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Biological processes are inherently complex and involve many unknown relationships and mechanisms at different scales. Despite many efforts, researchers still can't explain all of the observed phenomena and, if necessary, make any desirable changes in the dynamics. Recently, it has become apparent that a research opportunity lies in complementing the traditional, heuristic experimental approach with mathematical modeling and computer simulations. Achieving a simulation scale that corresponds, for instance, to clinically detectable tumor sizes is still a huge challenge, however, this scale is necessary to understand and control complex biological processes. This article presents a novel, high-performance computational approach allowing simulations of 3D cell colony dynamics at a previously unavailable tissue scale. Due to its high parallel scalability, the method achieves simulation of cell colonies composed of 109 cells, which allows for describing tumor growth in its early clinical stage.