Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Mathematical modelling of tumor growth in mice following electrotherapy and bleomycin treatment
Mathematics and Computers in Simulation - Special issue on mathematical modeling
Mathematical model of prevascular growth of a spherical carcinoma
Mathematical and Computer Modelling: An International Journal
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We show that the observed oscillatory pattern in the growth dynamics of a multicellular tumor may be successfully simulated with a classical field limit nonlinear matter wave equation given by the mean-field Gross-Pitaevskii model. Constructing and scaling the many-body Hamiltonian we account for the overall physics of the cell aggregate (e.g., the kinetic pressure, the cell-cell interaction, and the external trapping of the cells) together with the nonconservative effect of mitosis and necrosis, and find a compelling agreement with the tumor culture data for the V79 cells both in qualitative and quantitative sense. Results, obtained through an scaling of the characteristic length @/h/mw (h = h/2@p, h = Planck's constant; m = mass; @w = frequency) associated with the wave equation by the ratio of an effective cell size in tumor to the effective atom size in a condensate, demonstrate a scaling behavior for the tumor and reveal the role of underlying physical interactions, in particular the presence and influence of nonlinear cell-cell interactions, in the growth dynamics.