Continuum‐mechanical modelling of apoptosis

Abstract

In cancer cells, the administration of drugs, such as TRAIL, can induce a mode of cell death (apoptosis). This applied reagent shifts the cell's internal inhibition and activation reactions towards the activation of caspases, triggering the cell death. In this contribution, a macroscopic model in the framework of the well-known Theory of Porous Media is introduced to model the apoptosis reaction for lung-cancer metastases located in brain tissue. Therein, the density-production terms describe the apoptosis via a set of ordinary differential equations. The model is adapted to apoptosis experiments, measuring the survival rate of lung-cancer cells in dependency of the TRAIL concentration. Thereby, the model is compared to a reduced model version using a constitutive logarithmic apoptosis function within the production terms.

Modelling basal‐cell carcinoma behaviour in avascular skin

“…Further parameters are chosen according to the literature [5][6][7] and meaningful constitutive assumptions are included, cf. [2][3][4]. The simulation starts with an accumulation of approx.…”

“…Investigating the growth and regression of malignant neoplasms from a continuum-biomechanical point of view, we propose a suited description of basal-cell carcinomas in avascular skin. The model proceeds from a quaternary drug-spreading model [2], which is extended towards metastatic behaviour in brain tissue [4]. The Theory of Porous Media, cf.…”