The influence of PDL principal fibers in a 3-dimensional analysis of orthodontic tooth movement

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.

The effects of material and structural properties of the periodontal ligament in mechanical function of tooth-PDL-bone complex in dental trauma: A sensitivity study using finiteelement analysis

Periodontal ligament (PDL) plays a crucial role in transferring load from tooth to its adjacent bone, and its role is more pronounced in case of trauma, due to its shock-absorbing character, which has not been fully understood yet. Different constitutive models have correlated mechanical function of PDL with its anisotropic, inhomogeneous, non-linear elastic nature, and it was variably modeled using Finite Element (FE) simulations of dental trauma. Furthermore, since capturing accurate dimension of PDL is difficult, various thicknesses were considered for PDL in FE reconstruction process. In this study, the sensitivity of FE analyses to variation in mechanical properties, including a large range of elastic properties for a linear elastic model, also a hyper-elastic material model, and various thicknesses of PDL was investigated by developing a CT-based FE model of tooth-PDL-bone complex. Results of this study highlighted the crucial role of PDL in absorption and dissipation of energy, as well as in stress distribution within alveolar bone during dental trauma. It was observed that as Young's modulus of PDL decreases and its thickness increases, its shock-absorbing capacity would be escalated. Moreover, it was found that inclusion of PDL reduces the maximum von Mises stress exerted on the alveolar bone by about 60% in some areas, compared to the case in which the PDL is absent. Results of this work underscore the need of presenting comprehensive constitutive models to describe mechanical behavior of PDL, with the goal of understanding the behavior of a tooth-PDL-bone complex in pathological conditions, such as trauma.

The effects of different types of periodontal ligament material models on stresses computed using finite element models

INTRODUCTION

Finite element (FE) method has been used to calculate stress in the periodontal ligament (PDL), which is crucial in orthodontic tooth movement. The stress depends on the PDL material property, which varies significantly in previous studies. This study aimed to determine the effects of different PDL properties on stress in PDL using FE analysis.

METHODS

A 3-dimensional FE model was created consisting of a maxillary canine, its surrounding PDL, and alveolar bone obtained from cone-beam computed tomography scans. One Newton of intrusion force was applied vertically to the crown. Then, the hydrostatic stress and the von Mises stress in the PDL were computed using different PDL material properties, including linear elastic, viscoelastic, hyperelastic, and fiber matrix. Young's modulus (E), used previously from 0.01 to 1000 MPa, and 3 Poisson's ratios, 0.28, 0.45, and 0.49, were simulated for the linear elastic model.

RESULTS

The FE analyses showed consistent patterns of stress distribution. The high stresses are mostly concentrated at the apical area, except for the linear elastic models with high E (E >15 MPa). However, the magnitude varied significantly from -14.77 to -127.58 kPa among the analyzed patients. The E-stress relationship was not linear. The Poisson's ratio did not affect the stress distribution but significantly influenced the stress value. The hydrostatic stress varied from -14.61 to -95.48 kPa.

CONCLUSIONS

Different PDL material properties in the FE modeling of dentition do not alter the stress distributions. However, the magnitudes of the stress significantly differ among the patients with the tested material properties.

Response of human periodontal ligament to orthodontic force using superb microvascular imaging

INTRODUCTION

Remodeling of the periodontal ligament (PDL) during orthodontic tooth movement is closely related to the vascularity of the PDL, which has not been thoroughly investigated in humans. This study aimed to measure the width and vascular parameters of human PDL using superb microvascular imaging for the first time.

METHODS

Patients aged 18-25 years were selected for participation. The intervention was randomly allocated from the maxillary canines to the first molars on both sides using 50 g or 150 g of force. The width and vascular parameters of the PDL were measured using superb microvascular imaging at different time intervals (baseline, 30 minutes, and 1, 3, 7, and 14 days).

RESULTS

Before the intervention, the width of the PDL ranged from 0.14 to 0.25 mm, and the vascular index ranged from 9.40% to 13.54%. After applying orthodontic forces, the cervical and middle PDL widths increased. The vascular index decreased slightly in 30 minutes, decreased to a minimum value after 1 day, increased to the maximum in 3-7 days, and returned to baseline values in 14 days. The values of other vascular parameters showed similar trends.

CONCLUSIONS

The width and vascular parameters of the PDL changed slightly after force application, underwent changes in the period of reconstruction for 3-7 days, and eventually returned to baseline in 14 days.

Finite element and clinical analyses of effects of a new intraoral device (VomPress) combined with extraoral RAMPA on improving the overjet of craniofacial complex

This research intends to investigate the effects of a new intraoral device, VomPress, combined with a Right Angle Maxillary Protraction Appliance (RAMPA) extraoral device on the treatment of maxillary hypoplasia. To this end, finite element (FE) method has been employed and a skull model, including all sutures, has been investigated. In addition, the effects of VomPress combined with RAMPA on a seven-year-old girl with the malocclusion and other side problems were monitored. The results of both FE simulations and the clinical data revealed that VomPress combined with RAMPA effectively improved the malocclusion and straight neck problem by creating more space in the patient's mouth and anterosuperior protraction effects.

The effects of a PDL analogue on occlusal contact forces

BACKGROUND

Previous bench-top studies examined the details of the mechanical environment of rigidly-fixed occluding teeth. It was demonstrated that during each chomp, contacting molar teeth experience in-occlusal-plane forces (F_lateral ) that are highly transient in magnitude and direction.

OBJECTIVES

The objectives of this study are to identify F_lateral behaviors that are attributable to the presence of a visco-elastic periodontal ligament (PDL) analogue, and to asses the necessity of incorporating it into future studies.

