Finite element analysis of dental implant loading on atrophic and non-atrophic cancellous and cortical mandibular bone – a feasibility study

The first aim of this study was to assess displacements and micro-strain induced on different grades of atrophic cortical and trabecular mandibular bone by axially loaded dental implants using finite element analysis (FEA). The second aim was to assess the micro-strain induced by different implant geometries and the levels of bone-to-implant contact (BIC) on the surrounding bone. Six mandibular bone segments demonstrating different grades of mandibular bone atrophy and various bone volume fractions (from 0.149 to 0.471) were imaged using a micro-CT device. The acquired bone STL models and implant (Brånemark, Straumann, Ankylos) were merged into a three-dimensional finite elements structure. The mean displacement value for all implants was 3.1±1.2 µm. Displacements were lower in the group with a strong BIC. The results indicated that the maximum strain values of cortical and cancellous bone increased with lower bone density. Strain distribution is the first and foremost dependent on the shape of bone and architecture of cancellous bone. The geometry of the implant, thread patterns, grade of bone atrophy and BIC all affect the displacement and micro-strain on the mandible bone. Preoperative finite element analysis could offer improved predictability in the long-term outlook of dental implant restorations.     

Micro-mechanical damage of trabecular bone–cement interface under selected loading conditions: a finite element study

In this study, two micro finite element models of trabecular bone–cement interface developed from high resolution computed tomography (CT) images were loaded under compression and validated using the in situ experimental data. The models were then used under tension and shear to examine the load transfer between the bone and cement and the micro damage development at the bone–cement interface. In addition, one models was further modified to investigate the effect of cement penetration on the bone–cement interfacial behaviour. The simulated results show that the load transfer at the bone–cement interface occurred mainly in the bone cement partially interdigitated region, while the fully interdigitated region seemed to contribute little to the mechanical response. Consequently, cement penetration beyond a certain value would seem to be ineffective in improving the mechanical strength of trabecular bone–cement interface. Under tension and shear loading conditions, more cement failures were found in denser bones, while the cement damage is generally low under compression.     

Fatigue creep damage at the cement–bone interface: An experimental and a micro-mechanical finite element study

The goal of this study was to quantify the micromechanics of the cement–bone interface under tensile fatigue loading using finite element analysis (FEA) and to understand the underlying mechanisms that play a role in the fatigue behavior of this interface. Laboratory cement–bone specimens were subjected to a tensile fatigue load, while local displacements and crack growth on the specimen's surface were monitored. FEA models were created from these specimens based upon micro-computed tomography data. To accurately model interfacial gaps at the interface between the bone and cement, a custom-written erosion algorithm was applied to the bone model. A fatigue load was simulated in the FEA models while monitoring the local displacements and crack propagation. The results showed the FEA models were able to capture the general experimental creep damage behavior and creep stages of the interface. Consistent with the experiments, the majority of the deformation took place at the contact interface. Additionally, the FEA models predicted fatigue crack patterns similar to experimental findings. Experimental surface cracks correlated moderately with FEA surface cracks (r²=0.43), but did not correlate with the simulated crack volume fraction (r²=0.06). Although there was no relationship between experimental surface cracks and experimental creep damage displacement (r²=0.07), there was a strong relationship between the FEA crack volume fraction and the FEA creep damage displacement (r²=0.76). This study shows the additional value of FEA of the cement–bone interface relative to experimental studies and can therefore be used to optimize its mechanical properties.     

Influence of morphology and material properties on the range of motion of the costovertebral joint – a probabilistic finite element analysis

Abstract

The motion of the costovertebral joint (CVJ) is governed by the material properties and its morphology. The goal of this numerical study was to identify the material and morphology parameters with the greatest influence on the motion of the CVJ. A fully parametric finite element model of the anatomy and material properties of the CVJ was developed. The impact of five morphology and thirteen material parameters was investigated and compared to in vitro data. The motion was influenced in particular by the rotational stiffness of the articulatio capitis costae and the lateral position of the fovea costalis transveralis.     

