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.     

Measuring system for in vivo recording of force systems in orthodontic treatment-concept and analysis of accuracy

The aim of our developments is three-dimensional in vivo recording of those orthodontic force systems inducing tooth movements during treatment with fixed appliances. The concept presented here is the first to permit the forces and torques of these statically multiply undetermined systems to be recorded in vivo. For this purpose the force systems transmitted to the teeth from the archwire are isolated from the respective tooth by means of divisible special-design brackets and introduced into a 3D force torque sensor via a gripping appliance. The sensor is fixed with a purpose-developed device relative to the patient's dental arch. The patient's head is positioned relative to the system by means of a bite fork as well as a forehead and chin support. Electrical measurement of the mechanical quantities is carried out by a six-axis force torque sensor with semiconductor strain gauge elements, an electronical evaluator and a mobile measuring computer (PC). Extensive calibration of the sensor system has shown that the measuring uncertainty of the electrical measuring is less than 2%. Precise spatial fixing of bracket slot and archwire in the therapeutic position is crucial to the measuring accuracy of the system, as even minimum displacements affect the force system to be measured. Movements of the measuring system up to 0.04 mm result from a therapeutic force of 1.5 N. The results of extensive in vitro studies have already demonstrated that the system developed by us is suitable for the specified in vivo measuring function.     

In vivo 3-dimensional measurement of the force exerted on a tooth during clenching

We have developed a three-dimensional (3D) force-measuring device for teeth and used it to measure functional forces in vivo. It comprises an inner part forming a metal core (abutment), a 3D piezoelectric force transducer, and an outer part forming a metal crown, all joined together with a steel screw. The force transducer can measure +/- 500 N along the z-axis and +/- 150 N along the x- and y-axes. We evaluated the relationship between output and load and the effects of hysteresis and temperature on the output. The transducer had high linearity (r>0.9999), low hysteresis (1.7% at maximum), and high thermal stability (0.05% per degree) along each axis. The measuring device was mounted on the maxillary left second molar of a healthy male subject; the tooth had been endodontically treated (neurovascular bundle removed) and prepared for metal abutment and a crown. The 3D load calculated from the outputs of the transducer was expressed as a vector of the coordinates based on the Frankfort horizontal (x-y) and sagittal (y-z) planes. The force measured during maximum voluntary clenching was about 170 N; the force vector was directed from the crown to the root medially at an angle of about 10 degrees from the y-z plane and posteriorly at an angle of about 3 degrees from the x-z plane. This transducer will enable measurement of forces applied to different types of prosthetic appliances and has the potential to provide important basic in vivo data for analysis using computer simulation.     

Factors influencing the anterior component of occlusal force

We hypothesized that the anterior component of occlusal force (ACF) generated by mandibular molars was a function of molar inclination, height of the transverse condylar axis above the occlusal plane, steepness of the occlusal plane, gape, molar root dimensions, interproximal tooth contact force when not biting, and bite force. Our research aim was to identify those biomechanical factors which determine ACF. Mandibular second molars were axially loaded with a 90 N force (10 mm second molar gape) in 15 subjects, and the resulting ACF was measured at the mandibular first molar-second premolar contact using a recording technique based on interproximal frictional forces. Morphologic measurements were obtained from lateral cephalometric radiographs of each subject and included: Frankfort mandibular plane angle, occlusal plane angle, angles formed by the longitudinal axis of the second molar and the occlusal and mandibular planes, perpendicular distance from the top of the condyle to the occlusal plane, and second molar root width and root length. For ten subjects, ACF resulting from axial loads of 50, 100, 150, and 200 N was measured. For ten subjects, ACF resulting from an axial load of 50 N and second molar gapes of 10 mm, 14 mm, 18 mm, and 22 mm were measured. ACF increased with increasing gape and increased proportionally to increasing bite force. Correlation and stepwise regression analyses revealed that ACF varies with interproximal tooth contact force when not biting (contact ‘tightness’) and molar root width (model R² = 0.71, p < 0.01). The hypothesis that ACF is a function of bite force, gape, molar root width, and interproximal contact tightness has been supported, and the hypothesis that ACF is a function of molar inclination, occlusal plane steepness, condylar axis height, and root length was rejected.     