METHODS

A weighted maxillary molar denture tooth was lowered onto, and raised from, a matching mandibular molar 10 times. The latter was supported by a load cell that continuously measured F_lateral . For statistical purposes, the test was repeated with 21 (n = 21) different occlusal relationships obtained with 0.05 mm incremental shifts of the lower assembly.

RESULTS

Overall, the results are similar to those of rigid attachment but the details of the F_lateral profiles are very different.

CONCLUSION

The PDL plays a major role in the mechanical environment of occlusion, suggesting that, in general (not necessarily always), it should be integrated into studies of occlusion.

Peak loads on teeth from a generic mouthpiece of a vibration device for accelerating tooth movement

INTRODUCTION

The effect of vibrational force (VF) on accelerating orthodontic tooth movement depends on the ability to control the level of stimulation in terms of its peak load (PL) on the tooth. The objective of this study was to investigate the PL distribution on the teeth when a commercial VF device is used.

METHODS

Finite element models of a human dentition from cone-beam computed tomography images of an anonymous subject and a commonly used commercial VF device were created. The device consists of a mouthpiece and a VF source. The maxilla and mandible bites on the mouthpiece with the VF applied to it. Interface elements were used between the teeth and the mouthpiece, allowing relative motion at the interfaces. The finite element model was validated experimentally. Static load and VF with 2 frequencies were used, and the PL distributions were calculated. The effects of mouthpiece materials and orthodontic appliances on the PL distribution were also investigated.

RESULTS

The PL distribution of this kind of analyzed device is uneven under either static force or VF. Between the anterior and posterior segments, the anterior segment receives the most stimulations. The mouthpiece material affects the PL distribution. The appliance makes the PL more concentrated on the incisors. The VF frequencies tested have a negligible influence on both PL magnitude and distribution.

CONCLUSIONS

The device analyzed delivers different levels of stimulation to the teeth in both maxilla and mandible. Changing the material property of the mouthpiece alters the PL distribution.

Where is the center of resistance of a maxillary first molar? A 3-dimensional finite element analysis

INTRODUCTION

The center of resistance (C_Res) is regarded as the fundamental reference point for predictable tooth movement. Accurate estimation can greatly enhance the efficiency of orthodontic tooth movement. Only a handful of studies have evaluated the C_Res of a maxillary first molar; however, most had a low sample size (in single digits), used idealized models, or involved 2-dimensional analysis. The objectives of this study were to: (1) determine the 3-dimensional (3D) location of the C_Res of maxillary first molars, (2) evaluate its variability in a large sample, and (3) investigate the effects of applying orthodontic load from 2 directions on the location of the C_Res.

METHODS

Cone-beam computed tomography scans of 50 maxillary molars from 25 patients (mean age, 20.8 ± 8.7 years) were used. The cone-beam computed tomography volume images were manipulated to extract 3D biological structures via segmentation. The segmented structures were cleaned and converted into virtual mesh models made of tetrahedral triangles having a maximum edge length of 1 mm. The block, which included the molars and periodontal ligament, consisted of a mean of 7753 ± 2748 nodes and 38,355 ± 14,910 tetrahedral elements. Specialized software was used to preprocess the models to create an assembly and assign material properties, interaction conditions, boundary conditions, and load applications. Specific loads were applied, and custom-designed algorithms were used to analyze the stress and strain to locate the C_Res. The C_Res was measured in relation to the geometric center of the buccal surface of the molar and the trifurcation of the molar roots.

RESULTS

The average location of the C_Res for the maxillary first molar was 4.94 ± 1.39 mm lingual, 2.54 ± 2.7 mm distal, and 7.86 ± 1.66 mm gingival relative to the geometric center of the buccal surface of the molar and 0.136 ± 1.51 mm lingual (P <0.01), 1.48 ± 2.26 mm distal (P <0.01), and 0.188 ± 1.75 mm gingival (P >0.01) relative to the trifurcation of the molar roots. In the anteroposterior (y-axis) and the vertical (z-axis) planes, the C_Res showed significant association with root divergence (P <0.01).

CONCLUSIONS

The C_Res of the maxillary first molar was located apical and distal to the trifurcation area. It showed significant variation in its location. The 3D location of and also varied with the force direction. In some samples, this deviation was large. For accurate and predictable movement, tooth-specific C_Res need to be calculated.

Finite element simulations of the effects of an extraoral device, RAMPA, on anterosuperior protraction of the maxilla and comparison with gHu-1 intraoral device

OBJECTIVES

To investigate the effects of an extraoral device, right-angle maxillary protraction appliance (RAMPA), combined with a semi-rapid maxillary expansion intraoral device (gHu-1) on the anterosuperior protraction of maxillary bone.

MATERIALS AND METHODS

The finite element (FE) model included craniofacial bones and all sutures. The linear assumption was assumed for the FE simulations and the material properties of bones and sutures. The gHu-1 was simulated under screw activations equal to Δx = 0.25 and 0.5 mm in the lateral direction with and without RAMPA under a set of external forces {F1 = 2.94, F2 = 1.47, F3 = 4.44} N.

RESULTS

Displacement contours, nodal displacements of 12 landmarks, and von Mises stresses were compared. Combining RAMPA and gHu-1 (with Δx = 0.25 mm) resulted in changes in the displacement of the front part of the maxilla near the mid-palatal suture from (0.02, -0.1, -0.02) mm to (0.02, 0.3, 0.8) mm. For gHu-1 with Δx = 0.5 mm, the displacement of the same part changed from (0.04, -0.04, -0.2) mm to (0.04, 0.3, 0) mm. Similar trends were found in other locations.

CONCLUSIONS

The findings are in agreement with the previous cephalometric clinical data of an 8-year-old patient and prove the positive effects of RAMPA on the anterosuperior protraction of the maxilla when it is combined with the intraoral device gHu-1. In addition, RAMPA does not interfere with the lateral expansion generated by the intraoral device.

