Biomechanical study on orthodontic tooth movement: changes in biomechanical property of the periodontal tissue in terms of tooth mobility

The magnitude of tooth mobility has been frequently used for evaluating biomechanical response of the periodontal tissue to applied forces. However, tooth mobility during orthodontic tooth movement has not been measured. The purpose of this study was to investigate changes in biomechanical property of the periodontal tissue during canine retraction, in terms of tooth mobility. The upper canines on both sides of ten orthodontic patients were moved in the distal direction for about four weeks with an initial force of 200 gf. An amount of tooth movement and a magnitude of tooth mobility were measured every 3 or 4 days during retraction. A distally directed force up to 500 gf was continuously applied to each canine and tooth mobility was measured with a noncontact type of eddy current displacement sensor. A two-dimensional finite element model was constructed and displacements of the finite element model were calculated with various Young's moduli in loading with a 100 gf force in the distal direction. In comparison with the magnitudes of the tooth mobility, Young's modulus of the periodontal membrane before retraction and the influence of the biomechanical factors on changes in tooth mobility were investigated. The tooth movement curve was divided into three phases; an initial phase, a lag phase and a post-lag phase. The magnitudes of tooth mobility at the initial phase were significantly larger than those before retraction within the range of 250 gf to 500 gf and these magnitudes decreased during the lag phase. The magnitudes of tooth mobility at the post-lag phase significantly increased, within the range of 50 gf to 500 gf, than those before retraction. As a result of curveliniar regression analysis, the tooth mobility curves approximated to delta = AFB, where delta and F denote tooth mobility and force respectively. The coefficients A and B changed according to the phases of tooth movement. An inclination of the tooth mobility curve expressed by a tangent at the 400 gf force was the largest at the initial phase, and this inclination at the 100 gf force was the largest at the post-lag phase. Young's modulus of the periodontal membrane before retraction was determined to be approximately 35 gf/mm2 and Young's modulus of the periodontal membrane was the most important factor on the increase of tooth mobility. Tooth mobility significantly varied associated with tooth movement. It was indicated that biomechanical property of the periodontal tissue changes in response to each phase of tooth movement. In particular, Young's modulus of the periodontal membrane decreased at the post-lag phase of the orthodontic tooth movement.     

Numerical simulation of canine retraction by sliding mechanics.

BACKGROUND: Bone remodeling laws have been used to simulate the movement of a single tooth, but the calculations for simulating the movement of several teeth simultaneously are time-consuming. The purpose of this article is to discuss a method that allows the simulation of more complex tooth movements. METHODS: A 3-dimensional finite element method was used to simulate the orthodontic tooth movement (retraction) of a maxillary canine by sliding mechanics and any associated movement of the anchor teeth. Absorption and apposition of the alveolar bone were produced in proportion to the stress of the periodontal ligament. RESULTS: In a reference case, the canine was retracted by a 2N force with 0.016-in square wire. The frictional coefficient between wire and bracket was 0.2. The movement of both the canine and the anchor teeth could be calculated with the elastic deformation of wire. The canine tipped during the initial unsteady state and then moved bodily during the steady state. It became upright when the orthodontic force was removed. The anchor teeth moved in the steady state and tipped in the mesial direction. The decrease in applied force by friction was about 70%. The tipping of the canine decreased when the wire size was increased or when the applied force was decreased. CONCLUSIONS: Simple assumptions were used in this calculation to simulate orthodontic tooth movements. The calculated results were reasonable in mechanical considerations. This method might enable one to estimate various tooth movements clinically. However, precise comparisons between calculated and clinical results, and the improvement of the calculation model, are left for a future study.     

Numerical simulations of canine retraction with T-loop springs based on the updated moment-to-force ratio

The purpose of this study was to develop a new finite element method for simulating long-term tooth movements and to compare the movement process occurring in canine retraction using a T-loop spring having large bends and with that having small bends. Orthodontic tooth movement was assumed to occur in the same manner as the initial tooth movement, which was controlled by the moment-to-force (M/F) ratios acting on the tooth. The M/F ratios were calculated as the reaction forces from the spring ends. For these M/F ratios, the teeth were moved based on the initial tooth movements, which were calculated by using the bilinear elastic model of the periodontal ligament. Repeating these calculations, the teeth were moved step by step while updating the M/F ratio. In the spring with large bends, the canine at first moved bodily, followed by root distal tipping. The bodily movement was quickly achieved, but over a short distance. In the spring with small bends, the canine at first rotated and root mesial tipping occurred, subsequently the canine uprighted and the rotation decreased. After a long time elapsed, the canine moved bodily over a long distance. It was found that the long-term tooth movement produced by the T-loop springs could be simulated by the method proposed in this study. The force system acting on the teeth and the movement type remarkably changed during the long-term tooth movement. The spring with large bends could move the canine bodily faster than that with small bends.     

