Table 1.

The parameters in our model.

Parameter	Description	Value Taken	Reference
A	The maximum rate of proliferation of cancerous cells	1.4 × 10−6 s−1	Grote et al. (1977)
B	The maximum rate of necrosis of cells	2.1 × 10−6 s−1	A posteriori estimation
Ĉm	The non-dimensional critical oxygen concentration in Michaelis-Menten proliferation kinetics	0.1	A posteriori estimation
Ĉd	The non-dimensional critical oxygen concentration in Michaelis-Menten based necrosis kinetics	0.1	A posteriori estimation
σ	A parameter in the cell necrosis kinetic	0.9	A posteriori estimation
α	The rate at which proliferating cells become quiescent outside the proliferating rim	1.4 × 10−6 s−1	A posteriori estimation
β	The rate at which quiescent cells become proliferative inside the proliferating rim	1.4 × 10−6 s−1	A posteriori estimation
R	The width of the proliferating rim	80 µm	LaRue et al. (2004); Casciari et al. (1992); Buckley et al. (1999)
ν	The rate of linear decay of necrotic cells	2.8 × 10−7 s−1	A posteriori estimation
λ	The ratio of the rate of proliferation of non-cancerous cells to cancerous cells	0.3	See text
VL	The mean volume of a live cell	3 × 10−9 cm3	Landry et al. (1981, 1982)
VN	The mean volume of a necrotic cell	1.5 × 10−9 cm3	Landry et al. (1981, 1982)
𝒱	The cell volume fraction	0.66	Buckley et al. (1999)
D	The diffusion coefficient of oxygen	2 × 10−5 cm2 s−1	Grote et al. (1977); Hlatky and Alpen (1985)