Mechanical environment for lower canine T-loop retraction compared to en-masse space closure with a power-arm attached to either the canine bracket or the archwire

OBJECTIVES

To assess the mechanical environment for three fixed appliances designed to retract the lower anterior segment.

MATERIALS AND METHODS

A cone-beam computed tomography scan provided three-dimensional morphology to construct finite element models for three common methods of lower anterior retraction into first premolar extraction spaces: (1) canine retraction with a T-loop, (2) en-masse space closure with the power-arm on the canine bracket (PAB), and (3) power-arm directly attached to the archwire mesial to the canine (PAW). Half of the symmetric mandibular arch was modeled as a linear, isotropic composite material containing five teeth: central incisors (L1), lateral incisor (L2), canine (L3), second premolar (L4), and first molar (L5). Bonded brackets had 0.022-in slots. Archwire and power-arm components were 0.016 × 0.022 in. An initial retraction force of 125 cN was used for all three appliances. Displacements were calculated. Periodontal ligament (PDL) stresses and distributions were calculated for four invariants: maximum principal, minimum principal, von Mises, and dilatational stresses.

RESULTS

The PDL stress distributions for the four invariants corresponded to the displacement patterns for each appliance. T-loop tipped the canine(s) and incisors distally. PAB rotated L3 distal in, intruded L2, and extruded L1. PAW distorted the archwire resulting in L3 extrusion as well as lingual tipping of L1 and L2. Maximum stress levels in the PDL were up to 5× greater for the PAW than the T-loop and PAB methods.

CONCLUSIONS

T-loop of this type is more predictable because power-arms can have rotational and archwire distortion effects that result in undesirable paths of tooth movement.

Mechanical effects of distributed fibre orientation in the periodontal ligament of an idealised geometry

In this study, we computationally assess the effects of the distributed fibre orientation in the periodontal ligament (PDL) on mechanical responses of the tooth-PDL complex. An idealised axial-symmetric geometry of a tooth-PDL complex was constructed. The fibre orientation in the PDL was modelled as a trigonometric function based on anatomical knowledge, and the PDL was modelled as a transversely isotropic hyperelastic material dependent on fibre orientations. Parametric studies of the fibre orientation on the mechanical responses of the tooth-PDL complex were conducted. Obtained results showed that the anatomically consistent fibre orientation functions as a supporting structure against not only vertical but also horizontal loads.

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.

Effect of variable periodontal ligament thickness and its non-linear material properties on the location of a tooth's centre of resistance

In orthodontics, the 3D translational and rotational movement of a tooth is determined by the force-moment system applied and the location of the tooth's centre of resistance (CR). Because of the practical constraints of in-vivo experiments, the finite element (FE) method is commonly used to determine the CR. The objective of this study was to investigate the geometric model details required for accurate CR determination, and the effect of material non-linearity of the periodontal ligament (PDL). A FE model of a human lower canine derived from a high-resolution µCT scan (voxel size: 50 µm) was investigated by applying four different modelling approaches to the PDL. These comprised linear and non-linear material models, each with uniform and realistic PDL thickness. The CR locations determined for the four model configurations were in the range 37.2-45.3% (alveolar margin: 0%; root apex: 100%). We observed that a non-linear material model introduces load-dependent results that are dominated by the PDL regions under tension. Load variation within the range used in clinical orthodontic practice resulted in CR variations below 0.3%. Furthermore, the individualized realistic PDL geometry shifted the CR towards the alveolar margin by 2.3% and 2.8% on average for the linear and non-linear material models, respectively. We concluded that for conventional clinical therapy and the generation of representative reference data, the least sophisticated modelling approach with linear material behaviour and uniform PDL thickness appears sufficiently accurate. Research applications that require more precise treatment monitoring and planning may, however, benefit from the more accurate results obtained from the non-linear constitutive law and individualized realistic PDL geometry.

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.

Can interfaces at bracket-wire and between teeth in multi-teeth finite element model be simplified?

OBJECTIVE

Finite element (FE) method's correctness depends heavily on modeling method. This study aimed at determining whether the interfaces at bracket-wire and between teeth can be simplified for multi-teeth FE analysis.

METHOD

A three-dimensional FE model of a mandible was created from cone-beam computed tomography scan. Due to symmetry, only a half of the mandible was modeled, which consisted of five teeth (first premolar extraction and only first molar), brackets and archwire, periodontal ligament (PDL), cortical bone, and cancellous bone. All the bone, teeth, and PDL were considered to be isotropic and linear. The En-masse retraction case was simulated. A detailed model, which has contact elements between the bracket and archwire and between teeth, was developed to allow relative motion at the interfaces. A model with simplified interfacial conditions, which does not allow the relative motion, was also created. The stresses and displacements as results of the treatment on these two models were calculated and compared.

RESULTS

The stress and displacement distributions from the detailed model were more close to reality based on the expected displacement pattern of the clinical case than from the simplified model. The maximum stresses from the two methods were also different. The highest stress from the detailed model is twice as high as from the simplified model.

CONCLUSIONS

The detailed model provides much more reasonable results than the simplified model. Thus, the simplified model should not be used to replace the detailed model if the stress magnitude and highest stress location are the expected outcomes.

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.

