Christopher G. Provatidis

A comparative FEM-study of tooth mobility using isotropic and anisotropic models of the periodontal ligament

Orthodontic tooth movement is usually characterized by two centres: the centre of resistance and the centre of rotation. A literature survey shows that both centres vary to a significant extent in both clinical and computational experiments. This paper reports on studies upon five different hypothetical mechanical representations of the periodontal ligament (PDL) which plays the most significant role in tooth mobility. The first model considers the PDL as an isotropic and linear-elastic continuum without fibres; it also discusses some preliminary visco-elastic aspects. The next three models assume a nonlinear and anisotropic material composed of fibres only that are arranged in three different orientations, two hypothetical that have appeared previously in the literature and one more consistent with actual morphological data. The fifth model considers the PDL as an orthotropic material consisting of both a continuum and of fibres. Results were obtained by applying the Finite Element Method (FEM) on a maxillary central incisor. It was found that the isotropic linear-elastic PDL leads to occlusal positions of both centres in comparison with those obtained through the well-known Burstones theoretical formula, while histological anisotropic fibres locate them apically and eccentrically.

Evaluation of craniofacial effects during rapid maxillary expansion through combined in vivo/in vitro and finite element studies.

It is well documented in the literature that a contracted maxilla is commonly associated with nasal obstruction. Midpalatal splitting using the rapid maxillary expansion (RME) technique produces separation of the maxillary halves with consequent widening of the nasal cavity. Although clinicians agree about many of the indications for and outcomes of RME, some disagreements persist in relation to the biomechanical effects induced. The present research was based on the parametric analysis of a finite element model (FEM) of a dry human skull with the RME appliance cemented in place in order to evaluate these effects on the overall craniofacial complex with different suture ossification. The behaviour of the FEM was compared with the findings of a clinical study and to an in vitro experiment of the same dry skull. Comparisons refer to the opening pattern and associated displacements of four anatomical points located at the left and right maxilla (MI, UM, EM, CN). It was found that the maxillolacrymal, the frontomaxillary, the nasomaxillary, the transverse midpalatal sutures, and the suture between the maxilla and pterygoid process of the sphenoid bone did not influence the outcome of RME, while the zygomatico-maxillary suture influenced the response of the craniofacial complex to the expansion forces. Moreover, the sagittal suture at the level of the frontal part of the midpalatal suture plays an important role in the degree and manner of maxillary separation. Maximum displacements were observed in the area of maxilla below the hard palate, from the central incisors to second premolars, which dissipated at the frontal and parietal bone and nullified at the occipital bone.

An analytical model for stress analysis of a tooth in translation

Closed-form analytical formulas for a tooth of paraboloidal shape in pure translation are presented. These formulas are based on both the approximation of normal and tangential strains in terms of the translational displacement of the tooth and the tooth equilibrium of the thin surrounding periodontal membrane (or on the strain energy conservation equivalently). The tooth is considered to be a rigid body while the surrounding membrane is assumed to be an elastic foundation of uniform thickness. The proposed formulas are capable of determining the most important quantities involved in the case of tooth translation; these are the stiffness of the tooth-support in translation, the distribution of strain and stress tensors in the membrane, the maximum value of hydrostatic stress, as well as the location of the center of resistance. It was found that the proposed formulas involve not only the root length h, as the previous literature reports, but also the root diameter D. The theory is successfully compared to three-dimensional finite element results for an upper central incisor.

Structural characterization of textile fabrics using surface roughness data

The surface of the textile fabrics is not absolutely flat and smooth. Its geometrical roughness within certain extents is considerable. The surface roughness influences the fabric hand and it plays a significant role in the end use of the fabric. In parallel, the periodic variations of the fabric surface level due to the regular interlaced patterns of the yarns cause a respective variation of the geometrical roughness measurement. Thus, the fabric roughness data measured using the Kawabata Evaluation System for Fabrics and imposed to a certain process of numerical calculations result into the retrieval of the structural parameters of the fabric. The principle of the method has a non‐destructive character and can be applied to woven or knitted fabrics.

Weight minimisation of displacement-constrained truss structures using a strain energy criterion

This paper discusses a new method for the solution of the general truss weight-minimisation problem under simultaneous stress and displacement constraints. The method introduces a novel strain-energy-density criterion that refers to the ratio of the virtual strain energy per unit volume in each structural member to its average value on the whole structure. The virtual strain energy comes from the unit-load theorem and it is proportional to the product of the axial member forces due to both the actual loads and a virtual unit load that is applied at the node with the maximum displacement. A simple recursive formula for updating the cross-sectional areas, based on displacement constraints, is presented. A general subsequent algorithm applicable to both single and multiple load cases follows this formula. The results are encouraging since in all test cases the method was found to be robust and generally led to the same weight level as the literature, in both small and large structures.

