Contribution to collective works (Parts of books)
Reliable and efficient numerical simulation of a model of tissue differentiation in a bone chamber model
Gerisch, A.; Geris, Liesbet; Van Oosterwyck, Hans et al.
2005In Bischoff, G. (Ed.) Micro- and Nanostructures of Biological Systems
 

Files


Full Text
Nano2004-Gerisch-final.pdf
Author postprint (307.69 kB)
Request a copy

All documents in ORBi are protected by a user license.

Send to



Details



Abstract :
[en] For the study of peri-implant tissue differentiation, a repeated sampling bone chamber has been developed. Mathematical models, which describe tissue differentiation, help to gain insight into the processes taking place in the chamber. We consider here the numerical solution of a taxis-diffusion-reaction partial differential equation model. The general approach is the method of lines and we pay special attention to transfer qualitative features of the solution to the numerical approximation. These features are the conservation of mass principle and the nonnegativity of concentration values. This is achieved by following the finite volume idea and by employing positivity preserving spatial discretization, respectively. An instructive example is given. The time integration is performed with ROWMAP, a suitable implicit time integration method with time step size control. Altogether, this yields a reliable and efficient numerical solution technique. A numerical simulation of the tissue differentiation process in the chamber is presented and discussed.
Disciplines :
Biochemistry, biophysics & molecular biology
Computer science
Mechanical engineering
Author, co-author :
Gerisch, A.
Geris, Liesbet  ;  Université de Liège - ULiège > Département d'aérospatiale et mécanique > Génie biomécanique
Van Oosterwyck, Hans
Vander Sloten, Jos
Weiner, R.
Language :
English
Title :
Reliable and efficient numerical simulation of a model of tissue differentiation in a bone chamber model
Publication date :
2005
Main work title :
Micro- and Nanostructures of Biological Systems
Editor :
Bischoff, G.
ISBN/EAN :
3-8322-3868-9
Pages :
60-76
Available on ORBi :
since 26 August 2010

Statistics


Number of views
30 (2 by ULiège)
Number of downloads
0 (0 by ULiège)

Bibliography


Similar publications



Contact ORBi