A mathematical model of bone regeneration including angiogenesis: relevance for tissue engineering strategies

in European Cells and Materials (2008), Vol. 14(Suppl. 1,), 29

Mathematical modelling of bone regeneration including angiogenesis: design of treatment strategies for atrophic non-unions

in Proceedings of the 54th Annual Meeting of the Orthopaedic Research Society (2008)

Modelling of peri-implant osteogenesis by means of a fracture healing mode

in Journal of Biomechanics (2008), 41(S1), 289

Application of mechanoregulatory models to simulate peri-implant tissue formation in an in vivo bone chamber

in Journal of Biomechanics (2008), 41(1), 145-154

Several mechanoregulatory tissue differentiation models have been proposed over the last decade. Corroboration of these models by comparison with experimental data is necessary to determine their ... [more ▼]

Several mechanoregulatory tissue differentiation models have been proposed over the last decade. Corroboration of these models by comparison with experimental data is necessary to determine their predictive power. So far, models have been applied with various success rates to different experimental set-ups investigating mainly secondary fracture heating. In this study, the mechanoregulatory models are applied to simulate the implant osseointegration process in a repeated sampling in vivo bone chamber, placed in a rabbit tibia. This bone chamber provides a mechanically isolated environment to study tissue differentiation around titanium implants loaded in a controlled manner. For the purpose of this study, bone formation around loaded cylindrical and screw-shaped implants was investigated. Histologically, no differences were found between the two implant geometries for the global amount of bone formation in the entire chamber. However, a significantly larger amount of bone-to-implant contact was observed for the screw-shaped implant compared to the cylindrical implant. In the simulations, a larger amount of bone was also predicted to be in contact with the screw-shaped implant. However, other experimental observations could not be predicted. The simulation results showed a distribution of cartilage, fibrous tissue and (im)mature bone, depending on the mechanoregulatory model that was applied. In reality, no cartilage was observed. Adaptations to the differentiation models did not lead to a better correlation between experimentally observed and numerically predicted tissue distribution patterns. The hypothesis that the existing mechanoregulatory models were able to predict the patterns of tissue formation in the in vivo bone chamber could not be fully sustained. (c) 2007 Elsevier Ltd. All rights reserved. [less ▲]

Mathematical modelling of growth factor induced bone regeneration: importance of angiogenesis

in Tissue Engineering (2007)

Bone Formation around Immediately Loaded Implants: a Bone Chamber Model

in Proceedings of the 84th General Session & Exhibition of the IADR (2006)

Mathematical modeling of bone regeneration including the angiogenic process

in Journal of Biomechanics (2006), 39(S1), 411-412

Numerical simulation and experimental validation of murine fracture healing

in Proceedings of the fifth national day on biomedical engineering (2005)

De invloed van mechanische parameters op de weefselrespons bij immediaat belaste titanium implantaten

in Proceedings van het Congres Verbond der Vlaamse Tandartsen (2005)

Reliable and efficient numerical simulation of a model of tissue differentiation in a bone chamber model

in Bischoff, G. (Ed.) Micro- and Nanostructures of Biological Systems (2005)

For the study of peri-implant tissue differentiation, a repeated sampling bone chamber has been developed. Mathematical models, which describe tissue differentiation, help to gain insight into the ... [more ▼]

For the study of peri-implant tissue differentiation, a repeated sampling bone chamber has been developed. Mathematical models, which describe tissue differentiation, help to gain insight into the processes taking place in the chamber. We consider here the numerical solution of a taxis-diffusion-reaction partial differential equation model. The general approach is the method of lines and we pay special attention to transfer qualitative features of the solution to the numerical approximation. These features are the conservation of mass principle and the nonnegativity of concentration values. This is achieved by following the finite volume idea and by employing positivity preserving spatial discretization, respectively. An instructive example is given. The time integration is performed with ROWMAP, a suitable implicit time integration method with time step size control. Altogether, this yields a reliable and efficient numerical solution technique. A numerical simulation of the tissue differentiation process in the chamber is presented and discussed. [less ▲]