Approach towards the porous fibrous structure of the periodontal ligament using micro-computerized tomography and finite element analysis

The periodontal ligament (PDL) is a porous and fibrous soft tissue situated around the tooth, which plays a key role in the transmission of loads from the tooth to the alveolar bone of the mandible. Although several studies have tried to characterize its mechanical properties, the behaviour of this tissue is not clear yet. In this study, a new simulation methodology based on a material model which considers the contribution of porous and fibrous structure with different material model formulations depending on the effort direction is proposed. The defined material model was characterized by a non-linear approximation of the porous fibrous matrix to experimental results obtained from samples of similar species and was validated by rigorous test simulations under tensile and compressive loads. The global PDL response was also validated using the parameters of the characterization in a finite element model of full human canine tooth obtained by micro-tomography. The results suggest that the porous contribution has high influence during compression because the bulk modulus of the material depends on the ability of interstitial fluid to drain. On the other hand, the collagen fibres running along the load direction are the main responsible of the ligament stiffness during tensile efforts. Thus, a material model with distinct responses depending of the load direction is proposed. Furthermore, the results suggest the importance of considering 3D finite element models based of the real morphology of human PDL for representing the irregular stress distribution caused by the coupling of complex material models and irregular morphologies.

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.

Computational design and engineering of polymeric orthodontic aligners

Transparent and removable aligners represent an effective solution to correct various orthodontic malocclusions through minimally invasive procedures. An aligner-based treatment requires patients to sequentially wear dentition-mating shells obtained by thermoforming polymeric disks on reference dental models. An aligner is shaped introducing a geometrical mismatch with respect to the actual tooth positions to induce a loading system, which moves the target teeth toward the correct positions. The common practice is based on selecting the aligner features (material, thickness, and auxiliary elements) by only considering clinician's subjective assessments. In this article, a computational design and engineering methodology has been developed to reconstruct anatomical tissues, to model parametric aligner shapes, to simulate orthodontic movements, and to enhance the aligner design. The proposed approach integrates computer-aided technologies, from tomographic imaging to optical scanning, from parametric modeling to finite element analyses, within a 3-dimensional digital framework. The anatomical modeling provides anatomies, including teeth (roots and crowns), jaw bones, and periodontal ligaments, which are the references for the down streaming parametric aligner shaping. The biomechanical interactions between anatomical models and aligner geometries are virtually reproduced using a finite element analysis software. The methodology allows numerical simulations of patient-specific conditions and the comparative analyses of different aligner configurations. In this article, the digital framework has been used to study the influence of various auxiliary elements on the loading system delivered to a maxillary and a mandibular central incisor during an orthodontic tipping movement. Numerical simulations have shown a high dependency of the orthodontic tooth movement on the auxiliary element configuration, which should then be accurately selected to maximize the aligner's effectiveness.

New finite element study protocol: Clinical simulation of orthodontic tooth movement

The aim of this work was to model tooth movement in a more clinically-exact fashion, thanks to the use of new IT tools and imaging systems (cone-beam). Image segmentation and 3D reconstruction now enable us to model the anatomy realistically, while finite element (FE) analysis makes it possible to evaluate stresses and their distribution on the level of the tooth, the periodontal ligament (PDL) and the alveolar bone when a force is applied. The principle is to monitor tooth movement by obtaining optical impressions at each stage of treatment. The model corresponds to a genuine clinical situation. FE analysis is correlated with the clinically-observed displacement. The protocol remains long and complex. It nevertheless makes it possible to obtain, throughout the duration of treatment, patient-specific models that can be exploited using finite element methods. It requires further validation in more thorough studies but offers interesting prospects: precise study of induced tooth movement, distribution of stresses in the PDL, and development of a customized previsualization tool.

Mechanical environment change in root, periodontal ligament, and alveolar bone in response to two canine retraction treatment strategies

OBJECTIVE

To investigate the initial mechanical environment (ME) changes in root surface, periodontal ligament (PDL), and alveolar bone due to two treatment strategies, low or high moment-to-force ratio (M/F).

SETTING AND SAMPLE POPULATION

Indiana University-Purdue University Indianapolis. Eighteen patients who underwent maxillary bilateral canine retraction.

MATERIAL AND METHOD

Finite element models of the maxillary canines from the patients were built based on their cone beam computed tomography scans. For each patient, the canine on one side had a specially designed T-loop spring with the M/F higher than the other side. Four stress invariants (1st principal/dilatational/3rd principal/von Mises stress) in the tissues were calculated. The stresses were compared with the bone mineral density (BMD) changes reported previously for linking the ME change to bone modeling/remodeling activities. The correlation was tested by the mixed-model anova.

RESULTS

The alveolar bone in the direction of tooth movement is primarily in tension, while the PDL is in compression; the stresses in the opposite direction have a reversed pattern. The M/F primarily affects the stress in root. Three stress invariants (1st principal/3rd principal/dilatational stress) in the tooth movement direction have moderate correlations with BMD loss.

CONCLUSIONS

The stress invariants may be used to characterize what the osteocytes sense when ME changes. Their distributions in the tissues are significantly different, meaning the cells experience different stimuli. The higher bone activities along the direction of tooth movement may be related to the initial volumetric increase and decrease in the alveolar bone.

Numerical Analysis of Dental Caries Effect on the Biomechanical Behavior of the Periodontal System

The aim of this study was to investigate the effect of dental caries on the stability of the periodontal system. This study presents a numerical analysis performed with three-dimensional (3D) finite element (FE) method to evaluate stresses in the bone surrounding the tooth with dynamic mastication combined loadings. In this work, we present a comparative study on infected and healthy periodontal systems. The infected tooth was modeled and a caries defect was introduced to the tooth coronal part. The infected tooth was evaluated and equivalent von Mises interface stress values were obtained for comparison with the ones exhibited by the healthy tooth. Our results by 3D FE analysis indicated that maximum stresses occurred primarily at the cervical level of root and alveolar bone. In the cortical bone, the stress value was greater in infected system (21.641 MPa) than in healthy system (15.752 MPa), i.e., a 37.4% increase. However, in the trabecular bone we observed only 1.6% increase in the equivalent stress values for the infected tooth model. Stress concentration at the cervical level may cause abnormal bone remodeling or bone loss, resulting loss of tooth attachment or bone damage. Our findings showed that decayed single-rooted teeth are more vulnerable to apical root resorption than healthy teeth. The numerical method presented in this study not only can aid the elucidation of the biomechanics of teeth infected by caries but also can be implemented to investigate the effectiveness of new advanced restorative materials and protocols.

