Stress distribution and displacement analysis during an intermaxillary disjunction--a three-dimensional FEM study of a human skull

The goal of this study was to contribute to an understanding of how much expansion force is needed during a maxillary expansion (ME) and where bony reaction takes place. A finite element (FE) model of a dry human male skull was generated from CT scans. The FE model, which consists of cortical and cancellous bone and teeth, was loaded with the same force magnitudes, directions and working points as in rapid maxillary expansion (RME). A three-dimensional finite element stress analysis (FESA) of the forces and displacement was performed. The highest stress was observed in the maxilla in the region where the forces were applied, and spreads more or less throughout almost the whole frontal skull structures. The displacement distribution which causes stress in the skull is highly dependant on the thickness of the bone and its structure. All areas with high compressive and tensile stress are exactly the regions which determine the maximal amount of force to be used during the maxillary expansion and should be examined in case of any complication during a patient's treatment. Regions with significant compressive and tensile stress are the regions observed to have an increase in cellular activity. Further simulations with a given displacement (0.5mm) showed that displacement simulations need extra caution otherwise they will lead to very high forces which are not realistic in an orthodontic treatment.     

A three-dimensional inverse finite element analysis of the heel pad

Quantification of plantar tissue behavior of the heel pad is essential in developing computational models for predictive analysis of preventive treatment options such as footwear for patients with diabetes. Simulation based studies in the past have generally adopted heel pad properties from the literature, in return using heel-specific geometry with material properties of a different heel. In exceptional cases, patient-specific material characterization was performed with simplified two-dimensional models, without further evaluation of a heel-specific response under different loading conditions. The aim of this study was to conduct an inverse finite element analysis of the heel in order to calculate heel-specific material properties in situ. Multidimensional experimental data available from a previous cadaver study by Erdemir et al. ("An Elaborate Data Set Characterizing the Mechanical Response of the Foot," ASME J. Biomech. Eng., 131(9), pp. 094502) was used for model development, optimization, and evaluation of material properties. A specimen-specific three-dimensional finite element representation was developed. Heel pad material properties were determined using inverse finite element analysis by fitting the model behavior to the experimental data. Compression dominant loading, applied using a spherical indenter, was used for optimization of the material properties. The optimized material properties were evaluated through simulations representative of a combined loading scenario (compression and anterior-posterior shear) with a spherical indenter and also of a compression dominant loading applied using an elevated platform. Optimized heel pad material coefficients were 0.001084 MPa (μ), 9.780 (α) (with an effective Poisson's ratio (ν) of 0.475), for a first-order nearly incompressible Ogden material model. The model predicted structural response of the heel pad was in good agreement for both the optimization (<1.05% maximum tool force, 0.9% maximum tool displacement) and validation cases (6.5% maximum tool force, 15% maximum tool displacement). The inverse analysis successfully predicted the material properties for the given specimen-specific heel pad using the experimental data for the specimen. The modeling framework and results can be used for accurate predictions of the three-dimensional interaction of the heel pad with its surroundings.     

Sensitivity of vertebral compressive strength to endplate loading distribution

The sensitivity of vertebral body strength to the distribution of axial forces along the endplate has not been comprehensively evaluated. Using quantitative computed tomography-based finite element models of 13 vertebral bodies, an optimization analysis was performed to determine the endplate force distributions that minimized (lower bound) and maximized (upper bound) vertebral strength for a given set of externally applied axial compressive loads. Vertebral strength was also evaluated for three generic boundary conditions: uniform displacement, uniform force, and a nonuniform force distribution in which the interior of the endplate was loaded with a force that was 1.5 times greater than the periphery. Our results showed that the relative difference between the upper and lower bounds on vertebral strength was 14.2 +/- 7.0% (mean +/- SD). While there was a weak trend for the magnitude of the strength bounds to be inversely proportional to bone mineral density (R2 = 0.32, p = 0.02), both upper and lower bound vertebral strength measures were well predicted by the strength response under uniform displacement loading conditions (R2 = 0.91 and R2 = 0.99, respectively). All three generic boundary conditions resulted in vertebral strength values that were statistically indistinguishable from the loading condition that resulted in an upper bound on strength. The results of this study indicate that the uncertainty in strength arising from the unknown condition of the disc is dependent on the condition of the bone (whether it is osteoporotic or normal). Although bone mineral density is not a good predictor of strength sensitivity, vertebral strength under generic boundary conditions, i.e., uniform displacement or force, was strongly correlated with the relative magnitude of the strength bounds. Thus, explicit disc modeling may not be necessary.     

