Preliminary Studies on the Optimum Shape of Dental Bridges

Several pre-existing anterior and posterior dental bridge models using Finite elements and the new ceramic material In-Ceram have been developed. The mechanical behaviour of these models has been compared with optimised profiles obtained from a newly developed evolutionary algorithm known as Evolutionary Structural Optimisation (ESO).

The results show that the mechanical behaviour of the bridges was mainly restricted by the properties of the porcelain veneer and the design of the bridges themselves. For the case of the anterior bridge, it was found that there existed a specific thickness of veneer that minimised the maximum principal stress. This was related to peak stresses that occurred at the bridge surface. Peak stresses also occurred in the material interface between the In-Ceram and the veneer. These extreme stresses were attributed to the notch size and shape. For the case of the posterior bridge, it was concluded that the shape of the bottom of the Pontic tooth is crucial in reducing the magnitude of the maximum principal tensile stress. The ESO process produced bridge designs which have uniformly stressed bridge surfaces, and which also have significantly lower maximum principal tensile stresses compared to the pre-existing designs (up to 44%).     

Three-dimensional finite element analysis of glass-ceramic dental crowns

Because of the improved esthetic potential of glass-ceramic crowns as dental restorations, they are sometimes preferred over metal-ceramic crowns for restoration of anterior teeth. Because of their relatively high strength, these ceramic crowns are also frequently used for restoration of posterior teeth. However, due to the larger magnitude of biting forces on posterior teeth, intraoral fracture of all-ceramic crowns tends to occur more frequently in posterior crowns (Moffa, 1988). The objective of this study was to determine the relative influence of load orientation and the occlusal thickness of posterior ceramic crowns on the stress distribution which develops under these loading and design conditions. Three-dimensional finite element models for a molar crown were developed to determine the stress distribution under simulated applied loads. Glass-ceramic crowns with occlusal thicknesses of 0.5, 1.5, and 3.0 mm were considered. The largest principal tensile stresses induced in ceramic due to a distributed load of 600 N applied in a cuspal region were approximately 12 and 182 MPa for vertical and horizontal loading orientations, respectively. Stresses which developed in the facial and lingual marginal regions were primarily compressive under vertical loads. However, tensile stresses developed when the load was applied horizontally. Differences in stress distribution within crowns with the three occlusal thicknesses occurred only near the site of loading. Because of the relatively large failure rates of ceramic crowns in the posterior regions, these restorations should be strengthened by improvement in design, composition, and thermal processing conditions. Before any significant progress is made in these areas, these restorations should be used for the anterior teeth. The results of this study suggest that orientation of the applied load has a more important effect on development of large tensile stresses than the occlusal thickness of ceramic.     

Viscoelastic finite element analysis of an all-ceramic fixed partial denture

In recent years metal-free ceramic systems have become increasingly popular in dental practice because of their superior aesthetics, chemical durability and biocompatibility. Recently, manufacturers have proposed new dental ceramic systems that are advertised as being suitable for posterior fixed partial dentures (FPDs). Reports indicate that some of these systems have exhibited poor clinical performance. The objective of this study was to use the viscoelastic option of the ANSYS finite element program to calculate residual stresses in an all-ceramic FPD for four ceramic-ceramic combinations. A three-dimensional finite element model of the FPD was constructed from digitized scanning data and calculations were performed for four systems: (1) IPS Empress 2, a glass-veneering material, and Empress 2 core ceramic; (2) IPS Eris a low fusing fluorapatite-containing glass-veneering ceramic, and Empress 2 core ceramic; (3) IPS Empress 2 veneer and an experimental lithium-disilicate-based core ceramic; and (4) IPS Eris and an experimental lithium-disilicate-based core ceramic. The maximum residual tensile stresses in the veneer layer for these combinations are as follows: (1) 77 MPa, (2) 108 MPa, (3) 79 MPa, and (4) 100 MPa. These stresses are relatively high compared to the flexural strengths of these materials. In all cases, the maximum residual tensile stresses in the core frameworks were well below the flexural strengths of these materials. We conclude that the high residual tensile stresses in all-ceramic FPDs with a layering ceramic may place these systems in jeopardy of failure under occlusal loading in the oral cavity.     

Location-dependent variations in the material properties of the anterior cruciate ligament.

