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On the mechanics of a growing tumor D. Ambrosi a,*

Summary: On the mechanics of a growing tumor
D. Ambrosi a,*
, F. Mollica b
Dipartimento di Matematica, Politecnico di Torino, corso Duca degli Abruzzi 24, 10129 Torino, Italy
CNR Institute for Technology of Composite Materials, Piazzale Tecchio 80, 80125 Napoli, Italy
Received 14 November 2001; accepted 21 November 2001
(Submitted by K.R. RAJAGOPAL)
In this paper we study tumor growth within the framework of Continuum Mechanics, considering a
tumor as a specific case of a growing soft tissue. Using the notion of multiple natural configurations we
introduce a mechanical description that splits volumetric growth and mechanical response into two sep-
arate contributions. Growth is described as an increase of the mass of the particles of the body and not as
an increase of their number. As tumor growth strongly depends upon the availability of nutrients and on
the presence of chemical signals, such as growth factors, their diffusion through the growing material is
introduced in the description. The model is then applied to describe the homogeneous growth inside a rigid
cylinder, a model mimicking the growth of a ductal carcinoma, and to the growth of a multicell spheroid
fed by a non-homogeneous diffusion of nutrients. In the latter case residual stresses are generated because
the non-uniform distribution of nutrients leads to inhomogeneous growth. 2002 Elsevier Science Ltd.


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


Collections: Mathematics