|Reference : A Finite Volume Spatial Discretisation for taxis-diffusion-reaction systems with axi-...|
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|Life sciences : Microbiology|
Physical, chemical, mathematical & earth Sciences : Mathematics
|A Finite Volume Spatial Discretisation for taxis-diffusion-reaction systems with axi-symmetry: application to fracture healing|
|Gerisch, Alf [Martin-Luther-Universitat Halle-Wittenberg, Institut fur Numerische Mathematik, 06099 Halle (Saale), Germany > > > >]|
|Geris, Liesbet [K.U. Leuven, Faculty of Engineering, Division of Biomechanics and Engineering Design, Celestijnenlaan 300C, B-3001 Leuven, Belgium > > > >]|
|Advances in Mathematical Modeling of Biological Systems|
|de Vries, G.|
|[en] Taxis-diffusion-reaction model ; axi-symmetry ; numerical method ; finite volume discretisation ; fracture healing|
|[en] 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.
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