Finite element-based force/moment-driven simulation of orthodontic tooth movement

The objectives of this study were to develop a numerically controlled experimental set-up to predict the movement caused by the force systems of orthodontic devices and to experimentally verify this system. The presented experimental set-up incorporated an artificial tooth fixed via a 3D force/moment sensor to a parallel kinematics robot. An algorithm determining the initial movement of the tooth in its elastic embedding controlled the set-up. The initial tooth movement was described by constant compliances. The constants were obtained prior to the experiment in a parameterised finite element (FE) study on the basis of a validated FE model of a human molar. The long-term tooth movement was assembled by adding up a multiple of incremental steps of initial tooth movements. A pure translational movement of the tooth of about 8 mm resulted for a moment to force ratio of ? 8.85 mm, corresponding to the distance between the bracket and the centre of resistance. The correct behaviour of this linear elastic model in its symmetry plane allows for simulating single tooth movement induced by orthodontic devices.     

Computational and clinical investigation on the role of mechanical vibration on orthodontic tooth movement

The aim of this study is to investigate the biomechanics for orthodontic tooth movement (OTM) subjected to concurrent single-tooth vibration (50 Hz) with conventional orthodontic force application, via a clinical study and computational simulation. Thirteen patients were recruited in the clinical study, which involved distal retraction of maxillary canines with 1.5 N (150 g) force for 12 weeks. In a split mouth study, vibration and non-vibration sides were randomly assigned to each subject. Vibration of 50 Hz, of approximately 0.2 N (20 g) of magnitude, was applied on the buccal surface of maxillary canine for the vibration group. A mode-based steady-state dynamic finite element analysis (FEA) was conducted based on an anatomically detailed model, complying with the clinical protocol. Both the amounts of space closure and canine distalization of the vibration group were significantly higher than those of the control group, as measured intra-orally or on models (p < 0.05). Therefore it is indicated that a 50 Hz and 20 g single-tooth vibration can accelerate maxillary canine retraction. The volume-average hydrostatic stress (VHS) in the periodontal ligament (PDL) was computationally calculated to be higher with vibration compared with the control group for maxillary teeth and for both linguo-buccal and mesial-distal directions. An increase in vibratory frequency further amplified the PDL response before reaching a local natural frequency. An amplification of PDL response was also shown to be induced by vibration based on computational simulation. The vibration-enhanced OTM can be described by mild, vigorous and diminishing zones among which the mild zone is considered to be clinically beneficial.     

A visco-elastic model for the prediction of orthodontic tooth movement

This study presents a biomechanical model of orthodontic tooth movement. Although such models have already been presented in the literature, most of them incorporate computationally expensive finite elements (FE) methods to determine the strain distribution in the periodontal ligament (PDL). In contrast, the biomechanical model presented in this work avoids the use of FE methods. The elastic deformation of the PDL is modelled using an analytical approach, which does not require setting up a 3D model of the tooth. The duration of the lag phase is estimated using the calculated hydrostatic stresses, and bone remodelling is predicted by modelling the alveolar bone as a viscous material. To evaluate the model, some typically used motion patterns were simulated and a sensitivity analysis was carried out on the parameters. Results show that despite some shortcomings, the model is able to describe commonly used motion patterns in orthodontic tooth movement, in both single- and multi-rooted teeth.     

Muscle-driven finite element simulation of human foot movements

This paper describes a finite element scheme for realistic muscle-driven simulation of human foot movements. The scheme is used to simulate human ankle plantar flexion. A three-dimensional anatomically detailed finite element model of human foot and lower leg is developed and the idea of generating natural foot movement based entirely on the contraction of the plantar flexor muscles is used. The bones, ligaments, articular cartilage, muscles, tendons, as well as the rest soft tissues of human foot and lower leg are included in the model. A realistic three-dimensional continuum constitutive model that describes the biomechanical behaviour of muscles and tendons is used. Both the active and passive properties of muscle tissue are accounted for. The materials for bones and ligaments are considered as homogeneous, isotropic and linearly elastic, whereas the articular cartilage and the rest soft tissues (mainly fat) are defined as hyperelastic materials. The model is used to estimate muscle tissue deformations as well as stresses and strains that develop in the lower leg muscles during plantar flexion of the ankle. Stresses and strains that develop in Achilles tendon during such a movement are also investigated.     

