Computational Modeling of Tumor Response to Vascular-Targeting Therapies—Part I: Validation

Table 1

Summary of variables and parameters used in the model.

Variable	Definition
𝑣(𝑥,𝑦,𝑡)	Concentration of VEGF (𝜇M)
𝑎1(𝑥,𝑦,𝑡)	Concentration of Ang-1 (𝜇M)
𝑎2(𝑥,𝑦,𝑡)	Concentration of Ang-2 (𝜇M)
𝑟𝑣0(𝑥,𝑦,𝑡)	Concentration of unbound VEGFR-2 (𝜇M)
𝑟𝑎0(𝑥,𝑦,𝑡)	Concentration of unbound Tie-2 (𝜇M)
𝑟𝑣(𝑥,𝑦,𝑡)	Concentration of VEGFR-2 bound by VEGF (𝜇M)
𝑟𝑎1(𝑥,𝑦,𝑡)	Concentration of Tie-2 bound by Ang-1 (𝜇M)
𝑟𝑎2(𝑥,𝑦,𝑡)	Concentration of Tie-2 bound by Ang-2 (𝜇M)
𝑒𝑖(𝑥,𝑦,𝑡)	EC indicator function
ℎ𝑖(𝑥,𝑦,𝑡)	Hypoxic cell indicator function
𝑝𝑖(𝑥,𝑦,𝑡)	Proliferative cell indicator function
𝑛𝑖(𝑥,𝑦,𝑡)	Necrotic cell indicator function
ℎ(𝑥,𝑦,𝑡)	Concentration of hypoxic cells (𝜇M)
PDE parameters	Definition	Value
𝐷𝑣	Diffusion coefficient of VEGF	𝐷𝑣=3.6×10^−4 mm^2/h
𝐷𝑎2	Diffusion coefficient of Ang-2	𝐷𝑎2=3.6×10^−4 mm^2/h
𝑏𝑣	Production rate of VEGF by hypoxic cells	𝑏𝑣=0.05 h^−1
𝑏𝑎1	Production rate of Ang-1 by ECs	𝑏𝑎1=0.01 h^−1
𝑏𝑎2	Production rate of Ang-2 by ECs	𝑏𝑎2=0.08 h^−1
𝑏𝑎2	Production rate of Ang-2 by hypoxic cells	𝑏𝑎2=0.05 h^−1
𝜇𝑣	Decay rate of VEGF	𝜇𝑣=0.001 h^−1
𝜇𝑎1	Decay rate of Ang-1	𝜇𝑎1=0.003 h^−1
𝜇𝑎2	Decay rate of Ang-2	𝜇𝑎2=0.002 h^−1
𝑘0	Association rate of VEGF/VEGFR-2	𝑘0=46.8𝜇M^−1·h^−1
𝑘−0	Dissociation rate of VEGF/VEGFR-2	𝑘−0=0.2268 h^−1
𝑘1	Association rate of Ang-1/Tie-2	𝑘1=36𝜇M^−1·h^−1
𝑘−1	Dissociation rate of Ang-1/Tie-2	𝑘−1=0.1332 h^−1
𝑘2	Association rate of Ang-2/Tie-2	𝑘2=41.7𝜇M^−1·h^−1
𝑘−2	Dissociation rate of Ang-2/Tie-2	𝑘−2=0.108 h^−1
𝐾𝑣	Carrying capacity of VEGF	𝐾𝑣=10^−2 𝜇M
𝐾𝑎	Carrying capacity of angiopoietins	𝐾𝑎=1.5×10^−2 𝜇M
𝑒0	Endothelial cell concentration per blood vessel	𝑒0=10^−4 𝜇M
Treatment parameters	Definition	Value
𝑇1	AI treatment parameter is 𝑏𝑣/𝑇1	𝑇1=10,100,1000
𝑇2	Fraction of proliferative cells killed by cytotoxic agent	𝑇2=0.24,0.34,0.44
𝑇3	Fraction of angiogenic vessels destroyed by VDA	𝑇3=0.1,0.3,0.6,0.9