Biomechanical response of the human mandible to impacts of the chin

The purpose of this study was to determine the force-time and force-displacement response of the human mandible under direct loading at the chin. Sub-fracture response of the mandible and temporomandibular joint (TMJ) were analyzed from 10 cadavers that were impacted at the chin with a 2.8-kg mass at drop heights of 300, 400 and 500 mm and a 5.2-kg mass at 500 mm. Motion of radio-opaque markers adhered to the surface of the bone was recorded at 1000 Hz by a bi-planar X-ray and converted to three-dimensional coordinates. Peak force ranged from 0.90 to 4.54 kN causing chin displacement of 1.2-4.4 mm. A bi-linear response was observed with stiffness of 475.1+/-199.8 kN/m for chin displacement resulting from loading up to 0.6 kN and 2381.6+/-495.7 kN/m for loads from 0.6 to 3.25 kN. This defines the biomechanical response of the mandible for chin motion under impact loading. The response of different segments of the mandible and TMJ are also documented. Force-time and force-displacement response corridors for the mandible can be used for finite element model and/or the development and validation of a biomechanical surrogate.     

In-vitro results of rapid maxillary expansion on adults compared with finite element simulations

This study was mainly performed to investigate the effects of high maxillary expansion forces on the skull with fresh and thiel-fixed human skulls. The maxillary suture was not weakened except in one experiment. This study compares the strain measured on the zygomatic process of the skull with the results of a finite element model generated for this purpose. An increasing transversal force was applied on the alveolar process (teeth) until rupture. Strain on the zygomatic process, maxilla displacement and the expanding forces were registered.The results of this study show linear material behaviour of the skull before rupture. The highest stress during the experiments and FE simulation was observed on the alveolar process.Conclusions of this study are the necessity of the existence of appropriate models and that female specimens seem to rupture at a lower force than male ones. Both male and female specimens show a similar linear behaviour in the force/strain curve within each gender group. The probability of maxillary suture opening in adults during ultra-rapid maxillary expansion with tooth anchorage is very low. Complications and unwanted rupture could occur.     

Mechanics of blast loading on the head models in the study of traumatic brain injury using experimental and computational approaches

Blast waves generated by improvised explosive devices can cause mild, moderate to severe traumatic brain injury in soldiers and civilians. To understand the interactions of blast waves on the head and brain and to identify the mechanisms of injury, compression-driven air shock tubes are extensively used in laboratory settings to simulate the field conditions. The overall goal of this effort is to understand the mechanics of blast wave–head interactions as the blast wave traverses the head/brain continuum. Toward this goal, surrogate head model is subjected to well-controlled blast wave profile in the shock tube environment, and the results are analyzed using combined experimental and numerical approaches. The validated numerical models are then used to investigate the spatiotemporal distribution of stresses and pressure in the human skull and brain. By detailing the results from a series of careful experiments and numerical simulations, this paper demonstrates that: (1) Geometry of the head governs the flow dynamics around the head which in turn determines the net mechanical load on the head. (2) Biomechanical loading of the brain is governed by direct wave transmission, structural deformations, and wave reflections from tissue–material interfaces. (3) Deformation and stress analysis of the skull and brain show that skull flexure and tissue cavitation are possible mechanisms of blast-induced traumatic brain injury.     

