title: Predicting the growth of glioblastoma multiforme spheroids using a multiphase porous media model.
abstract: Tumor spheroids constitute an effective in vitro tool to investigate the avascular stage of tumor growth. These three-dimensional cell aggregates reproduce the nutrient and proliferation gradients found in the early stages of cancer and can be grown with a strict control of their environmental conditions. In the last years, new experimental techniques have been developed to determine the effect of mechanical stress on the growth of tumor spheroids. These studies report a reduction in cell proliferation as a function of increasingly applied stress on the surface of the spheroids. This work presents a specialization for tumor spheroid growth of a previous more general multiphase model. The equations of the model are derived in the framework of porous media theory, and constitutive relations for the mass transfer terms and the stress are formulated on the basis of experimental observations. A set of experiments is performed, investigating the growth of U-87MG spheroids both freely growing in the culture medium and subjected to an external mechanical pressure induced by a Dextran solution. The growth curves of the model are compared to the experimental data, with good agreement for both the experimental settings. A new mathematical law regulating the inhibitory effect of mechanical compression on cancer cell proliferation is presented at the end of the paper. This new law is validated against experimental data and provides better results compared to other expressions in the literature.
authors.affiliation: Dipartimento di Ingegneria Civile Edile ed Ambientale, Università di Padova, Via Marzolo 9, 35131, Padova, Italy. pietro.mascheroni@dicea.unipd.it.
authors.forename: Pietro
authors.initials: P
authors.lastname: Mascheroni
authors.affiliation: Nanomedicine Department, Houston Methodist Research Institute, 6670 Bertner Street, 77030, Houston, TX, USA.
authors.forename: Cinzia
authors.initials: C
authors.lastname: Stigliano
authors.affiliation: Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy.
authors.forename: Melania
authors.initials: M
authors.lastname: Carfagna
authors.affiliation: Dipartimento di Ingegneria Civile Edile ed Ambientale, Università di Padova, Via Marzolo 9, 35131, Padova, Italy.
authors.forename: Daniela P
authors.initials: DP
authors.lastname: Boso
authors.affiliation: Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy.
authors.forename: Luigi
authors.initials: L
authors.lastname: Preziosi
authors.affiliation: Department of Drug Design and Development, Fondazione Istituto Italiano di Tecnologia, 16163, Genova, Italy.
authors.forename: Paolo
authors.initials: P
authors.lastname: Decuzzi
authors.affiliation: Dipartimento di Ingegneria Civile Edile ed Ambientale, Università di Padova, Via Marzolo 9, 35131, Padova, Italy.|Nanomedicine Department, Houston Methodist Research Institute, 6670 Bertner Street, 77030, Houston, TX, USA.
authors.forename: Bernhard A
authors.initials: BA
authors.lastname: Schrefler
mesh_terms: D002452:Cell Count; D045744:Cell Line, Tumor; D049109:Cell Proliferation; D003198:Computer Simulation; D005909:Glioblastoma / Q000473:pathology*; D006801:Humans; D008954:Models, Biological; D061848:Optical Imaging; D016062:Porosity; D018874:Spheroids, Cellular / Q000473:pathology*; D013314:Stress, Mechanical
keywords: Cancer growth; Growth inhibition; Mathematical modeling; Mechanical compression of spheroids; U-87MG spheroids