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Angiogenesis, the formation of new bloods vessels from the existing vasculature, is a process that is essential during development and regeneration of tissues, and that plays a major role in diseases like cancer. Computational models have been designed to obtain a better understanding of the mechanisms behind angiogenesis. In this paper we review computational models of sprouting angiogenesis. These models can be subdivided into three categories: models that mainly focus on tip cell migration, models that make a distinction between the role of tip cells and stalk cells, and models that consider cell shape dynamics. Many models combine dis- crete modeling of individual cells with continuous modeling of the extracellular matrix (ECM) and diffusing solutes, in this way resulting in a hybrid model. We discuss their merits in unrav- eling the role of certain factors for vascular network formation, such as the role of (chemotactic, haptotactic, contact) guidance cues in the dynamics and morphology of vascular network forma- tion, and the role of cell-cell interactions that govern tip cell selection and phenotypic changes in general. At the same time, we identify a need for the inclusion of cell mechanical principles in models of angiogenesis, in particular for the description of cell migration, cell-matrix and cell-cell interaction, as the generation of cellular forces is key to cell migration. To further underline this we review models of single cell migration that incorporate such principles, which could be the starting point for formulating novel models of angiogenesis that respect the fundamental laws of classical mechanics at the cell level. As the generation of cellular forces is strongly mediated by pro-angiogenic signals, such models must couple cell mechanical principles to molecular signal- ing into multiscale mechanochemical models of angiogenesis. Finally, a tight coupling between models and experiments will be required to facilitate model improvements and the generation of novel insights on the regulation of angiogenesis. [ABSTRACT FROM AUTHOR]

The objective of this study was to see whether a mathematical model of fracture healing was able to mimic bone formation around an unloaded screw-shaped titanium implant as it is well-believed that both processes exhibit many biological similarities. This model describes the spatio-temporal evolution of cellular activities, ranging from mesenchymal stem cell migration, proliferation, differentiation to bone formation, which are initiated and regulated by the growth factors present at the peri-implant site. For the simulations, a finite volume code was used and adequate initial and boundary conditions were applied. Two sets of analyses have been performed, in which either initial and boundary condition or model parameter values were changed with respect to the fracture healing model parameter values. For a number of combinations, the spatio-temporal evolution of bone density was well-predicted. However reducing cell proliferation rate and increasing osteoblast differentiation and osteogenic growth factor synthesis rates, the simulation results were in agreement with the experimental data. [ABSTRACT FROM AUTHOR]

While mathematical models are able to capture essential aspects of biological processes like fracture healing and distraction osteogenesis, their predictive capacity in peri-implant osteogenesis remains uninvestigated. We tested the hypothesis that a mechano-regulatory model has the potential to predict bone regeneration around implants. In an in vivo bone chamber set-up allowing for controlled implant loading (up to 90 µm axial displacement), bone tissue formation was simulated and compared qualitatively and quantitatively with histology. Furthermore, the model was applied to simulate excessive loading conditions. Corresponding to literature data, implant displacement magnitudes larger than 90 µm predicted the formation of fibrous tissue encapsulation of the implant. In contradiction to findings in orthopedic implant osseointegration, implant displacement frequencies higher than 1 Hz did not favor the formation of peri-implant bone in the chamber. Additional bone chamber experiments are needed to test these numerical predictions. [ABSTRACT FROM AUTHOR]

A finite element (FE) numerical model of an oral implant was implemented with the theory of bone adaptation to predict the response over time of the bone tissue to the implant and to explain a phenomenon regarding the clinical situation: the bone loss due to an overload stress. An adaptation routine, based on Beaupré theory, was developed to interface with the FE packages. The value of the mechanical stimulus, corresponding to the overload stress, was evaluated by applying the Taylor crack propagation theory. The predictions obtained by the numerical analyses demonstrated that the overload resorption is blocked only with spongy bone of 'good quality'. [ABSTRACT FROM AUTHOR]