Our recent anterior drawer studies in human cadaveric knees [Guan and Butler, Adv. Bioengng 17, 5 (1990); Guan et al., Trans. orthop. Res. Soc. 16, 589 (1991)] have suggested that anterior bundles of the anterior cruciate ligament (ACL) develop higher load-related material properties than posterior bundles. This was confirmed when we reevaluated the axial failure data for these bundle-bone specimens from an earlier study [Butler et al., J. Biomechanics 19, 425-432 (1986)]. The purpose of this study was to determine, in a larger data set, if anteromedial and anterolateral bundles of the anterior cruciate ligament exhibit significantly larger load-related material properties than the posterior ligament bundles. Seven ACL-bone units from seven donors (the three tissues from the original study plus four new ones) were subdivided into three subunits, preserving the bone insertions. The subunits were failed in tension at a constant strain rate (100% s-1) and four material properties were compared within and between donors. The anterior bundles developed significantly larger moduli, maximum stresses, and strain energy densities to maximum stress than the posterior subunits. Moduli for the anterior vs posterior subunits averaged 284 MPa vs 155 MPa, maximum stresses averaged 38 MPa vs 15 MPa, and strain energy densities averaged 2.7 N m cc-1 vs 1.1 N m cc-1, respectively. No significant differences were found, however, among strains to maximum stress or between any of the other properties for the two anterior subunits. These results are important to the design of ligament replacements and suggest new experiments designed to distinguish in vivo force levels in these ACL bands, a possible reason for the material differences.     

Material properties and effect of preconditioning of human sclera,optic nerve,and optic nerve sheath

The optic nerve (ON) is a recently recognized tractional load on the eye during larger horizontal eye rotations. In order to understand the mechanical behavior of the eye during adduction, it is necessary to characterize material properties of the sclera, ON, and in particular its sheath. We performed tensile loading of specimens taken from fresh postmortem human eyes to characterize the range of variation in their biomechanical properties and determine the effect of preconditioning. We fitted reduced polynomial hyperelastic models to represent the nonlinear tensile behavior of the anterior, equatorial, posterior, and peripapillary sclera, as well as the ON and its sheath. For comparison, we analyzed tangent moduli in low and high strain regions to represent stiffness. Scleral stiffness generally decreased from anterior to posterior ocular regions. The ON had the lowest tangent modulus, but was surrounded by a much stiffer sheath. The low-strain hyperelastic behaviors of adjacent anatomical regions of the ON, ON sheath, and posterior sclera were similar as appropriate to avoid discontinuities at their boundaries. Regional stiffnesses within individual eyes were moderately correlated, implying that mechanical properties in one region of an eye do not reliably reflect properties of another region of that eye, and that potentially pathological combinations could occur in an eye if regional properties are discrepant. Preconditioning modestly stiffened ocular tissues, except peripapillary sclera that softened. The nonlinear mechanical behavior of posterior ocular tissues permits their stresses to match closely at low strains, although progressively increasing strain causes particularly great stress in the peripapillary region.

     

Formation of lamellar cross bridges in the annulus fibrosus of the intervertebral disc is a consequence of vascular regression

Cross bridges are radial structures within the highly organized lamellar structure of the annulus fibrosus of the intervertebral disc that connect two or more non-consecutive lamellae. Their origin and function are unknown. During fetal development, blood vessels penetrate deep within the AF and recede during postnatal growth. We hypothesized that cross bridges are the pathways left by these receding blood vessels.Initially, the presence of cross bridges was confirmed in cadaveric human discs aged 25 and 53 years. Next, L1-L2 intervertebral discs (n = 4) from sheep ranging in age from 75 days fetal gestation to adult were processed for paraffin histology. Mid-sagittal sections were immunostained for endothelial cell marker PECAM-1. The anterior and posterior AF were imaged using differential interference contrast microscopy, and the following parameters were quantified: total number of distinct lamellae, total number of cross bridges, percentage of cross bridges staining positive for PECAM-1, cross bridge penetration depth (% total lamellae), and PECAM-1 positive cross bridge penetration depth.Cross bridges were first observed at 100 days fetal gestation. The overall number peaked in neonates then remained relatively unchanged. The percentage of PECAM-1 positive cross bridges declined progressively from almost 100% at 100 days gestation to less than 10% in adults. Cross bridge penetration depth peaked in neonates then remained unchanged at subsequent ages. Depth of PECAM-1 positive cross bridges decreased progressively after birth. Findings were similar for both the anterior and posterior.The AF lamellar architecture is established early in development. It later becomes disrupted as a consequence of vascularization. Blood vessels then recede, perhaps due to increasing mechanical stresses in the surrounding matrix. In this study we present evidence that the pathways left by receding blood vessels remain as lamellar cross bridges. It is unclear whether the presence of cross bridges in the aging and degenerating intervertebral disc would be advantageous or detrimental, and this question should be addressed by future studies.     