The influence of social deprivation on bone donation: a 10 year retrospective study

An audit identifying all surgical bone donors over a 10 year period was conducted. Postcodes were used to link data from the index of multiple deprivation (IMD) 2007 to give each donor a deprivation score. An audit from 2000 to 2010 of primary total hip replacement (THR) patients was also conducted, and similarly a deprivation score was identified for each patient. IMD scores are split into quintiles. A high IMD score indicates a high degree of social deprivation. Conversely low IMD scores indicate a more affluent community. The mean IMD 2007 score was 13.36 (95 % CI 13.12–13.60). The national mean IMD score is 21.7 (CI 21.52–21.88). The difference is significant (p < 0.0001). The mean IMD 2007 score of primary THR patients identified in the arthroplasty database was 19.19 (CI 19.00–19.38). The difference between the mean arthroplasty score and the mean score of donors is significant (p < 0.0001). The donation rate increases as social deprivation decreases from quintile to quintile in both: the older patients (CI 1.08–1.14; p < 0.0001) and the general population (CI 1.20–1.25; p < 0.0001). Bone donors are substantially less deprived than their donor pool of THR patients. Donor rates are consistently lower in quintiles which are more deprived.     

The combined impact of mechanical factors on the wall stress of the human ascending aorta – a finite elements study

Background

Biomechanical factors influence stress in the aortic wall. The aim of this study was to assess how the diameter and shape of the vessel, blood pressure and longitudinal systolic aortic stretching (SAS) caused by the contraction of the myocardium influence stress in the aortic wall.

Methods

Three computational models of the non-dilated aorta and aneurysms of the ascending aorta and aortic root were created. Then, finite elements analyses were carried out. The models were subjected to blood pressure (120 mmHg and 160 mmHg) and longitudinal systolic aortic stretching (0 mm, 5 mm, 10 mm and 15 mm). The influence of wall elasticity was examined too.

Results

Blood pressure had a smaller impact on the stress than the SAS. An increase in blood pressure from 120 mmHg to 160 mmHg increased the peak wall stress (PWS) on average by 0.1 MPa in all models. A 5 mm SAS caused a 0.1–0.2 MPa increase in PWS in all the models. The increase in PWS caused by a 10 mm and 15 mm SAS was 0.2 MPa and 0.4 MPa in the non-dilated aorta, 0.2–0.3 MPa and 0.3–0.5 MPa in the aneurysm of the ascending aorta, and 0.1–0.2 MPa and 0.2–0.3 MPa in the aortic root aneurysm model, respectively. The loss of elasticity of the aneurysmal wall resulted in an increase of PWS by 0.1–0.2 MPa.

Conclusions

Aortic geometry, wall stiffness, blood pressure and SAS have an impact on PWS. However, SAS had the biggest impact on wall stress. The results of this study may be useful in future patient-specific computational models used to assess the risk of aortic complications.

     

The effect of direct and indirect force transmission on peri-implant bone stress – a contact finite element analysis

In almost all finite element (FE) studies in dentistry, virtual forces are applied directly to dentures. The purpose of this study was to develop a FE model with non-linear contact simulation using an antagonist as force transmitter and to compare this with a similar model that uses direct force transmission. Furthermore, five contact situations were created in order to examine their influence on the peri-implant bone stresses, which are relevant to the survival rate of implants. It was found that the peri-implant bone stresses were strongly influenced by the kind of force transmission and contact number.     

Impact of material and morphological parameters on the mechanical response of the lumbar spine – A finite element sensitivity study

Finite element models are frequently used to study lumbar spinal biomechanics. Deterministic models are used to reflect a certain configuration, including the means of geometrical and material properties, while probabilistic models account for the inherent variability in the population. Because model parameters are generally uncertain, their predictive power is frequently questioned. In the present study, we determined the sensitivities of spinal forces and motions to material parameters of intervertebral discs, vertebrae, and ligaments and to lumbar morphology. We performed 1200 model simulations using a generic model of the human lumbar spine loaded under pure moments. Coefficients of determination and of variation were determined for all parameter and response combinations. Material properties of the vertebrae displayed the least impact on results, whereas those of the discs and morphology impacted most. The most affected results were the axial compression forces in the vertebral body and in several ligaments during flexion and the facet-joint forces during extension. Intervertebral rotations were considerably affected only when several parameters were varied simultaneously. Results can be used to decide which model parameters require careful consideration in deterministic models and which parameters might be omitted in probabilistic studies. Findings allow quantitative estimation of a model׳s precision.     

