Bone ingrowth on the surface of endosseous implants. Part 1: Mathematical model

Effect of customized abutment taper configuration on bone remodeling and peri-implant tissue around implant-supported single crown: A 3D nonlinear finite element study

PURPOSE

The optimal configuration of a customized implant abutment plays a crucial role in promoting bone remodeling and maintaining the peri-implant gingival contour. However, the biomechanical effects of abutment configuration on bone remodeling and peri-implant tissue remain unclear. This study aimed to evaluate the influence of abutment taper configurations on bone remodeling and peri-implant tissue.

MATERIALS AND METHODS

Five models with different abutment taper configurations (10°, 20°, 30°, 40°, and 50°) were analyzed using finite element analysis (FEA) to evaluate the biomechanical responses in peri-implant bone and the hydrostatic pressure in peri-implant tissue.

RESULTS

The results demonstrated that the rate of increase in bone density was similar in all models. On the other hand, the hydrostatic pressure in peri-implant gingiva revealed significantly different results. Model 10° showed the highest maximum and volume-averaged hydrostatic pressures (69.31 and 4.5 mmHg), whereas Model 30° demonstrated the lowest values (57.83 and 3.88 mmHg) with the lowest excessive pressure area. The area of excessive hydrostatic pressure decreased in all models as the degree of abutment taper increased from 10° to 30°. In contrast, Models 40° and 50° exhibited greater hydrostatic pressure concentration at the cervical region.

CONCLUSION

In conclusion, the abutment taper configuration had a slight effect on bone remodeling but exerted a significant effect on the peri-implant gingiva above the implant platform via hydrostatic pressure. Significant decreases in greatest and average hydrostatic pressures were observed in the peri-implant tissues of Model 30°. However, the results indicate that implant abutment tapering wider than 40° could result in a larger area of excessive hydrostatic pressure in peri-implant tissue, which could induce gingival recession.

Peri-implant cell differentiation in delayed and immediately-loaded dental implant: A mechanobiological simulation

OBJECTIVE

This study aimed to investigate the effect of immediate versus delayed dental implant placement strategies on cell differentiation in a dental callus.

DESIGN

The implant was placed in the mandible with two nearby teeth using an idealized two-dimensional finite element model. Eight weeks after surgery, the mechanobiological modeling of healing was used to estimate cell differentiation. It was assumed that the callus was initially filled by mesenchymal cells. The model then transformed mechanical stimuli received by the callus from loadings in terms of distortional and dilatational strains into predictions of the cellular phenotypes, including fibroblasts, chondrocytes, and osteoblasts, or whether they would remain unchanged or die.

RESULTS

The results demonstrated that delayed loading led to greater bone formation than immediate loading. Osteoblast colonies were observed in the base of threads in the immediately-loaded implant, whereas the delayed loading caused distant bone formation from the surrounding bone side towards the implant. The osteoblasts were differentiated from both intramembranous and endochondral mechanisms of ossification. After eight weeks, approximately 61 % of the callus was ossified in the delayed placement model compared to 35 % in the immediate placement model, resulting in a greater amount of fibrocartilaginous tissue on the bone side of the callus.

CONCLUSIONS

Immediate and delayed loading models generated different results. In the delayed strategy, bone cells were supplied appropriately during the first few weeks following surgery, whereas the immediate loading caused fibrocartilaginous tissue differentiation. In the form of distant osseointegration, the secondary stability of the dental implant was higher and faster due to the delayed placement.

Improving the Endoprosthesis Design and the Postoperative Therapy as a Means of Reducing Complications Risks after Total Hip Arthroplasty

One of the most high-tech, efficient and reliable surgical procedures is Total Hip Arthroplasty (THA). Due to the increase in average life expectancy, it is especially relevant for older people suffering from chronic joint disease, allowing them to return to an active lifestyle. However, the rejuvenation of such a severe joint disease as osteoarthritis requires the search for new solutions that increase the lifespan of a Total Hip Replacement (THR). Current trends in the development of this area are primarily focused on the creation of new materials used in THR and methods for their processing that meet the requirements of biocompatibility, long-term strength, wear resistance and the absence of an immune system response aimed at rejection. This study is devoted to the substantiation of one of the possible approaches to increase the reliability and durability of THR, based on the improvement of the implant design and postoperative rehabilitation technology, potentially reducing the risk of complications in the postoperative period.

