Occurrence and Treatment of Bone Atrophic Non-Unions Investigated by an Integrative Approach

in PLoS Computational Biology (2010), 6(9), 1000915

Recently developed atrophic non-union models are a good representation of the clinical situation in which many nonunions develop. Based on previous experimental studies with these atrophic non-union ... [more ▼]

Recently developed atrophic non-union models are a good representation of the clinical situation in which many nonunions develop. Based on previous experimental studies with these atrophic non-union models, it was hypothesized that in order to obtain successful fracture healing, blood vessels, growth factors, and (proliferative) precursor cells all need to be present in the callus at the same time. This study uses a combined in vivo-in silico approach to investigate these different aspects (vasculature, growth factors, cell proliferation). The mathematical model, initially developed for the study of normal fracture healing, is able to capture essential aspects of the in vivo atrophic non-union model despite a number of deviations that are mainly due to simplifications in the in silico model. The mathematical model is subsequently used to test possible treatment strategies for atrophic non-unions (i.e. cell transplant at post-osteotomy, week 3). Preliminary in vivo experiments corroborate the numerical predictions. Finally, the mathematical model is applied to explain experimental observations and identify potentially crucial steps in the treatments and can thereby be used to optimize experimental and clinical studies in this area. This study demonstrates the potential of the combined in silico-in vivo approach and its clinical implications for the early treatment of patients with problematic fractures. [less ▲]

Cross-talk Modeling of Wnt, BMP and ERK Pathways during Osteochondrogenic Differentiation

in Proceedings of the TERMIS-EU meeting (2010, June)

The biology of orthodontic tooth movement: a mathematical model

in Middleton, J.; Jacobs, C.; Walker, B. (Eds.) et al 9th International symposium on Computer Methods in Biomechanics and Biomedical Engineering (2010, February)

Mathematical Modeling in Wound Healing, Bone Regeneration and Tissue Engineering

in Acta Biotheoretica (2010), 58(4), 355-367

The processes of wound healing and bone regeneration and problems in tissue engineering have been an active area for mathematical modeling in the last decade. Here we review a selection of recent models ... [more ▼]

The processes of wound healing and bone regeneration and problems in tissue engineering have been an active area for mathematical modeling in the last decade. Here we review a selection of recent models which aim at deriving strategies for improved healing. In wound healing, the models have particularly focused on the inflammatory response in order to improve the healing of chronic wound. For bone regeneration, the mathematical models have been applied to design optimal and new treatment strategies for normal and specific cases of impaired fracture healing. For the field of tissue engineering, we focus on mathematical models that analyze the interplay between cells and their biochemical cues within the scaffold to ensure optimal nutrient transport and maximal tissue production. Finally, we briefly comment on numerical issues arising from simulations of these mathematical models. [less ▲]

In vivo, in vitro, in silico: computational tools for tissue engineering

in proceedings of the 2nd International Conference on Innovation for Sustainable Production i-SUP (2010)

Mathematical modelling of cell aggregates for bone tissue engineering using continuum methods

in Middleton, J.; Jacobs, C.; Walker, B. (Eds.) et al 9th International symposium on Computer Methods in Biomechanics and Biomedical Engineering (2010)

Numerical simulation of two-dimensional and three-dimensional axisymmetric advection-diffusion systems with complex geometries using finite-volume methods

in Proceedings : Mathematical, Physical & Engineering Sciences (2010), 466(2118), 1621-1643

A finite-volume method has been developed that can deal accurately with complicated, curved boundaries for both two-dimensional and three-dimensional axisymmetric advection-diffusion systems. The ... [more ▼]

A finite-volume method has been developed that can deal accurately with complicated, curved boundaries for both two-dimensional and three-dimensional axisymmetric advection-diffusion systems. The motivation behind this is threefold. Firstly, the ability to model the correct geometry of a situation yields more accurate results. Secondly, smooth geometries eliminate corner singularities in the calculation of, for example, mechanical variables and thirdly, different geometries can be tested for experimental applications. An example illustrating each of these is given: fluid carrying a dye and rotating in an annulus, bone fracture healing in mice, and using vessels of different geometry in an ultracentrifuge. [less ▲]

In silico design of treatment strategies in wound healing and bone fracture healing

in Philosophical Transactions : Mathematical, Physical & Engineering Sciences (2010), 368(1920), 2683-2706

Wound and bone fracture healing are natural repair processes initiated by trauma. Over the last decade, many mathematical models have been established to investigate the healing processes in silico, in ... [more ▼]

Wound and bone fracture healing are natural repair processes initiated by trauma. Over the last decade, many mathematical models have been established to investigate the healing processes in silico, in addition to ongoing experimental work. In recent days, the focus of the mathematical models has shifted from simulation of the healing process towards simulation of the impaired healing process and the in silico design of treatment strategies. This review describes the most important causes of failure of the wound and bone fracture healing processes and the experimental models and methods used to investigate and treat these impaired healing cases. Furthermore, the mathematical models that are described address these impaired healing cases and investigate various therapeutic scenarios in silico. Examples are provided to illustrate the potential of these in silico experiments. Finally, limitations of the models and the need for and ability of these models to capture patient specificity and variability are discussed. [less ▲]

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 ▲]