A biomechanical model to simulate the effect of a high vertical loading on trunk flexural stiffness

A human trunk model was developed to simulate the effect of a high vertical loading on trunk flexural stiffness. A force–length relationship is attributed to each muscle of the multi-body model. Trunk stiffness and muscle forces were evaluated experimentally and numerically for various applied loads. Experimental evaluation of trunk stiffness was carried out by measuring changes in reaction force following a sudden horizontal displacement at the T10 level prior to paraspinal reflexes induction. Results showed that the trunk stiffness increases under small applied loads, peaks when the loads were further increased and decreases when higher loads are applied. A sensitivity analysis to muscle force–length relationship is provided to determine the model's limitations. This model pointed out the importance of taking into account the changes in muscle length to evaluate the effect of spinal loads beyond the safe limit that cannot be evaluated experimentally and to predict the trunk instability under vertical load.     

Rate-independent characteristics of an arthroscopically implantable force probe in the human achilles tendon

The effect of loading rate on specimen calibration was investigated for an implantable force sensor of the two-point loading variety. This variety of sensor incorporates a strain gage to measure the compressive load applied to the sensor due to tensile loading in a soft tissue specimen. The Achilles tendon in each of four human cadaveric lower extremities was instrumented with a force sensor and then loaded in tension using a materials testing machine. Each specimen was tensile tested at three different displacement rates, 0.25, 2.5 and 12.7 cm s(-1), corresponding with mean loading rates of 33.8, 513.2, and 2838.6 N s(-1), respectively. A calibration curve relating the force sensor signal and applied tendon tension was generated for each specimen/ displacement rate combination. For each specimen, calibration curves were compared by calculating an RMS error for the entire data set (eRMS = 1.6% of the full load value) and a coefficient of determination, R2, of a curve fit through all of the data (R2 = 99.6%). Over the range of rates tested, no measurable change in sensor sensitivity due to loading rate was observed. Hysteresis for all displacement rates was on the order of 2.4%.     

Deformation analysis of microcapsules compressed by two rigid parallel plates

Alginate-poly(l)lysine-alginate microcapsules with a diameter of 200–300 μm were produced and subjected to compression experiments using two rigid parallel plates. The deformed shape was observed, and the relationship between the applied force and the displacement of the plate was measured. A practical analysis method is proposed for the prediction of mechanical properties of microcapsules, namely, the changes in force, transmural pressure, and deformed shape due to the change in the displacement of the plate. The analysis is based on a microcapsule model comprising an axi-symmetric elastic membrane with a constant capsule volume during deformation. Young’s modulus of the membrane, which is used in the analysis, was determined by applying the Hertz contact theory to the experimental results obtained by using an atomic force microscope. The bending stiffness and permeability of the membrane as well as the frictional force between the membrane and the plate were neglected in the analysis. A non-dimensional relationship between the applied force and the displacement of the plate was shown. The theoretically predicted compression force was smaller than the experimentally measured force in the small displacement region, whereas both forces were in good agreement in the large displacement region. The effects of change in Poisson’s ratio, which varied from 0 to 0.5, on the force, transmural pressure, and deformed shape were shown. Under the same displacement conditions, it was observed that the calculated deformed shape was almost coincident with the shape observed in the experiment.     

Measuring single cardiac myocyte contractile force via moving a magnetic bead

One of the biggest problems of heart failure is the heart's inability to effectively pump blood to meet the body's demands, which may be caused by disease-induced alterations in contraction properties (such as contractile force and Young's modulus). Thus, it is very important to measure contractile properties at single cardiac myocyte level that can lay the foundation for quantitatively understanding the mechanism of heart failure and understanding molecular alterations in diseased heart cells. In this article, we report a novel single cardiac myocyte contractile force measurement technique based on moving a magnetic bead. The measuring system is mainly composed of 1), a high-power inverted microscope with video output and edge detection; and 2), a moving magnetic bead based magnetic force loading module. The main measurement procedures are as follows: 1), record maximal displacement of single cardiac myocyte during contraction; 2), attach a magnetic bead on one end of the myocyte that will move with myocyte during the contraction; 3), repeat step 1 and record contraction processes under different magnitudes of magnetic force loading by adjusting the magnetic field applied on the magnetic bead; and 4), derive the myocyte contractile force base on the maximal displacement of cell contraction and magnetic loading force. The major advantages of this unique approach are: 1), measuring the force without direct connections to the cell specimen (i.e., "remote sensing", a noninvasive/minimally invasive approach); 2), high sensitivity and large dynamic range (force measurement range: from pico Newton to micro Newton); 3), a convenient and cost-effective approach; and 4), more importantly, it can be used to study the contractile properties of heart cells under different levels of external loading forces by adjusting the magnitude of applied magnetic field, which is very important for studying disease induced alterations in contraction properties. Experimental results demonstrated the feasibility of proposed approach.     