Stresses in the midpalatal suture in the maxillary protraction therapy: a 3D finite element analysis

Background

The aim of the present work was to evaluate the stress magnitudes and directions along the midpalatal suture in the maxillary protraction therapy.

Methods

The geometry of the maxilla and teeth were digitally reconstructed based on computer tomography images obtained from the skull of a girl in a mixed dentition stage with skeletal and dental class III malocclusion. An appliance commonly used for rapid palatal expansion (RPE) was also digitally modeled for anchorage of the protraction force and meshed for finite element analysis. The maxillary protraction was simulated applying 600 cN (300 cN for each side) directed 30° forward and downward to the maxillary occlusal plane.

Results

The principal stresses, through the force application, exhibited similar distribution patterns. A higher stress area was observed in the region of the midpalatal suture located in front of the incisive canal. All the sections showed vectors of compressive nature.

Conclusions

Because of the compressive nature of the stresses distributed along the midpalatal suture in the maxillary protraction therapy simulation, which is opposite to the natural growth transversal tendency, maxillary expansion is advisable in clinical cases.

Expression analysis of α-smooth muscle actin and tenascin-C in the periodontal ligament under orthodontic loading or in vitro culture

α-smooth muscle actin (α-SMA) and tenascin-C are stress-induced phenotypic features of myofibroblasts. The expression levels of these two proteins closely correlate with the extracellular mechanical microenvironment. We investigated how the expression of α-SMA and tenascin-C was altered in the periodontal ligament (PDL) under orthodontic loading to indirectly reveal the intrinsic mechanical microenvironment in the PDL. In this study, we demonstrated the synergistic effects of transforming growth factor-β1 (TGF-β1) and mechanical tensile or compressive stress on myofibroblast differentiation from human periodontal ligament cells (hPDLCs). The hPDLCs under higher tensile or compressive stress significantly increased their levels of α-SMA and tenascin-C compared with those under lower tensile or compressive stress. A similar trend was observed in the tension and compression areas of the PDL under continuous light or heavy orthodontic load in rats. During the time-course analysis of expression, we observed that an increase in α-SMA levels was matched by an increase in tenascin-C levels in the PDL under orthodontic load in vivo. The time-dependent variation of α-SMA and tenascin-C expression in the PDL may indicate the time-dependent variation of intrinsic stress under constant extrinsic loading.

Estimating the location of the center of resistance of canines

OBJECTIVE

To develop a method to quickly estimate the location of center of resistance (CR) in mesial-distal (MD) and buccal-lingual (BL) directions from the tooth's image.

MATERIALS AND METHODS

The maxillary cone-beam computed tomography (CBCT) scans of 18 patients were used. Finite element (FE) models of the canines and their surrounding tissues were built based on their CBCT scans to calculate the locations of CR. Root length, centroid of the contact surface (CCS), and centroid of projection of the contact surface (CPCS) were also obtained from the images. The CCS and CPCS locations were projected on the tooth's long axis, which were represented as percentages of the root length measured from the root's apex.

RESULTS

Using the FE results as the standards, the errors of using CCS or CPCS to estimate CR were calculated. The average location of CR calculated using the FE method was 60.2% measured from the root's apex in the MD direction and 58.4% in the BL direction. The location of the CCS was 60.9%. The difference in CR was 0.7% in the MD direction and 2.5% in the BL direction. The location of CPCS was 60.2% in the MD direction and 59.1% in the BL direction, which resulted in a 0.1% and 0.8% difference with the reference CR, respectively. The average difference of CR in the MD and BL directions was small but statistically significant (P < .05).

CONCLUSION

The locations of the CR of a human canine in the MD and BL directions can be estimated by finding the CPCSs in those directions.

In vivo measurements and numerical analysis of the biomechanical characteristics of the human periodontal ligament

The periodontal ligament is a complex tissue with respect to its biomechanical behaviour. It is important to understand the mechanical behaviour of the periodontal ligament during physiological loading in healthy patients as well as during the movement of the tooth in orthodontic treatment or in patients with periodontal disease, as these might affect the mechanical properties of the periodontal ligament (PDL). Up to now, only a limited amount of in vivo data is available concerning this issue. The aim of this study has been to determine the time dependent material properties of the PDL in an experimental in vivo study, using a novel device that is able to measure tooth displacement intraorally. Using the intraoral loading device, tooth deflections at various velocities were realised in vivo on human teeth. The in vivo investigations were performed on the upper left central incisors of five volunteers aged 21-33 years with healthy periodontal tissue. A deflection, applied at the centre of the crown, was linearly increased from 0 to 0.15mm in a loading period of between 0.1 and 5.0s. Individual numerical models were developed based on the experimental results to simulate the relationship between the applied force and tooth displacement. The numerical force/displacement curves were fitted to the experimental ones to obtain the material properties of the human PDL. For the shortest loading time of 0.1s, the experimentally determined forces were between 7.0 and 16.2N. The numerically calculated Young's modulus varied between 0.9MPa (5.0s) and 1.2MPa (0.1s). By considering the experimentally and numerically obtained force curves, forces decreased with increasing loading time. The experimental data gained in this study can be used for the further development and verification of a multiphasic constitutive law of the PDL.

Finite element method analysis of the periodontal ligament in mandibular canine movement with transparent tooth correction treatment

Background

This study used the 3D finite element method to investigate canine’s displacements and stresses in the canine’s periodontal ligament (PDL) during canine’s translation, inclination, and rotation with transparent tooth correction treatment.