Nowadays, there is a growing consensus on the impact of mechanical loading on bone biology. A bone chamber provides a mechanically isolated in vivo environment in which the influence of different parameters on the tissue response around loaded implants can be investigated. This also provides data to assess the feasibility of different mechanobiological models that mathematically describe the mechanoregulation of tissue differentiation. Before comparing numerical results to animal experimental results, it is necessary to investigate the influence of the different model parameters on the outcome of the simulations. A 2D finite element model of the tissue inside the bone chamber was created. The differentiation models developed by Prendergast, et al. ["Biophysical stimuli on cells during tissue differentiation at implant interfaces", Journal of Biomechanics , 30 (6), (1997), 539-548], Huiskes et al. ["A biomechanical regulatory model for periprosthetic fibrous-tissue differentiation", Journal of Material Science: Materials in Medicine , 8 (1997) 785-788] and by Claes and Heigele ["Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing", Journal of Biomechanics , 32 (3), (1999) 255-266] were implemented and integrated in the finite element code. The fluid component in the first model has an important effect on the predicted differentiation patterns. It has a direct effect on the predicted degree of maturation of bone and a substantial indirect effect on the simulated deformations and hence the predicted phenotypes of the tissue in the chamber. Finally, the presence of fluid also causes time-dependent behavior. Both models lead to qualitative and quantitative differences in predicted differentiation patterns. Because of the different nature of the tissue phenotypes used to describe the differentiation processes, it is however hard to compare both models in terms of their validity. [ABSTRACT FROM AUTHOR]

Inappropriate implant loading has been suggested as one of the most important factors for late failures of endosseous oral implants. In order to quantify peri-implant bone stresses and strains for a controlled load applied during an animal experiment, an anatomical finite element model was built. Marginal bone loss that occurred during the animal experiment could only partially be related to overload. Furthermore, it is hypothesised that relative motion between bone and implant could have also played a role in the marginal bone response. In order to further explore the relation between marginal bone resorption and overload, a computer algorithm was developed that simulates overload-induced marginal bone loss. It was found that marginal bone resorption can be arrested due to a redistribution of the peri-implant bone stresses. [ABSTRACT FROM AUTHOR]

This paper describes a methodology that allows in vitro and in vivo quantification and qualification of forces on oral implants. Strain gauges are adapted to the outer surface of 5·5 and 7 mm standard abutments (Brånemark System®, Nobel Biocare, Sweden). The readings of the strain gauges are transformed into a numerical representation of the normal force and the bending moment around the X- and Y-axis. The hardware and the software of the 3D measuring device based on the strain gauge technology is explained and its accuracy and reliability tested. The accuracy level for axial forces and bending moments is 9.72 N and 2.5 N·cm, respectively, based on the current techniques for strain gauged abutments. As an example, an in vivo force analysis was performed in a patient with a full fixed prosthesis in the mandible. Since axial loads of 450 N and bending moments of 70 N·cm were recorded, it was concluded that the accuracy of the device falls well within the scope of our needs. Nevertheless, more in vivo research is needed before well defined conclusions can be drawn and strategies developed to improve the biomechanics of oral implants. [ABSTRACT FROM AUTHOR]

This study investigated the influence of prosthesis material on the distribution and magnitude of load on oral implants carrying a fixed prosthesis by an in vivo quantification and qualification of this load. Eight patients with 9 three-unit prostheses on 2 implants and 3 patients with 4 two-unit fixed prostheses on 2 implants were selected. Both metal and acrylic resin prostheses were made for the patients. Strain-gauged abutments were used to measure the load on the supporting implants during controlled application of 50 N on selected positions. A significantly better distribution of bending moments was observed with metal prostheses compared to resin prostheses. No other difference was noted. It was concluded that there may be a clinically significant increased risk of bending overload with acrylic long-span prostheses or acrylic resin prostheses with extensions. [ABSTRACT FROM AUTHOR]

The article investigates the influence of mechanical parameters on the phenomena of tissue differentiation, appositional bone growth and de nova bone formation around a cylindrical turned acid-etched titanium immediately loaded implant. A description is given on the highly controlled immediate loading experiments. The degree of tissue differentiation in the bone chamber, expressed by the variable bone and osteoid volume fraction, was found to be influenced by the duration of immediate loading.

The article examines the effect of various degrees of implant micromotion on the tissue differentiation around immediately loaded titanium implants. The experiments involving the tibia of rabbits are described. The smaller total tissue volume for the unloaded condition is probably due to the fact that implant motion initially helped to spread blood and cells around in the bone chamber.