Fig 1.
Cross-section of a tumor spheroid of radius ro.
The anoxic radius is denoted by rn. The radius rp depicts the radial extent of pm, the minimal oxygen level required for mitosis. The orange part of the image is the region rp ≤ r ≤ ro, the purple part corresponds to rn ≤ r ≤ rp and the central anoxic core (r ≤ rn) is shown in gray.
Fig 2.
Representative images (maximum intensity projections) of five cell lines that were fluorescently labelled for estimating cell volume using 3D confocal microscopy.
Merged images show the simultaneous staining of the nucleus (blue, Hoechst 33342, 3.2μM) and the cell membrane (green, PKH26, 2μM) in (A) HeLa cells and in (B) the MDA-468, HCT116, Ls-174T, and SCC25 cells. Scale bars represent 10μm.
Table 1.
Summary of Spheroids used for growth curves.
Fig 3.
Theoretical best fits for (a) MDA-MB-231 (b) U-87 and (c) Hamster V-79 spheroids.
Data for the V-79 cells is from previously published investigations by Freyer [4] and standard errors are not shown on this plot. (d) SCC-25. While best fits are shown in this figure, there are several possible combinations of diffusion limit (rl) and doubling time (td) that produce similarly high co-efficients of determination so these results may not be uniquely determined.
Fig 4.
Plots of experimental data and model growth curves for (a) HCT 116 (b) LS 174T (c) MDA-MB-468 and (d) SCC-25 spheroids.
In all plots the growth curve due to mean experimentally estimated OCR a is denoted by a solid blue line, with one standard deviation above average OCR marked by a dashed red line and one standard deviation below average consumption marked with a dotted green line. Best fit doubling times td and co-efficient of determination are shown for each value with high goodness of fit obtained for each estimated consumption rate within the confidence intervals of experimental data. The shaded area corresponds to range of ± 2 standard deviations for OCR.
Table 2.
Experimentally measured cell mass / OCR.
Fig 5.
(a) A HCT 116 control spheroid stained for proliferating cells using Ki-67 (green) and for hypoxia using EF5 (red) (b) a HCT 116 spheroid treated with 50 nM of gemcitabine showing markedly smaller hypoxic centre than untreated spheroid. (c) OCR estimated from stained cross-sections by previously outlined method [26] for 4 control spheroids and 7 spheroids treated with 50nM gemcitabine.
Average OCR for treated spheroids is 6.18 ×10−7 m3 kg−1 s−1 (18.75 mmHg / s) versus 9.05 ×10−7 m3 kg−1 s−1 (27.43 mmHg / s) for untreated spheroids (P-Value < 0.01 using a two-tailed Welch’s correction t-test,α = 0.05). This suggests a marked decrease in OCR for treated spheroids.
Fig 6.
Best fit degeneracy for U-87 growth curve.
While most values of rl / td yield negative co-efficients of determination, there is a relatively narrow-band (shown in color) that produces a good fit to observed data (R2 > 0.95). In this case, values of rl between 160–215 μm (8.56–15.46 ×10−7 m3 kg−1 s−1) can yield good fits, with these values yielding doubling times between 0.6–2.1 days. The range value is due to inherent degeneracy between diffusion limit and doubling time.