Mechanobiological model to study the influence of screw design and surface treatment on osseointegration

This study aims at suggesting a new approach to peri-implant healing models, providing a set of taxis-diffusion-reaction equations under the combined influence of mechanical and biochemical factors. Early events of osseointegration were simulated for titanium screw implants inserted into a pre-drilled trabecular bone environment, up to 12 weeks of peri-implant bone healing. Simulations showed the ability of the model to reproduce biological events occurring at the implant interface through osteogenesis. Implants with shallow healing chamber showed higher proportions of lamellar bone, enhanced by the increase of mechanical stimulation. Osteoconduction was observed through the surface treatment model and similar bone healing patterns compared to in vivo studies.

Multiscale modeling of bone tissue mechanobiology

Mechanical environment has a crucial role in our organism at the different levels, ranging from cells to tissues and our own organs. This regulatory role is especially relevant for bones, given their importance as load-transmitting elements that allow the movement of our body as well as the protection of vital organs from load impacts. Therefore bone, as living tissue, is continuously adapting its properties, shape and repairing itself, being the mechanical loads one of the main regulatory stimuli that modulate this adaptive behavior. Here we review some key results of bone mechanobiology from computational models, describing the effect that changes associated to the mechanical environment induce in bone response, implant design and scaffold-driven bone regeneration.

Numerical simulations on periprosthetic bone remodeling: a systematic review

BACKGROUND AND OBJECTIVE

The aim of the present study was to review the literature concerning the analysis of periprosthetic bone remodeling through finite element (FE) simulation.

METHODS

A systematic review was conducted on 9 databases, taking into account a ten-year time period (from 2009 until 2020). The inclusion criteria were: articles published in English, publication date after 2009, full text articles, articles containing the keywords both in the abstract and in the title. The articles were classified through the following parameters: dimensionality of the simulation, modelling of the bone-prosthesis interface, output parameters, type of simulated prosthesis, bone remodeling algorithm.

RESULTS

Sixty-seven articles were included in the study. Femur and tooth were the most evaluated bone segment (respectively 41.8% and 29.9%). The 55.2% of the evaluated articles used a bonded bone-prosthesis interface, 73% used 3D simulations, 67.2% of the articles (45 articles) evaluate the bone remodeling by the bone density variation. At last, 59.7% of the articles employed algorithms based on a specific remodeling function.

CONCLUSIONS

Increasing interest in the bone remodeling FE analysis in different bone segments emerged from the review, and heterogeneous solutions were adopted. An optimal balance between computational cost and accuracy is needed to accurately simulate the bone remodeling phenomenon in the post-operative period.

Spatial extension of a bone remodeling dynamics model and its finite element analysis

There are many works dealing with the dynamics of bone remodeling, proposing increasingly complex and complete models. In the recent years, the efforts started to focus on developing models that not only reproduce the temporal evolution, but also include the spatial aspects of this phenomenon. In this work, we propose the spatial extension of an existing model that includes the dynamics of osteocytes. The spatial dependence is modeled in terms of a linear diffusion, as proposed in previous works dealing with related problems. The resulting model is then written in its variational form, and fully discretized using the well-known finite element method and a combination of the implicit and explicit Euler schemes. The numerical algorithm is then analyzed, proving some a priori error estimates and its linear convergence. Finally, we extend the examples already published for the temporal model to one and two dimensions, showing the dynamics of the solution in the spatial domain.

