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Mathematical Models and Methods in Applied Sciences Vol. 12, No. 5 (2002) 737754
 

Summary: Mathematical Models and Methods in Applied Sciences
Vol. 12, No. 5 (2002) 737754
c World Scientific Publishing Company
ON THE CLOSURE OF MASS BALANCE MODELS
FOR TUMOR GROWTH
D. AMBROSI and L. PREZIOSI
Dipartimento di Matematica, Politecnico di Torino,
Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
ambrosi@calvino.polito.it
preziosi@polito.it
Received 27 September 2001
Revised 7 January 2002
Communicated by N. Bellomo
Mass balance equations typically adopted to describe tumor growth are to be closed by
introducing a suitable velocity field. The first part of this paper is devoted to a critical
review of some approaches devised to this aim in the relevant literature. In the second
part we start from the observation that the phenomenological description of a tumor
spheroid suggests to model it as a growing and deformable porous material. The concept
of volume fraction and the essentials of the mechanics of multicomponent continua are
then introduced and applied to the problem at hand. The system of equations regulating

  

Source: Ambrosi, Davide - Dipartimento di Matematica, Politecnico di Torino
Preziosi, Luigi - Dipartimento di Matematica, Politecnico di Torino

 

Collections: Mathematics