References of "Gerisch, Alf"
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See detailA hybrid bioregulatory model of angiogenesis during bone fracture healing
Peiffer, Veronique; Gerisch, Alf; Vandepitte, Dirk et al

in Biomechanics & Modeling in Mechanobiology (2011), 10(3), 383-395

Bone fracture healing is a complex process in which angiogenesis or the development of a blood vessel net work plays a crucial role. In this paper, a mathematicalmodel is presented that simulates the ... [more ▼]

Bone fracture healing is a complex process in which angiogenesis or the development of a blood vessel net work plays a crucial role. In this paper, a mathematicalmodel is presented that simulates the biological aspects of fracture healing including the formation of individual blood vessels. The model consists of partial differential equations, several of which describe the evolution in density of the most important cell types, growth factors, tissues and nutrients. The other equations determine the growth of blood vessels as a result of themovement of leading endothelial (tip) cells. Branching and anastomoses are accounted for in the model. The model is applied to a normal fracture healing case and subjected to a sensitivity analysis. The spatiotemporal evolution of soft tissues and bone, as well as the development of a blood vessel network are corroborated by comparison with experimental data. Moreover, this study shows that the proposed mathematical framework can be a useful tool in the research of impaired healing and the design of treatment strategies. [less ▲]

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See detailMathematical Modeling in Wound Healing, Bone Regeneration and Tissue Engineering
Geris, Liesbet ULg; Gerisch, Alf; Schugart, Richard C.

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 ▲]

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See detailA hybrid model for the simulation of angiogenesis during bone fracture healing
Geris, Liesbet ULg; Peiffer, Veronique; Gerisch, Alf et al

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

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See detailAngiogenesis in bone fracture healing: a bioregulatory model.
Geris, Liesbet ULg; Gerisch, Alf; Sloten, Jos Vander et al

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 ▲]

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See detailA Finite Volume Spatial Discretisation for taxis-diffusion-reaction systems with axi-symmetry: application to fracture healing
Gerisch, Alf; Geris, Liesbet ULg

in Deutsch, A.; Brusch, L.; Byrne, H. (Eds.) et al Advances in Mathematical Modeling of Biological Systems (2007)

We consider the numerical simulation of a time-dependent taxis-diffusion-reaction model of fracture healing in mice using the method of lines. The partial differential equation problem has an axi ... [more ▼]

We consider the numerical simulation of a time-dependent taxis-diffusion-reaction model of fracture healing in mice using the method of lines. The partial differential equation problem has an axi-symmetric structure and this is employed to properly reduce the model to an equivalent problem in two-dimensional (2D) space leading subsequently to an efficient spatial discretisation. Special care is given to respect conservation of mass and the non-negativity of the solution. The numerical simulation results are contrasted to those obtained from a simplistic reduction of the axi-symmetric model to 2D space (at the same computational cost).We observe quantitative and qualitative differences. [less ▲]

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See detailMathematical modeling of fracture healing in mice: comparison between experimental data and numerical simulation results.
Geris, Liesbet ULg; Gerisch, Alf; Maes, Christa et al

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 ▲]

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See detailEfficient and robust simulation of tissue differentiation in fracture healing
Gerisch, Alf; Geris, Liesbet ULg

in Proceedings of the European Conference on Mathematical and Theoretical Biology (2005)

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See detailTissue differentiation during fracture healing in mice: comparison of an experimental and numerical study
Geris, Liesbet ULg; Gerisch, Alf; Maes, Christa et al

in Proceedings of the first thematic workshop of the European Society of Biomechanics on Mechanobiology of Cells and Tissue Engineering (2005)

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