Towards the continuum‐mechanical modelling of metastatic tumour growth in the brain

Abstract

The growth of metastases in the brain increases the state of stress, create leaky blood vessels and disrupt regular brain cells. Essential steps during the development of metastases are the infiltration of the tissue, the nutrient-dependent growth and the stimulation of blood-vessel sprouting. A promising medical treatment can be obtained by the direct infusion of a therapeutic solution into the tissue. Besides experiments, computational models can improve the understanding of brain metastases. In this regard, the liquid-saturated brain tissue represents a porous material. Therefore, the framework of the Theory of Porous Media (TPM) provides an excellent tool for its description. The continuum-mechanical theory of a multi-constituent model and mechanisms of metastases growth are presented in this contribution.

Continuum‐mechanical modelling of apoptosis

“…The growth part of the solid volume fraction is n S g , cf. [7]. The apoptosis process is modelled using the density production terms of the drug and the metastases.…”