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In this contribution, open cell ceramic foam structures composed of regular/irregular shape cells and containing a macroscopic central notch/crack were investigated in terms of their cracking upon the tensile loading and their strength was predicted using the FE simulations. The developed model of the real ceramic foam specimen containing a central notch/crack was subjected to a tension, resulting in a failure beginning at the tip of the notch. The work discusses an approach how to predict the critical failure load and also the crack path in the foam structure. Various cell irregularity and size of the macroscopic notch was considered in the investigations. Predictions of the foam structure cracking were performed using the beam element based FE model having characteristics of the real foam structure and by utilization of the stress criterion which considers failure of particular struts, when the maximum stress on them reaches the tensile strength of the ceramic material. Outputs from simulations were compared with available experimental observations and with an estimation of the critical failure load calculated using the developed analytical model.

Patient-specific approach is gaining a wide popularity in computational simulations of biomechanical systems. Simulations (most often based on the finite element method) are to date routinely created using data from imaging devices such as computed tomography which makes the models seemingly very complex and sophisticated. However, using a computed tomography in finite element calculations does not necessarily enhance the quality or even credibility of the models as these depend on the quality of the input images. Low-resolution (medical-)CT datasets do not always offer detailed representation of trabecular bone in FE models and thus might lead to incorrect calculation of mechanical response to external loading. The effect of image resolution on mechanical simulations of bone-implant interaction has not been thoroughly studied yet. In this study, the effect of image resolution on the modeling procedure and resulting mechanical strains in bone was analyzed on the example of cranial implant. For this purpose, several finite element models of bone interacting with fixation-screws were generated using seven computed tomography datasets of a bone specimen but with different image resolutions (ranging from micro-CT resolution of 25 μm to medical-CT resolution of 1250 μm). The comparative analysis revealed that FE models created from images of low resolution (obtained from medical computed tomography) can produce biased results. There are two main reasons: 1. Medical computed tomography images do not allow generating models with complex trabecular architecture which leads to substituting of the intertrabecular pores with a fictitious mass; 2. Image gray value distribution can be distorted resulting in incorrect mechanical properties of the bone and thus in unrealistic or even completely fictitious mechanical strains. The biased results of calculated mechanical strains can lead to incorrect conclusion, especially when bone-implant interaction is investigated. The image resolution was observed not to significantly affect stresses in the fixation screw itself; however, selection of bone material representation might result in significantly different stresses in the screw.

This work deals with a computational analysis and quantification of the influence of processing (primarily crack-like) defects of various amount on the (tensile) strength of open cell ceramic foam structures. This information is essential e.g. for application of these materials in the mechanically loaded application, where a design with certain reliability to operating conditions is required. The analysed ceramic foam structures are composed of both regular and irregular cells and crack-like defects (pre-cracked struts) are simulated inside them. The foam structure is modelled using a 3D FE beam element based model created by utilization of the Voronoi tessellation technique. The tensile strength upon presence of various amount of pre-cracked struts is analysed based upon an iterative FE simulation on whose base the critical failure force leading to specimen fracture is determined. The performed parametric study relates the tensile strength of the foam structure to the amount of initial defects. With increasing amount of these defects, the foam strength decreases by approximately 30% with every 10% of broken struts. This information can be directly used for a fast estimation of the foam tensile strength if the fraction of broken struts to the intact ones is known (e.g. from a microscopic analysis).

It is widely accepted that bones have the ability to adapt to new biomechanical environment by changing their material properties, geometry and inner architecture. Bones have also an exceptional ability to self-repair, to remove microcracks and to prevent the bone damage caused by the fatigue failure. These abilities are enabled through coupled processes of bone resorption and bone formation, the processes collectively referred to as bone remodeling. Numerous studies have shown that bone remodeling is governed by combination of mechanical stimulus (strains) and its frequency, both sensed by sensor cells (osteocytes). Through mechanotransduction, the stimulus is transmitted to actor cells (osteoclasts, osteoblasts) that actually do the bone resorption or formation. Several theories have been proposed to predict bone remodeling and several finite-element-based algorithms have been introduced. The vast majority of them uses strain energy density as the mechanical stimulus. The purpose of this paper is to investigate and discuss the applicability of also other strain-based representations of the mechanical stimulus in simulations of remodeling of bone with an initial microcrack. The need for developing more reliable models is essential for both clinicians and engineers who are interested, for instance, in prediction of bone performance when various implants are involved.

