Table 1.

The values of the parameters used in the proposed model.

Parameters	Values	Units	Descriptions
$\rho$	993.3	kg/${\mathrm{m}}^3$	Density of water at 37 °C, [28]
Μ	6.92$\times {10}^{-4}$	Pa·s	Viscosity of water at 37 °C, [28]
$D_{glucose-water}$	9.27$\times {10}^{-10}$	${\mathrm{m}}^2/\mathrm{s}$	Diffusion coefficient of glucose through water [28]
$D_{O_2-water}$	2.6$\times {10}^{-9}$	${\mathrm{m}}^2/\mathrm{s}$	Diffusion coefficient of oxygen through water [28]
$D_1$	4.22$\times {10}^{-11}$	${\mathrm{m}}^2/\mathrm{s}$	Diffusion coefficient of glucose through EMT6/Ro cancerous tissue [26]
$D_2$	1.65$\times {10}^{-9}$	${\mathrm{m}}^2/\mathrm{s}$	Diffusion coefficient of oxygen through EMT6/Ro cancerous tissue [26]
$C_{glucose-critical}$	0.06	mM	Critical concentration of glucose for EMT6/Ro spheroid [26]
$C_{O_2-critical}$	0.02	mM	Critical concentration of oxygen for EMT6/Ro spheroid [26]
$V_1$	4.36$\times {10}^{-2}$	mol/${\mathrm{m}}^3/\mathrm{s}$	Maximum consumption rate of glucose for EMT6/Ro spheroid [29]
$V_2$	2.74$\times {10}^{-2}$	mol/${\mathrm{m}}^3/\mathrm{s}$	Maximum consumption rate of oxygen for EMT6/Ro spheroid [29]
$K_1$	4$\times {10}^{-2}$	mol/${\mathrm{m}}^3$	Michaelis constant of glucose for EMT6/Ro spheroid [28]
$K_2$	4.64$\times {10}^{-3}$	mol/${\mathrm{m}}^3$	Michaelis constant of oxygen for EMT6/Ro spheroid, Casciari et al. [12]
$A_p$	1.2153$\times {10}^{-9}$	1/s	Apoptosis rate constant for EMT6/Ro spheroid, Mahmood et al. [30]
$A_n$	2$\times {10}^{-6}$	1/s	Necrosis rate constant for EMT6/Ro spheroid, Mahmood et al. [30]
$A$	$3.3\times {10}^{-2}$ *	1/h	Proliferation rate constant for 0.8 mM glucose and 0.28 mM oxygen for EMT6/Ro spheroid [14]

* Obtained from the exponential cell doubling time (21 h).