The Effects of Implant Length and Diameter Prior to and After Osseointegration: A 2-D Finite Element Analysis

A two-dimensional finite element analysis was used to evaluate the effects of implant length and diameter on the stress distribution of a single-implant supported crown and the strain distribution of its surrounding bone prior to and after the phase of osseointegration. The effect of length was investigated using implants with a diameter of 3.75 mm and lengths of 8 mm, 10 mm, 12 mm, and 14 mm. The effect of diameter was investigated using implants with a length of 10 mm and diameters of 3 mm, 3.75 mm, 4.5 mm, and 5mm. The phase prior to osseointegration was simulated by assuming a coefficient of friction for the interface between the implant and the surrounding bone, while the phase after osseointegration was simulated by assuming a fixed bond on the interface between the implant and the surrounding bone. The FEA results indicated a tendency towards stress reduction on the implant, both prior to and after osseointegration, when the length was increased. However, the calculated stresses on the implant were lower after the phase of osseointegration. Although no specific correlation could be seen regarding the influence of implant diameter, the calculated stresses on the implant were again lower after the phase of osseointegration. For all these cases, the maximum stress concentration occurred at the abutment-implant interface. As far as bone tissue was concerned, there was a tendency towards strain reduction, before and after osseointegration, when the length of the implant was increased from 10 mm up to 14 mm. This tendency was not manifested for the range of 8 to 10 mm. The effect of implant diameter on bone tissue was not clear. It appears that implants of a diameter more than 5 mm are not preferable for immediate loading. Finally, it seems that cortical bone is not influenced by the phase of osseointegration, while trabecular bone is highly affected.

Analysis of axisymmetric structures using Coons' interpolation

This paper investigates the performance of global shape functions in axisymmetric elastic structures. The main idea behind the proposed theory is the use of the interpolation formula developed by Coons for CAD purposes in automotive industry, in which it is shown that it is capable of interpolating the displacements within a large patch on the axial cross-section of a structure. The degrees of freedom appear only at the patch boundaries and can be used in the solution of displacement and stress analysis problems. Two different schemes for the interpolation of the boundary data, using B-splines and/or linear global shape functions, are investigated. Numerical results are presented for three typical test cases where the proposed method is successfully compared with conventional finite elements and closed analytical solutions.

Numerical Estimation of the Centres of Rotation and Resistance in Orthodontic Tooth Movement

The position of the centre of resistance (Cre) as well as the centre of rotation (Cro) of a tooth under a force-system is still an open question. This paper presents a reliable and efficient three-dimensional rigid-body finite element technique to accurately estimate these centres. The influence of not only the root length but also the root diameter, the thickness of the periodontal ligament, as well as its material properties on the position of the Cre and Cro is investigated. Additionally, an explanation is given for the meaning of the coefficient (0.068 h(2) ) involved in Burstones theoretical formula which is generalised and is expressed as the ratio of the flexibilities of tooth support in translation and pure moment rotation, respectively. The former ratio determines the position of the centres of rotation as a function of the applied moment-to-force ratio (M/F) and the relevant curve remains an isosceles hyperbola for any arbitrary-shaped tooth. The present study focuses on single-rooted teeth, such as maxillary canines and maxillary incisors, but the proposed methodology is generally applicable to any tooth.

Large Diameter Femoral Heads Impose Significant Alterations on the Strains Developed on Femoral Component and Bone: A Finite Element Analysis

Total Hip Arthroplasty aims at fully recreating a functional hip joint. Over the past years modular implant systems have become common practice and are widely used, due to the surgical options they provide. In addition Big Femoral Heads have also been implemented in the process, providing more flexibility for the surgeon. The current study aims at investigating the effects that femoral heads of bigger diameter may impose on the mechanical behavior of the bone-implant assembly. Using data acquired by Computed Tomographies and a Coordinate Measurement Machine, a cadaveric femur and a Profemur-E modular stem were fully digitized, leading to a three dimensional finite element model in ANSYS Workbench. Strains and stresses were then calculated, focusing on areas of clinical interest, based on Gruen zones: the calcar and the corresponding below the greater trochanter area in the proximal femur, the stem tip region and a profile line along linea aspera. The performed finite elements analysis revealed that the use of large diameter heads produces significant changes in strain development within the bone volume, especially in the lateral side. The application of Frost’s law in bone remodeling, validated the hypothesis that for all diameters normal bone growth occurs. However, in the calcar area lower strain values were recorded, when comparing with the reference model featuring a 28mm femoral head. Along line aspera and for the stem tip area, higher values were recorded. Finally, stresses calculated on the modular neck revealed increased values, but without reaching the yield strength of the titanium alloy used.

Effects of Foot Posture on Fifth Metatarsal Fracture Healing: A Finite Element Study

The goal of this study was to evaluate the effects of maintaining different foot postures during healing of proximal fifth metatarsal fractures for each of 3 common fracture types. A 3-dimensional (3D) finite element model of a human foot was developed and 3 loading situations were evaluated, including the following: (1) normal weightbearing, (2) standing with the affected foot in dorsiflexion at the ankle, and (3) standing with the affected foot in eversion. Three different stages of the fracture-healing process were studied, including: stage 1, wherein the material interposed between the fractured edges was the initial connective tissue; stage 2, wherein connective tissue had been replaced by soft callus; and stage 3, wherein soft callus was replaced by mature bone. Thus, 30 3D finite element models were analyzed that took into account fracture type, foot posture, and healing stage. Different foot postures did not statistically significantly affect the peak-developed strains on the fracture site. When the fractured foot was everted or dorsiflexed, it developed a slightly higher strain within the fracture than when it was in the normal weightbearing position. In Jones fractures, eversion of the foot caused further torsional strain and we believe that this position should be avoided during foot immobilization during the treatment of fifth metatarsal base fractures. Tuberosity avulsion fractures and Jones fractures seem to be biomechanically stable fractures, as compared with shaft fractures. Our understanding of the literature and experience indicate that current clinical observations and standard therapeutic options are in accordance with the results that we observed in this investigation, with the exception of Jones fractures.