  We use a theoretical approach to examine the effect of a radial fluid flow or
electric current on the growth and homeostasis of a cell spheroid. Such
conditions may be generated by a drain of micrometric diameter. To perform this
analysis, we describe the tissue as a continuum. We include active mechanical,
electric, and hydraulic components in the tissue material properties. We
consider a spherical geometry and study the effect of the drain on the dynamics
of the cell aggregate. We show that a steady fluid flow or electric current
imposed by the drain could be able to significantly change the spheroid
long-time state. In particular, our work suggests that a growing spheroid can
systematically be driven to a shrinking state if an appropriate external field
is applied. Order-of-magnitude estimates suggest that such fields are of the
order of the indigenous ones. Similarities and differences with the case of
tumors and embryo development are briefly discussed.