Modeling and simulation of novel antenna for the treatment of hepatocellular carcinoma using finite element method

In this article, new interstitial antenna operating at a frequency of 2.45 GHz for the treatment of hepatocellular carcinoma (HCC) using microwave ablation has been investigated. This antenna is basically an asymmetrical miniaturized choke dipole antenna with a pointed needle at the tip. A commercial finite element method (FEM) package, COMSOL Multiphysics 3.4a, has been used to simulate the performance of needle tip choke antenna. The performance of the antenna has been evaluated numerically, taking into account the specific absorption rate, antenna impedance matching and geometry of the obtained thermal lesion, and the temperature distribution plot obtained shows that maximum temperature was attained in this simulation. The antenna is also capable of creating a spherical-shaped ablation zone. The size and shape of the ablation zone can be slightly adjusted by adjusting the choke position in order to maintain spherical ablation zones.     

Mechanical significance of femoral head trabecular bone structure in Loris and Galago evaluated using micromechanical finite element models

Work on the interspecific and intraspecific variation of trabecular bone in the proximal femur of primates demonstrates important architectural variation between animals with different locomotor behaviors. This variation is thought to be related to the processes of bone adaptation whereby bone structure is optimized to the mechanical environment. Micromechanical finite element models were created for the proximal femur of the leaping Galago senegalensis and the climbing and quadrupedal Loris tardigradus by converting bone voxels from high-resolution X-ray computed tomography scans of the femoral head to eight-noded brick elements. The resulting models had approximately 1.8 million elements each. Loading conditions representing takeoff phase of a leap and more generalized load orientations were applied to the models, and the models were solved using the iterative "row-by-row" matrix-vector multiplication algorithm. The principal strain and Von Mises stress results for the leaping model were similar for both species at each load orientation. Similar hip joint reaction forces in the range of 4.9 x to 12 x body weight were calculated for both species under each loading condition, but the hip reaction values estimated for Loris were higher than predicted based on locomotor behavior. These results suggest that functional adaptation to hip joint loading may not fully explain the differences in femoral head trabecular bone structure in Galago and Loris. The finite element method represents a unique and useful tool for analyzing the functional adaptation of trabecular bone in a diversity of animals and for reconstructing locomotor behavior in extinct taxa.     

Prediction of the structural response of the femoral shaft under dynamic loading using subject-specific finite element models

The goal of this study was to predict the structural response of the femoral shaft under dynamic loading conditions using subject-specific finite element (SS-FE) models and to evaluate the prediction accuracy of the models in relation to the model complexity. In total, SS-FE models of 31 femur specimens were developed. Using those models, dynamic three-point bending and combined loading tests (bending with four different levels of axial compression) of bare femurs were simulated, and the prediction capabilities of five different levels of model complexity were evaluated based on the impact force time histories: baseline, mass-based scaled, structure-based scaled, geometric SS-FE, and heterogenized SS-FE models. Among the five levels of model complexity, the geometric SS-FE and the heterogenized SS-FE models showed statistically significant improvement on response prediction capability compared to the other model formulations whereas the difference between two SS-FE models was negligible. This result indicated the geometric SS-FE models, containing detailed geometric information from CT images with homogeneous linear isotropic elastic material properties, would be an optimal model complexity for prediction of structural response of the femoral shafts under the dynamic loading conditions. The average and the standard deviation of the RMS errors of the geometric SS-FE models for all the 31 cases was 0.46 kN and 0.66 kN, respectively. This study highlights the contribution of geometric variability on the structural response variation of the femoral shafts subjected to dynamic loading condition and the potential of geometric SS-FE models to capture the structural response variation of the femoral shafts.     

Biomechanical analysis of foot with different foot arch heights: a finite element analysis

Clinically, different foot arch heights are associated with different tissue injuries to the foot. To investigate the possible factors contributing to the difference in foot arch heights, previous studies have mostly measured foot pressure in either low-arched or high-arched feet. However, little information exists on stress variation inside the foot with different arch heights. Therefore, this study aimed to implement the finite element (FE) method to analyse the influence of different foot arches. This study established a 3D foot FE model using software ANSYS 11.0. After validating the FE model, this study created low-arched, high-arched and normal-arched foot FE models. The FE analysis found that both the stress and strain on the plantar fascia and metatarsal were higher in the high-arched foot, whereas the stress and strain on the calcaneous, navicular and cuboid were higher in low-arched foot. Additionally, forefoot pressure was increased with an increase in arch height.     