Deconvoluting the Bioactivity of Calcium Phosphate-Based Bone Graft Substitutes: Strategies to Understand the Role of Individual Material Properties

Calcium phosphate (CaP)-based ceramics are the most widely applied synthetic biomaterials for repair and regeneration of damaged and diseased bone. CaP bioactivity is regulated by a set of largely intertwined physico-chemical and structural properties, such as the surface microstructure, surface energy, porosity, chemical composition, crystallinity and stiffness. Unravelling the role of each individual property in the interaction between the biomaterial and the biological system is a prerequisite for evolving from a trial-and-error approach to a design-driven approach in the development of new functional biomaterials. This progress report critically reviews various strategies developed to decouple the roles of the individual material properties in the biological performance of CaP ceramics. It furthermore emphasizes on the importance of a comprehensive and adequate material characterization that is needed to enhance our knowledge of the property-function relationship of biomaterials used in bone regeneration, and in regenerative medicine in general.

Characteristics of contact and distance osteogenesis around modified implant surfaces in rabbit tibiae

Purpose

Contact and distance osteogenesis occur around all endosseous dental implants. However, the mechanisms underlying these processes have not been fully elucidated. We hypothesized that these processes occur independently of each other. To test this, we used titanium (Ti) tubes to physically separate contact and distance osteogenesis, thus allowing contact osteogenesis to be measured in the absence of possible triggers from distance osteogenesis.

Methods

Sandblasted and acid-etched (SLA) and modified SLA (modSLA) implants were used. Both types had been sandblasted with large grit and then etched with acid. The modSLA implants then underwent additional treatment to increase hydrophilicity. The implants were implanted into rabbit tibiae, and half were implanted within Ti tubes. The bone-to-implant contact (BIC) ratio was calculated for each implant. Immunohistochemical analyses of bone morphogenetic protein (BMP)-2 expression and new bone formation (Masson trichrome stain) were performed.

Results

The implants outside of Ti tubes were associated with good bone formation along the implant surface. Implantation within a Ti tube significantly reduced the BIC ratio (P<0.001). Compared with the modSLA implants, the SLA implants were associated with significantly higher BIC ratios, regardless of the presence or absence of Ti tubes (P=0.043). In the absence of Ti tubes, the bone adjacent to the implant had areas of new bone formation that expressed BMP-2 at high levels.

Conclusions

This study disproved the null hypothesis and suggested that contact osteogenesis is initiated by signals from the old bone that undergoes distance osteogenesis after drilling. This signal may be BMP-2.

Biocompatibility Analyses of Al₂O₃-Treated Titanium Plates Tested with Osteocyte and Fibroblast Cell Lines

Osseointegration of a titanium implant is still an issue in dental/orthopedic implants durable over time. The good integration of these implants is mainly due to their surface and topography. We obtained an innovative titanium surface by shooting different-in-size particles of Al₂O₃ against the titanium scaffolds which seems to be ideal for bone integration. To corroborate that, we used two different cell lines: MLO-Y4 (murine osteocytes) and 293 (human fibroblasts) and tested the titanium scaffolds untreated and treated (i.e., Al₂O₃ shot-peened titanium surfaces). Distribution, density, and expression of adhesion molecules (fibronectin and vitronectin) were evaluated under scanning electron microscope (SEM) and confocal microscope (CM). DAPI and fluorochrome-conjugated antibodies were used to highlight nuclei, fibronectin, and vitronectin, under CM; cell distribution was analyzed after gold-palladium sputtering of samples by SEM. The engineered biomaterial surfaces showed under SEM irregular morphology displaying variously-shaped spicules. Both SEM and CM observations showed better outcome in terms of cell adhesion and distribution in treated titanium surfaces with respect to the untreated ones. The results obtained clearly showed that this kind of surface-treated titanium, used to manufacture devices for dental implantology: (i) is very suitable for cell colonization, essential prerequisite for the best osseointegration, and (ii) represents an excellent solution for the development of further engineered implants with the target to obtain recovery of stable dental function over time.

