Orthodontic Force Systems Research Articles

Digital Models and 3D Biomechanics Analysis in Orthodontics. Part 1: Vector Calculations

Biomechanics is essential for optimizing orthodontic appliances and controlling dental movement. Charles J. Burstone pioneered a three-dimensional (3D) approach in orthodontics, advocating for a shift beyond appliance-focused methods. Initially, biomechanics studies were constrained to two-dimensional (2D) analysis due to the complexities of 3D evaluation. Despite progress in computational tools and digital modeling, orthodontic biomechanics has largely maintained a 2D orientation. This paper advances orthodontic biomechanics into 3D, re-evaluating concepts previously limited to 2D frameworks. A dedicated software, DDP-Ortho (Ortolab, Poland), is introduced to enable orthodontists to analyze and resolve biomechanical challenges in 3D, facilitating appliance designs with precise 3D force systems. The representation and calculation of force vectors and moments in 3D are detailed, emphasizing the inherent complexity absent computational support. Key processes such as vector subtraction and addition, fundamental for assessing and refining orthodontic force systems, are explained. Additionally, the vector split (couple replacement) method, previously described in 2D, is extended to 3D, addressing the unique constraints and challenges of this approach. These tools promise to refine the accuracy and effectiveness of orthodontic treatments, setting the stage to examine the interactions between 3D force systems and dental movement, which will be addressed in a subsequent paper, to broaden the potential of contemporary orthodontic therapy.

Effect of 3D anchorage attachment on the alleviating tipping/extrusion of premolars for en-mass distalization of maxillary molars with clear aligners: A finite element study

This study aimed to explore the optimal invisible orthodontic force system during the en-mass distalization of two maxillary molars to minimize the side effect of anchorage loss by changing the direction of the application of the orthodontic force system. A high bio-fidelity 3D finite element model including maxilla, periodontal ligament, dentition, clear aligner, 3D anchorage attachment and mini-implant was established. Different lengths of lateral hooks of 3D-printed anchorage attachments and mini-implant positions into the palatal alveolus were considered. A 200 ​g distal force was applied to the lateral hooks of different horizontal lengths (3.26 ​mm, 6.52 ​mm and 9.78 ​mm) with the mini-implant as the application point. Using ABAQUS software, orthodontic tooth movements under 12 different clinical treatment designs were analyzed and calculated. The 3D anchorage attachment enhanced the anchorage of anterior teeth and alleviated the tipping/extrusion of premolars. In contrast to without clear aligners, length of the lateral hook had a negligible effect on both mesial tipping and buccal tipping with clear aligners, which could then be ignored. The change in mesial tipping was less and nearly remained constant despite of the different heights of the mini-implant. The 3D anchorage attachment assisted clear aligner can avoid the side effects of anterior tooth proclination caused by insufficient anchorage. The length of the lateral hook, and height of the mini-implant in this invisible orthodontic force system hardly affects the tooth movement of anchorage units. Clear aligners can effectively control the rotation and tipping of anchorage units caused by 3D anchorage attachment.

Analysis of Coating Loss from Coated Stainless Steel Orthodontic Wire

The leaching of metal ions from orthodontic appliances into the oral cavity is problematic for metal-allergic patients. Non-metal orthodontic appliances, such as plastic and ceramic brackets and elastomeric materials, have been clinically used and are effective for treatment of metal-allergic patients. However, only a few types of orthodontic wire are available for use in patients with metal allergies, thus restricting the establishment of orthodontic force systems in these patients. Wire surfaces can be coated with various substances to prevent leaching of metal ions. However, detachment of the coating may occur during orthodontic procedures, resulting in metal ion leaching from the substrate material. This study was performed to examine the resilience of various types of coated stainless steel wire to low pH, bending, and brushing. Wire surface characteristics were examined by stereomicroscopy and scanning electron microscopy. The degree of coating detachment due to bending of the wire was quantified by determining the change in the amount of metal ions eluted from the site of the bend immersed in hydrochloric acid. Exposure of the substrate metal by brushing was investigated by energy dispersive spectrometry. The results indicated that polyethylene naphthalate (PEN)-coated wire is resilient to bending, while gold (Au)-coated and titanium nitride (TiN)-coated wires are resilient to brushing.