Development of a novel intraoral measurement device to determine the biomechanical characteristics of the human periodontal ligament

Periodontal diseases like gingivitis and periodontitis have damaging effects on the periodontium and commonly affect the mechanical properties of the periodontal ligament (PDL), which in the end might lead to loss of teeth. Monitoring tooth mobility and changes of the material properties of the PDL might help in early diagnosis of periodontal diseases and improve their prognosis. It was the aim of this study to develop a novel intraoral device to determine the biomechanical characteristics of the periodontal ligament. This includes the measurement of applied forces and resulting tooth displacement in order to investigate the biomechanical behaviour of the periodontium with varying loading protocols with respect to velocity and tooth displacement. The developed device uses a piezoelectric actuator to apply a displacement to a tooth's crown, and the resulting force is measured by an integrated force sensor. To measure the tooth displacement independently and non-invasively, two magnets are fixed on the teeth. The change in the magnetic field caused by the movement of the magnets is measured by a total of 16 Hall sensors. The displacement of the tooth is calculated from the movement of the magnets. The device was tested in vitro on premolars of four porcine mandibular segments and in vivo on two volunteers. The teeth were loaded with varying activation curves. Comparing the force progression of different activation velocities, the forces decreased with decreasing velocity. Intensive testing demonstrated that the device fulfils all requirements. After acceptance of the ethical committee, further testing in clinical measurements is planned.     

In vivo tendon force measurement of 2-week duration in sheep

Tendon tension in vivo may be determined indirectly by measuring intratendinous pressure, by using a buckle transducer or by measuring the tendon strain. All of these methods require appropriate calibration, which is highly dependent on various variables. To measure the tendon load in vivo during a period of 2 weeks in sheep, a measurement technique has been developed using a force sensor interposed serially between the humeral head and the tendon end. Within a supporting frame, a flexion-sensitive force transducer is subjected to three-point bending stress. The load is transmitted by sutures from the tendon end through a hole in the sensor frame, orthogonal to the force transducer. In this configuration, the sensor measures the tensile force acting on the tendon, largely independent of the loading direction. The sensor was screwed to the humeral head and connected to the tendon end which was previously released from its insertion site along with a bone chip, using sutures. Connecting wires passed subcutaneously to a skin outlet about 30 cm away from the transducer. The sensor output was linear to the measured load up to 300 N, with maximum hysteresis of 18% full scale. All sensors worked in vivo without drift over a period of up to 14 days with no change in the calibration data. Forces up to 310 N have been recorded in vivo with daily tension measurements. This study shows that serial tendon tension measurement is feasible and allows for reliable, repeatable recording of the absolute tendon tension at the expense of tendon integrity.     

Residual force enhancement exceeds the isometric force at optimal sarcomere length for optimized stretch conditions.

Residual force enhancement (FE) following stretch of an activated muscle is a well accepted property of skeletal muscle contraction. However, the mechanism underlying FE remains unknown. A crucial assumption on which some proposed mechanisms are based is the idea that forces in the enhanced state cannot exceed the steady-state isometric force at a sarcomere length associated with optimal myofilament overlap. Although there are a number of studies in which forces in the enhanced state were compared with the corresponding isometric forces on the plateau of the force-length relationship, these studies either did not show enhanced forces above the plateau or, if they did, they lacked measurements of sarcomere lengths confirming the plateau region. Here, we revisited this question by optimizing stretch conditions and measuring the average sarcomere lengths in isolated fibers, and we found that FE exceeded the maximal isometric reference force obtained at the plateau of the force-length relationship consistently (mean+/-SD: 4.8+/-2.1%) and by up to 10%. When subtracting the passive component of FE from the total FE, the enhanced forces remained greater than the isometric plateau force (mean+/-SD: 4.3+/-2.0%). Calcium-induced increases in passive forces, known to be present in single fibers and myofibrils, are too small to account for the FE observed here. We conclude that FE cannot be explained exclusively with a stretch-induced development of sarcomere length nonuniformities, that FE in single fibers may be associated with the recruitment of additional contractile force, and that isometric steady-state forces in the enhanced state are not uniquely determined by sarcomere lengths.     

