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Table 1 Description of the variables and parameters used in the vascular tumour growth and the two-compartmental pharmacokinetic bevacizumab models

From: Numerical simulation of vascular tumour growth under antiangiogenic treatment: addressing the paradigm of single-agent bevacizumab therapy with the use of experimental data

Mathematical Symbol Description Units Valuea Referencea
Vascular tumour growth model
t Time day n/a -
V Tumour volume mm3 n/a -
K Tumour carrying capacity mm3 n/a -
λ 1 Gompertzian growth constant day−1 0.192 [31, 43]
λ 2 Proportionality constant related to the natural mortality of endothelial cells day−1 0 [31, 43]
c Proportionality constant related to the term reflecting endogenous stimulation of the tumour upon the vasculature mg/(day · mm3p · kg) 5.85 [31, 43]
d Proportionality constant related to the term reflecting endogenous inhibition of tumour vasculature day−1 · mm−2 0.00873 [31]
α Parameter reflecting the stimulator clearance rate mg/(mm3p · kg) 1 [43]
β Parameter reflecting the extent of the abnormal phenotype of tumour vasculature mm3p 1 [43]
p Parameter reflecting the extent of the abnormal phenotype of tumour vasculature - 0 [43]
I Drug concentration in plasma mg/kg n/a -
Two-compartmental pharmacokinetic bevacizumab model
t Time-point day n/a -
I Bevacizumab concentration in plasma mg/ml n/a -
n Number of infusions to be administered - 9 [60]
D Dose mg dosage*weight -
T Infusion duration day 1/48 [66]
V c Volume of central compartment ml 7.975 [64]
k 12 Transfer constant from central to peripheral compartment day−1 0.7536 [64]
k 21 Transfer constant from peripheral to central compartment day−1 0.3144 [64]
k e Rate of elimination day−1 0.3888 [64]
d Dosage mg/kg 5 [60, 61, 65]
w Host’s weight kg 0.025 [60, 64]
t D Administration time-point of anti-angiogenic treatment day t1 = 1 -
t2 = 4
t3 = 8
t4 = 11
t5 = 15
t6 = 18
t7 = 22
t8 = 25
t9 = 29
  1. aUsed for indicative free growth and/or Intermittent bevacizumab monotherapy simulations