Finite element and experimental analyses of polymer-based dental bridges reinforced by ceramic bars

Dental bridges made of polymer materials reveal only low loading capacity. This paper analyzes possible improvements of the loading capacity of polymer-based dental bridges reinforced by incorporated ceramic bars. Finite element (FE) analyses were performed to study the stress distribution caused by the mastication process in the bridge material. In the experimental part of the study, the fracture load of dental bridges with and without ceramic bar reinforcement was evaluated. Critical stresses occur in the connector area between abutment and pontic of bridges without bar reinforcement. A suitably shaped ceramic bar incorporated into the polymer-based bridge can significantly reduce these critical stresses. The fracture load of the bridge was increased from 515 to 1603N by the bar reinforcement. We conclude from our study that a ceramic bar can significantly improve the loading capacity of a polymer-based dental bridge. The FE and the experimental analyses revealed that the detailed design of the ceramic bar is of decisive importance for the effectiveness of the suggested ceramic reinforcement.     

Three-dimensional finite element stress analysis of the dentate human mandible.

The biomechanical events which accompany functional loading of the human mandible are not fully understood. The techniques normally used to record them are highly invasive. Computer modelling offers a promising alternative approach in this regard, with the additional ability to predict regional stresses and strains in inaccessible locations. In this study, we built two three-dimensional finite element (FE) models of a human mandible reconstructed from tomographs of a dry dentate jaw. The first model was used for a complete mechanical characterization of physical events. It also provided comparative data for the second model, which had an increased vertical corpus depth. In both cases, boundary conditions included rigid restraints at the first right molar and endosteal cortical surfaces of the articular eminences of temporal bones. Groups of parallel multiple vectors simulated individual masticatory muscle loads. The models were solved for displacements, stresses, strains, and forces. The simulated muscle loads in the first model deformed the mandible helically upward and toward its right (working) side. The highest principal stresses occurred at the bite point, anterior aspects of the coronoid processes, symphyseal region, and right and left sides of the mandibular corpus. In general, the observed principal stresses and strains were highest on the periosteal cortical surface and alveolar bone. At the symphyseal region, maximum principal stresses and strains were highest on the lower lingual mandibular aspect, whereas minimum principal stresses and strains were highest on its upper labial side. Subcondylar principal strains and condylar forces were higher on the left (balancing or nonbiting) side than on the right mandibular side, with condylar forces more concentrated on the anteromedial aspect of the working-side condyle and on the central and lateral aspects of the left. When compared with in vivo strain data from macaques during comparable biting events, the predictive strain values from the first model were qualitatively similar. In the second model, the reduced tensile stress on the working-side, and decreased shear stress bilaterally, confirmed that lower stresses occurred on the lower mandibular border with increased jaw depth. Our results suggested that although the mandible behaved in a beam-like manner, its corpus acted more like a combination of open and closed cross sections due to the presence of tooth sockets, at least for the task modelled.(ABSTRACT TRUNCATED AT 400 WORDS)     

The Biomechanics of Tree Fork Design

Two biomechanically different types of tree fork are described: the “compression fork” where the two jointed stems are pressed against each other at the contact face by the action of reaction wood, and the “tension fork” where the two connected stems are bent away from each other by gravity or wind action leading to tensile stresses in the connective zone. It is well known that trees permanently try to improve their own designs by adaptive growth in order to maintain a state of constant mechanical stress at the tree surface. In the case of these two different types of tree fork, adaptive growth also takes different ways in order to avoid high localized stress peaks which could lead to failure of the tree under wind loading. In this paper only the tension fork is assessed with respect to its shape optimization by computer simulation of adaptive growth. It is shown that the tensile fork is shape optimized in a very perfect way in order to avoid any dangerous localized stress peaks (notch stresses) which could lead to failure of the tree.     

