A mathematical, in silico implemented, modular model for tumor growth in   a spatially inhomogeneous, time-varying chemical environment (1st unrevised   edition)
  During the last decades, medical observations and multiscale data concerning tumor growth are mounting. At the same time, contemporary imaging techniques well established in clinical practice, provide a variety of information on real-time, in-vivo tumor growth. Mathematical and in-silico modeling has been widely recruited to provide means for further understanding of pertinent biological phenomena. However, despite the vast amounts of new evidence compiled by medical doctors, there are still many aspects of tumor growth that remain largely unknown. There is still a large variety of mechanisms to be better understood and therefore, many hypotheses to be tested. To approach this problem, starting from mathematical elaborations, we have developed a model of the early phases of tumor growth consisting of several algorithmic modules, each one corresponding to a particular biological mechanism. The modularity of the model allows keeping track of the assumptions made in each step and facilitates re-adjustment, in case new hypotheses need to be considered. Simulations showed good qualitative agreement with biological observations, and revealed a non-trivial interplay between between oxygen requirements of cancer cells and their maximum mitosis rates. The proposed model has, at least in principle, the potential to exploit data from contemporary imaging techniques and is eligible for utilizing multicore computation. 
Markos Antonopoulos and Georgios Stamatakos
q-bio.TO