Influence of single-level lumbar degenerative disc disease on the behavior of the adjacent segments—A finite element model study

The current study investigated mechanical predictors for the development of adjacent disc degeneration. A 3-D finite element model of a lumbar spine was modified to simulate two grades of degeneration at the L4–L5 disc. Degeneration was modeled by changes in geometry and material properties. All models were subjected to follower preloads of 800 N and moment loads in the three principal directions of motion using a hybrid protocol. Degeneration caused changes in the loading and motion patterns of the segments above and below the degenerated disc. At the level (L3–L4) above the degenerated disc, the motion increased due to moderate degeneration by 21% under lateral bending, 26% under axial rotation and 28% under flexion/extension. At the level (L5-S1) below the degenerated disc, motion increased only during lateral bending by 20% due to moderate degeneration. Both the L3–L4 and L5-S1 segment showed a monotonic increase in both the maximum von Mises stress and shear stress in the annulus as degeneration progressed for all loading directions, expect extension at L3–L4. The most significant increase in stress was observed at the L5-S1 level during axial rotation with nearly a ten-fold increase in the maximum shear stress and 103% increase in the maximum von Mises stress. The L5-S1 segment also showed a progressive increase in facet contact force for all loading directions with degeneration. Nucleus pressure did not increase significantly for any loading direction at either the caudal or cephalic adjacent segment. Results suggest that single-level degeneration can increase the risk for injury at the adjacent levels.     

The influence of solvent on conformational properties of peptides with Aib residue—a DFT study

The conformational propensities of the Aib residue on the example of two model peptides Ac-Aib-NHMe (1) and Ac-Aib-NMe₂ (2), were studied by B3LYP and M06-2X functionals, in the gas phase and in the polar solvents. To verify the reliability of selected functionals, we also performed MP2 calculations for the tested molecules in vacuum. Polarizable continuum models (PCM and SMD) were used to estimate the solvent effect. Ramachandran maps were calculated to find all energy minima. Noncovalent intramolecular interactions due to hydrogen-bonds and dipole attractions between carbonyl groups are responsible for the relative stabilities of the conformers. In order to verify the theoretical results, the available conformations of similar X-ray structures from the Cambridge Crystallographic Data Center (CCDC) were analyzed. The results of the calculations show that both derivatives with the Aib residue in the gas phase prefer structures stabilized by intramolecular N–H?O hydrogen bonds, i.e., C₅ and C₇ conformations, while polar solvent promotes helical conformation with φ, ψ values equal to +/?60°, +/?40°. In addition, in the case of molecule 2, the helical conformation is the only one available in the polar environment. This result is fully consistent with the X-ray data.

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Graphical abstract Effect of solvent on the Ramachandran maps of the model peptides with Aib residue

     

Is the sheep a suitable model to study the mechanical alterations of disc degeneration in humans? A probabilistic finite element model study

Intervertebral disc degeneration is one major source of low back pain, which because of its complex multifactorial nature renders the treatment challenging and thus necessitates extensive research. Experimental animal models have proven valuable in improving our understanding of degenerative processes and potentially promising therapies. Currently, the sheep is the most frequently used large animal in vivo model in intervertebral disc research. However, despite its undoubted value for investigations of the complex biological and cellular aspects, to date, it is unclear whether the sheep is also suited to study the mechanical aspects of disc degeneration in humans.A parametric finite element (FE) model of the L4–5 spinal motion segment was developed. Using this model, the geometry and the material properties of both the human and the ovine spinal segment as well as different appearances of disc degeneration can be depicted. Under pure and combined loads, it was investigated whether degenerative changes to both the human and the ovine model equivalent caused the same mechanical response.Different patterns of degeneration resulted in large variations in the ranges of motion, intradiscal pressure, ligament and facet loads. In the human, but not in the ovine model, all these results differed significantly between different degrees of degeneration.This FE model study highlighted possible differences in the mechanical response to disc degeneration between human and ovine intervertebral discs and indicates the necessity of further, more detailed, investigations.     

Configuration of anchorage holes affects fixation of the acetabular component in cemented total hip replacement—a finite element study

Our survey of current practice among UK orthopaedic surgeons shows wide variations in fixation techniques. The aim of this study, is to investigate the effect of drilling different configurations of anchorage holes in the acetabulum on implant stability. To avoid variables that could incur during in vitro testing, we used commercially available COSMOS finite element analysis package to investigate the stress distributions, deformations, and strains on the cement mantle when drilling three large anchorage holes and six smaller ones, with straight and rounded cement pegs. The results, which are in line with our in vitro studies on simulated reconstructed acetabulae, indicate better stability of the acetabular component when three larger holes than six smaller holes are drilled and when the necks of the anchorage holes are rounded. The longevity of total hip replacements could be improved by drilling three large anchorage holes, rather than many smaller ones, as initially proposed by Charnley.     