A numerical simulation of orthodontic tooth movement produced by a canine retraction spring

Tooth movements produced by a canine retraction spring were calculated. Although a gable bend and an anti-rotational bend were incorporated into the spring, the canine tipped and rotated initially. Retraction force decreased and moment-to-force ratio increased after the spring legs closed. Then, the initial tipping and rotation began to be corrected. As a result, the canine moved almost bodily after a prolonged period of time. Such tooth movements cannot be estimated from the initial force system. The gable bend decreased tipping movement, but increased rotational movement. On the other hand, the anti-rotational bend decreased rotational movement but increased tipping movement. In other words, one bend decreased the effect of the other, when both bends were incorporated in the spring.     

Application of Bone Remodeling Theories in the Simulation of Orthodontic Tooth Movements

A numerical model that calculates bone apposition and resorption around a tooth root on the basis of bone remodeling theories was developed to simulate orthodontic tooth movements. The model was used to calculate different kinds of orthodontic tooth movements, that were then compared with the expected movements based on clinical experience. For simulation of the movements the root of a canine was modeled in an idealized way in the form of an elliptical paraboloid and was processed with a finite element program. The finite element model was loaded with defined force systems. Two model assumptions were used to calculate the bone remodeling process. The mechanical loads firstly in the periodontal ligament and secondly in the alveolar bone were taken to simulate the following tooth movements: 1. mesial tipping around the center of resistance (force system at the bracket: isolated torque MY = 5 Nmm), 2. rotation around the long axis of the tooth (MZ = 5 Nmm), 3. uncontrolled tipping around the root tip (FX = 1 N, MZ = 5 Nmm), 4. canine retraction (FX = 1 N, MY = -9.5 Nmm, MZ = 5 Nmm), 5. and 6. extrusion/intrusion (FZ = +/- 0.5 N, MX = +/- 2.5 Nmm). Comparison with clinical experience was performed by calculating the orthodontic tooth movements based on the assumption of a fixed position of the center of resistance. It could be demonstrated that the numerical model of orthodontic bone remodeling can be used to calculate orthodontic tooth movements. However, the results are strongly dependent on the model assumptions. The model simulating the bone remodeling on the basis of the loading of the periodontal ligament delivers results that are in very good accordance with the biomechanical assumptions of the position of the center of resistance. However, marked side effects occurred with the second model, especially in the simulations of uncontrolled tipping, translation and intrusion/extrusion. Clinically, these side effects cannot be observed.     

Determination of the centre of resistance in an upper human canine and idealized tooth model

The purpose of this investigation was to analyse the influence of geometric and material parameters of a human canine on initial tooth mobility, and the stress and strain profiles in the periodontal ligament. While the material parameters of tooth and bony structures are known within an uncertain limit of approximately a factor of 10, values reported for the elasticity parameters of the periodontal ligament differ significantly. In the course of this study, bilinear behaviour was assumed for the mechanical property of the periodontium. The finite element model of an elliptical paraboloid was created as an approximation to the geometry of a human canine to reduce calculation time and to determine influences of the geometry on numerical results. The results were compared with those obtained for a realistic human canine model. The root length of both models was 19.5 mm. By calculating pure rotational and pure tipping movements, the centre of resistance (CR) was determined for both models. They were located on the long axis of the tooth approximately 7.2 mm below the alveolar crest for the idealized model and 8.2 mm for the canine model. Thus, the centre of resistance of a human canine seems to be located around two-fifths of the root length from the alveolar margin. Using these results, uncontrolled tipping (1 N of mesializing force and 5 Nmm of derotating momentum), as well as pure translation (additionally about 10 Nmm of uprighting momentum) were calculated. Comparing the idealized and the realistic models, the uncontrolled tipping was described by the parabolic-shaped model within an accuracy limit of 10 per cent as compared with the canine model, whereas the results for bodily movement differed significantly showing that it is very difficult to achieve a pure translation with the realistic canine model.     

