A multi-patient analysis of the center of rotation trajectories using finite element models of the human mandible

Studying different types of tooth movements can help us to better understand the force systems used for tooth position correction in orthodontic treatments. This study considers a more realistic force system in tooth movement modeling across different patients and investigates the effect of the couple force direction on the position of the center of rotation (CRot). The finite-element (FE) models of human mandibles from three patients are used to investigate the position of the CRots for different patients’ teeth in 3D space. The CRot is considered a single point in a 3D coordinate system and is obtained by choosing the closest point on the axis of rotation to the center of resistance (CRes). A force system, consisting of a constant load and a couple (pair of forces), is applied to each tooth, and the corresponding CRot trajectories are examined across different patients. To perform a consistent inter-patient analysis, different patients’ teeth are registered to the corresponding reference teeth using an affine transformation. The selected directions and applied points of force on the reference teeth are then transformed into the registered teeth domains. The effect of the direction of the couple on the location of the CRot is also studied by rotating the couples about the three principal axes of a patient’s premolar. Our results indicate that similar patterns can be obtained for the CRot positions of different patients and teeth if the same load conditions are used. Moreover, equally rotating the direction of the couple about the three principal axes results in different patterns for the CRot positions, especially in labiolingual direction. The CRot trajectories follow similar patterns in the corresponding teeth, but any changes in the direction of the force and couple cause misalignment of the CRot trajectories, seen as rotations about the long axis of the tooth.

Comparative evaluation of interrupted and intermittent forces on canine retraction: an in vivo study

Introduction: Various force systems are used in orthodontics to move teeth, such as continuous, intermittent and interrupted. Teeth responds differently to these orthodontic forces. Aims: The aim of the study is to compare the rate of canine retraction with intermittent and interrupted forces. Materials and Methods: A split mouth study was carried among eighteen participants. One side of maxillary arch randomly received interrupted force with elastomeric powerchain while other received intermittent force with elastics with magnitude of 150-170g for canine retraction on each side. For 15 weeks, participants were asked to wear the elastics 8 hours a day whereas the elastomeric powerchains were replaced by operator every 5 weeks. The outcomes were assessed using scanned images of study models collected at the beginning (T0) and 15 weeks later (T3) as well on OPG. Linear and angular measurements were used to measure the distal movement, rotation as well tipping of canines and the results were statistically analysed using Independent t-test. Results: The distal movement of canine on the interrupted force side was 0.98mm/5weeks and on the intermittent force side was 1.06mm/5weeks. The distopalatal rotation on interrupted and intermittent force side was 8.38° and 5.72°. Tipping measured on OPG was 5.72° and 5.27° for interrupted and intermittent force. No statistically significant differences were found. Conclusion: The rate of canine retraction with interrupted force and intermittent force showed no statistically significant differences. Less canine rotation and tipping with intermittent force compared to interrupted force though not statistically significant.

Finite Element Analysis in Orthodontics

One of the governing ideologies in orthodontics is gradually imposing remodeling, which involves progressive and irreversible bone deformations using specific force systems on the teeth. Bone remodeling results in the movement of the teeth into new positions, with two tissues having a major influence along with it: the periodontal ligament and the alveolar bone. There is a definite connection between the mechanical, biological and physiological reactions to the orthodontic forces. The development of the Finite Element Analysis and administration of this new age computer-aided method in orthodontics applies to this chapter. Finite Element Analysis is a computational procedure to calculate the stress in an element, which can show a model solution. The FEM analyses the biomechanical effects of various treatment modalities and calculates the deformation and the stress distribution in the bodies exposed to the external forces. The ideology behind this particular chapter is to introduce this scientific approach to the orthodontist and to reinforce the effects and advantages to the ones who are already aware of the same. In this chapter there is a detail discussion and explanation systematically on Finite element analysis method and its application strictly in and around orthodontics without much deviation from the subject.

