Reference : A Finite Volume Spatial Discretisation for taxis-diffusion-reaction systems with axi-...
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A Finite Volume Spatial Discretisation for taxis-diffusion-reaction systems with axi-symmetry: application to fracture healing
Gerisch, Alf mailto [Martin-Luther-Universitat Halle-Wittenberg, Institut fur Numerische Mathematik, 06099 Halle (Saale), Germany > > > >]
Geris, Liesbet mailto [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
Deutsch, A.
Brusch, L.
Byrne, H.
de Vries, G.
Herzel, H.
[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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