Table 1 Model parameters and their abbreviations.

Concentration of A (ng/ml)

[A]

Hypoxia inducible factor (HIF1α)

Hα

Vascular endothelial growth factor

VEGF

Matrix metalloproteinase

MMP

Notch ligand Delta-like 4

Dll4

Gradient (concentration of species A) (ng/ml/μm)

∇A

Standard deviation

σ

Probability distribution

ϕ

Cell position

X(i,j,k)

Velocity (μm/s)

ν(i,j,k)

Directional vector

d

Persistence

p

Degree of randomness

μ

Length (μm)

ℓ

Time (hr)

t

Elongation constant

ε

Total tip cell movement

m_total

Migration of the tip cell (μm)

M_tip

Elongation of the tip cell (μm)

E_tip

Elongation of the adjacent stalk cell segment (μm)

E_stalk

Proliferation of tip cell (% volume increase)

P_tip

Proliferation of stalk cell (% volume increase)

P_stalk

Cell volume (μm³)

V

Total stalk cell volume in a sprout (μm³)

V_sproutStalk

Radius of cell (μm)

R

Radius after proliferation (μm)

R_P

Outer radius of existing capillary (μm)

R_cap

Radius of inner lumen in existing capillary (μm)

r_lumen

Length of tip cell (μm)

ℓ_tip

Length of adjacent stalk cell segment (μm)

ℓ_Stalk

Length due to stalk cell growth (μm)

${\ell }_{{\text{P}}_{\text{stalk}}}$

Length due to tip cell growth (μm)

${\ell }_{{\text{P}}_{\text{tip}}}$

Length due to stalk cell stretching (μm)

${\ell }_{{\text{E}}_{\text{stalk}}}$

Random number generator

rgen

Grid height (μm)

g_H

Grid width (μm)

g_W

Grid length (μm)

g_l