Correspondence between time-evolution dynamics of a tumor and an attractively interacting Bose-Einstein Condensate with feeding and dissipation

Abstract

The morphology and time-evolution of tumors are expected to depend heavily on the detailed balance of the overall physics of the cell assembly (e.g., the kinetic pressure, the cell-cell interaction, and the external trapping by the tissue) and the biological processes of mitosis, necrosis, etc. Here, for the first time, we include such a detailed balance in a theoretical model by exploiting the {\it ab initio} mathematical framework of atomic Bose-Einstein Condensation (BEC) with feeding and dissipation, to study tumor evolution dynamics. We show that, with a characteristic length scaling, the Gross-Pitaevskii (GP) equation, which describes the many-body atomic BEC characteristics, indeed explains the detailed features of a prevascular tumor culture data. The agreement suggests the prevascular that the prevascular carcinoma may be a natural analog to BEC and predicts an intercellular wave connecting the cells.