3D finite element models of shoulder muscles for computing lines of actions and moment arms

Accurate representation of musculoskeletal geometry is needed to characterise the function of shoulder muscles. Previous models of shoulder muscles have represented muscle geometry as a collection of line segments, making it difficult to account for the large attachment areas, muscle–muscle interactions and complex muscle fibre trajectories typical of shoulder muscles. To better represent shoulder muscle geometry, we developed 3D finite element models of the deltoid and rotator cuff muscles and used the models to examine muscle function. Muscle fibre paths within the muscles were approximated, and moment arms were calculated for two motions: thoracohumeral abduction and internal/external rotation. We found that muscle fibre moment arms varied substantially across each muscle. For example, supraspinatus is considered a weak external rotator, but the 3D model of supraspinatus showed that the anterior fibres provide substantial internal rotation while the posterior fibres act as external rotators. Including the effects of large attachment regions and 3D mechanical interactions of muscle fibres constrains muscle motion, generates more realistic muscle paths and allows deeper analysis of shoulder muscle function.     

Simulation of 3D tumor cell growth using nonlinear finite element method

We propose a novel parallel computing framework for a nonlinear finite element method (FEM)-based cell model and apply it to simulate avascular tumor growth. We derive computation formulas to simplify the simulation and design the basic algorithms. With the increment of the proliferation generations of tumor cells, the FEM elements may become larger and more distorted. Then, we describe a remesh and refinement processing of the distorted or over large finite elements and the parallel implementation based on Message Passing Interface to improve the accuracy and efficiency of the simulation. We demonstrate the feasibility and effectiveness of the FEM model and the parallelization methods in simulations of early tumor growth.     

Three-dimensional finite element analysis of the maxillary central incisor in two different situations of traumatic impact

Dental trauma is one of the most common events in dental practice. However, few studies have investigated the biomechanical characteristics of these injuries. The objective of this study was to analyse the stress distribution in the dentoalveolar structures of a maxillary central incisor subjected to two situations of impact loading. The following loading forces were applied using a 3D finite element model: a force of 2000 N acting at an angle of 90°on the buccal surface of the crown and a vertical 2000 N force acting in the cleidocranial direction on the incisal surface of the tooth. Harmful stresses were observed in both situations, causing damage to both the tooth and adjacent tissue. However, the damage found in soft tissues such as periodontal ligament and dental pulp was negligible. In conclusion, injuries resulting from the traumatic situations were more damaging to the integrity of the tooth and its associated hard-tissue structures.     

Validation performance comparison for finite element models of the human brain

The objective of this study was to compare the performance of six validated brain finite element (FE) models to localized brain motion validation data in five experimental configurations. Model performance was measured using the objective metric CORA (CORrelation and Analysis), where higher ratings represent better correlation. The KTH model achieved the highest average CORA rating, and the ABM received the highest average rating among models robustly validated against five cadaver impacts in three directions. This technique can be more frequently employed to build better models and, when associated limitations are well understood, to compare inter-model performance under similar conditions.     

Evaluation of accuracy of non-linear finite element computations for surgical simulation: study using brain phantom

In this paper, the accuracy of non-linear finite element computations in application to surgical simulation was evaluated by comparing the experiment and modelling of indentation of the human brain phantom. The evaluation was realised by comparing forces acting on the indenter and the deformation of the brain phantom. The deformation of the brain phantom was measured by tracking 3D motions of X-ray opaque markers, placed within the brain phantom using a custom-built bi-plane X-ray image intensifier system. The model was implemented using the ABAQUS^TM finite element solver. Realistic geometry obtained from magnetic resonance images and specific constitutive properties determined through compression tests were used in the model. The model accurately predicted the indentation force–displacement relations and marker displacements. Good agreement between modelling and experimental results verifies the reliability of the finite element modelling techniques used in this study and confirms the predictive power of these techniques in surgical simulation.     

Development of a finite element musculoskeletal model with the ability to predict contractions of three-dimensional muscles

Representation of realistic muscle geometries is needed for systematic biomechanical simulation of musculoskeletal systems. Most of the previous musculoskeletal models are based on multibody dynamics simulation with muscles simplified as one-dimensional (1D) line-segments without accounting for the large muscle attachment areas, spatial fibre alignment within muscles and contact and wrapping between muscles and surrounding tissues. In previous musculoskeletal models with three-dimensional (3D) muscles, contractions of muscles were among the inputs rather than calculated, which hampers the predictive capability of these models. To address these issues, a finite element musculoskeletal model with the ability to predict contractions of 3D muscles was developed. Muscles with realistic 3D geometry, spatial muscle fibre alignment and muscle-muscle and muscle-bone interactions were accounted for. Active contractile stresses of the 3D muscles were determined through an efficient optimization approach based on the measured kinematics of the lower extremity and ground force during gait. This model also provided stresses and strains of muscles and contact mechanics of the muscle-muscle and muscle-bone interactions. The total contact force of the knee predicted by the model corresponded well to the in vivo measurement. Contact and wrapping between muscles and surrounding tissues were evident, demonstrating the need to consider 3D contact models of muscles. This modelling framework serves as the methodological basis for developing musculoskeletal modelling systems in finite element method incorporating 3D deformable contact models of muscles, joints, ligaments and bones.     

