A hybrid model for the simulation of angiogenesis during bone fracture healing

in Proceedings of the 17th conference of the European Society of Biomechanics (2010)

Crosstalk Modeling of Wnt, BMP and ERK Pathways during osteochondrogenic differentiation

in proceedings of the International Symposium on Biomechanics and Biology of Bone Regeneration “From Functional Assessment To Guided Tissue Formation (2009, November)

The in vitro engineering of tissues may be achieved by mimicking in vivo tissue development. Although multiple skeletal tissue engineering applications already exist, the underlying mechanisms at protein ... [more ▼]

The in vitro engineering of tissues may be achieved by mimicking in vivo tissue development. Although multiple skeletal tissue engineering applications already exist, the underlying mechanisms at protein level are often poorly understood. Growth factors and protein pathways precisely navigate mesenchymal stem cells trough the correct cascades. A detailed understanding of these cascades will enable us to develop efficient and robust production methods, which are required for large scale tissue engineering applications. Multiple studies hypothesize that the Wnt/β-catenin pathway acts as a switching mechanism to determine the differential fate of esenchymal cells in osteoblasts or chondrocytes during skeletogenesis. The concentration of β-catenin is a key factor in this mechanism. Wnt upregulates the productionof β-catenin which in turn upregulates Runx2 and downregulates Sox9. High concentrations of Runx2 relative to Sox9 lead to osteoblasts, while the opposite situation leads to chondrocytes. Crosstalks of the Wnt pathway with other pathways such as that of BMP and ERK expand the amount of factors that can influence β-catenin, turning the linear signaling cascade into a complex network with multiple starting conditions. A mathematical model was derived from literature describing the pathways of BMP, Wnt and ERK as well as various crosstalks between these pathways that were suggested in literature. CellDesigner™ was used to formulate, solve and visualize the Ordinary Differential Equations describing the temporal evolution of the various model constituents. Multiple starting conditions (various concentrations of BMP, Wnt and ERK) were examined to clarify the crosstalk effect. Modeling various crosstalks proposed in literature resulted in a mutual inhibitory effect between Wnt and BMP signaling, an effect independently described in literature. Experiments are ongoing to corroborate the model predictions. [less ▲]

Mathematical modeling of bone regeneration during fracture healing

in proceedings of the National Conference on Theoretical and Applied Mechanics (2009)

The biology of bone formation in orthodontic tooth movement: a mathematical model

in Proceedings of the International Conference on Mathematical Biology 2009 (2009)

In silico biology of bone modelling and remodelling: regeneration.

in Philosophical Transactions : Mathematical, Physical & Engineering Sciences (2009), 367(1895), 2031-53

Bone regeneration is the process whereby bone is able to (scarlessly) repair itself from trauma, such as fractures or implant placement. Despite extensive experimental research, many of the mechanisms ... [more ▼]

Bone regeneration is the process whereby bone is able to (scarlessly) repair itself from trauma, such as fractures or implant placement. Despite extensive experimental research, many of the mechanisms involved still remain to be elucidated. Over the last decade, many mathematical models have been established to investigate the regeneration process in silico. The first models considered only the influence of the mechanical environment as a regulator of the healing process. These models were followed by the development of bioregulatory models where mechanics was neglected and regeneration was regulated only by biological stimuli such as growth factors. The most recent mathematical models couple the influences of both biological and mechanical stimuli. Examples are given to illustrate the added value of mathematical regeneration research, specifically in the in silico design of treatment strategies for non-unions. Drawbacks of the current continuum-type models, together with possible solutions in extending the models towards other time and length scales are discussed. Finally, the demands for dedicated and more quantitative experimental research are presented. [less ▲]

Modelling the early phases of bone regeneration around an endosseous oral implant

in Computer Methods in Biomechanics & Biomedical Engineering (2009), 12(4), 459-468

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 ... [more ▼]

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. [less ▲]

Mathematical modelling of atrophic non-union and its treatment

in Proceedings of the International symposium on Biomechanics and Biology of Bone Healing (2008)

Development of a mechanobiological model of bone formation in orthodontic tooth movement

in Proceedings of the European Conference on Mathematical and Theoretical Biology (2008)

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)