Injury tolerance and moment response of the knee joint to combined valgus bending and shear loading

Valgus bending and shearing of the knee have been identified as primary mechanisms of injuries in a lateral loading environment applicable to pedestrian-car collisions. Previous studies have reported on the structural response of the knee joint to pure valgus bending and lateral shearing, as well as the estimated injury thresholds for the knee bending angle and shear displacement based on experimental tests. However, epidemiological studies indicate that most knee injuries are due to the combined effects of bending and shear loading. Therefore, characterization of knee stiffness for combined loading and the associated injury tolerances is necessary for developing vehicle countermeasures to mitigate pedestrian injuries. Isolated knee joint specimens (n=40) from postmortem human subjects were tested in valgus bending at a loading rate representative of a pedestrian-car impact. The effect of lateral shear force combined with the bending moment on the stiffness response and the injury tolerances of the knee was concurrently evaluated. In addition to the knee moment-angle response, the bending angle and shear displacement corresponding to the first instance of primary ligament failure were determined in each test. The failure displacements were subsequently used to estimate an injury threshold function based on a simplified analytical model of the knee. The validity of the determined injury threshold function was subsequently verified using a finite element model. Post-test necropsy of the knees indicated medial collateral ligament injury consistent with the clinical injuries observed in pedestrian victims. The moment-angle response in valgus bending was determined at quasistatic and dynamic loading rates and compared to previously published test data. The peak bending moment values scaled to an average adult male showed no significant change with variation in the superimposed shear load. An injury threshold function for the knee in terms of bending angle and shear displacement was determined by performing regression analysis on the experimental data. The threshold values of the bending angle (16.2 deg) and shear displacement (25.2 mm) estimated from the injury threshold function were in agreement with previously published knee injury threshold data. The continuous knee injury function expressed in terms of bending angle and shear displacement enabled injury prediction for combined loading conditions such as those observed in pedestrian-car collisions.     

Influence of the lateral ventricles and irregular skull base on brain kinematics due to sagittal plane head rotation

Two-dimensional physical models of the human head were used to investigate how the lateral ventricles and irregular skull base influence kinematics in the medial brain during sagittal angular head dynamics. Silicone gel simulated the brain and was separatedfrom the surrounding skull vessel by paraffin that provided a slip interface between the gel and vessel. A humanlike skull base model (HSB) included a surrogate skull base mimicking the irregular geometry of the human. An HSBV model added an elliptical inclusion filled with liquid paraffin simulating the lateral ventricles to the HSB model. A simplified skull base model (SSBV) included ventricle substitute but approximated the anterior and middle cranial fossae by a flat and slightly angled surface. The models were exposed to 7600 rad/s2 peak angular acceleration with 6 ms pulse duration and 5 deg forced rotation. After 90 deg free rotation, the models were decelerated during 30 ms. Rigid body displacement, shear strain and principal strains were determined from high-speed video recorded trajectories of grid markers in the surrogate brains. Peak values of inferior brain surface displacement and strains were up to 10.9X (times) and 3.3X higher in SSBV than in HSBV. Peak strain was up to 2.7X higher in HSB than in HSBV. The results indicate that the irregular skull base protects nerves and vessels passing through the cranial floor by reducing brain displacement and that the intraventricular cerebrospinal fluid relieves strain in regions inferior and superior to the ventricles. The ventricles and irregular skull base are necessary in modeling head impact and understanding brain injury mechanisms.     

