Modeling and simulation of multicellular tumor growth using a nonlinear matter wave equation

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 √ħ/mw (ħ = h/2π, h = Planck's constant; m = mass; ω ≡ 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.