Table 4 Summary of the parameter values used in the simulation depicted in Figs. 2 and 3

C _hyp

Threshold of hypoxia

5.5

M

\(C_{\textit {hyp}}^{sev}\)

Threshold of severe hypoxia

1.52

M

C _nec

Threshold of necrosis

0.02

M

D _{C,m a x}

Maximum diffusion of oxygen

1

mm ² h ⁻¹

D _{α,m a x}

Maximum diffusion of VEGF

0.1875

mm ² h ⁻¹

ε

Percentage of loss of diffusion

20

%

C _sou

Oxygen concentration in functional blood vessels

8

M h ⁻¹

λ _C

Degradation rate of oxygen

0.01

h ⁻¹

ε _C

Rate of oxygen consumption by proliferative cells

3

cells ⁻¹ mm ² h ⁻¹

β _C

Rate of oxygen consumption by quiescent cells

1.5

cells ⁻¹ mm ² h ⁻¹

C _max

Maximum concentration of oxygen

8

M

λ _α

Degradation rate of VEGF

1.25×10⁻⁴

h ⁻¹

π

Binding rate of VEGF to endothelial cells

0.791

cells ⁻¹ mm ² h ⁻¹

α _sou

Production rate of VEGF

2.11

M cells ⁻¹ mm ² h ⁻¹

α _max

Maximum concentration of VEGF

2.11

M

α _half

Shape parameter of f _{ρ ρ}

1.25×10⁻³

M

χ _chemo

Maximum effect of VEGF on endothelial chemotaxis

1.25×10⁻²

mm ² M ⁻¹ h ⁻¹

χ _prol

Maximum effect of VEGF on endothelial proliferation

5×10⁻²

h ⁻¹