Modeling and simulation of platelet reaction and diffusion towards an electro-stimulating dental implant

Electrical stimulation (ES) has been used clinically to promote bone ingrowth on implant surface. The osseointegration of biomaterials in bone requires complex biological interactions between different bone cells species. At the early stages of bone healing, it is reported in literature that platelets play an important role in stimulating stem cells, osteogenic cells and osteoblasts. This work studies the coupling of the reaction-diffusion model of platelets with external ES. For this, we introduce a mathematical model framework consisting of a system of coupled partial differential equations. Platelets' migration and interaction within a realistic 3D model adapted from an electro-stimulating dental implant is studied. DC voltage of 3.1 V is applied at the electrodes. The electric field distribution around the electro-stimulating dental implant is simulated. High concentration of platelets around the implant surface is achieved after one day of healing. Based on these results, it is shown that osseointegration of dental implants in bone could be enhanced and accelerated by means of ES.

Diffusion model to describe osteogenesis within a porous titanium scaffold

In this study, we develop a two-dimensional finite element model, which is derived from an animal experiment and allows simulating osteogenesis within a porous titanium scaffold implanted in ewe's hemi-mandible during 12 weeks. The cell activity is described through diffusion equations and regulated by the stress state of the structure. We compare our model to (i) histological observations and (ii) experimental data obtained from a mechanical test done on sacrificed animal. We show that our mechano-biological approach provides consistent numerical results and constitutes a useful tool to predict osteogenesis pattern.

Early stages of bone fracture healing: formation of a fibrin-collagen scaffold in the fracture hematoma

This work is concerned with the sequence of events taking place during the first stages of bone fracture healing, from bone breakup until the formation of early fibrous callus (EFC). The latter provides a scaffold over which subsequent remodeling processes will eventually result in successful bone repair. Specifically, some mathematical models are proposed to estimate the time required for (1) the formation immediately after fracture of a fibrin clot, described in terms of a phase transition in a polymerization process, and (2) the onset of EFC which is produced when fibroblasts arising from differentiation of chemotactically recruited mesenchymal stem cells remodel a previous fibrin clot by releasing a collagen matrix over it. An attempt has been made to keep models as simple as possible, so that a explicit dependence of the estimates obtained on relevant biochemical parameters involved is obtained.

Finite-element modeling and analysis in nanomedicine and dentistry

This article aims to provide a brief background to the current applications of finite-element analysis (FEA) in nanomedicine and dentistry. FEA was introduced in orthopedic biomechanics in the 1970s in order to assess the stresses and deformation in human bones during functional loadings and in the design and analysis of implants. Since then, it has been applied with great frequency in orthopedics and dentistry in order to analyze issues such as implant design, bone remodeling and fracture healing, the mechanical properties of biomedical coatings on implants and the interactions at the bone–implant interface. More recently, FEA has been used in nanomedicine to study the mechanics of a single cell and to gain fundamental insights into how the particulate nature of blood influences nanoparticle delivery.

Numerical investigation into blood clotting at the bone-dental implant interface in the presence of an electrical stimulus

The insertion of a dental implant activates a sequence of wound healing events ending with bone formation and implant osseointegration. This sequence starts with the blood coagulation process and the formation of a fibrin network that detains spilt blood. Fibrin formation can be simplified as the kinetic reaction between thrombin and fibrinogen preceding the conversion of fibrinogen into fibrin. Based on experimental observations of the electrical properties of these molecules, we present a hypothesis for the mechanism of a static electrical stimulus in controlling the formation of the blood clot. Specifically, the electrical stimulus increases the fibrin network formation in such a way that a preferential region of higher fibrin density is obtained. This hypothesis is validated by means of a numerical model for the blood clot formation at the bone-dental implant interface. Numerical results compare favorably to experimental observations for blood clotting with and without the static electrical stimulus. It is concluded that the density of the fibrin network depends on the strength of the static electrical stimulus, and that the blood clot formation has a preferential direction of formation in the presence of the electrical signal.

