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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.

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.

Channel morphology step-pool represents a morphodynamic complex influenced by large woody debris and litter-fall. The aim of this paper is to determine the impact of litter-fall on the channel morphology step-pool. General conclusions regarding the influence of litter-fall on channel morphology step-pool were based on results of geomorphological analyses. The study showed differences between river segments with or without foliaged steps. The pools following foliaged steps have a finer grain size composition of sediment. They are also larger, shallower and have a higher retention capacity. Foliaged steps help to decrease potential energy of water more effectively. If the litter-fall is permanently preserved at the step, it makes it more resistant to extreme water flows. As a result, it enables the development of a fully functional channel morphology step-pool.

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.

This study investigated the effect of implant thickness and material on deformation and stress distribution within different components of cranial implant assemblies. Using the finite element method, two cranial implants, differing in size and shape, and thicknesses (1, 2, 3 and 4 mm, respectively), were simulated under three loading scenarios. The implant assembly model included the detailed geometries of the mini-plates and micro-screws and was simulated using a sub-modeling approach. Statistical assessments based on the Design of Experiment methodology and on multiple regression analysis revealed that peak stresses in the components are influenced primarily by implant thickness, while the effect of implant material is secondary. On the contrary, the implant deflection is influenced predominantly by implant material followed by implant thickness. The highest values of deformation under a 50 N load were observed in the thinnest (1 mm) Polymethyl Methacrylate implant (S mall defect: 0.296 mm; Large defect: 0.390 mm). The thinnest Polymethyl Methacrylate and Polyether Ether Ketone implants also generated stresses in the implants that can potentially breach the materials' yield limit. In terms of stress distribution, the change of implant thickness had a more significant impact on the implant performance than the change of Young's modulus of the implant material. The results indicated that the stresses are concentrated in the locations of fixation; therefore, the detailed models of mini-plates and micro-screws implemented in the finite element simulation provided a better insight into the mechanical performance of the implant-skull system.

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.

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.

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.

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.

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.

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.

This study aimed to introduce a procedure for determining the bilinear elastic moduli (E1 and E2) of the periodontal ligament for a mathematical tooth model to analyse stress in the mandible. The bone and tooth morphology were scanned from a dry skull and an extracted intact tooth, respectively, and reconstructed in a three-dimensional finite element model. The model showed good agreement with previously reported in vivo premolar movement when an E1 for the first phase tooth movement of 0.05 MPa and an E2 for the second phase of 8.0 MPa with ε(12) of 0.075 were adopted. The mandible model analysis indicated that a remarkably high maximum compressive stress in the cervical cortical bone and the tensile stress in areas of masticatory muscle attachment were found. Future stress analyses using a jaw model may follow the process of determination of bilinear moduli to enhance accurate simulation with less calculation time.