to determine the dynamic loads. For validating the results of inverse identification, an experimental force-measuring system was developed by using a 3-dimensional piezoelectric transducer to measure the dynamic load in the I-FPD structure in vivo. The computationally identified loads were presented with different noise levels to determine their influence on the identification accuracy. The errors between the measured load and identified counterpart were calculated for evaluating the practical applicability of the proposed procedure in biomechanical engineering. This study is expected to serve as a demonstrative role in identifying dynamic loading in biomedical systems, where a direct in vivo measurement may be rather demanding in some areas of interest clinically.

Inclusion of periodontal ligament fibres in mandibular finite element models leads to an increase in alveolar bone strains

Alveolar bone remodelling is vital for the success of dental implants and orthodontic treatments. However, the underlying biomechanical mechanisms, in particular the function of the periodontal ligament (PDL) in bone loading and remodelling, are not well understood. The PDL is a soft fibrous connective tissue that joins the tooth root to the alveolar bone and plays a critical role in the transmission of loads from the tooth to the surrounding bone. However, due to its complex structure, small size and location within the tooth socket it is difficult to study in vivo. Finite element analysis (FEA) is an ideal tool with which to investigate the role of the PDL, however inclusion of the PDL in FE models is complex and time consuming, therefore consideration must be given to how it is included. The aim of this study was to investigate the effects of including the PDL and its fibrous structure in mandibular finite element models. A high-resolution model of a human molar region was created from micro-computed tomography scans. This is the first time that the fibrous structure of the PDL has been included in a model with realistic tooth and bone geometry. The results show that omission of the PDL creates a more rigid model, reducing the strains observed in the mandibular corpus which are of interest when considering mandibular functional morphology. How the PDL is modelled also affects the strains. The inclusion of PDL fibres alters the strains in the mandibular bone, increasing the strains in the tooth socket compared to PDL modelled without fibres. As strains in the alveolar bone are thought to play a key role in bone remodelling during orthodontic tooth movement, future FE analyses aimed at improving our understanding and management of orthodontic treatment should include the fibrous structure of the PDL.