A mathematical model for cell differentiation, as an evolutionary and regulated process

We introduce an approach which allows one to introduce the concept of cell plasticity into models for tissue regeneration. In contrast to most of the recent models for tissue regeneration, cell differentiation is considered a gradual process, which evolves in time and which is regulated by an arbitrary number of parameters. In the current approach, cell differentiation is modelled by means of a differentiation state variable. Cells are assumed to differentiate into an arbitrary number of cell types. The differentiation path is considered as reversible, unless differentiation has fully completed. Cell differentiation is incorporated into the partial differential equations (PDEs), which model the tissue regeneration process, by means of an advection term in the differentiation state space. This allows one to consider the differentiation path of cells, which is not possible if a reaction-like term is used for differentiation. The boundary conditions, which should be specified for the general PDEs, are derived from the flux of the fully non-differentiated cells and from the irreversibility of the fully completed differentiation process. An application of the proposed model for peri-implant osseointegration is considered. Numerical results are compared with experimental data. Potential lines of further development of the present approach are proposed.

Stability analysis for a peri-implant osseointegration model

We investigate stability of the solution of a set of partial differential equations, which is used to model a peri-implant osseointegration process. For certain parameter values, the solution has a 'wave-like' profile, which appears in the distribution of osteogenic cells, osteoblasts, growth factor and bone matrix. This 'wave-like' profile contradicts experimental observations. In our study we investigate the conditions, under which such profile appears in the solution. Those conditions are determined in terms of model parameters, by means of linear stability analysis, carried out at one of the constant solutions of the simplified system. The stability analysis was carried out for the reduced system of PDE's, of which we prove, that it is equivalent to the original system of equations, with respect to the stability properties of constant solutions. The conclusions, derived from the linear stability analysis, are extended for the case of large perturbations. If the constant solution is unstable, then the solution of the system never converges to this constant solution. The analytical results are validated with finite element simulations. The simulations show, that stability of the constant solution could determine the behavior of the solution of the whole system, if certain initial conditions are considered.

A mathematical model of medial collateral ligament repair: migration, fibroblast proliferation and collagen formation

The partial rupture of ligament fibres leads to an injury known as grade 2 sprain. Wound healing after injury consists of four general stages: swelling, release of platelet-derived growth factor (PDGF), fibroblast migration and proliferation and collagen production. The aim of this paper is to present a mathematical model based on reaction-diffusion equations for describing the repair of the medial collateral ligament when it has suffered a grade 2 sprain. We have used the finite element method to solve the equations of this. The results have simulated the tissue swelling at the time of injury, predicted PDGF influence, the concentration of fibroblasts migrating towards the place of injury and reproduced the random orientation of immature collagen fibres. These results agree with experimental data reported by other authors. The model describes wound healing during the 9 days following such injury.

A finite element method approach for the mechanobiological modeling of the osseointegration of a dental implant

The aim of this paper is to introduce a new mathematical model using a mechanobiological approach describing the process of osseointegration at the bone-dental implant interface in terms of biological and mechanical factors and the implant surface. The model has been computationally implemented by using the finite element method. The results show the spatial-temporal patterns distribution at the bone-dental implant interface and demonstrate the ability of the model to reproduce features of the wound healing process such as blood clotting, osteogenic cell migration, granulation tissue formation, collagen-like matrix displacements and new osteoid formation. The model might be used as a methodological basis for designing a dental tool useful to predict the degree of osseointegration of dental implants and subsequent formulation of mathematical models associated with different types of bone injuries and different types of implantable devices.