Biomechanical comparison of conventional and anatomical calcaneal plates for the treatment of intraarticular calcaneal fractures – a finite element study

Initial stability is essential for open reduction internal fixation of intraarticular calcaneal fractures. Geometrical feature of a calcaneal plate is influential to its endurance under physiological load. It is unclear if conventional and pre-contoured anatomical calcaneal plates may exhibit differently in biomechanical perspective. A Sanders’ Type II-B intraarticular calcaneal fracture model was reconstructed to evaluate the effectiveness of calcaneal plates using finite element methods. Incremental vertical joint loads up to 450 N were exerted on the subtalar joint to evaluate the stability and safety of the calcaneal plates and bony structure. Results revealed that the anatomical calcaneal plate model had greater average structural stiffness (585.7 N/mm) and lower von Mises stress on the plate (774.5 MPa) compared to those observed in the conventional calcaneal plate model (stiffness: 430.9 N/mm; stress on plate: 867.1 MPa). Although both maximal compressive and maximal tensile stress and strain were lower in the anatomical calcaneal plate group, greater loads on fixation screws were found (average 172.7 MPa compared to 82.18 MPa in the conventional calcaneal plate). It was noted that high magnitude stress concentrations would occur where the bone plate bridges the fracture line on the lateral side of the calcaneus bone. Sufficient fixation strength at the posterolateral calcaneus bone is important for maintaining subtalar joint load after reduction and fixation of a Sanders’ Type II-B calcaneal fracture. In addition, geometrical design of a calcaneal plate should worth considering for the mechanical safety in practical usage.     

Effect of hematocrit on wall shear rate in oscillatory flow: do the elastic properties of blood play a role?

Porcine blood was used to examine the relationship between hematocrit levels and wall shear rate patterns in straight and curved artery models under fixed oscillatory flow conditions characteristic of larger arteries. It is demonstrated that porcine blood models both the viscous and elastic components of the 2 Hz complex viscosity of human blood quite accurately over a broad range of shear rates (1-1000 s-1) and hematocrits (20%-80%). For a fixed oscillatory flow waveform (Poiseuille peak shear rate = 168 s-1; mean shear rate 84 s-1), increases in hematocrit produced a decrease in the peak wall shear rate in both the straight and curved artery models and a corresponding decrease in wall shear rate reversal on the inside wall of the curved artery model. The same trends were also observed for oscillatory flows of aqueous glycerin solutions of increasing viscosity in the range of viscosity of the blood samples tested. Aqueous glycerin solutions produced wall shear rate waveforms of the same magnitude and shape as the porcine blood. This indicates that variations in the shear rate, and therefore the shear stress, were caused primarily by changes in the viscous and not the elastic properties of blood. The results suggest that simple Newtonian fluids may be sufficient for in vitro determination of the first order effects to be expected of human blood flow in large vessels having complex geometries and shear rates in or above the range of the present study.     

Can the diverse elastic properties of trabecular and cortical bone be attributed to only a few tissue-independent phase properties and their interactions?

As candidates for tissue-independent phases of cortical and trabecular bone we consider (i) hydroxyapatite, (ii) collagen, (iii) ultrastructural water and non-collagenous organic matter, and (iv) marrow (water) filling the Haversian canals and the intertrabecular space. From experiments reported in the literature, we assign stiffness properties to these phases (experimental set I).On the basis of these phase definitions, we develop, within the framework of continuum micromechanics, a two-step homogenization procedure: (i) at a length scale of 100–200 nm, hydroxyapatite (HA) crystals build up a crystal foam (polycrystal), and water and non-collagenous organic matter fill the intercrystalline space (homogenization step I); (ii) at the ultrastructural scale of mineralized tissues (5–10 microns), collagen assemblies composed of collagen molecules are embedded into the crystal foam, acting mechanically as cylindrical templates. At an enlarged material scale of 5–10 mm, the second homogenization step also accommodates the micropore space as cylindrical pore inclusions (Haversian and Volkmann canals, inter-trabecular space) that are suitable for both trabecular and cortical bone. The inputs for this micromechanical model are the tissue-specific volume fractions of HA, collagen, and of the micropore space. The outputs are the tissue-specific ultrastructural and microstructural (=macroscopic=apparent) elasticity tensors.A second independent experimental set (composition data and experimental stiffness values) is employed to validate the proposed model. We report a small mean prediction error for the macroscopic stiffness values. The validation suggests that hydroxyapatite, collagen, and water are tissue-independent phases, which define, through their mechanical interaction, the elasticity of all bones, whether cortical or trabecular.     

