Mechanics in Tumor Growth

Mathematical model of tumour cord growth along the source of nutrient

“…Σ(φ) may also be chosen to be vanishing for φ below a certain threshold, to describe a situation when the cells are so scarce, than no longer interact. Selection of Σ was discussed in more details in [19].…”

Multiphase Models of Tumour Growth

“…Examples of applications can be found in [BBL02, BBL03, BKMP03, BP04, CGP06, FBK + 03, FBM + 03, FK03] while [AP02, AM05,GP07] are review papers on this approach and on the mechanical aspects related to tumour growth. Here, we shall deduce a general multiphase modelling framework for few but essential constituents (cells, extracellular matrix, and extracellular liquid with the solutes dissolved in it).…”

“…Section 4 is in large part devoted to the description of the interaction between the cells and the extracellular matrix. In Section 5 we address the issue of how to deduce a proper constitutive model for the stress, though the reader is referred to more specific literature for further details [AP02,AP07,AM05,GP07]. Finally, in the last three sections, the general model is specialized to describe tumour growth in an immutabile ECM (rigid, non-remodelling), including the mechanical interaction with the host tissue, the growth in a rigid remodelling ECM with the aim of showing the formation of fibrosis, and the growth of a vascularized tumour, with a particular focus on how to relate cell metabolism to growth terms.…”

A Mechano-Chemical Model of a Solid Tumor for Therapy Outcome Predictions

“…In our model, proliferation is constrained by the availability of oxygen [7,9] and space [10]. We account for tumor cells proliferation, apoptosis and necrosis.…”

“…We continue to rely on the established methods from solid mechanics and chemical engineering. The finite element method (FEM) is particularly suitable for describing strain-induced cellular responses, gaining acceptance as an influential player in simulating tissue development [6,7]. With such a representation we can account for mechanical tissue deformations induced by developing pathologies and capture its interplay with the chemical environment.…”