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Digital Object Identifier (DOI): 10.1007/s00285-003-0238-2
 

Summary: Digital Object Identifier (DOI):
10.1007/s00285-003-0238-2
J. Math. Biol. 48, 477­499 (2004)
Mathematical Biology
D. Ambrosi · F. Mollica
The role of stress in the growth of a multicell spheroid
Received: 19 February 2003 / Revised version: 5 August 2003 /
Published online: 2 December 2003 ­ c Springer-Verlag 2003
Abstract. Ratherrecentexperimentalresultsdemonstratethenon­negligibleroleofmechan-
ical stress in the growth of a multicell spheroid. In this paper we discuss a theoretical frame-
work for volumetric growth suitable for modeling the growth of soft tissues exhibiting the
properties of a solid. After a proper kinematic decomposition, balance equations for mass,
momentum and energy are discussed together with constitutive relationships. The mathe-
matical model is then applied to avascular tumor growth. We show by numerical simulation
that, under assumption of spherical symmetry, the mathematical model is able to reproduce
the experimental data with a satisfying qualitative agreement.
Introduction
It is well known that macroscopic stress, the mechanical mutual interaction among
cells observed at the macroscale, influences the growth of soft tissues such as arter-
ies, blood tissue, the heart, the trachea and tendons [23]. It is therefore rather natural

  

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

 

Collections: Mathematics