Methods

Finite element models were developed to simulate dynamic orthodontic treatments of the translation, inclination, and rotation of the left mandibular canine with transparent tooth correction system. Piecewise static simulations were performed to replicate the dynamic process of orthodontic treatments. The distribution and change trends of canine’s displacements and stresses in the canine’s PDL during the three types of tooth movements were obtained.

Results

Maximum displacements were observed at the crown and middle part in the translation case, at the crown in the inclination case, and at the crown and root part in the rotation case. The relative maximum von Mises and principal stresses were mainly found at the cervix of the PDL in the translation and inclination cases. In the translation case, tensile stress was mainly observed on the mesial and distal surfaces near the lingual side and compressive stress was located at the bottom of the labial surface. In the inclination case, tensile stress was mainly observed at the labial cervix and lingual apex and compressive stress was located at the lingual cervix and labial apex. In the rotation case, von Mises stress was mainly located at the cervix and inside the lingual surface, tensile stress was located on the distal surface, and compressive stress was detected on the mesial surface. The stress and displacement value rapidly decreased in the first few steps and then reached a plateau.

Conclusions

Canine’s movement type significantly influences the distribution of canine’s displacement and stresses in the canine’s PDL. Changes in canine’s displacement and stresses in the canine’s PDL were exponential in transparent tooth correction treatment.

A finite element analysis of the maxillary first molar PDL with maxillary protraction in a mixed dentition Class III malocclusion

OBJECTIVES

To analyze the stress distribution on the PDL of the maxillary first molar in a mixed dentition Class III malocclusion, using a Hyrax-type appliance and maxillary protraction.

SETTING AND SAMPLE POPULATION

A Class III malocclusion in the mixed dentition was reconstructed based on CBCT images.

MATERIAL AND METHODS

The 3D FEM comprised the maxilla, alveolar bone, right first permanent molar teeth, and PDL and consisted of 1 133 497 nodes and 573 726 elements. Maxillary protraction force was applied to a hook positioned close to the deciduous canines with 600 g and at 15°, 30°, and 45° downward angles to the maxillary occlusal plane.

RESULTS

Analysis was carried out from the top and buccal view of the sagittal plane. The magnitude of the stresses at 15°, 30°, and 45° of protraction angulation resulted in the highest stress magnitude being in the region between the distobuccal and palatal roots, as well as on the distal surface of the mesial root. The vector direction in this area showed traction and mesial movement. With 30° and 45° protraction angulations, the stress was located only between the distobuccal and palatal roots, and the vector direction was more extrusive at 15°.

CONCLUSIONS

The suggested orthodontic movement is in the mesial direction with a small amount of extrusion with 15° angulation and greater extrusion with 30° and 45°.

Evaluation of Effects and Effectiveness of Various α and β Angulations for Three Different Loop Made of Stainless Steel Arch Wires - A FEM Study

INTRODUCTION

Evaluations on retraction loop designs have been limited to describe the force systems applied to the buccal surfaces of the tooth that can be in different planes resulting undesirable effects, needing corrective action in future. By initially understanding these effects, modifications to the loop design can essentially counteract the undesired affects.

AIM

To deter-mine Moments & M/F ratios produced by different gabling in the three retraction loops (Tear drop loop, T-loop, Open vertical loop) and movement of the anterior teeth and posterior teeth) of the maxillary arch in an extraction model, on activation of three retraction loops by1 mm.

MATERIALS AND METHODS

A PC with Quad core processor, 8GB RAM, 1TB storage space and Graphic Accelerator was used. Computer Software: ANSYS Version11, PRO/ENGINEER was used in the study. The first step is modeling, done by using Pro/Engineer software and for creating a model the CT scan data is required. The maxilla with teeth of a patient is scanned at various sections at regular intervals of 0.5 mm. These scanned images are then imported into Pro/E software to various offset planes. Once imported, the software can do an automatic meshing and establishes contact automatically.

RESULTS

When angulations increases intrusive or extrusive movements and movements in horizontal direction of crown tip and root tip increases. All values of T-loop are more than Teardrop loop and less than Open vertical loop.

CONCLUSION

FEM study concludes that Teardrop loop with 10-20(α-β) combination is preferred for Group A anchorage.

The biomechanical function of periodontal ligament fibres in orthodontic tooth movement

Orthodontic tooth movement occurs as a result of resorption and formation of the alveolar bone due to an applied load, but the stimulus responsible for triggering orthodontic tooth movement remains the subject of debate. It has been suggested that the periodontal ligament (PDL) plays a key role. However, the mechanical function of the PDL in orthodontic tooth movement is not well understood as most mechanical models of the PDL to date have ignored the fibrous structure of the PDL. In this study we use finite element (FE) analysis to investigate the strains in the alveolar bone due to occlusal and orthodontic loads when PDL is modelled as a fibrous structure as compared to modelling PDL as a layer of solid material. The results show that the tension-only nature of the fibres essentially suspends the tooth in the tooth socket and their inclusion in FE models makes a significant difference to both the magnitude and distribution of strains produced in the surrounding bone. The results indicate that the PDL fibres have a very important role in load transfer between the teeth and alveolar bone and should be considered in FE studies investigating the biomechanics of orthodontic tooth movement.

Favorable effect of myofibroblasts on collagen synthesis and osteocalcin production in the periodontal ligament

INTRODUCTION

In this study, we aimed to explore the expressions of α-smooth muscle actin, collagen type I, collagen type III, and osteocalcin in the periodontal ligament (PDL) under orthodontic loading, and to investigate the effect of myofibroblasts on collagen synthesis and osteocalcin production.