Effect of the Maxillary Sinus on Tooth Movement during Orthodontics Based on Biomechanical Responses of Periodontal Ligaments

The maxillary sinus is a common anatomic limitation for orthodontic tooth movement. The effect of orthodontic forces on a particular anatomy can be studied using finite element analysis (FEA). Our study aimed to determine the effect of different tooth penetration depths into the maxillary sinus floor (MSF) on the orthodontic force system for bodily tooth movement. Using the cone-beam computed tomography of a patient with low MSF, we modeled the geometry of canine, premolar, and molar teeth with their periodontal ligaments and the alveolar bone surrounding them. The models were manually modified to simulate different root penetration depths. Thereafter, the center of resistance and stress distributions for teeth penetrating into the MS were determined using FEA. Moreover, the force systems for teeth with a low MSF to varying degree were evaluated based on the FEA results. During orthodontic tooth movement, the individual differences in the periodontal anatomy should be considered. The CR position decreases with the penetration depth, while the average hydrostatic stress in the PDL increases rapidly. In this paper, we present the correction coefficients of the orthodontic force and moment for a tooth penetrating into the MSF, which is necessary for personalized treatment planning.

Comparative Evaluation of the Stress Distribution and Transverse Displacement of the Circummaxillary Sutural System by Four Different Designs of Rapid Maxillary Expansion Appliances Using 3D Finite Element model: A Study Protocol

Background: In adolescent patient’s Rapid maxillary skeletal expansion (RME) is used with predictable clinical results for correcting transverse maxillary skeletal contraction. During RME, heavy force is directed towards the maxillary skeletal base. These forces also have effect on the palatal bone, adjacent skeletal structures and dentition. Tooth supported RME apply significant pressure on the teeth leading to varying amount of buccal inclination of premolars and molars and dental expansion. Implant assisted expanders take skeletal anchorage thus minimizing or negating the effect of heavy pressure on the teeth and supporting structures. Finite Element Analysis is a form of computer simulation. It is a non-invasive, precise method for obtaining quantitative and comprehensive knowledge about the physiological responses that occur in tissues. It outperforms other experimental methods because it creates a three-dimensional model that allows for simulation and analysis of orthodontic force systems in all three dimensions.
 Objective: The present study intends to make an assessment of four different RME designs (Banded HYRAX, Banded MARPE, MSE expander, Orthoeasy PAL expander) in terms of distribution of stress in the circummaxillary Sutural system and resulting displacement of the bones in the craniofacial complex upon activation of the respective appliance.
 Methodology: CBCT scan data of an adolescent patient will be taken from archives of a reputed scan centre. 3D skull model will be generated using CBCT data and .stl/ DICOM format will be converted into Finite Element model. The different types of RME appliances will be designed over the FE model. The expanders will be activated and the stresses generated at the sites of interest would be studied.
 Results: The study is expected to permit a clinician to select the design of RME appliances, which will produce suitable stress and displacement that will help to increase transverse width of maxilla to correct the underlying skeletal discrepancy.
 Conclusion: This study will help to arrive at a conclusion about which designs of RME will best suit clinical application of mechanics for orthopaedic expansion in a particular case.

Finite element analysis of maxillary anterior teeth retraction of posterior teeth with different alveolar bone absorption heights under orthodontic force

This study applied the direct orthodontic force system to explore the applicability of the finite element method in the simulation of alveolar bone absorption and analyze periodontal stress distribution and the overall displacement trend. The horizontal balanced alveolar bones of model 2, 3 and 4 were reduced by 2, 4, and 6 mm by deleting elements in reference to the established height of the normal alveolar bone model 1. Then, stress distribution on the posterior set of teeth and initial total tooth displacement under the simulated load of 1.47 N of orthodontic force were investigated. The total displacement of posterior teeth increased and parodontium Von Mises stress gradually increased as the alveolar bone height decreased. The total displacement trend and parodontium stress drastically increased when alveolar bone absorp-tion reached the height of 4 mm. When treating patients with alveolar bone loss, stress should be avoided or drasti-cally reduced to prevent irreversible damage to periodontal tissue and to improve the quality of medical treatment.

