Abstract
Multicellular tumor spheroids are an important in vitro model of the pre-vascular phase of solid tumors, for sizes well below the diagnostic limit: therefore a biophysical model of spheroids has the ability to shed light on the internal workings and organization of tumors at a critical phase of their development. To this end, we have developed a computer program that integrates the behavior of individual cells and their interactions with other cells and the surrounding environment. It is based on a quantitative description of metabolism, growth, proliferation and death of single tumor cells, and on equations that model biochemical and mechanical cell-cell and cell-environment interactions. The program reproduces existing experimental data on spheroids, and yields unique views of their microenvironment. Simulations show complex internal flows and motions of nutrients, metabolites and cells, that are otherwise unobservable with current experimental techniques, and give novel clues on tumor development and strong hints for future therapies.
Highlights
Multicellular tumor spheroids (MTS) stand out as the most important in vitro model of pre-vascular solid tumors [1,2,3,4,5,6,7,8]
MTS often have a regular, almost spherical structure, and their apparent simplicity has led to repeated attempts to capture their features with neat mathematical models
Since cells communicate with other cells and the environment, the other actors of this complex play are the concentration gradients of important molecular species that depend on the structure of the extracellular space and of the facilitated transport processes into and out of individual cells, and the mechanical forces that push and pull cells as they proliferate with repeated mitoses and shrink after death [20]
Summary
Multicellular tumor spheroids (MTS) stand out as the most important in vitro model of pre-vascular solid tumors [1,2,3,4,5,6,7,8]. Since cells communicate with other cells and the environment, the other actors of this complex play are the concentration gradients of important molecular species that depend on the structure of the extracellular space and of the facilitated transport processes into and out of individual cells, and the mechanical forces that push and pull cells as they proliferate with repeated mitoses and shrink after death [20]. These processes mix with complex nonlinear interactions between the biochemical and the mechanical part, and this highlights again the importance of an effective model at the single-cell level
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