The paper deals with crack bridging modelling in Bioglass ® based scaffolds due the presence of a special polymer coating. This includes a careful modelling of the scaffold which is based on x-ray computed micro-tomography (micro-CT) scans and identification of bridging mechanism with the aid of extensive fractographic observations of coated, broken struts. A replacement of the real structure of scaffold by a periodic model utilizing Kelvin cell whose size corresponds to the mean cell size of the real foam is discussed. The struts of the idealized foam are modelled using the beam elements. A detailed computational analysis of crack bridging due to coating film fibrils under plane strain conditions is presented and an improvement of fracture resistance of coated scaffolds is explained.

The purpose of this study was to investigate the effect of load-induced local mechanical strain on bone cell activity of peri-implant bone in mice. Titanium implants were placed in the maxillae of 13-week-old male C57BL/6J mice and subjected to intermittent 0.15 N, 0.3 N, or 0.6 N loads for 30 min/day for 6 days. The animals were sacrificed 2 days after the final loading. Unloaded mice were used as controls. An animal-specific three-dimensional finite element model was constructed based on morphological data retrieved from in vivo microfocus computed tomography for each mouse to calculate the mechanical strain distribution. Strain distribution images were overlaid on corresponding histological images of the same site in the same animal. The buccal cervical region of the peri-implant bone was predetermined as the region of interest (ROI). Each ROI was divided by four strain intensity levels: 0-20 με, 20-60 με, 60-100 με, and ≥100 με, and the bone histomorphometric parameters were analyzed by the total area of each strain range for all loaded samples. The distance between the calcified front and calcein labeling as a parameter representing the mineral apposition rate was significantly greater in the areas with strain intensity ≥100 με than in the area with strain intensity100 με, suggesting that the bone formation activity of osteoblasts was locally enhanced by a higher mechanical strain. However, the shrunken osteocytes and the empty osteocyte lacunae were significantly lower in the highest strain area, suggesting that osteoclastogenesis was more retarded in higher strain areas than in lower strain areas. The histomorphometric parameters were not affected geometrically in the unloaded animals, suggesting that the load-induced mechanical strain caused differences in the histomorphometric parameters. Our findings support the hypothesis that bone cell activity related to bone resorption and formation is local strain-dependent on implant loading.

Using porous bioceramics became recently an alternative approach to increase bone density which is a key factor for successful dental implant application. These novel biomaterials should substitute missing natural trabecular structures in terms of material strength as well as deformation characteristics. However, mechanical behavior of these materials used as bone fillers are still in question. This problem is made more difficult by the fact that bone structure itself exhibits a complex mechanical behavior which is still in question as well and, therefore, appropriate analytical criteria should to be established. The purpose of this paper is to determine typical mechanical behavior of trabecular structure of mandibular cancellous bone using computational simulations which can serve as a basis for establishing such criteria. For this purpose, four bone specimens of various bone density were μCT-scanned and high-level finite element models including detailed trabecular structure were created on their basis to analyze relevant mechanical quantities for various loadings in terms of bone density and various histomorphometric parameters.

In this study, different patient-specific computational models of the skull, which are often used in literature, were investigated, analysed and compared. The purpose of this study was to demonstrate the differences in computational model creation and results in case different computational models based on same computed tomography (CT) dataset are used. The selection of computational model directly influences the values of investigated parameters. The effort is to demonstrate, how the selection of the computational model influences the results of biomechanically relevant parameters. The comparison was based on total displacement of the skull and von Mises strain investigated around predefined paths around the skull. The strain values were evaluated according to criterion from literature. The results were obtained using finite element method. The values of the displacement of the skull were higher in case of considering cancellous bone tissue due to its poor material properties or heterogeneous material properties. The same situation occurred during the evaluation of strain. The values were higher in models which include cancellous bone tissue in the structure.