Efficient Design of a Clear Aligner Attachment to Induce Bodily Tooth Movement in Orthodontic Treatment Using Finite Element Analysis

Clear aligner technology has become the preferred choice of orthodontic treatment for malocclusions for most adult patients due to their esthetic appeal and comfortability. However, limitations exist for aligner technology, such as corrections involving complex force systems. Composite attachments on the tooth surface are intended to enable active control of tooth movements. However, unintended tooth movements still occur. In this study, we present an effective attachment design of an attachment that can efficiently induce tooth movement by comparing and analyzing the movement and rotation of teeth between a general attachment and an overhanging attachment. The 3D finite element modes were constructed from CBCT data and used to analyze the distal displacement of the central incisor using 0.5- and 0.75-mm-thick aligners without an attachment, and with general and overhanging attachments. The results show that the aligner with the overhanging attachment can effectively reduce crown tipping and prevent axial rotation for an intended distal displacement of the central incisor. In all models, an aligner with or without attachments was not capable of preventing the lingual inclination of the tooth.

The Generalized Hamilton Principle and Non-Hermitian Quantum Theory

The Hamilton principle is a variation principle describing the isolated and conservative systems, its Lagrange function is the difference between kinetic energy and potential energy. By Feynman path integration, we can obtain the Hermitian quantum theory, i.e., the standard Schrodinger equation. In this paper, we have generalized the Hamilton principle to the generalized Hamilton principle, which can describe the open system (mass or energy exchange systems) and nonconservative force systems or dissipative systems, and given the generalized Lagrange function, it has to do with the kinetic energy, potential energy and the work of nonconservative forces to do. With the Feynman path integration, we have given the non-Hermitian quantum theory of the nonconservative force systems. Otherwise, with the generalized Hamilton principle, we have given the generalized Hamiltonian for the particle exchanging heat with the outside world, which is the sum of kinetic energy, potential energy and thermal energy, and further given the equation of quantum thermodynamics. PACS: 03.65.-w, 05.70.Ce, 05.30.Rt

Versatile Uses of Crimpable Hooks

The crimpable hook is a widely accepted tool onto which active elements can be fixed to aid in orthodontic tooth movement. This clinical pearl aims at showing the different ways in which crimpable hooks can be used to better orthodontic treatment mechanics, which are Crimpable hooks used for buccolingual force mechanics and Crimpable hooks used in conjunction with orthodontic miniscrews. The above-mentioned simple methods aim to facilitate and make easy the attachment of force elements for various kinds of tooth movements. It can help the operator to save time, prevent unwanted side effects of forces, as well as reduce the need for ligature wires for the attachment of force systems onto implant heads or lingual sheaths.

On the regularity of curvature fields in stress-driven nonlocal elastic beams

Elastostatic problems of Bernoulli–Euler nanobeams, involving internal kinematic constraints and discontinuous and/or concentrated force systems, are investigated by the stress-driven nonlocal elasticity model. The field of elastic curvature is output by the convolution integral with a special averaging kernel and a piecewise smooth source field of elastic curvature, pointwise generated by the bending interaction. The total curvature is got by adding nonelastic curvatures due to thermal and/or electromagnetic effects and similar ones. It is shown that fields of elastic curvature, associated with piecewise smooth source fields and bi-exponential kernel, are continuously differentiable in the whole domain. The nonlocal elastic stress-driven integral law is then equivalent to a constitutive differential problem equipped with boundary and interface constitutive conditions expressing continuity of elastic curvature and its derivative. Effectiveness of the interface conditions is evidenced by the solution of an exemplar assemblage of beams subjected to discontinuous and concentrated loadings and to thermal curvatures, nonlocally associated with discontinuous thermal gradients. Analytical solutions of structural problems and their nonlocal-to-local limits are evaluated and commented upon.

Analytical graphic statics

Graphic statics is undergoing a renaissance, with computerized visual representation becoming both easier and more spectacular as time passes. While methods of the past are revived, little emphasis has been placed on studying the mathematics behind these methods. Due to the considerable advances of our mathematical understanding since the birth of graphic statics, we can learn a lot by examining these old methods from a more modern viewpoint. As such, this work shows the mathematical fabric joining different aspects of graphic statics, like dualities, reciprocal diagrams, and discontinuous stress functions. This is done by introducing a new, three dimensional force diagram (containing the old two dimensional force diagram) depicting the three dimensional equilibrium of planar force systems. A corresponding three dimensional “form diagram” (dual diagram) is introduced, in which forces are treated as linear functionals (dual vectors). It is shown that the polyhedral stress function introduced by Maxwell is in fact a linear combination of these functionals; and the projective dualities connecting these three dimensional diagrams are also explained.