Fig. 5: Spheroid number and its implications.

a The spheroid number fit uses the known data points found by using the experimental values of q_S, R, and D_S with the part of the equation in red (y-axis) to fit the value of \(\tilde S\) with the part of the equation in black (y-axis). b Two spheroids were chosen as typical. The small spheroid (red) with a 1.7 spheroid number has a diameter of 285 μm, and the large spheroid (blue) with a 2.7 spheroid number has a diameter of 453 μm. The scale bar is 200 μm. The images were taken at the initial time point, when the bulk glucose levels were \(c_{g0}^ \ast\) = 150 μM in the hanging-drop compartment. With this initial glucose level, we plotted the expected glucose distribution through the spheroids for the spheroid numbers fitted in subfigure a. The radial distance from the center of the microtissue was normalized by the spheroid radius to emphasize the difference in the expected initial glucose distribution. The heterogeneous glucose distribution will lead to a metabolism that diverges from ideal homogeneous consumption. c The proportion of cells that participate in the metabolization of glucose (metabolism ratio) is plotted as a function of the spheroid number. This function is found by normalizing Eq. (9) by an assumption that all cells in the spheroid consume glucose uniformly: \(\frac{{Q_S}}{{c_g^ \ast v_S}} = \frac{3}{{\tilde S^2}}\left( {\tilde S\coth \tilde S - 1} \right)\). At low spheroid numbers, 100% of cells participate in metabolic activity; at high spheroid numbers, only a few cells participate in metabolic activity. The relative metabolic activities of the typical spheroids are 85% and 70% for the smaller and larger spheroids, respectively.