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The energy balance in stationary multicellular spheroids. (English) Zbl 1187.92052

Summary: The paper addresses the question of how to formulate a mathematical model allowing to predict the size of a multicellular spheroid once it has reached equilibrium. All previous models postulate some law of removal of necrotic material from the spheroid, compensating the new cellular volume produced by proliferation. However, such removal process has not been described on physical grounds, but has been rather presented as a postulate. We adopt a different point of view, claiming that equilibrium is the result of an energy balance: the proliferating cells have to supply the mechanical power which is dissipated within the spheroid due to cell-cell and liquid-cell friction. Adopting the two-fluid model for the mechanics of the spheroid, we compute the explicit expression of the mechanical energy dissipation rate as a function of the spheroid size. With reference to a specific experimental case (for which the equilibrium size is known) we deduce the average value of the power to be supplied by proliferating cells and we formulate the general requirement that (depending on environmental conditions) the terminal size of the spheroid is such to fulfill the balance between power dissipation and power production. As a by-product we compute the stress profile in the spheroid.

MSC:

92C50 Medical applications (general)
92C15 Developmental biology, pattern formation
92C05 Biophysics
92C37 Cell biology
37N25 Dynamical systems in biology
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