Loss of control biomechanics of the human arm-elbow system

An experimental study was conducted to determine whether external disturbance oscillations, such as those that could be created by hand held tools, alter the dynamic response characteristics of the human arm-muscle system. A special arm-test frame was used to induce external sinusoidal torque oscillations of various amplitudes and frequencies, while the reaction force and angular displacement were monitored. Two different output variable frequency responses were determined using input/output cross-spectrum analysis. The angular displacement of the test frame and a component of hand reaction force were the output variables used, while the test frame torque was the input. Test results from one subject are presented in this paper. Changes in the magnitude and phase angle of the frequency responses were observed for different frequencies of the disturbance torque. These changes indicate that the stability margin and response amplitude of the human arm-muscle system do change as a function of the frequency and amplitude of external disturbance oscillations. This suggests that at certain operating frequencies hand held tools can induce large reaction amplitudes or even loss of control.     

Brief communication: comparing loading scenarios in lower first molar supporting bone structure using 3D finite element analysis

Finite element analysis (FEA) is a widespread technique to evaluate the stress/strain distributions in teeth or dental supporting tissues. However, in most studies occlusal forces are usually simplified using a single vector (i.e., point load) either parallel to the long tooth axis or oblique to this axis. In this pilot study we show how lower first molar occlusal information can be used to investigate the stress distribution with 3D FEA in the supporting bone structure. The LM₁ and the LP²‐LM¹ of a dried modern human skull were scanned by μCT in maximum intercuspation contact. A kinematic analysis of the surface contacts between LM₁ and LP²‐LM¹ during the power stroke was carried out in the occlusal fingerprint analyzer (OFA) software to visualize contact areas during maximum intercuspation contact. This information was used for setting the occlusal molar loading to evaluate the stress distribution in the supporting bone structure using FEA. The output was compared to that obtained when a point force parallel to the long axis of the tooth was loaded in the occlusal basin. For the point load case, our results indicate that the buccal and lingual cortical plates do not experience notable stresses. However, when the occlusal contact areas are considered, the disto‐lingual superior third of the mandible experiences high tensile stresses, while the medio‐lingual cortical bone is subjected to high compressive stresses. Developing a more realistic loading scenario leads to better models to understand the relationship between masticatory function and mandibular shape and structures. Am J Phys Anthropol, 2012. © 2011 Wiley Periodicals, Inc.     

Three-dimensional model of the human craniofacial skeleton: method and preliminary results using finite element analysis

The purpose of this study was to develop a three-dimensional finite element model of the craniofacial skeleton using a dry human skull. The model consisted of 2918 nodes and 1776 solid elements, and was used to investigate the biomechanical effect of a distally directed orthopaedic force on the craniofacial complex. The force was applied at the level of the maxillary first molar. The results indicated that in response to the force system applied: the nasomaxillary complex displaces in a backward and downward direction and rotates in clockwise sense; the nasomaxillary complex, including the zygomatic bone, experiences high stress levels in comparison with those at the remaining bones; the stress distribution in the maxillary basal bone area is relatively uniform; and the stress distribution across the opposing surface of the bony margins of the sutures is non-uniform.     

Force–displacement measurements of earlywood bordered pits using a mesomechanical tester

The elastic properties of pit membranes are reported to have important implications in understanding air‐seeding phenomena in gymnosperms, and pit aspiration plays a large role in wood technological applications such as wood drying and preservative treatment. Here we present force–displacement measurements for pit membranes of circular bordered pits, collected on a mesomechanical testing system. The system consists of a quartz microprobe attached to a microforce sensor that is positioned and advanced with a micromanipulator mounted on an inverted microscope. Membrane displacement is measured from digital image analysis. Unaspirated pits from earlywood of never‐dried wood of Larix and Pinus and aspirated pits from earlywood of dried wood of Larix were tested to generate force–displacement curves up to the point of membrane failure. Two failure modes were observed: rupture or tearing of the pit membrane by the microprobe tip, and the stretching of the pit membrane until the torus was forced out of the pit chamber through the pit aperture without rupture, a condition we refer to as torus prolapse.     