Biomechanical design and clinical evaluation of a new canine-retraction spring

Use of the sectional arch technique facilitates the creation of an optimal force system fulfilling the biomechanical requirements imperative for planned tooth movements. Controlled canine retraction, usually in extraction cases, requires the creation of a biomechanical system to deliver a predetermined force and a relatively constant moment-to-force ratio in order to avoid distal tipping and rotation. The responsive couple delivered to the anchorage unit should be adjusted in such a way that no single tooth is subjected to unwanted side effects and that undesirable changes in the occlusal plane are avoided. On the basis of a series of theoretical considerations described in the present report, a canine-retraction spring was constructed from 0.016 X 0.022 inch stainless steel wire, the principal element being a double ovoid loop 10 mm in height. A "sweep" bend was incorporated to avoid unwanted side effects at the second premolar. Load deflection and moment/force curves were derived experimentally and demonstrate the ability of the spring to generate and maintain biomechanical conditions necessary for optimal canine retraction (that is, load deflection = 45 gm per millimeter of activation, antitip moment/force ratio of approximately 11:1, and antirotation moment/force ratio of approximately 7:1). The clinical applicability of the spring is demonstrated in the present report by the presentation of two treated cases.     

A finite element study of canine retraction with a palatal spring

The use of a removable appliance to retract a maxillary canine tooth into a first premolar extraction space is one of the most commonly performed orthodontic procedures. However, unwanted movements may occur, including excessive tipping, rotation, and flaring of the tooth. The present investigation by the use of a finite element model quantifies some of the initial stresses produced within the periodontal ligament when two obliquely directed forces are applied to a maxillary canine tooth. In simulating the action of a removable appliance it attempts to relate the stress patterns to the nature of the subsequent tooth movement.     

Human interleukin-1 beta and interleukin-1 receptor antagonist secretion and velocity of tooth movement

The cytokines interleukin-1 beta (IL-1 beta) and IL-1 receptor antagonist (IL-1RA) probably play a part in orthodontic tooth movement. Here, the force magnitudes and the area of force application in the compressed periodontal ligament (PDL) were controlled and the velocity of tooth movement correlated with concentrations of IL-1 beta and IL-1RA in the gingival crevicular fluid (GCF). Seven individuals undergoing orthodontic treatment involving maxillary first premolar extractions and distal movement (bodily retraction) of the maxillary canines participated in the 84-day study. For each participant, continuous retraction forces were applied so that they received equivalent PDL stresses of 13 kPa for one canine and 4 kPa for the other. GCF cytokine concentrations from experimental and control teeth were expressed relative to total protein in the GCF and compared using an 'Activity Index' (AI)=Experimental (IL-1 beta/IL-1RA)/Control (IL-1 beta/IL-1RA). The results showed that the velocity of tooth movement in an individual was related to their AI. The correlation between AI and tooth movement was stronger from the distal (R(d)=0.78) than from the mesial (R(m)=0.65) of retracted teeth. The results demonstrate that equivalent force systems produce individual differences in cytokine production, which correlate with interindividual differences in the velocity of canine retraction.     

A finite element model of apical force distribution from orthodontic tooth movement

This study was undertaken to determine the types of orthodontic forces that cause high stress at the root apex. A 3-dimensional finite element model of a maxillary central incisor, its periodontal ligament (PDL), and alveolar bone was constructed on the basis of average anatomic morphology. The maxillary central incisor was chosen for study because it is one of the teeth at greatest risk for apical root resorption. The material properties of enamel, dentin, PDL, and bone and 5 different load systems (tipping, intrusion, extrusion, bodily movement, and rotational force) were tested. The finite element analysis showed that purely intrusive, extrusive, and rotational forces had stresses concentrated at the apex of the root. The principal stress from a tipping force was located at the alveolar crest. For bodily movement, stress was distributed throughout the PDL; however, it was concentrated more at the alveolar crest. We conclude that intrusive, extrusive, and rotational forces produce more stress at the apex. Bodily movement and tipping forces concentrate forces at the alveolar crest, not at the apex.     

Anchorage loss during canine retraction using intermittent versus continuous force distractions; a split mouth randomized clinical trial

ObjectivesThe aim of this study was to evaluate the anchorage loss, amount and time of canine retraction, and canine tipping concomitant with periodontal ligament distraction (PLD) using intermittent and continuous forces.Materials and methodsThis was a split mouth randomized clinical trial involving 30 patients in need of first premolar extraction. For each patient, one side was randomly allocated to receive a screw-based dental distractor, and the other side a continuous force coil spring distractor. Molar and canine movements were recorded on study casts using the rugae as reference. Changes in the long axis of the canines were evaluated from pre- and post distraction panoramic radiographs.ResultsOn the screw side, molars moved mesially 2.5 ± 0.9 mm. The canine tipped distally a mean of 10.5°±3.1°. The average time needed for canine retraction was 5.3 ± 1.3 weeks. In the coil side, the molar mesial movement was not statistically different from the screw group (2.8 ± 1.5 mm). The canine moved bodily with a mean distal tip of 0.27°±1.75° in a period of 27.8 ± 6.6 weeks.ConclusionsAnchorage loss occurs with dental distraction using either intermittent or continuous force. No significant difference in anchorage loss was found with either type of force. The surgical intervention did not shorten the time needed for canine retraction using the continuous force. Continuous force leads to slow bodily retraction of the canine unlike the intermittent force which leads to rapid tipping of the canine.     