Versatile and inexpensive Hall-Effect force sensor for mechanical characterization of soft biological materials

Mismatch of hierarchical structure and mechanical properties between tissue-engineered implants and native tissue may result in signal cues that negatively impact repair and remodeling. With bottom-up tissue engineering approaches, designing tissue components with proper microscale mechanical properties is crucial to achieve necessary macroscale properties in the final implant. However, characterizing microscale mechanical properties is challenging, and current methods do not provide the versatility and sensitivity required to measure these fragile, soft biological materials. Here, we developed a novel, highly sensitive Hall-Effect based force sensor that is capable of measuring mechanical properties of biological materials over wide force ranges (μN to N), allowing its use at all steps in layer-by-layer fabrication of engineered tissues. The force sensor design can be easily customized to measure specific force ranges, while remaining easy to fabricate using inexpensive, commercial materials. Although we used the force sensor to characterize mechanics of single-layer cell sheets and silk fibers, the design can be easily adapted for different applications spanning larger force ranges (>N). This platform is thus a novel, versatile, and practical tool for mechanically characterizing biological and biomimetic materials.     

Alternative dental measurements: proposals and relationships with other measurements

Most archaeological and fossil teeth are heavily worn, and this greatly limits the usefulness of tooth crown diameter measurements, as they are usually defined at the widest points of the crown. There are alternatives, particularly measurements at the cervix of the tooth, where the crown joints the root, and measurements along a diagonal axis in molars, that are much less affected by wear. These would allow a wider range of specimens to be included, e.g., in the study of dental reduction in Upper Palaeolithic and Mesolithic Homo sapiens. In addition, they would allow the little-worn teeth of children to be compared directly with well-worn teeth in adults. These alternatives, however, have been little used, and as yet there have not been any studies of the repeatability with which they can be measured, or of the extent to which they are related to the more usual crown diameters. The present study is based on a group of unworn teeth, where direct comparisons could be made between the alternative measurements, which are not much affected by wear, with the usual crown diameters, which are very much affected. In an interobserver-error study of this material, cervical and diagonal measurements could be recorded as reliably as the usual crown diameters. The buccolingual cervical measurement was strongly correlated with the normal bucclingual crown diameter in all teeth, whereas the mesiodistal cervical measurement was highly correlated with the normal mesiodistal crown diameter in incisors and canines, but less so in premolars and molars. The molar diagonal measurements showed high correlations with all other measurements. Crown areas (robustness index) calculated from the usual diameters were strongly correlated with crown areas calculated from cervical measurements, and crown areas calculated from molar diagonals were strongly correlated with both other areas. Despite the long usage of the more usual maximum crown diameters, the alternative dental measurements could be measured just as reliably, could record similar information about tooth crown size, and would be better measures for the worn dentitions seen in archaeological and fossil material.     

An analysis of the measurement principle of smart brackets for 3D force and moment monitoring in orthodontics

Measuring the three-dimensional (3D) force-moment (F/M) systems applied for correcting tooth malposition is highly desirable for accurate spatial control of tooth movement and for reducing traumatic side effects such as irreversible root resorption. To date, suitable tools for monitoring the applied F/M system during therapy are lacking. We have previously introduced a true-scale orthodontic bracket with an integrated microelectronic stress sensor system for 3D F/M measurements on individual teeth with a perspective for clinical application. The underlying theoretical concept assumes a linear correlation between externally applied F/M systems and mechanical stresses induced within the smart bracket. However, in combined applications of F/M components the actual wire-bracket contacts may differ from those caused by separate applications of corresponding individual F/M components, thus violating the principle of linear superposition of mechanical stresses. This study systematically evaluates this aspect using finite element (FE) simulations and measurements with a real smart bracket. The FE analysis indicated that variability in the wire-bracket contacts is a major source for measurement errors. By taking the critical F/M combinations into account in the calibration of the real smart bracket, we were able to reduce the mean measurement error in five of the six F/M components to values <0.12 N and <0.04 N cm. Bucco-lingually directed forces still showed mean errors up to 0.21 N. Improving the force measurement accuracy and integrating components for telemetric energy and data transfer are the next steps towards clinical application of intelligent orthodontic appliances based on smart brackets.     