A finite element model of an anthropomorphic test device lower limb to assess risk of injuries during vertical accelerative loading

Improvised explosive devices (IEDs) were used extensively to target occupants of military vehicles during the conflicts in Iraq and Afghanistan (2003–2011). War fighters exposed to an IED attack were highly susceptible to lower limb injuries. To appropriately assess vehicle safety and make informed improvements to vehicle design, a novel Anthropomorphic Test Device (ATD), called the Warrior Injury Assessment Manikin (WIAMan), was designed for vertical loading. The main objective of this study was to develop and validate a Finite Element (FE) model of the WIAMan lower limb (WIAMan-LL). Appropriate materials and contacts were applied to realistically model the physical dummy. Validation of the model was conducted based on experiments performed on two different test rigs designed to simulate the vertical loading experienced during an under-vehicle explosion. Additionally, a preliminary evaluation of the WIAMan and Hybrid-III test devices was performed by comparing force responses to post-mortem human surrogate (PMHS) corridors. The knee axial force recorded by the WIAMan-LL when struck on the plantar surface of the foot (2 m/s) fell mostly within the PMHS corridor, but the corresponding data predicted by the Hybrid-III was almost 60% higher. Overall, good agreements were observed between the WIAMan-LL FE predictions and experiments at various pre-impact speeds ranging from 2 m/s up to 5.8 m/s. Results of the FE model were backed by mean objective rating scores of 0.67–0.76 which support its accuracy relative to the physical lower limb dummy. The observations and objective rating scores show the model is validated within the experimental loading conditions. These results indicate the model can be used in numerical studies related to possible dummy design improvements once additional PMHS data is available. The numerical lower limb is currently incorporated into a whole body model that will be used to evaluate the vehicle design for underbody blast protection.     

Dynamic unconfined compression of articular cartilage under a cyclic compressive load

To study the effect of dynamic mechanical force on cartilage metabolism, many investigators have applied a cyclic compressive load to cartilage disc explants in vitro. The most frequently used in vitro testing protocol has been the cyclic unconfined compression of articular cartilage in a bath of culture medium. Cyclic compression has been achieved by applying either a prescribed cyclic displacement or a prescribed cyclic force on a loading platen placed on the top surface of a cylindrical cartilage disc. It was found that the separation of the loading platen from the tissue surface was likely when a prescribed cyclic displacement was applied at a high frequency.The purpose of the present study was to simulate mathematically the dynamic behavior of a cylindrical cartilage disc subjected to cyclic unconfined compression under a dynamic force boundary condition protocol, and to provide a parametric analysis of mechanical deformations within the extracellular matrix. The frequency-dependent dynamic characteristics of dilatation, hydrostatic pressure and interstitial fluid velocity were analyzed over a wide range of loading frequencies without the separation of the loading platen. The result predicted that a cyclic compressive force created an oscillating positive-negative hydrostatic pressure together with a forced circulation of interstitial fluid within the tissue matrix. It was also found that the load partitioning mechanism between the solid and fluid phases was a function of loading frequency. At a relatively high loading frequency, a localized dynamic zone was developed near the peripheral free surface of the cartilage disc, where a large dynamic pressure gradient exists, causing vigorous interstitial fluid flow.     

Evaluation of dentinal fluid flow behaviours: a fluid-structure interaction simulation

This study uses the fluid-structure interaction (FSI) method to investigate the fluid flow in dental pulp. First, the FSI method is used for the biomechanical simulation of dental intrapulpal responses during force loading (50, 100 and 150 N) on a tooth. The results are validated by comparison with experimental outcomes. Second, the FSI method is used to investigate an intact tooth subjected to a mechanical stimulus during loading at various loading rates. Force loading (0–100 N) is applied gradually to an intact tooth surface with loading rates of 125, 62.5, 25 and 12.5 N/s, respectively, and the fluid flow changes in the pulp are evaluated. FSI analysis is found to be suitable for examining intrapulpal biomechanics. An external force applied to a tooth with a low loading rate leads to a low fluid flow velocity in the pulp chamber, thus avoiding tooth pain.