METHODS

The teeth in the right maxillae of the rats were orthodontically loaded while the contralateral teeth remained unloaded as controls. The total 30 rats were divided into 5 groups, with each group corresponding to a treatment duration (0, 3, 5, 7, or 14 days, respectively). The expressions of α-smooth muscle actin, collagen type I, collagen type III, and osteocalcin in the tension area of the PDL over time were analyzed by immunochemistry staining. For the in-vitro study, the expressions of α-smooth muscle actin, collagen type I, collagen type III, and osteocalcin in the myofibroblasts and human osteoblast-like cells (MG63) coculture and PDL cells-MG63 coculture systems were examined by Western blot and real-time polymerase chain reaction.

RESULTS

Enhanced expression of α-smooth muscle actin, collagen type I, collagen type III, and osteocalcin in the tension area of the PDL under orthodontic loading were observed in vivo, and increased expressions of α-smooth muscle actin, collagen type I, collagen type III, and osteocalcin in the myofibroblasts-MG63 coculture system were observed compared with the controls.

CONCLUSIONS

Expressions of α-smooth muscle actin, collagen type I, collagen type III, and osteocalcin are up-regulated in the PDL under orthodontic tensile loading. Myofibroblasts have a more positive effect on collagen synthesis and osteocalcin expression than do PDL cells.

An analytical approach to 3D orthodontic load systems

OBJECTIVE

To present and demonstrate a pseudo three-dimensional (3D) analytical approach for the characterization of orthodontic load (force and moment) systems.

MATERIALS AND METHODS

Previously measured 3D load systems were evaluated and compared using the traditional two-dimensional (2D) plane approach and the newly proposed vector method.

RESULTS

Although both methods demonstrated that the loop designs were not ideal for translatory space closure, they did so for entirely different and conflicting reasons.

CONCLUSIONS

The traditional 2D approach to the analysis of 3D load systems is flawed, but the established 2D orthodontic concepts can be substantially preserved and adapted to 3D with the use of a modified coordinate system that is aligned with the desired tooth translation.

Effect of bite force on orthodontic mini-implants in the molar region: Finite element analysis

Objective

To examine the effect of bite force on the displacement and stress distribution of orthodontic mini-implants (OMIs) in the molar region according to placement site, insertion angle, and loading direction.

Methods

Five finite element models were created using micro-computed tomography (microCT) images of the maxilla and mandible. OMIs were placed at one maxillary and two mandibular positions: between the maxillary second premolar and first molar, between the mandibular second premolar and first molar, and between the mandibular first and second molars. The OMIs were inserted at angles of 45° and 90° to the buccal surface of the cortical bone. A bite force of 25 kg was applied to the 10 occlusal contact points of the second premolar, first molar, and second molar. The loading directions were 0°, 5°, and 10° to the long axis of the tooth.

Results

With regard to placement site, the displacement and stress were greatest for the OMI placed between the mandibular first molar and second molar, and smallest for the OMI placed between the maxillary second premolar and first molar. In the mandibular molar region, the angled OMI showed slightly less displacement than the OMI placed at 90°. The maximum Von Mises stress increased with the inclination of the loading direction.

Conclusions

These results suggest that placement of OMIs between the second premolar and first molar at 45° to the cortical bone reduces the effect of bite force on OMIs.

Estimation of periodontal ligament's equivalent mechanical parameters for finite element modeling

INTRODUCTION

Young's modulus (E) and Poisson's ratio (v) of the periodontal ligament are needed in a finite element analysis for investigating the biomechanical behavior of a tooth, periodontal ligament, and bone complex. However, large discrepancies in E (0.01-1,750 MPa) and v (0.28-0.49) were reported previously. The objective of this study was to narrow the ranges and to provide equivalent E and v pairs suitable for finite element modeling of a tooth, periodontal ligament, and bone complex by using a reported crown load-displacement relationship as the criterion.

METHODS

A 3-dimensional finite element model of a 3-tooth, periodontal ligament, and bone complex, consisting of a maxillary central incisor with 2 adjacent teeth, from a cone-beam computed tomography scan was created. The dimensions, constraints, and loading condition were kept similar to those reported in the human study. With the load applied to the crown, both v and E were adjusted independently, and the corresponding crown displacements were calculated. The resulting load-displacement curves were compared with those reported in the human study. The mean absolute displacement difference method was used to find the best fit. The E and v pairs that generated the minimum mean absolute displacement difference were identified.

RESULTS

The finite element model with 1 of the 3 E and v pairs (v = 0.35, E = 0.87 MPa; v = 0.4, E = 0.71 MPa; and v = 0.45, E = 0.47 MPa) simulated the tooth, periodontal ligament, and bone complex well. The mean absolute displacement differences were 0.0135, 0.0138, and 0.0138 mm, respectively; these are less than 8% of 0.175 mm, which was the crown displacement of the tooth, periodontal ligament, and bone complex under the load of 500 cN.

CONCLUSIONS

The E and v values close to the 3 pairs might be used for finite element modeling of the tooth, periodontal ligament, and bone complex.

Periodontal ligament influence on the stress distribution in a removable partial denture supported by implant: a finite element analysis

ABSTRACT

Objective

The non-homogenous aspect of periodontal ligament (PDL) has been examined using finite element analysis (FEA) to better simulate PDL behavior. The aim of this study was to assess, by 2-D FEA, the influence of non-homogenous PDL on the stress distribution when the free-end saddle removable partial denture (RPD) is partially supported by an osseointegrated implant.

Material and Methods

Six finite element (FE) models of a partially edentulous mandible were created to represent two types of PDL (non-homogenous and homogenous) and two types of RPD (conventional RPD, supported by tooth and fibromucosa; and modified RPD, supported by tooth and implant [10.00x3.75 mm]). Two additional FE models without RPD were used as control models. The non-homogenous PDL was modeled using beam elements to simulate the crest, horizontal, oblique and apical fibers. The load (50 N) was applied in each cusp simultaneously. Regarding boundary conditions the border of alveolar ridge was fixed along the x axis. The FE software (Ansys 10.0) was used to compute the stress fields, and the von Mises stress criterion (σvM) was applied to analyze the results.