In this study 6 pre-operative designs for PMMA based reconstructions of cranial defects were evaluated for their mechanical robustness using finite element modeling. Clinical experience and engineering principles were employed to create multiple plan options, which were subsequently computationally analyzed for mechanically relevant parameters under 50N loads: stress, strain and deformation in various components of the assembly. The factors assessed were: defect size, location and shape. The major variable in the cranioplasty assembly design was the arrangement of the fixation plates. An additional study variable introduced was the location of the 50N load within the implant area. It was found that in smaller defects, it was simpler to design a symmetric distribution of plates and under limited variability in load location it was possible to design an optimal for expected loads. However, for very large defects with complex shapes, the variability in the load locations introduces complications to the intuitive design of the optimal assembly. The study shows that it can be beneficial to incorporate multi design computational analyses to decide upon the most optimal plan for a clinical case. V této studii bylo provedeno 6 předoperačních návrhů pro rekonstrukci kraniálních defektů pomocí PMMA implantátů, které byly hodnoceny z mechanického hlediska pomocí výpočtového modelování metodou konečných prvků. Pomocí inženýrského přístupu a klinických zkušeností byly vytvořeny různé varianty výpočtových modelů. Veličinami, které byly následně výpočetně analyzovány při zatížení 50N jsou napětí, deformace a deformace. Hodnotící faktory byly: velikost defektu, umístění a tvar. Posouzení sestavy s kranioplastikou bylo provedeno pro různé uspořádání fixačních desek. Dále byla analyzována poloha zatížení 50N v oblasti implantátu.

Medical grade 3D printing offers the possibility to manufacture patient-specific implants to treat cranial defects. The performance of the implant assembly depends on many factors, such as material, thickness, size and manufacturing accuracy. A significant factor in the stability and success of the assembly is the fixation method. Cranial implants are usually fixed to the skull by means of mini-plates. Biomechanical assessment of fixing the implant to the skull might be helpful not only for mini-plate design but might be beneficial also for the surgeons. In this study, four different mini-plate designs were analyzed and compared based on the stress-strain analysis of one cranial implant fixed at three locations by mini-plates. Computational simulations were done using Finite Element Method.

In this paper, the restricted form of the principle of quasi work – the so-called modified Betti׳s theorem – is used for developing an alternative analytical solution of beams on an elastic foundation. A brief review of this principle is provided along with the reminder of the classical Winkler׳s model. A methodology is based on the calculation of the deflection of beam on an elastic foundation from the deflection of a reference beam which is topologically equivalent. Fundamental formulae for the reference beam on an elastic foundation are derived and thoroughly discussed. Applying the modified Betti׳s theorem, these formulae can be used for analysis of any arbitrary topologically equivalent beam on an elastic foundation. The applicability of this methodology is proved and a detailed guidance for its use is provided as well. The methodology is illustrated by three representative examples. The beam on an elastic foundation is a structure which is often used in many areas of technical practice including civil engineering, aerospace engineering etc; thus, the presented alternative way of its analytical solution might be found helpful, mainly for quick calculation and for its simple algorithmization.

Dental implants induce diverse forces on their surrounding bone. However, when excessive unphysiological forces are applied, resorption of the neighbouring bone may occur. The aim of this study was to assess possible causes of bone loss around failing dental implants using finite element analysis. A further aim was to assess the implications of progressive bone loss on the strains induced by dental implants. Between 2003 and 2009 a total of 3700 implant operations were performed in a private clinic. Ten patients with 16 fixtures developed severe marginal bone defects. Finite element analysis was used to assess the effective strains produced at the bone-implant interface under unidirectional axial loading. These simulations were carried out on 4 specific implant types – Camlog Plus, Astra Osseo Speed, Straumann BL and Straumann S/SP. All implant types exhibited degraded performance under circular and horizontal bone loss conditions. This is evidenced by increased distribution of pathological strain intensities (>3000 μe), in accordance with the mechanostat hypothesis, in the surrounding bone. Among the implants, the Camlog design seemed to have performed poorly, especially at the chamfer in the implant collar (>25000 μe). Implants are designed to perform under nearly ideal conditions from insertion till osseointegration. However, when the surrounding bone undergoes remodelling, implant geometries can have varied performance, which in some cases can exacerbate bone loss. The results of this study indicate the importance of evaluating implant geometries under clinically observed conditions of progressive bone loss.

Introduction The process of fabricating physical medical skull models requires many steps, each of which is a potential source of geometric error. The aim of this study was to demonstrate inaccuracies and differences caused by DICOM to STL conversion in additively manufactured medical skull models. Material and methods Three different institutes were requested to perform an automatic reconstruction from an identical DICOM data set of a patients undergoing tumour surgery into an STL file format using their software of preference. The acquired digitized STL data sets were assessed and compared and subsequently used to fabricate physical medical skull models. The three fabricated skull models were then scanned, and differences in the model geometries were assessed using established CAD inspection software methods. Results A large variation was noted in size and anatomical geometries of the three physical skull models fabricated from an identical (or “a single”) DICOM data set. Conclusions A medical skull model of the same individual can vary markedly depending on the DICOM to STL conversion software and the technical parameters used. Clinicians should be aware of this inaccuracy in certain applications.

