Table 1 Parameters and values used in the mathematical models

Tumour blood flow

Tumour capillary radius

R_C

100 (μm)

[33]

Tumour interstitium radius

R_T

1200 (μm)

Estimated

Tumour length

L

1 (cm)

[33]

Blood density

ρ

1000 (kg/m³)

[32]

Blood viscosity

μ

0.004 (Pa∙s)

[35]

Vascular hydraulic conductivity

L _p

0.36-2.8 × 10^-6 (cm/mmHg∙s)

[36]

Tissue hydraulic conductivity

K

0.4-2.0 × 10^-7 (cm²/mmHg∙s)

[36]

Vascular inlet pressure

P _A

15 (mmHg)

[37]

Vascular outlet pressure

P _V

0

[36]

Ambient pressure

P ₀

0

[36]

Drug transport (Doxorubicin)

D _E

1.5778 × 10^-6 (cm²/s)

[17]

DOX diffusion coefficient

Rate of transmembrane transport

V ₁ , V ₂

0.28 (ng/(10⁵cells)/min)

[14]

(V₁ = V₂)

Diffusive permeability for DOX

P _E

2.778 × 10^-4 (cm/s)

[17]

Michaelis constant for transmembrane transport

k ₁

0.219 (μg/ml)

[14]

Michaelis constant for transmembrane transport

k ₂

1.37 (ng/(10⁵cells))

[14]

Tumour cell density

Initial tumour cell density

c _t,0

10⁶ (cells/mm³)

[17]

Tumour cell growth rate

a ₁

0.5 (day^-1)

Estimated

Saturation constant in logistic equation

b

0.02592 (mm³/(10⁵cells)/day)

Estimated

Tumour cell natural decay rate

a ₂

0.24 (day^-1)

Estimated

Intracellular signalling:

Bistable switch

Michaelis Menten constants

V _f

27 (hr^-1)

[38]

Michaelis Menten constants

V _r

0.459 (hr^-1)

[38]

Michaelis Menten constants

K _m1

100

[38]

Michaelis Menten constants

K _m2

0.01

[38]

Kinetic parameter mediating feedback strength

k _fb

2.927 (hr^-1)

[38]

Basal level in the bistable switch

p

0.7

Estimated

Parameter mediating input regulation in the bistable switch

q

0.3(ng/(10⁵cells))^-1

Estimated

Monostable switch

Kinetic parameter reflecting the time scale of the response

k

0.432 (hr^-1)

Estimated

Associated constant

k _h

1 (ng/(10⁵cells))

Estimated

Hill coefficient

n

10

Estimated

R₁ protein activation rate

k _f

3.6 (hr^-1)

Estimated

R₁ protein degradation rate

k _r

0.144 (hr^-1)

Estimated

R₁ Threshold for apoptosis switch

R ₁ , _th

0.9

Estimated