Angiogenesis in bone fracture healing: a bioregulatory model.

in Journal of Theoretical Biology (2008), 251(1), 137-58

The process of fracture healing involves the action and interaction of many cells, regulated by biochemical and mechanical signals. Vital to a successful healing process is the restoration of a good ... [more ▼]

The process of fracture healing involves the action and interaction of many cells, regulated by biochemical and mechanical signals. Vital to a successful healing process is the restoration of a good vascular network. In this paper, a continuous mathematical model is presented that describes the different fracture healing stages and their response to biochemical stimuli only (a bioregulatory model); mechanoregulatory effects are excluded here. The model consists of a system of nonlinear partial differential equations describing the spatiotemporal evolution of concentrations and densities of the cell types, extracellular matrix types and growth factors indispensable to the healing process. The model starts after the inflammation phase, when the fracture callus has already been formed. Cell migration is described using not only haptokinetic, but also chemotactic and haptotactic influences. Cell differentiation is controlled by the presence of growth factors and sufficient vascularisation. Matrix synthesis and growth factor production are controlled by the local cell and matrix densities and by the local growth factor concentrations. Numerical simulations of the system, using parameter values based on experimental data obtained from literature, are presented. The simulation results are corroborated by comparison with experimental data from a standardised rodent fracture model. The results of sensitivity analyses on the parameter values as well as on the boundary and initial conditions are discussed. Numerical simulations of compromised healing situations showed that the establishment of a vascular network in response to angiogenic growth factors is a key factor in the healing process. Furthermore, a correct description of cell migration is also shown to be essential to the prediction of realistic spatiotemporal tissue distribution patterns in the fracture callus. The mathematical framework presented in this paper can be an important tool in furthering the understanding of the mechanisms causing compromised healing and can be applied in the design of future fracture healing experiments. [less ▲]

Mathematical modeling of bone regeneration during fracture healing and implant osseointegration

Doctoral thesis (2007)

Despite the extensive body of literature on bone regeneration, many questions remain on e.g. the regulatory mechanisms and potential treatment strategies of pathological regeneration cases. The hypothesis ... [more ▼]

Despite the extensive body of literature on bone regeneration, many questions remain on e.g. the regulatory mechanisms and potential treatment strategies of pathological regeneration cases. The hypothesis underlying this work states that mathematical models of bone regeneration can make a substantial contribution to this domain by proposing pathological regeneration mechanisms and designing therapies, which can subsequently be tested experimentally. In the first part of this work, existing mechanoregulatory and bioregulatory models of bone regeneration are implemented and applied to both implant osseointegration and fracture healing set-ups. A quantitative comparison with experimental results is performed. Thorough sensitivity analyses are carried out to assess the influence of various modelling aspects on the simulation outcome. Shortcomings of these models are identified and suggestions for improvements are made. In the second part of this work, a novel bioregulatory model of bone regeneration is developed in which several of the previously defined shortcomings are addressed. This model includes key aspects of the regeneration process such as intramembranous and endochondral ossification, angiogenesis and directed cell motion. The results obtained with this novel model are corroborated both qualitatively and quantitatively by comparison with experimental data for normal fracture healing. Cases of pathological fracture healing are simulated and experimentally testable therapeutic strategies are implemented. The last part of this work describes the establishment of a mathematical framework, based on the previously developed bioregulatory model, in which the regulatory influence of both biological and mechanical factors is combined. This is the first model of bone regeneration in which the coupling between mechanical loading and angiogenesis is made in an explicit and mechanistic manner. Several examples are given to illustrate the added value of this approach in simulating normal and pathological bone regeneration. In summary, this work demonstrates the potential of mathematical models in advancing the knowledge on bone regeneration and designing treatment strategies for pathological healing cases. [less ▲]

The effect of mechanical loading on peri-implant osteogenesis

in proceedings of the 17th annual meeting of the Dutch society for calcium and bone metabolism (2007)

Influence of controlled immediate loading and implant design on peri-implant bone formation.

in Journal of Clinical Periodontology (2007), 34(2), 172-81

AIM: Tissue formation at the implant interface is known to be sensitive to mechanical stimuli. The aim of the study was to compare the bone formation around immediately loaded versus unloaded implants in ... [more ▼]

AIM: Tissue formation at the implant interface is known to be sensitive to mechanical stimuli. The aim of the study was to compare the bone formation around immediately loaded versus unloaded implants in two different implant macro-designs. MATERIAL AND METHODS: A repeated sampling bone chamber with a central implant was installed in the tibia of 10 rabbits. Highly controlled loading experiments were designed for a cylindrical (CL) and screw-shaped (SL) implant, while the unloaded screw-shaped (SU) implant served as a control. An F-statistic model with alpha=5% determined statistical significance. RESULTS: A significantly higher bone area fraction was observed for SL compared with SU (p<0.0001). The mineralized bone fraction was the highest for SL and significantly different from SU (p<0.0001). The chance that osteoid- and bone-to-implant contact occurred was the highest for SL and significantly different from SU (p<0.0001), but not from CL. When bone-to-implant contact was observed, a loading (SL versus SU: p=0.0049) as well as an implant geometry effect (SL versus CL: p=0.01) was found, in favour of the SL condition. CONCLUSIONS: Well-controlled immediate implant loading accelerates tissue mineralization at the interface. Adequate bone stimulation via mechanical coupling may account for the larger bone response around the screw-type implant compared with the cylindrical implant. [less ▲]

Impact of implant geometry and loading on early bone formation, Clinical Oral Implants Research

in Clinical Oral Implants Research (2007), 18(5), 71-72

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 fracture healing in mice: comparison between experimental data and numerical simulation results.

in Medical & Biological Engineering & Computing (2006), 44(4), 280-9

The combined use of experimental and mathematical models can lead to a better understanding of fracture healing. In this study, a mathematical model, which was originally established by Bailon-Plaza and ... [more ▼]

The combined use of experimental and mathematical models can lead to a better understanding of fracture healing. In this study, a mathematical model, which was originally established by Bailon-Plaza and van der Meulen (J Theor Biol 212:191-209, 2001), was applied to an experimental model of a semi-stabilized murine tibial fracture. The mathematical model was implemented in a custom finite volumes code, specialized in dealing with the model's requirements of mass conservation and non-negativity of the variables. A qualitative agreement between the experimentally measured and numerically simulated evolution in the cartilage and bone content was observed. Additionally, an extensive parametric study was conducted to assess the influence of the model parameters on the simulation outcome. Finally, a case of pathological fracture healing and its treatment by administration of growth factors was modeled to demonstrate the potential therapeutic value of this mathematical model. [less ▲]

A novel mathematical model to simulate and predict tissue regeneration

in Middleton, J.; Jones, M. L.; Shrive, N. (Eds.) Proceedings of the 7th international symposium on Computer Methods in Biomechanics and Biomedical Engineering (2006)

Numerical simulation and experimental validation of murine fracture healing

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