Modelling of lung‐metastases apoptosis within brain tissue

Abstract

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.

Continuum‐mechanical modelling of apoptosis

“…The parameter estimation is based on maximising the likelihood of the error log(ε) = log(y data ) − log(ȳ simu ), such that the simulation resultȳ simu given by the parameters resemble the experimental dataȳ data , cf. [4]. For the introduced apoptotic cellular pathway model, all kinetic reaction parameters are optimised.…”

“…For the introduced apoptotic cellular pathway model, all kinetic reaction parameters are optimised. Furthermore, these results are compared to the model introduced in [4], which only differentiates in the metastases decline which consists of a constitutive logarithmic density production termρ SC ⊖ = n ST ρ SR (µ SC init ⊖ + c ID m µ SC max ⊖ ). Hereby, µ SC init ⊖ represents an initial apoptosis rate, while a maximum rate µ SC max ⊖ is related to the drug concentration.…”

“…Additionally, energy supplying nutrients ϕ IN , the death-receptor agonist (drug) ϕ ID and the solvent ϕ IL form the interstitial fluid as a mixture of miscible components, cf. [4]. The adapted governing balance relations are the concentration balances for the miscible components, the volume balances for the pore liquids and the overall momentum equation as introduced in [4].…”

“…[4]. The adapted governing balance relations are the concentration balances for the miscible components, the volume balances for the pore liquids and the overall momentum equation as introduced in [4]. This system of equations is solved numerically for the primary variables solid displacement field u S , concentrations c IN m and c ID m as well as the effective pore-liquid pressures p BR and p IR .…”

“…The optimised results are compared to the experimental data as well as a previously introduced apoptosis model, cf. [4]. The considered in-situ experiments were conducted at the Institute of Cell Biology and Immunology at the University of Stuttgart, Germany.…”