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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]