Human tooth movement in response to continuous stress of low magnitude.

Conventional orthodontic therapy often uses force magnitudes in excess of 100 g to retract canine teeth. Typically, this results in a lag phase of approximately 21 days before tooth movement occurs. The current project was undertaken to demonstrate that by using lower force magnitudes, tooth translation can start without a lag phase and can occur at velocities that are clinically significant. Seven subjects participated in the 84-day study. A continuous retraction force averaging 18 g was applied to 1 of the maxillary canines, whereas a continuous retraction force averaging 60 g was applied to the other. The magnitude was adjusted for each canine to produce equivalent compressive stresses between subjects. Estimated average compressive stress on the distal aspect of the canine teeth was 4 kPa or 13 kPa. The moment-to-force ratios were between 9 and 13 mm. Tooth movement in 3 linear and 3 rotational dimensions was measured with a 3-axis measuring microscope and a series of dental casts made at 1- to 14-day intervals. The results showed a statistical difference in the velocity of distal movement of the canines produced by the 2 stresses (P =.02). The lag phase was eliminated and average velocities were 0.87 and 1.27 mm/month for 18 and 60 g of average retraction force. Interindividual velocities varied as much as 3 to 1 for equivalent stress conditions. It was concluded that effective tooth movement can be produced with lower forces and that because loading conditions were controlled, cell biology must account for the variability in tooth velocities measured in these subjects.     

Effects of different types of tooth movement and force magnitudes on the amount of tooth movement and root resorption in rats

Objective:To investigate differences in the amount of tooth movement and root resorption that occurred after tipping and bodily movement of the maxillary first molar in rats.Materials and Methods:Ten-week-old female Wistar rats were divided into two groups according to type of tooth movement and subdivided into four subgroups according to the magnitude of applied force. Nickel-titanium closed-coil springs exerting forces of 10, 25, 50, or 100 g were applied to the maxillary left first molars to induce mesial tooth movement. We designed a novel orthodontic appliance for bodily tooth movement. Tooth movement distance and root resorption were measured using microcomputed tomography and scanning electron and scanning laser microscopy.Results:The amount of tooth movement in the bodily tooth movement group was less than half that in the tipping tooth movement group. The greatest amount of tooth movement occurred in the 10-g tipping and 50-g bodily tooth movement subgroups, and the amount of tooth movement decreased with the application of an excessive magnitude of force. Conversely, root resorption increased when the heavier orthodontic force was applied in both groups. Root resorption in the tipping tooth movement group was approximately twice that in the bodily tooth movement group.Conclusions:Root resorption in the tipping tooth movement group was more pronounced than that in the bodily tooth movement group. Although the amount of tooth movement decreased when extremely heavy forces were applied, root resorption increased in both the tipping and bodily tooth movement groups in rats.     

双钥匙曲整体内收上前牙的三维有限元研究

目的：探讨双钥匙曲整体内收上前牙的过程中不同的加力方式对上颌前牙生物力学效应的影响。方法：采用 CBCT采集患者上颌骨以及上牙列数据信息,利用 Mimics 软件进行三维重建,建立双钥匙曲整体内收上前牙的三维有限元模型;在ANSYS 软件中分别分析①末端回弯、②结扎丝加力以及③结扎丝加力联合双钥匙曲顶部连扎3种工况下上颌前牙的初始位移。结果：从工况1到工况3,矢状方向上：中切牙冠根位移差值由4．19E －03 mm 变为－8．85E －03 mm,表现为舌侧倾斜移动到整体移动后转变为唇侧倾斜移动。而侧切牙冠根位移差由7．99E －03 mm 减小到5．84E －04 mm,尖牙由9．47E －03 mm 变为8．54E －03 mm,显示侧切牙和尖牙由倾斜移动向整体移动转变;垂直方向上：切牙由伸长移动趋势变为压低,而尖牙的压低量也逐渐变大。结论：不同的加力方式上颌前牙的移动趋势不同,结扎丝加力和顶部连扎使前牙趋向于整体移动。     

Determining the center of resistance of maxillary anterior teeth subjected to retraction forces in sliding mechanics. An in vivo study

