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During the last decades, medical observations and multiscale data concerningtumor growth are mounting. At the same time, contemporary imaging techniqueswell established in clinical practice, provide a variety of information onreal-time, in-vivo tumor growth. Mathematical and in-silico modeling has beenwidely recruited to provide means for further understanding of pertinentbiological phenomena. However, despite the vast amounts of new evidencecompiled by medical doctors, there are still many aspects of tumor growth thatremain largely unknown. There is still a large variety of mechanisms to bebetter understood and therefore, many hypotheses to be tested. To approach thisproblem, starting from mathematical elaborations, we have developed a model ofthe early phases of tumor growth consisting of several algorithmic modules,each one corresponding to a particular biological mechanism. The modularity ofthe model allows keeping track of the assumptions made in each step andfacilitates re-adjustment, in case new hypotheses need to be considered.Simulations showed good qualitative agreement with biological observations, andrevealed a non-trivial interplay between between oxygen requirements of cancercells and their maximum mitosis rates. The proposed model has, at least inprinciple, the potential to exploit data from contemporary imaging techniquesand is eligible for utilizing multicore computation.

A mathematical, in silico implemented, modular model for tumor growth in  a spatially inhomogeneous, time-varying chemical environment (1st unrevised  edition)