Eur. Phys. J. E (2013) 36: 23
https://doi.org/10.1140/epje/i2013-13023-2

Regular Article

Mechano-transduction in tumour growth modelling

¹⁹⁸³⁶ Institut Jean le Rond d’Alembert, UMR CNRS 7190, Universitè Pierre et Marie Curie, Paris 6, 4 place Jussieu, Case 162, 75005, Paris, France
²⁹⁸³⁶ MOX Laboratory, Dipartimento di Matematica, Politecnico di Milano, piazza Leonardo da Vinci 32, 20133, Milano, Italy
³⁹⁸³⁶ Dipartimento di Scienze Matematiche, Politecnico di Torino, c.so Duca degli Abruzzi 24, 10123, Torino, Italy
⁴⁹⁸³⁶ Fondazione CEN, Centro Europeo di Nanomedicina, piazza Leonardo da Vinci 32, 20133, Milano, Italy

^* e-mail: pasquale.ciarletta@upmc.fr

Received: 14 November 2012
Revised: 19 December 2012
Accepted: 11 February 2013
Published online: 18 March 2013

Abstract

The evolution of biological systems is strongly influenced by physical factors, such as applied forces, geometry or the stiffness of the micro-environment. Mechanical changes are particularly important in solid tumour development, as altered stromal-epithelial interactions can provoke a persistent increase in cytoskeletal tension, driving the gene expression of a malignant phenotype. In this work, we propose a novel multi-scale treatment of mechano-transduction in cancer growth. The avascular tumour is modelled as an expanding elastic spheroid, whilst growth may occur both as a volume increase and as a mass production within a cell rim. Considering the physical constraints of an outer healthy tissue, we derive the thermo-dynamical requirements for coupling growth rate, solid stress and diffusing biomolecules inside a heterogeneous tumour. The theoretical predictions successfully reproduce the stress-dependent growth curves observed by in vitro experiments on multicellular spheroids.