The present overview is intended to point the readers' attention to the important subject of calcium orthophosphates (CaPO4). This type of materials is of the special significance for the human beings because they represent the inorganic part of major normal (bones, teeth and antlers) and pathological (i.e., those appearing due to various diseases) calcified tissues of mammals. For example, atherosclerosis results in blood vessel blockage caused by a solid composite of cholesterol with CaPO4, while dental caries and osteoporosis mean a partial decalcification of teeth and bones, respectively, that results in replacement of a less soluble and harder biological apatite by more soluble and softer calcium hydrogenorthophosphates. Therefore, the processes of both normal and pathological calcifications are just an in vivo crystallization of CaPO4. Similarly, dental caries and osteoporosis might be considered as in vivo dissolution of CaPO4. In addition, natural CaPO4 are the major source of phosphorus, which is used to produce agricultural fertilizers, detergents and various phosphorus-containing chemicals. Thus, there is a great significance of CaPO4 for the humankind and, in this paper, an overview on the current knowledge on this subject is provided.

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Calcium orthophosphates (CaPO4): occurrence and properties

Individual tooth segmentation from CT images using level set method with shape and intensity prior

/pdf/finite-element-investigation-of-the-center-of-resistance-of-5a25c8lvr1.pdf

Finite-element investigation of the center of resistance of the maxillary dentition

Orthodontic mechanotransduction and the role of the P2X7 receptor

The aim of this study was to develop a three-dimensional (3D) finite element (FE) model of a sound extracted human second premolar from micro-CT data using commercially available software tools. A detailed 3D FE model of the tooth could be constructed and was experimentally validated by comparing strains calculated in the FE model with strain gauge measurement of the tooth under loading. The regression coefficient and its standard error in the regression analysis between strains calculated by the FE model and measured with strain gauge measurement were 0.82 and 0.06, respectively, and the correlation coefficient was found to be highly significant. These results suggested that an FE model reconstructed from micro-CT data could be used as a valid model to estimate the actual strains with acceptable accuracy.

Three-dimensional finite element modeling from CT images of tooth and its validation.

Numeric modeling of torque capabilities of self-ligating and conventional brackets.

Direct comparison of experimental and theoretical results in biomechanical studies requires a careful reconstruction of specimen surfaces to achieve a satisfactory congruence for validation. In this paper a semi-automatic approach is described to reconstruct triangular boundary representations from images originating from, either histological sections or μCT-, CT- or MRI-data, respectively. In a user-guided first step, planar 2D contours were extracted for every material of interest, using image segmentation techniques. In a second step, standard 2D triangulation algorithms were used to derive high quality mesh representations of the underlying surfaces. This was accomplished by converting the 2D meshes into 3D meshes by a novel lifting procedure. The meshes can be imported as is into finite element programme packages such as Marc/Mentat or COSMOS/M. Accuracy and feasibility of the algorithm is demonstrated by reconstructing several specimens as examples and comparing simulated results with available meas...

3D Reconstruction of dental specimens from 2D histological images and μCT-Scans

Orthodontic biomechanics started in the early 1960s with the work of Burstone and later Nikolai. Experimental and theoretical studies using finite element methods (FEM) focused on the determination of the position of the center of resistance of single and multi-rooted teeth. Due to the complex structure of the system tooth/periodontal ligament/alveolar bone and because of the limited power of computers, the first numerical models were quite simple. Improved FE software, sophisticated programs for model generation and the explosion of computer power in the last decade resulted in more complex tooth-periodontium models and model assumptions. This paper describes the application of finite element methods in orthodontic biomechanics with the help of several typical examples. The examples cover aspects from basic orthodontic biomechanics to possible future applications in treatment planning using bone remodelling theories: determination of the mechanical properties of the periodontal ligament in a combined numerical and experimental study, calculation of the centers of resistance of different teeth, and simulation of orthodontic tooth movements. The examples show that nowadays finite element methods are a useful and easy-to-handle tool for the solution of a larger number of structure-mechanical and biomechanical problems. Nevertheless, in spite of the enormous technical progress in the last decade, many problems in orthodontic biomechanics remain to be solved.

Computer-aided analysis of the biomechanics of tooth movements.

This study aimed to predict the distribution of bone trabeculae, as a density change per unit time, around a dental implant based on applying a selected mathematical remodelling model. The apparent bone density change as a function of the mechanical stimulus was the base of the applied remodelling model that describes disuse and overload bone resorption. The simulation was tested in a finite element model of a screw-shaped dental implant in an idealised bone segment. The sensitivity of the simulation to different mechanical parameters was investigated; these included element edge length, boundary conditions, as well as direction and magnitude of the implant loads. The alteration in the mechanical parameters had a significant influence on density distribution and model stability, in particular at the cortical bone region. The remodelling model could succeed to achieve trabeculae-like structure around osseointegrated dental implants. The validation of this model to a real clinical case is required.

Computational simulation of internal bone remodelling around dental implants: a sensitivity analysis

Huang Y., Keilig L., Rahimi A., Reimann S., Bourauel C: Torque capabilities of self-ligating and conventional brackets under the effect of bracket width and free wire length Orthod Craniofac Res 2012;15:255–262. © John Wiley & Sons A/S



Structured Abstract

Objectives –  To numerically investigate the torque capacity of conventional and self-ligating brackets under the effect of varying bracket width and free wire length.



Material and Methods –  Finite element models of three kinds of orthodontic brackets in the 0.022-inch slot size were investigated: Discovery, Damon 3MX, Speed. Additionally, finite element (FE) models of Speed and Damon brackets were generated with the same width as the Discovery. From the left upper incisor to the right upper canine, four brackets each were modelled. The total wire length at the upper right incisor was kept constant at 12 mm for all brackets types. For the Discovery brackets, the wire length was increased from 12 to 16 mm in 2-mm steps. A torque of 20° was applied to the upper right incisor with 0.46 × 0.64 mm2 (0.018″ × 0.025″) and 0.48 × 0.64 mm2 (0.019″ × 0.025″) wires. Wires made of stainless steel, titanium molybdenum and nickel titanium were studied. Torque angle/moment characteristics were recorded.



Results –  Wider brackets showed more torque control capability (e.g. Discovery: 10.6 Nmm, Damon: 9.2 Nmm, Speed: 4.0 Nmm for the NiTi wire). Even with the same width as the Discovery bracket, Damon and Speed brackets showed lower torque capability than the Discovery bracket. Increasing the free wire length decreased the torsional stiffness of the wire and thus decreased the torque capability.



Conclusion –  The results showed that the bracket design has less influence on the torquing moment than other parameters, such as bracket width, free wire length, wire/slot play or misalignment.

Alireza Rahimi

Papers

Numeric modeling of torque capabilities of self-ligating and conventional brackets.

3D Reconstruction of dental specimens from 2D histological images and μCT-Scans

Computer-aided analysis of the biomechanics of tooth movements.

Computational simulation of internal bone remodelling around dental implants: a sensitivity analysis

Torque capabilities of self-ligating and conventional brackets under the effect of bracket width and free wire length