Microenvironmental influence on microtumour infiltration patterns: 3D-mathematical modelling supported by in vitro studies

LUJÁN, EMMANUEL; SOTO, DANIELA; ROSITO, MARÍA SOL; SOBA, ALEJANDRO; GUERRA, LILIANA N; CALVO, JUAN CARLOS; MARSHALL, GUILLERMO; SUÁREZ, CECILIA ANA

INTEGRATIVE BIOLOGY

ROYAL SOC CHEMISTRY

Lugar: CAMBRIDGE; Año: 2018

1757-9694

Mathematical modelling approaches have become increasingly abundant in cancer research. Tumour infiltration extent and its spatial organization depend both on the tumour type and stage as well as on the bio-physicochemical characteristics of the microenvironment. This sets a complex scenario that often requires a multidisciplinary and individually-adjusted approach. The ultimate goal of this work is to present an experimental/numerical combined method to develop a three-dimensional mathematical model able to reproduce the growth and infiltration pattern of a given avascular microtumour in response to different microenvironmental conditions. The model consists on a diffusion-convection-reaction equation that considers logistic proliferation, volumetric growth, a rim of proliferative cells at the tumour surface, and invasion with diffusive and convective components. Parameter values of the model were fitted to experimental results while radial velocity and diffusion coefficients were made spatially variable in a case-specific way through the introduction of a shape function and a diffusion-limited-aggregation (DLA)-derived fractal matrix, respectively, according to the infiltration pattern observed. The in vitro model consists of multicellular tumour spheroids (MTS) of an epithelial mammary tumour cell line (LM3) immersed in a collagen I gel matrix with standard culture medium ("naive" matrix) or conditioned medium from adipocytes or preadipocytes ("conditioned" matrix). It was experimentally determined that both adipocyte and preadipocyte conditioned media are able to change the MTS infiltration pattern from a collective and laminar to an individual and atomized one. Numerical simulations were able to adequately reproduce qualitatively and quantitatively both kinds of infiltration patterns, which was determined by area quantification, analysis of fractal dimensions and lacunarity, and a Bland-Altman analysis. These results suggest that the combined approach presented here could be established as a new framework with interesting potential applications both at the basic and clinical levels of the oncology area.