How does the geometry affect the internal biomechanics of a lumbar spine bi-segment finite element model? Consequences on the validation process

Numerical modelling can provide a thorough understanding of the mechanical influence on the spinal tissues and may offer explanations to mechanically linked pathologies. Such objective might be achieved only if the models are carefully validated. Sensitivity study must be performed in order to evaluate the influence of the approximations inherent to modelling. In this study, a new geometrically accurate L3-L5 lumbar spine bi-segmental finite-element model was acquired by modifying a previously existing model. The effect of changes in bone geometry, ligament fibres distribution, nucleus position and disc height was investigated in flexion and extension by comparison of the results obtained from the model before and after the geometrical update. Additional calculations were performed in axial rotation and lateral bending in order to compare the computed ranges of motion (ROM) with experimental results. It was found that the geometrical parameters affected the stress distribution and strain energy in the zygapophysial joints, the ligaments, and the intervertebral disc, changing qualitatively and quantitatively their relative role in resisting the imposed loads. The predicted ROM were generally in good agreement with the experimental results, independently of the geometrical changes. Hence, although the model update affected its internal biomechanics, no conclusions could be drawn from the experimental data about the validation of a particular geometry. Hence the validation of the lumbar spine model should be based on the relative role of its structural components and not only on its global mobility.     

Mineral in skeletal elements of the terrestrial crustacean Porcellio scaber: SRμCT of function related distribution and changes during the moult cycle

Terrestrial isopods moult first the posterior and then the anterior half of the body, allowing for storage and recycling of CaCO₃. We used synchrotron-radiation microtomography to estimate mineral content within skeletal segments in sequential moulting stages of Porcellio scaber. The results suggest that all examined cuticular segments contribute to storage and recycling, however, to varying extents. The mineral within the hepatopancreas after moult suggests an uptake of mineral from the ingested exuviae. The total maximum loss of mineral was 46% for the anterior and 43% for the posterior cuticle. The time course of resorption of mineral and mineralisation of the new cuticle suggests storage and recycling of mineral in the posterior and anterior cuticle. The mineral in the anterior pereiopods decreases by 25% only. P. scaber has long legs and can run fast; therefore, a less mineralised and thus lightweight cuticle in pereiopods likely serves to lower energy consumption during escape behaviour. Differential demineralisation occurs in the head cuticle, in which the cornea of the complex eyes remains completely mineralised. The partes incisivae of the mandibles are mineralised before the old cuticle is demineralised and shed. Probably, this enables the animal to ingest the old exuviae after each half moult.     

Tissue viscoelasticity is related to tissue composition but may not fully predict the apparent-level viscoelasticity in human trabecular bone – An experimental and finite element study

Trabecular bone is viscoelastic under dynamic loading. However, it is unclear how tissue viscoelasticity controls viscoelasticity at the apparent-level. In this study, viscoelasticity of cylindrical human trabecular bone samples (n = 11, male, age 18–78 years) from 11 proximal femurs were characterized using dynamic and stress-relaxation testing at the apparent-level and with creep nanoindentation at the tissue-level. In addition, bone tissue elasticity was determined using scanning acoustic microscope (SAM). Tissue composition and collagen crosslinks were assessed using Raman micro-spectroscopy and high performance liquid chromatography (HPLC), respectively. Values of material parameters were obtained from finite element (FE) models by optimizing tissue-level creep and apparent-level stress-relaxation to experimental nanoindentation and unconfined compression testing values, respectively, utilizing the second order Prony series to depict viscoelasticity. FE simulations showed that tissue-level equilibrium elastic modulus (E_eq) increased with increasing crystallinity (r = 0.730, p = .011) while at the apparent-level it increased with increasing hydroxylysyl pyridinoline content (r = 0.718, p = .019). In addition, the normalized shear modulus g₁ (r = −0.780, p = .005) decreased with increasing collagen ratio (amide III/CH₂) at the tissue-level, but increased (r = 0.696, p = .025) with increasing collagen ratio at the apparent-level. No significant relations were found between the measured or simulated viscoelastic parameters at the tissue- and apparent-levels nor were the parameters related to tissue elasticity determined with SAM. However, only E_eq, g₂ and relaxation time τ₁ from simulated viscoelastic values were statistically different between tissue- and apparent-levels (p < .01). These findings indicate that bone tissue viscoelasticity is affected by tissue composition but may not fully predict the macroscale viscoelasticity in human trabecular bone.     

Estimating the elastic properties of the eye from differential tonometry by the Schiøtz tonometer: Analysis of the measurement procedure on the basis of a two-component mathematical model

Biophysics - The procedure of differential tonometry by the Schiøtz tonometer is modeled using a two-component model of the eyeball in which the cornea is represented by a momentless...