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.

Obtaining Influence Coefficients in Different Formats With Reduced Number of Trial Runs on Two-Plane Balancing

Previously conversion equations of influence coefficients between multi-plane and static(in-phase)-couple(180 degrees out-of-phase) methods have been established. Sometimes one may have influence coefficients due to weight from one end only, but not both ends, plus those due to static or couple pair weight only but not both pairs. It has been found now that obtaining or knowing half of influence coefficients in the first method, plus half of those in the second method, can yield the other half of influence coefficients in both methods. In the other words, all influence coefficients in different formats can be obtained without a further trial run once one has half of influence coefficients in both methods. The above findings and conversion equations have been obtained analytically and verified by experimental results. A real application example is presented to demonstrate its efficiency in dealing with balancing tasks. The corresponding spreadsheets that can easily convert influence coefficients between different formats have been developed and used in real cases. Up to this point, all possible conversion equations of influence coefficients in different formats have been successfully discovered.

Combination of multicomponent KA2 and Pauson–Khand reactions: short synthesis of spirocyclic pyrrolocyclopentenones

The Cu-catalyzed multicomponent ketone–amine–alkyne (KA2) reaction was combined with a Pauson–Khand cycloaddition to give access of unprecedented constrained spirocyclic pyrrolocyclopentenone derivatives following a DOS couple-pair approach. The polyfunctional molecular scaffolds were tested on the cyclopentenone reactivity to further expand the skeletal diversity, demonstrating the utility of this combined approach in generating novel spiro compounds as starting material for the generation of chemical libraries. The chemoinformatics characterization of the newly-synthesized molecules gave evidence about structural and physicochemical properties with respect to a set of blockbuster drugs, and showed that such scaffolds are drug-like but more spherical and three-dimensional in character than the drugs.

Diversity oriented multi-component reaction (DOS–MCR) approach to access natural product analogues: regio- and chemo-selective synthesis of polyheterocyclic scaffolds via one-pot cascade reactions

Skeletally diverse and complex polyheterocyclic hybrid scaffolds have been accessed via one-pot three-component reaction by exploiting the build/couple/pair strategy of diversity oriented synthesis.