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Biological processes are inherently very complex and involve many unknown relationships and mechanisms at different scales. Despite many efforts, one still cannot explain all the observed phenomena and, if necessary, make any desirable changes in the dynamics. Recently, it has become apparent that the opportunity lies in complementing the traditional, heuristic experimental approach with mathematical modelling and computer simulations. Achieving a simulation scale that corresponds for instance to clinically detectable tumour sizes is still a huge challenge, however it is necessary to understand and control complex biological processes. In this paper we present a novel high performance computational approach allowing simulations of 3D cell colony dynamics in previously unavailable tissue scale. Due to the high parallel scalability we are able to simulate cell colonies composed of 10^9 cells, which allows for instance to describe tumor growth in its early clinical stage.