Residual stress distribution in rabbit limb bones

The presence of the residual stresses in bone tissue has been noted and the authors have reported that there are residual stresses in bone tissue. The aim of our study is to measure the residual stress distribution in the cortical bone of the extremities of vertebrates and to describe the relationships with the osteon population density. The study used the rabbit limb bones (femur, tibia/fibula, humerus, and radius/ulna) and measured the residual stresses in the bone axial direction at anterior and posterior positions on the cortical surface. The osteons at the sections at the measurement positions were observed by microscopy. As a result, the average stresses at the hindlimb bones and the forelimb bones were 210 and 149 MPa, respectively. In the femur, humerus, and radius/ulna, the residual stresses at the anterior position were larger than those at the posterior position, while in the tibia, the stress at the posterior position was larger than that at the anterior position. Further, in the femur and humerus, the osteon population densities in the anterior positions were larger than those in the posterior positions. In the tibia, the osteon population density in the posterior position was larger than that in the anterior position. Therefore, tensile residual stresses were observed at every measurement position in the rabbit limb bones and the value of residual stress correlated with the osteon population density (r=0.55, P<0.01).     

Finite element analysis of anterior tooth root stresses developed during endodontic treatment

Vertical tooth root fractures are diagnostically challenging, frustrating, and an increasingly common cause of failure of tooth restoration. These vertical root fractures have been associated with many causes, including the endodontic process itself. To investigate these endodontic causes, various phases of crown replacement for an anterior tooth were modeled using nonlinear, plane strain finite element (FE) analysis. Stresses developed during obturation, post positioning, crown placement, and masticatory and occlusal loading of the restored tooth were estimated using this analysis method. The minimum (compressive) principal stress was greatest during obturation of cones 1 and 2, and during mastication of the restored tooth. Although these stresses were significant (-150 to -280 MPa), they did not exceed the compressive strength of dentin. The maximum (tensile) principal stresses, 160 to 300 MPa, were also observed during obturation of cones 1 and 2. These peak stresses exceed the dentin tensile strength.     

Evidence of entropic elasticity of human bone trabeculae at low strains

We performed 60 microtensile tests on 6 single trabeculae excised from a human femur head at various maximum tensile loads. The obtained results show a clear dependence of the calculated stress-strain behaviour from the applied load and thus from the mean stress over the cross section of the trabecula. The pooled data were found in good agreement with a combination of both the model of the nonlinear stress-strain behaviour of collagen fibrils and that for the modulus of elasticity of staggered mineralized collagen. This circumstance could also suggest a realistic explanation of the extreme variability found in literature for the elastic modulus of the trabecular material. In particular, when the trabeculae are solicited with relatively low stresses, their mechanical properties are mainly affected by the entropic elasticity of collagen molecules. This work offers both experimental data and a reasonable interpretation of the behaviour of fully mineralized tissue at low strains, that is up to about 0.1%.     

Local variations in the micromechanical properties of mouse femur: the involvement of collagen fiber orientation and mineralization

In this study we sought to understand the material level basis for local variations in the uniaxial micromechanical properties of mouse cortical bone. It was hypothesized that the opposing anterior and posterior quadrants will significantly differ in terms of their mechanical function, such that, the anterior portion will be stronger in tension whereas the posterior quadrant will be stronger in compression. Mechanical properties were assessed via microtensile and microcompressive tests of standardized coupon-shaped specimens from femurs of Swiss Webster mice (9 weeks). The mineralization and mineral quality was assessed via Raman spectroscopy and the overall collagen orientation was investigated with quantitative polarized imaging. Micromechanical tests demonstrated that the modulus, yield stress, maximum stress and fracture energy of the posterior quadrant was 66%, 53%, 42% and 31% of anterior quadrant; however, the compressive properties did not differ between the two quadrants. Raman microspectroscopic analysis indicated that the mineral matrix ratio, mineral crystallinity and carbonation did not vary between the quadrants. However, the collagen fibers in the anterior quadrant were significantly (p<0.05) more oriented along the longer axis of the diaphyseal shaft than the collagen fibers of the posterior quadrant. Therefore, we concluded that the orientation of collagen fibers with respect to the anatomical loading axis has a profound effect on the uniaxial mechanical function of murine bone. It will be a matter of further research to reveal the role of local variations in the mode of stress on this material level dichotomy in tissue organization and mechanical function.     