Results

The peak of σvM in non-homogenous PDL was higher than that for the homogenous condition. The benefits of implants were enhanced for the non-homogenous PDL condition, with drastic σvM reduction on the posterior half of the alveolar ridge. The implant did not reduce the stress on the support tooth for both PDL conditions.

Conclusion

The PDL modeled in the non-homogeneous form increased the benefits of the osseointegrated implant in comparison with the homogeneous condition. Using the non-homogenous PDL, the presence of osseointegrated implant did not reduce the stress on the supporting tooth.

The oxytalan fibre network in the periodontium and its possible mechanical function

The biomechanical character of the periodontal ligament (PDL) is crucial in its response to functional and orthodontic forces. Collagen has been the primary subject of investigations in this field. Several studies, however, indicate that oxytalan fibres, which belong to the elastic fibre family, also contribute to the biomechanical character and behaviour of the PDL. In order to elucidate this, we have evaluated the available literature on the oxytalan fibre network within the PDL and supra-alveolar tissues with respect to development, morphology and distribution, and response to mechanical stimulation. To this end, we have combined the classical histological studies with more recent in vitro studies. Oxytalan fibres develop simultaneously with the root and the vascular system within the PDL. A close association between oxytalan fibres and the vascular system also remains later in life, suggesting a role in vascular support. Mechanical loading of the PDL, through orthodontic force application, appears to induce an increase in the number, size, and length of oxytalan fibres. In line with this, in vitro stretching of PDL fibroblasts (PDLFs) results in an increased production of fibrillin, a major structural component of the microfibrils that make up oxytalan fibres. The available data suggest a mechanical function for oxytalan, but to date experimental data are limited. Further research is required to clarify their exact mechanical function and possible role in orthodontic tooth movement.

Three-dimensional finite-element analysis of a central lower incisor under labial and lingual loads

INTRODUCTION

The aim was to evaluate the differences between labial and lingual application of an orthodontic force. This was achieved using a three-dimensional CAD design software model of a real lower incisor surrounded by a prismatic representation of the mandibular bone. This model was subjected to various loading conditions, with finite-element analysis.

MATERIALS AND METHODS

Cone-beam computed tomography scanning was used to create a three-dimensional geometric model of a lower incisor, together with its simulated periodontal ligament. This model was then meshed and analysed with commercial finite-element code. Various single and combined forces and moments were applied to each side of the simulated lower incisor at the centre of the clinical crown. To evaluate the effects of the various forces considered, the instantaneous displacement and stress generated in the bone and the periodontal ligament were measured, as a comparison of the labial and lingual loading sites.

RESULTS

Dental movement was only influenced by the side of the force application when an intrusive component was present. The simulations showed larger displacement when a vertical force was present at the lingual surface. In general, this movement was of the tipping type when the combined forces were applied, while there was greater intrusion upon application of combined forces and an anticlockwise moment to the labial surface.

CONCLUSIONS

Application of an intrusive lingual force to a lower incisor appears to generate bodily movement, while the same intrusive labial force appears to lead to labial tipping. Subject to further study, this should be taken into consideration when devising treatment plans for fixed appliances.

Experimentally determined mechanical properties of, and models for, the periodontal ligament: critical review of current literature

Introduction. This review is intended to highlight and discuss discrepancies in the literature of the periodontal ligament's (PDL) mechanical properties and the various experimental approaches used to measure them. Methods. Searches were performed on biomechanical and orthodontic publications (in databases: Compendex, EMBASE, MEDLINE, PubMed, ScienceDirect, and Scopus). Results. The review revealed that significant variations exist, some on the order of six orders of magnitude, in the PDL's elastic constants and mechanical properties. Possible explanations may be attributable to different experimental approaches and assumptions. Conclusions. The discrepancies highlight the need for further research into PDL properties under various clinical and experimental loading conditions. Better understanding of the PDL's biomechanical behavior under physiologic and traumatic loading conditions might enhance the understanding of the PDL's biologic reaction in health and disease. Providing a greater insight into the response of the PDL would be instrumental to orthodontists and engineers for designing more predictable, and therefore more efficacious, orthodontic appliances.

Apical force distribution due to orthodontic forces: a finite element study

AIM

This finite element study was conducted to calculate the distribution of stresses in the periodontal ligament when various orthodontic forces were applied, with emphasis on the effect on root apex.

MATERIALS AND METHODS

An in vitro finite element method was used to construct a three-dimensional finite element model of a maxillary central incisor, its periodontal ligament and alveolar bone was constructed on the basis of average anatomic morphology. To this model, five types of orthodontic forces namely tipping, bodily movement, intrusion, extrusion and rotations were applied at various points on the crown of the tooth model. After the application of the forces, initial stress and initial displacements of the periodontal ligament were evaluated. The principal stress obtained on the periodontal ligament due to various orthodontic loadings on the maxillary central incisor was analyzed using ANSYS 10 finite element software.

RESULTS

It showed that the greatest amount of relative stress at the apex of maxillary central incisor occurred with intrusion, extrusion and rotation. Bodily movement and tipping forces produce stress concentrated at the alveolar crest and not at the root apex.

CONCLUSION

Clinical implications of this study suggest that if the clinician is concerned about placing heavy stresses on the root apex, then vertical and rotational forces must be applied with caution.

CLINICAL SIGNIFICANCE

If heavy stresses are to be placed on the root apex, then vertical and rotational forces must be applied with caution during orthodontic therapy.