On the mechanics of a growing tumor

Abstract

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 separate 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.