Stress analysis of irradiated human tooth enamel using finite element methods

The objectives of this project were to use finite element methods to determine how changes in the elastic modulus due to oral cancer therapeutic radiation alter the distribution of mechanical stresses in teeth and to determine if observed failures in irradiated teeth correlate with changes in mechanical stresses. A thin slice section finite element (FE) model was constructed from micro CT sections of a molar tooth using MIMICS and 3-Matic software. This model divides the tooth into three enamel regions, the dentin-enamel junction (DEJ) and dentin. The enamel elastic modulus was determined in each region using nano indentation for three experimental groups namely – control (non-radiated), in vitro irradiated (simulated radiotherapy following tooth extraction) and in vivo irradiated (extracted subsequent to oral cancer patient radiotherapy) teeth. Physiological loads were applied to the tooth models at the buccal and lingual cusp regions for all three groups (control, in vitro and in vivo). The principal tensile stress and the maximum shear stress were used to compare the results from different groups since it has been observed in previous studies that delamination of enamel from the underlying dentin was one of the major reasons for the failure of teeth following therapeutic radiation. From the FE data, we observed an increase in the principal tensile stress within the inner enamel region of in vivo irradiated teeth (9.97 ± 1.32 MPa) as compared to control/non-irradiated teeth (8.44 ± 1.57 MPa). Our model predicts that failure occurs at the inner enamel/DEJ interface due to extremely high tensile and maximum shear stresses in in vivo irradiated teeth which could be a cause of enamel delamination due to radiotherapy.     

A simple method of estimating the stress acting on a bilaterally symmetric abdominal aortic aneurysm

We extended a method of estimating the stress acting on an axisymmetric abdominal aortic aneurysm (AAA) under a load in vivo (Elger, D. F., Blackketter, D. M., Budwig, R. S., Johansen, K. H. (1996) The influence of shape on the stresses in model abdominal aortic aneurysms, Journal of Biomechanical Engineering, 118, pp. 326-32.) to bilaterally-symmetric AAAs, which are symmetric about the sagittal plane. Stresses were calculated along the anterior and posterior median lines of the AAA wall. Of the two force equilibrium equations, the Laplace equation held in this study. The longitudinal equilibrium was extended to hold by approximating the meridional tension and the directional cosine of the wall surface as constants along the circumference. The estimated stresses were compared with the results of a finite element analysis. Comparisons showed that the maximal principal stress, usually the circumferential stress or sometimes the meridional stress depending on location, sufficiently represented the wall stress. The proposed method provides a reasonable index for evaluating the rupture risk using the peak value of the maximal principal stress and its location without using the stress-free geometry and constitutive equation.     

Morphogenesis in Volvox: analysis of critical variables.

Inversion, the process by which Volvox embryos turn inside out, was analyzed by a combination of geometrical and experimental techniques. It was shown that simple geometric figures are adequate to represent cell shapes during inversion and that cell volumes remain constant as cell shapes change and the embryo inverts. The first stage of inversion, phialopore opening, results from the release of compressive forces as the embryo withdraws from its surrounding vesicle during a two-stage contraction of each cell around its radial axis. Premature phialopore opening occurs when withdrawal of the embryo from the vesicle is elicited artificially by exposure to either calcium ionophore or hypertonic solutions. The major event of inversion, generation of negative curvature, requires both microtubule-driven elongation of cells (to produce a classical "flask" shape) and cytochalasin-sensitive active migration of cytoplasmic bridges to the outermost ends of flask cells. Colchicine, cyclic GMP and isobutyl methyl xanthine (individually) block both normal elongation and bridge migration; cytochalasin D blocks bridge migration selectively. Flask cell formation and bridge migration are adequate to account for the negative curvature observed. An asymmetric bending of flask cell stalks along the ring of maximum curvature accounts for the fact that the embryo is not constricted in a "purse-string" fashion as negative curvature is generated. Inversion of the posterior hemisphere involves an elastic snap-through resulting from a combination of compressive stresses generated by inversion of the anterior hemisphere and the circumferential restraint imposed by cells at the equator. We conclude that the observed changes in cell shape and the migration of cytoplasmic bridges are the result of an ordered process of membrane-cytoskeletal interactions, and both necessary and sufficient to account for the morphogenetic process of inversion in Volvox.     

