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Table 4 Summary of parameter values

From: How to schedule VEGF and PD-1 inhibitors in combination cancer therapy?

Notation

Description

Value used

References

d D

Death rate of DCs

0.1 day−1

[59]

\(d_{T_{1}}\)

Death rate of CD 4+ T cells

0.197day−1

[59]

\(d_{T_{8}}\)

Death rate of CD 8+ T cells

0.18day−1

[59]

\(d_{T_{r}}\)

Death rate of Tregs

0.2day−1

[61]

d E

Death rate of endothelial cells

0.69 day−1

[43]

d C

Death rate of tumor cells

0.17 day−1

[59]

\(d_{I_{12}}\)

Degradation rate of IL-12

1.38 day−1

[59]

\(d_{I_{2}}\)

Degradation rate of IL-2

2.376 day−1

[59]

\(d_{T_{\beta }}\)

Degradation rate of TGF-β

499.066 day−1

[15]

d W

Take-up rate of oxygen by cells

1.04 day−1

Estimated

d G

Degradation rate of VEGF

12.6 day−1

[43]

d A

Degradation rate of anti-PD-L1

0.34 day−1

Estimated

η 1

Killing rate of cancer cells by T1

30.19 cm3/g·day

Estimated

η 8

Killing rate of cancer cells by T8

60.375 cm3/g·day

Estimated

d B

Degradation rate of anti-VEGF

0.17 day−1

Estimated

μ PA

Blocking rate of PD-1 by anti-PD-1

4.33×107cm3/g·day

Estimated

μ AP

Degradation rate of anti-PD-1 in blocking PD-1

4.33×107cm3/g·day

Estimated

μ GB

Blocking rate of VEGF by anti-VEGF

2.19×107cm3/g·day

Estimated

μ BG

Degradation rate of anti-VEGF in blocking VEGF

1.31×108cm3/g·day

Estimated

K D

Half-saturation of CD 4+ T cells

4×10−4g/cm3

[15]

\(K_{T_{1}}\)

Half-saturation of CD 4+ T cells

2×10−3g/cm3

[15]

\(K_{T_{8}}\)

Half-saturation of CD 8+ T cells

1×10−3g/cm3

[15]

\(K_{T_{r}}\)

Half-saturation of Tregs

5×10−4g/cm3

[15]

K E

Half-saturation of endothelial cells

2.5×10−3g/cm3

[43]

K C

Half-saturation of tumor cells

0.4 g/cm3

[15]

\(K_{I_{12}}\)

Half-saturation of IL-12

8×10−10g/cm3

[15]

\(K_{I_{2}}\)

Half-saturation of IL-2

2.37×10−11g/cm3

[15]

\(K_{T_{\beta }}\)

Half-saturation of TGF-β

2.68×10−13g/cm3

[15]

K W

Half-saturation of oxygen

1.69×10−4g/cm3

[43]

K G

Half-saturation of VGEF

7×10−8g/cm3

[43]

\(K_{TT_{r}}\)

Inhibition of function of T cells by Tregs

5×10−4g/cm3

[15]

\(K^{\prime }_{TQ}\)

Inhibition of function of T cells by PD-1-PD-L1

1.68×10−18g2/cm6

Estimated

K PB

Block of anti-PD-1 perfusion by anti-VEGF (mice)

1×10−8g/cm3

Estimated

K PB

Block of anti-PD-1 perfusion by anti-VEGF (humans)

1×10−9g/cm3

Estimated

D 0

Density of immature DCs

2×10−5 g/ cm3

[59]

T 10

Density of naive CD 4+ T cells

4×10−4 g/ cm3

[15]

T 80

Density of naive CD 8+ T cells

2×10−4 g/ cm3

[15]

E M

Carrying capacity of endothelial cells

5×10−3 g/ cm3

[43]

C M

Carrying capacity of cancer cells

0.8 g/ cm3

[59]

G 0

Threshold VEGF concentration

3.65×10−10 g/ cm3

[43]

\(\hat T_{1}\)

Density of CD 4+ T cells from lymph node

4×10−3 g/ cm3

[15]

\(\hat T_{8}\)

Density of CD 8+ T cells from lymph node

2×10−3 g/ cm3

[15]

\(\hat E\)

Density of endothelial cells from outside of tumor

5×10−3 g/ cm3

Estimated

W ∗

Hypoxia threshold oxygen level

1.69×10−4 g/ cm3

[44]

W 0

Normal threshold oxygen level

4.65×10−4 g/ cm3

[44]