A preliminary approach in the prediction of orthodontic bone remodeling by coupling experiments, theory and numerical models

Orthodontic treatments are based on a prolonged application of mechanical forces on the teeth through orthodontic appliances, leading to tooth movement due to the remodeling of the surrounding bone. Bone response is dependent on the biological reactions occurring in the periodontal ligament (PDL) and more specifically on those related to vascular changes (Pavlin and Gluhak-Heinrich 2001). Hence, optimal forces and moments are required to obtain the desired tooth displacements without generating deleterious effects. Although the biological events occurring during orthodontic tooth movement are nowadays better understood, the correlation between orthodontic force systems, desmodontal reactions and bone remodeling is not well established (Meikle 2005). Little is known about the forces and moments developed on more than two adjacent teeth (Badawi et al. 2009). In this work, we focus our analysis on a buccal upper right canine in infraclusion and extract the experimental measurements of the mechanical forces developed onto the complete dental arch. These are then transferred into a numerical finite element (FE) model to determine the PDL deformation and hence, through a theoretical numerical model, quantify the cellular mechanobiological reactions at the root of orthodontic bone remodeling.

Residents' journal review

Residents' journal review

Development and modification of a device for three-dimensional measurement of orthodontic force system: The V-bend system re-visited.

We developed a device to evaluate the orthodontic force applied by systems requiring high operability. A life-sized, two-tooth model was designed, and the measurements were performed using a custom-made jointed attachment, referred to as an "action stick", to allow clearance for the oversized six-axis sensors. This tooth-sensor apparatus was accurately calibrated, and the error was limited. Vector analysis and rotating coordinate transformation were required to derive the force and moment at the tooth from the sensor readings. The device was then used to obtain measurements of the force and moment generated by the V-bend system. Our device was effective, providing results that were consistent with those of previous studies. This measurement device can be manufactured with force sensors of any size, and it can also be expanded to models with any number of teeth.

Self-ligating brackets in perspective of friction: A Review

No abstract available.

Biomechanical time dependency of the periodontal ligament: a combined experimental and numerical approach

The analysis of the non-linear and time-dependent viscoelasticity of the periodontal ligament (PDL) enables a better understanding of the biomechanical features of the key regulator tissue for tooth movement. This is of great significance in the field of orthodontics as targeted tooth movement remains still one of the main goals to accomplish. The investigation of biomechanical aspects of the PDL function, a difficult area of research, helps towards this direction. After analysing the time-dependent biomechanical properties of pig PDL specimens in an in vitro experimental study, it was possible to confirm that PDL has a viscoelastic anisotropic behaviour. Three-dimensional finite element models of mini-pig mandibular premolars with surrounding tissues were developed, based on micro-computed tomography (μCT) data of the experimental specimens. Tooth mobility was numerically analysed under the same force systems as used in the experiment. A bilinear material parameter set was assumed to simulate tooth displacements. The numerical force/displacement curves were fitted to the experimental curves by repeatedly calculating tooth displacements of 0.2mm varying the loading velocities and the parameters, which describe the nonlinearity. The experimental results showed a good agreement with the numerical calculations. Mean values of Young's moduli E1, E2 and ultimate strain ε12 were derived for the elastic behaviour of the PDL for all loading velocities. E1 and E2 values increased with increasing the velocity, while ε12 remained relatively stable. A bilinear approximation of material properties of the PDL is a suitable description of measured force/displacement diagrams. The numerical results can be used to describe mechanical processes, especially stress-strain distributions in the PDL, accurately. Further development of suitable modelling assumptions for the response of PDL under load would be instrumental to orthodontists and engineers for designing more predictable orthodontic force systems and appliances.

Evaluating orthodontic force system in clinical condition with a numerical method

The aim of this paper is to quantitatively evaluating orthodontic force system during orthodontic treatment with a numerical method. Dental cast models were made to obtain digital models with impressions of a patient’s dental arch at regular intervals. Then the displacement of each bracket for a period of time was obtained by computer aided inspection. The finite element model of archwire in free status and brackets engaged in archwire was built. With the derived displacements applied as the boundary condition, the orthodontic force system at a time point was derived by a finite element analysis. The error of this method, especially the influences of friction and material of archwire on the orthodontic force system were discussed at last. This method can quantitatively evaluate the orthodontic force system generated from elastic material in clinic condition, the deformation history of archwire need to be traced for the orthodontic force generated from shape memory alloy.

