No abstract

Cancer is one of the most serious diseases for human beings, especially when metastases come into play. In the present article, the example of lung-cancer metastases in the brain is used to discuss the basic problem of cancer growth and atrophy as a result of both nutrients and medication. As the brain itself is a soft tissue that is saturated by blood and interstitial fluid, the biomechanical description of the problem is based on the Theory of Porous Media enhanced by the results of medication tests carried out in in-vitro experiments on cancer-cell cultures. Based on theoretical and experimental results, the consideration of proliferation, necrosis and apoptosis of metastatic cancer cells is included in the description by so-called mass-production terms added to the mass balances of the brain skeleton and the interstitial fluid. Furthermore, the mass interaction of nutrients and medical drugs between the solid and the interstitial fluid and its influence on proliferation, necrosis and apoptosis of cancer cells are considered. As a result, the overall model is appropriate for the description of brain tumour treatment combined with stress and deformation induced by cancer growth in the skull.

Apoptosis, a form of programmed cell death, can be induced in lung-cancer cells by treatment with death-receptor ligands. In this contribution, the coupled multiphasic process is described using a continuum-mechanical model based on the Theory of Porous Media. Furthermore, the data-enriched model incorporates the crucial apoptosis parameters, which are estimated via the maximum likelihood estimation based on cell-culture experiments.

Originated from a lung tumour, cancer cells can spread via the blood-vessel system, travel to the cerebrum and may pass the blood-brain barrier. The extravasation is followed by migration, and the formation of micrometastases. Further proliferation causes interveined metastases. A pressure-driven infusion of a therapeutic solution counteracts the disturbance by the metastases within the brain. These processes are described with a continuum-mechanical model based on the Theory of Porous Media. Numerical applications demonstrate the feasibility of the model and include multicellular-tumour spheroid experiments in the macroscopic simulation of metastases growth and atrophy.

Malignant neoplasms are one of the most dangerous diseases. Within the framework of the well-established Theory of Porous Media (TPM), a multi-constituent model is derived. The model is mathematically formulated by a set of coupled partial differential equations which are solved within the well-known framework of the finite-element method. The general TPM model is applied to basal-cell carcinoma in the avascular skin and representative numerical examples show the capabilities of the model.