Distributed parameters deterministic model for treatment of brain tumors using Galerkin finite element method

In this paper, we present a distributed parameters deterministic model for treatment of brain tumors using Galerkin finite element method. The dynamic model comprises system of three coupled reaction-diffusion models, involving the tumor cells, the normal tissues and the drug concentration. An optimal control problem is formulated with the goal of minimizing the tumor cell density and reducing the side effects of the drug. A distributed parameters method based on the application of variational calculus is used on an integral-Hamiltonian, which is then used to obtain an optimal coupled system of forward state equations and backward co-state equations. The Galerkin finite element method is used to realistically represent the brain structure as well as to facilitate computation. Finally a three-dimensional test case is considered and partitioned into a set of spherical finite elements, using tri-linear basis functions, except for the elements affected by singularities of polar and azimuthal angles, as well as the origin.     

Numerical investigations of the mechanical properties of a braided non-vascular stent design using finite element method

This paper discusses various issues relating to the mechanical properties of a braided non-vascular stent made of a Ni–Ti alloy. The design of the stent is a major factor which determines its reliability after implantation into a stenosed non-vascular cavity. This paper presents the effect of the main structural parameters on the mechanical properties of braided stents. A parametric analysis of a commercial stent model is developed using the commercial finite element code ANSYS. As a consequence of the analytical results that the pitch of wire has a greater effect than other structural parameters, a new design of a variable pitch stent is presented to improve mechanical properties of these braided stents. The effect of structural parameters on mechanical properties is compared for both stent models: constant and variable pitches. When the pitches of the left and right quarters of the stent are 50% larger and 100% larger than that of the central portion, respectively, the radial stiffness in the central portion increases by 10% and 38.8%, while the radial stiffness at the end portions decreases by 128% and 164.7%, the axial elongation by 25.6% and 56.6% and the bending deflection by 3.96% and 10.15%. It has been demonstrated by finite element analysis that the variable pitch stent can better meet the clinical requirements.     

Comparative analysis of bone remodelling models with respect to computerised tomography-based finite element models of bone

Subject-specific finite element models are an extensively used tool for the numerical analysis of the biomechanical behaviour of human bones. However, bone modelling is not an easy task due to the complex behaviour of bone tissue, involving non-homogeneous and anisotropic mechanical properties. Moreover, bone is a living tissue and therefore its microstructure and mechanical properties evolve with time in a known process called bone remodelling. This phenomenon has been widely studied, many being the numerical models that have been formulated to predict density distribution and its evolution in several bones. The aim of the present study is to assess the capability of a bone remodelling model to predict the bone density distribution of different types of human bone (femur, tibia and mandible) comparing the obtained results with the bone density estimated by means of computerised tomography. Good accuracy was observed for the bone remodelling predictions including the thickness of the cortical layer.     

Validation of a full body finite element model (THUMS) for running-type impacts to the lower extremity

The purpose of this study was to determine whether modifying an existing, highly biofidelic full body finite element model [total human model for safety (THUMS)] would produce valid amplitude and temporal shock wave characteristics as it travels proximally through the lower extremity. Modifying an existing model may be more feasible than developing a new model, in terms of cost, labour and expertise. The THUMS shoe was modified to more closely simulate the material properties of a heel pad. Relative errors in force and acceleration data from experimental human pendulum impacts and simulated THUMS impacts were 22% and 54%, respectively, across the time history studied. The THUMS peak acceleration was attenuated by 57.5% and took 19.7 ms to travel proximally along the lower extremity. Although refinements may be necessary to improve force and acceleration timing, the modified THUMS represented, to a certain extent, shock wave propagation and attenuation demonstrated by living humans under controlled impact conditions.     

Centre of resistance and centre of rotation of a tooth: experimental determination,computer simulation and the effect of tissue nonlinearity

The centre of resistance and centre of rotation of a tooth are key concepts in orthodontics. Determining the coordinates of these points is essential for planning orthodontic tooth movement. The paper proposes a procedure for experimental determination of the two centres, verifies a previously developed mathematical theory through computer simulations and evaluates the effect of nonlinearity of the periodontal ligament on the parameters related to the centres. The paper relies on the mathematical theory of a rigid body embedded in an elastic medium, physical experiment, finite element method and a simple nonlinear theory of the tooth. The concept of the centre of resistance requires a revision if nonlinearity is taken into account.