The autotransplantation of an anklyosed maxillary canine

The clinical diagnosis of ankylosis can be made only when the affected tooth gives positive evidence of an inability to move. The inability to move is demonstrated either as a failure of the tooth to move with normal vertical dental alveolar growth or a failure of the tooth to move when the tooth is subjected to an orthodontic force system. This case report describes the autotransplantation of an ankylosed maxillary canine. [J Kor Acad Cons Dent 2011;36(4):336-339.]

Viscoelastic properties of an aesthetic translucent orthodontic wire

The objective of this study was to evaluate the time-dependent viscoelastic properties of an aesthetic orthodontic archwire. The wire is based on a recently developed translucent polyphenylene thermoplastic, whose rigid molecular structure provides high strength. While the wire has good instantaneous mechanical properties, over time all polymers may relax so it is important to understand the potential impact of the relaxation on orthodontic force systems. Four samples of 0.020 inch round and six samples of 0.021 × 0.025 inch rectangular wire were loaded in tension to a range of initial stresses, and relaxation of the stress was monitored for 7 days. Sixty-three additional samples were maintained in edgewise bracket pairs with vertical displacement for up to 6 weeks. The deformation of these wires was measured immediately after removal from the brackets and for 2 days as the samples recovered. Tensile stress decayed about 10-30 per cent over 24-48 hours depending on the initial stress. The relaxation behaviour was proportional to the initial tensile strain and therefore these data were combined into a single curve using regression. Deformation of the samples placed in the bracket pairs increased with increasing vertical displacement and time, evaluated with analysis of variance, but 19-100 per cent of the deformation was recoverable. The force systems from polyphenylene wires could vary with time and activation, but this behaviour is predictable.

Effects of cementum–dentine junction and cementum on the mechanical response of tooth supporting structure

Objectives The aim of the present work is to investigate the effects of cementum–dentine junction (CDJ) and cementum on the stress distribution in the periodontal ligament (PDL) and alveolar bone. Methods Based on the anatomical profiles and the recently reported theories about the tooth attachment mechanism, the finite element (FE) model of a mandibular second premolar along with its detailed supporting structures was developed. The effect of CDJ and cementum was evaluated by comparing the resulting stresses of FE models of the second mandibular premolar with and without CDJ and cementum in tooth supporting structure. Results The stress levels are higher in the structure without CDJ and cementum than that with CDJ and cementum. The function of CDJ and cementum is as a cushion pad decreasing the stress in the PDL and alveolar bone under loading. Conclusions As a major result of this study, it can be concluded that the CDJ and cementum significantly influence the stress distribution within the tooth supporting structure. However, most of the reported FE analysis did not take CDJ and cementum into account, which possibly resulted in overestimated stress values in the PDL and alveolar bone. From a bio-engineering perspective, the results of this study provide guidance for the design of dental implants and the application of orthodontic force system as well.

Quantification of three-dimensional orthodontic force systems of T-loop archwires

To demonstrate the three-dimensional (3D) orthodontic force systems of three commercial closing T-loop archwires using a new method and to quantify the force systems of the T-loop archwires. An orthodontic force tester (OFT) and a custom-made dentoform were developed to measure force systems. The system simulated the clinical environment for an orthodontic patient requiring space closure, which included measurement of three force components along, and three moment components about, three clinically defined axes on two target teeth. The archwires were attached to the dentoform and were activated following a standard clinical procedure. The resulting force system was measured using the OFT. The force systems of the T-loops on the teeth were 3D. Activation in one direction resulted in force and moment components in other directions (side effects). The six force and moment components as well as the moment-to-force ratios in the clinically defined coordinate system were quantified. The commercial archwires do not provide force systems for pure translation. Quantification of the force system is critical for the selection and design of optimal orthodontic appliances.

