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Mathematical Models of the Interaction of Cells and Cell Aggregates with the Extracellular Matrix

Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2167)

Abstract

It is nowadays understood that the interactions cells have with the fibrous environment they live in determine their behaviour. In fact, for instance, they play a fundamental role in cell motion, in tumour invasion and metastatization, in stem cell differentiation, and in tissue development.

In this chapter, we will describe several models that deal with different aspects characterizing these interactions. In particular, from the tutorial point of view, the topic will be used as a playground to briefly present several modelling frameworks, e.g., age-structured models, individual cell-based models, continuum mechanics, and mixture theory.

The models presented will be usually characterised by multiscale aspects because, for instance, the physical parameters determining cell motion and duplication are affected by the expression of proteins inside the cell and of receptors at its membrane. In turn, the behaviour of cellular aggregates and of tissues depends on the behaviour of single cells. For this reason, some upscaling tool will also be described.

Keywords

Interaction Force Traction Force Mass Balance Equation Monte Carlo Step Force Balance Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Dipartimento di Scienze MatematichePolitecnico di TorinoTorinoItaly

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