Biomechanical comparison of implant inclinations and load times with the all-on-4 treatment concept: a three-dimensional finite element analysis

The purpose of this study was to compare the effects of implant inclinations and load times on stress distributions in the peri-implant bone based on immediate- and delayed-loading models. Four 3D FEA models with different inclination angle of the posterior implants (0°, 15°, 30°, 45°) were constructed. A static load of 150?N in the multivectoral direction was applied unilaterally to the cantilever region. The stress distributions in the peri-implant bone were evaluated before and after osseointegration. The principal tensile stress (σ_max), mean principal tensile stress (σ_max), principal compressive stress (σ_min) and mean principal compressive stress (σ_min) of the bone and micromotion at the contact interface between the bone and implants were calculated. In all the models, peak principal stresses occurred in the bone surrounding the left tilted implant. The highest σ_max and σ_min were all observed in the 0° model for both immediate- and delayed-loading models. And the 0° and 15° models showed higher σ_max and σ_min values. The 0°models showed the largest micromotion. The observed stress distribution was better in the 30° and 45° models than in the 0° and 15° models.     

A comparison of uniaxial and biaxial mechanical properties of the annulus fibrosus: a porcine model

The annulus fibrosus of the intervertebral disk experiences multidirectional tension in vivo, yet the majority of mechanical property testing has been uniaxial. Therefore, our understanding of how this complex multilayered tissue responds to loading may be deficient. This study aimed to determine the mechanical properties of porcine annular samples under uniaxial and biaxial tensile loading. Two-layer annulus samples were isolated from porcine disks from four locations: anterior superficial, anterior deep, posterior superficial, and posterior deep. These tissues were then subjected to three deformation conditions each to a maximal stretch ratio of 1.23: uniaxial, constrained uniaxial, and biaxial. Uniaxial deformation was applied in the circumferential direction, while biaxial deformation was applied simultaneously in the circumferential and compressive directions. Constrained uniaxial consisted of a stretch ratio of 1.23 in the circumferential direction while holding the tissue stationary in the axial direction. The maximal stress and stress-stretch ratio (S-S) moduli determined from the biaxial tests were significantly higher than those observed during both the uniaxial tests (maximal stress, 97.1% higher during biaxial; p=0.002; S-S moduli, 117.9% higher during biaxial; p=0.0004) and the constrained uniaxial tests (maximal stress, 46.8% higher during biaxial; S-S moduli, 82.9% higher during biaxial). These findings suggest that the annulus is subjected to higher stresses in vivo when under multidirectional tension.     

Stress analysis of cemented glenoid prostheses in total shoulder arthroplasty

Glenoid component loosening is the most-frequently encountered problem in the total shoulder arthroplasty. The purpose of the study was to investigate whether failure of the glenoid component is caused by stresses generated within the cement mantle, implant materials and at the various interfaces during humeral abduction, using 3-D FE analyses of implanted glenoid structures. FE models, one total polyethylene and the other, metal backed polyethylene, were developed using CT-scan data and submodelling technique, which was based on an overall solution of a natural scapula model acted upon by all the muscles, ligaments and joint reaction forces. Material interfaces were assumed to be fully bonded. Based on the FE stress analysis, the following observations were made. (1) The submodelling technique, which required a large-size submodel and the use of prescribed displacements at cut-boundaries located far away from the glenoid, was crucial for evaluations on glenoid component. (2) Total polyethylene results in lower-peak stresses (tensile: 10 MPa, Von-Mises: 8.31 MPa) in the cement as compared to a metal-backed design (tensile: 11.5 MPa, Von-Mises: 9.81 MPa). The maximum principal (tensile) stresses generated in the cement mantle for both the designs were below its failure strength, but might evoke crack initiation. (3) The cement-bone interface adjacent to the tip of the keel seemed very likely to fail for both the designs. In case of metal-backed design, this interface adjacent to the tip of the keel appears even more likely to fail. (4) High metal-cement interface stresses for a moderate load might indicate failure at higher load. (5) It appears that both the designs were vulnerable to failure in some ways or the other. A part of the subchondral bone along the longitudinal axis of the glenoid cavity should be preserved to strengthen the glenoid structure and to reduce the use of cement.