Computational modelling of biomaterial surface interactions with blood platelets and osteoblastic cells for the prediction of contact osteogenesis

Surface microroughness can induce contact osteogenesis (bone formation initiated at the implant surface) around oral implants, which may result from different mechanisms, such as blood platelet-biomaterial interactions and/or interaction with (pre-)osteoblast cells. We have developed a computational model of implant endosseous healing that takes into account these interactions. We hypothesized that the initial attachment and growth factor release from activated platelets is crucial in achieving contact osteogenesis. In order to investigate this, a computational model was applied to an animal experiment [7] that looked at the effect of surface microroughness on endosseous healing. Surface-specific model parameters were implemented based on in vitro data (Lincks et al. Biomaterials 1998;19:2219-32). The predicted spatio-temporal patterns of bone formation correlated with the histological data. It was found that contact osteogenesis could not be predicted if only the osteogenic response of cells was up-regulated by surface microroughness. This could only be achieved if platelet-biomaterial interactions were sufficiently up-regulated as well. These results confirmed our hypothesis and demonstrate the added value of the computational model to study the importance of surface-mediated events for peri-implant endosseous healing.

Finite element method (FEM), mechanobiology and biomimetic scaffolds in bone tissue engineering

Techniques of bone reconstructive surgery are largely based on conventional, non-cell-based therapies that rely on the use of durable materials from outside the patient's body. In contrast to conventional materials, bone tissue engineering is an interdisciplinary field that applies the principles of engineering and life sciences towards the development of biological substitutes that restore, maintain, or improve bone tissue function. Bone tissue engineering has led to great expectations for clinical surgery or various diseases that cannot be solved with traditional devices. For example, critical-sized defects in bone, whether induced by primary tumor resection, trauma, or selective surgery have in many cases presented insurmountable challenges to the current gold standard treatment for bone repair. The primary purpose of bone tissue engineering is to apply engineering principles to incite and promote the natural healing process of bone which does not occur in critical-sized defects. The total market for bone tissue regeneration and repair was valued at $1.1 billion in 2007 and is projected to increase to nearly $1.6 billion by 2014.Usually, temporary biomimetic scaffolds are utilized for accommodating cell growth and bone tissue genesis. The scaffold has to promote biological processes such as the production of extra-cellular matrix and vascularisation, furthermore the scaffold has to withstand the mechanical loads acting on it and to transfer them to the natural tissues located in the vicinity. The design of a scaffold for the guided regeneration of a bony tissue requires a multidisciplinary approach. Finite element method and mechanobiology can be used in an integrated approach to find the optimal parameters governing bone scaffold performance.In this paper, a review of the studies that through a combined use of finite element method and mechano-regulation algorithms described the possible patterns of tissue differentiation in biomimetic scaffolds for bone tissue engineering is given. Firstly, the generalities of the finite element method of structural analysis are outlined; second, the issues related to the generation of a finite element model of a given anatomical site or of a bone scaffold are discussed; thirdly, the principles on which mechanobiology is based, the principal theories as well as the main applications of mechano-regulation models in bone tissue engineering are described; finally, the limitations of the mechanobiological models and the future perspectives are indicated.

Cell Cultivation on Porous Titanium Implants with Various Structures

The paper presents data on the cultivation of human dermal fibroblasts and rabbit mesenchymal stromal cells on two types of porous titanium implants, i.e., those with irregular pores formed by pressed titanium particles and those with regular pores formed by the cohesion of one-size titanium particles inside the implant. The goal of this study was to determine what type of titanium implant porosity ensured its strongest interaction with cells. Cells were cultivated on implants for 7 days. During this period, they formed a confluent monolayer on the implant surface. Cells grown on titanium implants were monitored by scanning electron microscopy. Fibroblasts interaction with implants depended on the implant porosity structure. On implants with irregular pores cells were more spread. On implants with regular pores fibroblasts enveloped particles and were only occasionally bound with neighboring particles by small outgrowths. There was no tight interaction of particles inside the implant. In implants formed by pressed particles, cells grow not only on surface, but also in the depth of the implant. Thus, we suppose that a tighter interaction of cells with the titanium implant and, supposedly, tissues with the implant in the organism will take place in the variant when the implant structure is formed by pressed titanium particles, i.e., cellular interaction was observed inside the implant. In implants with irregular pores, cells grew both on the surface and in the depth. Thus, cells exhibited more adequate interactions with irregular pore titanium implants in vitro and hopefully the same interaction will be true in tissues after the implantation of the prosthesis into the organism.