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.

The paper deals with a creation of computational model of a high porous ceramic material. This type of material has a large-scale industrial utilization. The computational model was created based on micro-CT data in the ANSYS 14.0 software using Finite Element Method. A creation of a porous ceramic struts model which respect a micro architecture is quite difficult (computer demanding and micro-CT data). The micro-CT slices are converted into a 3D model using image processing (used software STL Model Creator). The local first principle stress was analyzed because, ceramic is the brittle material. Furthermore, the influence of the thick layer around the individual struts was analyzed.

In recent years, particle reinforced composites are widely used due their mechanical properties as construction materials, high-performance engineering materials or protective organic coatings. The paper was mainly focused on the estimating of the interactions of the micro-crack and the particles in the particulate polymer composites. A non-linear material behavior of the matrix was obtained from the experiment and it was used to investigation by means of the finite element method - using ANSYS software. A two-dimensional numerical model was developed and a micro-crack propagation direction was calculated based on the assumption of the linear elastic fracture mechanics. The results indicated that the presence of the interphase between particle and matrix can improve the fracture toughness of the polymer particle composites through debonding process. The paper can contribute to a better understanding of the behavior and failure of the composites with the polymer matrix reinforced by the rigid particles.

The domain of the generalized stress intensity factors dominance ahead of the notch tip can be rather small with respect to the length of the perturbing cracks initiated from the tip of the notch. Thus the non-singular terms of the stress asymptotic expansion at the notch tip would play an important role in the notch tip stability. Following the procedures dealing with complex potential theory and path-independent two-state integrals developed for the singular stress analysis of the stress concentrators one can evaluate their magnitude and include them to the energy release rate of the preexisting crack initiated from the notch tip applying the matched asymptotic procedure. The presented analysis should lead to better understanding of the notch stability process and precising of the notch stability criteria.

This paper is focused on computational modeling of an interaction of dental implant with mandible bone. It describes creation of computational model including model of geometry, materials, loads and constraints. There is a comparative stress-strain analysis of the levels of cancellous bone model. Computations are performed with the use of finite element method. Results show differences between the model which includes trabecular architecture of cancellous bone tissue and the model with non-trabecular cancellous bone tissue. For better description of the processes in bone tissue and at the interface between bone tissue and implant, it is necessary to create the computational model on the highest possible level, i.e. with the trabecular bone tissue.

This article deals with presentation of data processing obtained from imaging CT (computer tomography) and micro CT devices. These methods enable to perform bone tissue density analysis by non-invasive way. The image processing methods, by which it is possible to determine mechanical properties of bone tissue, are described in this paper. Further, a creation of a computational model with different bone density of cancellous tissue is described and afterwards the stress strain analysis is performed. The mandible segments with different bone density were used as samples. Results show significantly higher stresses are reached in a cancellous bone tissue with worse bone quality.

This article is focused on computational modeling of an interaction of malleable lumbar spine fixation device with ambient bone tissue focusing on solving problems of clinical practise. It describes creation of computational model including model of geometry, materials, loads and constraints. There is a comparative stress strain analysis of spinal segment after fixation device application with its physiological state. Computations are performed with use of FEM method. To simulate natural way of loading we used the compression of motional spinal segment. Results show the difference between the system including intervertebral disc in between vertebras and the system with applied lumbar spinal fixation device.

The presented paper describes the creation of a computational model of highly porous materials, and a stress-strain analysis is performed. The computational model is created using micro-CT by the finite element method in the ANSYS 12.0 software. The micro-CT slices are converted into a 3D model using image processing. The local equivalent stress (HMH criterion) and struts deformation are analyzed. Commercially available ceramic foam, 85%Al2O3-14%SiO2- 1%MgO, was used in the experiment part of the paper.

This computational study investigates the effect of shape (defect contour curvature) and bone-implant interface (osteotomy angle) on the stress distribution within PMMA skull implants. Using finite element methodology, 15 configurations – combinations of simplified synthetic geometric shapes (circular, square, triangular, irregular) and interface angulations – were simulated under 50N static loads. Furthermore, the implant fixation devices were modelled and analysed in detail. Negative osteotomy configurations demonstrated the largest stresses in the implant (275 MPa), fixation devices (1258 MPa) and bone strains (0.04). The circular implant with zero and positive osteotomy performed well with maximum observed magnitudes of – implant stress (1.2 MPa and 1.2 MPa), fixation device stress (11.2 MPa and 2.2 MPa), bone strain (0.218e-3 and 0.750e-4). The results suggest that the preparation of defect sites is a critical procedure. Of the greatest importance is the angle at which the edges of the defect are sawed. If under an external load, the implant has no support from the interface and the stresses are transferred to the fixation devices. This can endanger their material integrity and lead to unphysiological strains in the adjacent bone, potentially compromising the bone morphology required for anchoring. These factors can ultimately weaken the stability of the entire implant assembly.

