Biomechanic approach of a growing tumor

• Based on the notion of multiple natural configurations a mechanical description is introduced.
• The availability of nutrients and their diffusion through the growing material are considered.
• A mathematical statement of the problem is written and a numerical algorithm is implemented.
• In order to validate the model, a comparison with experimental data is reported.

The growth and remodeling of soft tissues depend on a number of biological, chemical and mechanical factors, including the stress state. Tumor growth within the framework of continuum mechanics is studied, understanding the tumor as a continuous solid body. Based on the notion of multiple natural configurations, a mechanical description is introduced, which splits volumetric growth and mechanical response into two separate contributions. Growth is described as an increase of the mass of the cells of the body and not as an increase of their number. Besides the body does not rotate, but rather it is deformed varying its mass. In the model the availability of nutrients and their diffusion through the growing material are considered. Some different situations of growing tumors are studied and numerical solutions of the problems are given. The material parameters used in the computation were chosen from realistic tumor measurements and the results are compared with experimental works.