Location of the vector of jaw muscle force in mammals

Previous work has suggested that the third molar lies just in front of the point where the resultant vector of jaw muscle force, estimated from dissections, intersects the tooth row. This point meets the jaw such that the vector is 30% of jaw length from the jaw joint. Thus, the vector divides the jaw in the ratio of 3:7 when measurements are taken perpendicular to the vector. In practice, however, distances along mammalian jaws are typically measured on an easily determined line such as a line from one end of the tooth row to the other. The position of the jaw joint is then projected onto this line. As a rule, such a line is not perpendicular to the vector and so the distance from the projection of the joint, out to the rear of the third molar (and the vector's intersection), is different in different mammals. Rarely is this distance 30% of total jaw length. However, when the location of the vector's intersection is measured along the tooth row, this position varies directly with the inclination of the vector; a vector inclined posteriorly intersects the tooth row far from the projection of the joint and an anterior vector's intersection is relatively close. Only a vector perpendicular to the line from one end of the tooth row to the other intersects at 30%. This obvious point suggests a way to test the above hypotheses when the inclination of the vector is not known exactly. The predicted relationship between the distance to the molar, as a percentage of the total jaw length, and the approximate inclination of the vector derived from muscle weights (posterior or anterior depending on whether the temporalis or the masseter/pterygoid, respectively, is dominant) was observed in a sample of 46 different mammals.     

Comparison of dental measurement systems for taxonomic assignment of first molars

Morphometrics of the molar crown is based traditionally on diameter measurements but is nowadays more often based on 2D image analysis of crown outlines. An alternative approach involves measurements at the level of the cervical line. We compare the information content of the two options in a three-dimensional (3D) digital sample of lower and upper first molars (M(1) and M(1) ) of modern human and Neanderthal teeth. The cervical outline for each tooth was created by digitizing the cervical line and then sectioning the tooth with a best fit plane. The crown outline was projected onto this same plane. The curves were analyzed by direct extraction of diameters, diagonals, and area and also by principal component analysis either of the residuals obtained by regressing out these measurements from the radii (shape information) or directly by the radii (size and shape information). For M(1) , the crown and cervical outline radii allow us to discriminate between Neanderthals and modern humans with 90% and 95% accuracy, respectively. Fairly good discrimination between the groups (80-82.5%) was also obtained using cervical measurements. With respect to M(1) , general overlap of the two groups was obtained by both crown and cervical measurements; however, the two taxa were differentiable by crown outline residuals (90-97%). Accordingly, while crown diameters or crown radii should be used for taxonomic analysis of unworn or slightly worn M(1) s, the crown outline, after regressing out size information, could be promising for taxonomic assignment of lower M1s.     

Evaluation of a flexible force sensor for measurement of helmet foam impact performance

The association between translational head acceleration and concussion remains unclear and provides a weak predictive measure for this type of injury; thus, alternative methods of helmet evaluation are warranted. Recent finite element analysis studies suggest that better estimates of concussion risk can be obtained when regional parameters of the cranium, brain and surrounding tissues are included. Lacking, however, are empirical data at the head–helmet interface with regards to contact area and force. Hence, the purpose of this study was to evaluate a system to capture the impact force distribution of helmet foams. Thirteen Flexiforce^® sensors were arranged in a 5×5 cm array, secured to a load cell. Three densities of foam were repeatedly impacted with 5 J of energy during ambient (20 °C) and cold (?25 °C) conditions. RMS error, calculated relative to the global force registered by the load cell, was <1.5% of the measurement range during individual calibration of the Flexiforce^® sensors. RMS error was 5% of the measured range for the global force estimated by the sensor array. Load distribution measurement revealed significant differences between repeated impacts of cold temperature foams for which acceleration results were non-significant. The sensor array, covering only 36% of the total area, possessed sufficient spatial and temporal resolution to capture dynamic load distribution patterns. Implementation of this force mapping system is not limited to helmet testing. Indeed it may be adopted to assess other body regions vulnerable to contact injuries (e.g., chest, hip and shin protectors).     

Thermo-Mechanical Analysis of Restored Molar Tooth using Finite Element Analysis

The aim of the study is to find most optimum combination of crown material and adhesive to avoid loosening and thereby failure of restored tooth. This study describes the Thermo-Mechanical analysis of restored molar tooth crown for determination of the stress levels due to thermal and mechanical loads on restored molar tooth. The potential use of the 3-D model was demonstrated and analyzed using different materials for crown. Thermal strain, stress and deformation were measured at hot and cold conditions in ANSYS and correlated with analytical calculation and existing experimental data for model validation and optimization. It is concluded that amongst various material porcelain crown with composite resin adhesive cement closely simulates the behavior of natural crown and should ideally result into long lasting restoration.     