The response to the mechanical loading of bone tissue has been extensively investigated; however, precisely how much strain intensity is necessary to promote bone formation remains unclear. Combination studies utilizing histomorphometric and numerical analyses were performed using the established murine maxilla loading model to clarify the threshold of mechanical strain needed to accelerate bone formation activity. For 7 days, 191 kPa loading stimulation for 30 min/day was applied to C57BL/6J mice. Two regions of interest, the AWAY region (away from the loading site) and the NEAR region (near the loading site), were determined. The inflammatory score increased in the NEAR region, but not in the AWAY region. A strain intensity map obtained from [Formula: see text] images was superimposed onto the images of the bone formation inhibitor, sclerostin-positive cell localization. The number of sclerostin-positive cells significantly decreased after mechanical loading of more than [Formula: see text] in the AWAY region, but not in the NEAR region. The mineral apposition rate, which shows the bone formation ability of osteoblasts, was accelerated at the site of surface strain intensity, namely around [Formula: see text], but not at the site of lower surface strain intensity, which was around [Formula: see text] in the AWAY region, thus suggesting the existence of a strain intensity threshold for promoting bone formation. Taken together, our data suggest that a threshold of mechanical strain intensity for the direct activation of osteoblast function and the reduction of sclerostin exists in a murine maxilla loading model in the non-inflammatory region.

Large mandibular continuity defects pose a significant challenge in oral maxillofacial surgery. One solution to this problem is to use computer-guided surgical planning and additive manufacturing technology to produce patient-specific reconstruction plates. However, when designing customized plates, it is important to assess potential biomechanical responses that may vary substantially depending on the size and geometry of the defect. The aim of this study was to assess the design of two customized plates using finite element method (FEM). These plates were designed for the reconstruction of the lower left mandibles of two ameloblastoma cases (patient 1/plate 1 and patient 2/plate 2) with large bone resections differing in both geometry and size. Simulations revealed maximum von Mises stresses of 63 MPa and 108 MPa in plates 1 and 2, and 65 MPa and 190 MPa in the fixation screws of patients 1 and 2. The equivalent strain induced in the bone at the screw-bone interface reached maximum values of 2739 micro-strain for patient 1 and 19,575 micro-strain for patient 2. The results demonstrate the influence of design on the stresses induced in the plate and screw bodies. Of particular note, however, are the differences in the induced strains. Unphysiologically high strains in bone adjacent to screws can cause micro-damage leading to bone resorption. This can adversely affect the anchoring capabilities of the screws. Thus, while custom plates offer optimal anatomical fit, attention should be paid to the expected physiological forces on the plates and the induced stresses and strains in the plate-screw-bone assembly.

The mechanism of traumatic bone resorption in the denture-bearing bone has not yet been established with regard to the osteoclastic activity in relation to the mechanical stimulus. The purpose of this study was to clarify whether osteoclast appearance in maxilla depends on the strain intensity, using the murine loading model. The maxillary palate of thirteen-week-old male C57BL/6 mice was subjected to continuous pressure of 2 kPa (low stimulation, n = 4) or 7 kPa (high stimulation, n = 4) for 30 min/day for 7 consecutive days, and the mice were sacrificed after the last loading. The control group underwent the same protocol without load (n = 4). An animal-specific finite element model was constructed based on morphology and characteristics obtained from the micro-CT data and used to calculate the strain intensity of the bone. The bone histomorphometric technique revealed significant reduction of cortical bone volume and significant increase of bone resorption parameters such as osteoclast number in the bone tissue under the loading contact in comparison to the control (p < 0.05). The osteoclasts were observed in the subsurface region adjacent to the loading contact and the peripheral region of the marrow space in the intracortical region of the cortical bone in the mouse maxilla in both stimulation groups. An average of more than 90 % of the osteoclasts was observed in the areas with strain intensity higher than 85.0μ strain for the high stimulation group. The result suggests that the osteoclastic resorption is location-dependent and is also sensitive to the local strain intensity.