OBJECTIVE: To determine the location of center of resistance and the relationship between height of retraction force on power arm (power-arm length) and movement of anterior teeth (degree of rotation) during sliding mechanics retraction. MATERIALS AND METHODS: Three human subjects with maxillary protrusion were selected for this study. Initial tooth displacements of maxillary right central incisor under sliding mechanics with various heights of retraction forces were measured in vivo using a two-point three-dimensional displacement magnetic sensor device. By calculating the angle of rotation from the displacements measured, the location of the center of resistance was determined. RESULTS: The results suggested that different heights of retraction forces could affect the direction of anterior tooth movement. The higher the retraction force was applied, the lower the degree of rotation (crown-lingual tipping) would be. The tooth rotation was in the opposite direction (from crown-lingual to crown-labial) if the height of the force was raised above the level of the center of resistance. CONCLUSION: The location of the center of resistance of the maxillary central incisor was approximately 0.77 of the root length from the apex. During anterior tooth retraction with sliding mechanics, controlled crown-lingual tipping, bodily translation movement, and controlled crown-labial movement could be achieved by attaching a power-arm length that was lower, equivalent, or higher than the level of the center of resistance, respectively. The power-arm length could be the most easily modifiable clinical factor in determining the direction of anterior tooth movement during retraction with sliding mechanics.     

Material parameters and stress profiles within the periodontal ligament

Levels and profiles of initial stress in the periodontal ligament after application of various force systems were studied. Two finite-element models, based on sections of human autopsy material, were developed to simulate one full and one partial mandible. The validity of the finite-element model was improved by identification of material parameters; the mechanical properties of the tissue were described by means of strain-gauge measurements of initial tooth movements in human autopsy material. The multiple modeling technique, in which data from a coarse global model are transferred to a more detailed one, was used to identify bone structure and boundary conditions. Parameters known to influence the results were varied to establish the validity of the finite-element model. Iterative calculation methods were used to gain stable results. However, optimizing features of the bone structure and boundary conditions did not influence the results significantly. The elastic stiffness of the periodontal ligament was determined to 0.07 MPa and tau = 0.49 (tau being the Poisson's ratio). Stress profiles were obtained for various force systems--as in tipping, translation, and root movement. As we expected, there was a marked variation in the stress distribution from cervix to apex when tipping forces were applied. Bodily movement of the tooth produced an almost uniform stress distribution; root movement produced stress patterns opposite to those observed during tipping; and masticatory forces alone produced stress patterns almost identical to those achieved by masticatory force in combination with orthodontic forces.     

微植体支抗滑动法内收上颌前牙的三维有限元研究

目的探讨不同微螺钉种植体植入高度以及不同牵引钩高度对微植体支抗滑动法内收上颌前牙的生物力学效应的影响。方法采用高精度螺旋CT扫描结合MIMICS快速三维重建的方法建立微植体－直丝弓上颌前牙内收力系的三维有限元模型,并在准确构建托槽、牙齿、弓丝、微种植体的力学关系基础上计算当微种植体植入高度为4、8 mm时以及牵引钩高度为1、4、7、10 mm时上颌前牙的初始移动情况。结果随着牵引钩高度的增加,上颌前牙内收时逐渐从冠舌向倾斜移动变为冠唇向移动;微种植体高位植入更有利于上颌前牙内收时的压入移动。结论通过微种植体植入高度和牵引钩高度的变化可以有效控制上颌前牙内收的牙齿移动方式。     

Three-dimensional finite element analysis for stress in the periodontal tissue by orthodontic forces

This study was designed to investigate the stress levels induced in the periodontal tissue by orthodontic forces using the three-dimensional finite element method. The three-dimensional finite element model of the lower first premolar was constructed on the basis of average anatomic morphology and consisted of 240 isoparametric elements. Principal stresses were determined at the root, alveolar bone, and periodontal ligament (PDL). In all loading cases for the buccolingually directed forces, three principal stresses in the PDL were very similar. At the surface of the root and the alveolar bone, large bending stresses acting almost in parallel to the root were generally observed. During tipping movement, stresses nonuniformly varied with a large difference from the cervix to the apex of the root. On the other hand, in case of movement approaching translation, the stresses induced were either tensile or compressive at all occlusogingival levels with some difference of the stress from the cervix to the apex. The pattern and magnitude of stresses in the periodontium from a given magnitude of force were markedly different, depending on the center of rotation of the tooth.     

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

ObjectivesTo assess the mechanical environment for three fixed appliances designed to retract the lower anterior segment.Materials and MethodsA 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.ResultsThe 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.ConclusionsT-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.