Finite element method analysis of the tooth movement induced by orthodontic forces

The finite element method is a useful technique for measuring structural stress and for movement analyses. The objective of this investigation was to get a more accurate estimation of tooth movement depending on application point when a tipping orthodontic force is applied. The three-dimensional model of un upper canine, consisting of 4,000 hexahedron elements with 2,367 nodes was obtained. Horizontal, orally directed 1N tipping orthodontic force was applied to the model on five different levels of the tooth crown. The three-dimensional mathematical finite element model is useful in analyzing the tooth movement in response to orthodontic forces. The tipping tooth movement is greater if the force is applied closer to its neck, or more gingivally.     

A technique for conditioning and calibrating force-sensing resistors for repeatable and reliable measurement of compressive force

Miniature sensors that could measure forces applied by the fingers and hand without interfering with manual dexterity or range of motion would have considerable practical value in ergonomics and rehabilitation. In this study, techniques have been developed to use inexpensive pressure-sensing resistors (FSRs) to accurately measure compression force. The FSRs are converted from pressure-sensing to force-sensing devices. The effects of nonlinear response properties and dependence on loading history are compensated by signal conditioning and calibration. A fourth-order polynomial relating the applied force to the current voltage output and a linearly weighted sum of prior outputs corrects for sensor hysteresis and drift. It was found that prolonged (>20 h) shear force loading caused sensor gain to change by approximately 100%. Shear loading also had the effect of eliminating shear force effects on sensor output, albeit only in the direction of shear loading. By applying prolonged shear loading in two orthogonal directions, the sensors were converted into pure compression sensors. Such preloading of the sensor is, therefore, required prior to calibration. The error in compression force after prolonged shear loading and calibration was consistently <5% from 0 to 30 N and <10% from 30 to 40 N. This novel method of calibrating FSRs for measuring compression force provides an inexpensive tool for biomedical and industrial design applications where measurements of finger and hand force are needed.     

Concept for development of new individual treatment devices in orthodontics using 3-dimensional numerical simulation of bone remodeling]

The present study is part of a research project that includes different components for the simulation of orthodontic tooth movement and comparing experimental results. This concept includes the development of a bone remodelling algorithm, as well as experimental studies on tooth movement. After the acquisition and evaluation of specific experimental data of the patient's situation, the individual components have to be integrated to verify and forecast tooth movement. The aim is to design individual treatment devices as well as to shorten treatment while making it more effective. The geometry of the teeth and that of the surrounding alveolar bone both influence the orthodontic tooth movement. For this reason, an exact morphological tooth model for the valid simulation of the tooth movement is needed, and can be constructed from computed tomography data. Simulation of tooth movement can then be compared with "in vivo" measurements of the orthodontic tooth movement. In this study, a specially developed hybrid retraction spring is employed. This spring enables the application of a defined, almost constant force system. The "in vivo" determined tooth movement is simulated with the aid of special positioning and measuring devices. Meanwhile, the active force system can be determined by 6-component force/moment sensors. The experimentally measured force system, "in vivo" measurements of tooth movement and the CT model are now available for numerical simulation for the first time.     

History-dependence of isometric muscle force: effect of prior stretch or shortening amplitude

It is well-recognised that steady-state isometric muscle force is decreased following active shortening (force depression, FD) and increased following active stretch (force enhancement, FE). It has also been demonstrated that passive muscle force is increased following active stretch (passive FE). Several studies have reported that FD increases with shortening amplitude and that FE and passive FE increase with stretch amplitude. Here, we investigate whether these trends continue with further increases in shortening or stretch amplitude. Experiments were performed using in situ cat soleus muscles (n=8 for FD; n=7 for FE and passive FE). FD, FE and passive FE were measured after shortening or stretch contractions that covered as wide a range of amplitudes as practically possible without damaging the muscles. FD increased approximately linearly with shortening amplitude, over the full range of amplitudes investigated. This is consistent with the hypothesis that FD arises from a stress-induced inhibition of crossbridges. FE increased with stretch amplitude only up to a point, and then levelled off. Passive FE, and the transient increase in force at the end of stretch, showed relationships to stretch amplitude that were qualitatively very similar to the relationship for FE, increasing only until the same critical stretch amplitude had been reached. We conclude that FE and passive FE do not increase with stretch amplitude under all circumstances. This finding has important consequences for determining the mechanisms underlying FE and passive FE because any mechanism that is proposed to explain them must be able to predict it.