Three-dimensional orthodontic force measurements

Until recently, much of the orthodontic biomechanics literature was restricted to 2-dimensional experimental studies and, more recently, to assumption-based 3-dimensional computer modeling. There is little evidence in the literature regarding 3-dimensional experimental measurements and analysis of orthodontic force systems. The purpose of this study was the design, construction, and validation of a laboratory-based human mouth model capable of accurately measuring forces and moments applied by orthodontic fixed appliances on all teeth in 1 arch. A high canine malocclusion was simulated, and forces and moments acting on the canine, lateral incisor, and premolar were measured with passive and conventional ligation. We were successful in building this human mouth model. The error in force measurements of the 14 transducers was 1.54%. The force system resulting from passive ligation brackets was considerably different from that of conventional ligation. This method will allow us, for the first time in the history of our specialty, to determine with great accuracy the forces acting on orthodontically treated teeth. Future research will focus on simulating many types of orthodontic clinical applications of full-fixed or partial-fixed appliances.

Strains in periodontal ligament and alveolar bone associated with orthodontic tooth movement analyzed by finite element

Orthodontic tooth movement (OTM) is achieved by applying an orthodontic force system to the brackets. The (re)modeling processes of the alveolar support structures are triggered by alterations in the stress/strain distribution in the periodontium. According to the classical OTM theories, symmetric zones of compression and tension are present in the periodontium, but these do not consider the complex mechanical properties of the PDL, the alveolar structures' morphology, and the magnitude of the force applied. Human jaws segments obtained from autopsy were microCT-scanned and sample-specific finite element (FE) models were generated. The material behavior of the PDL was considered to be nonlinear and non-symmetric and the alveolar bone was modeled according to its actual morphology. A series of FE-analyzes investigated the influence of the moment-to-force ratio, force magnitude, and chewing forces on the stress/strain in the alveolar support structures and OTM. Stress/strain findings were dependent on alveolar bone's morphology. Because of the nonlinear behavior of the PDL, distinct areas of tension, and compression could not be detected. Secondary load transfer mechanisms were activated and the stress/strain distribution in the periodontium was concealed by occlusal forces. We could not confirm the classical ideas of distinct and symmetrical compressive and tensile areas in the periodontium in relation to different OTM scenarios. Light continuous orthodontics forces will be perceived as intermittent by the periodontium. Because roots and alveolar bone morphology are patient-specific, FE-analysis of orthodontic loading regime should not be based on general models.

Complete orthodontic load systems on teeth in a continuous full archwire: The role of triangular loop position

A novel approach to characterizing orthodontic spring-generated force and moment systems has been developed. This method allows simultaneous measurement of all 6 force and moment components acting on a tooth. A continuous full archwire space-closure technique was simulated, and the complete force and moment systems acting on the teeth adjacent to the extraction space were measured. The data showed that, in addition to the intended forces and moments, there are nontrivial activation-dependent interactions with the other load components, and these complex relationships are affected by the position of the triangular loop.

Force Systems in the Initial Phase of Orthodontic Treatment—a Comparison of Different Leveling Archwires

The determination of orthodontically-effective forces and moments places great demands on the technical equipment. Many patients report severe pain after fixed appliance insertion. Since it is assumed that pain from orthodontic appliances is associated with the force and moment levels applied to the teeth and since the occurrence of root resorption is a common therapeutic side effect, it would seem important to know the actual magnitudes of the components of the active orthodontic force systems. The aim of the present study was therefore to measure initial force systems produced by different leveling arch-wires in a complete multi-bracket appliance and to assess whether force and moment levels can be regarded as biologically acceptable or not. The actual bracket position in 42 patients was transferred onto a measurement model. Forces and moments produced by a super-elastic nickel-titanium (NiTi) archwire, a 6-strand stainless steel archwire, and a 7-strand super-elastic NiTi archwire were determined experimentally on different teeth. Average forces and moments produced by the super-elastic NiTi arch wires were found to be the highest. In spite if their larger diameter, the stranded arch wires' average force and moment levels were lower, especially that of the stranded super-elastic archwire. Nevertheless, maximum force levels sometimes exceeded recommended values in the literature and must be considered as too high. The measured arch wires' initial force systems differed significantly depending on the type of archwire and its material structure. Stranded arch wires produced lower force and moment levels, and we recommend their use in the initial phase of orthodontic treatment.