Most of the parameters for the anti-VEGF agent were taken from published data on bevacizumab. We assume a half-life of 21 days (4 (link)) for the anti-VEGF whether unbound or bound to VEGF121 or VEGF165, as bound and free bevacizumab exhibit the same pharmacokinetic profile (9 (link)). Kinetic parameters (kon, koff) for the binding and unbinding of the anti-VEGF to the vascular endothelial growth factor were taken to be 9.2 × 104 M-1·s-1 and 2.0 × 10-4 s-1 respectively, leading to a dissociation constant Kd of 2.2 nM (17 (link)).
Experiments have shown that bevacizumab may have multimeric binding to VEGF (9 (link), 18 (link)) and can bind to extracellular matrix-sequestered VEGF (19 (link)). For simplicity purposes, we limit our model to monomeric binding to VEGF and neglect binding to VEGF sequestered by the extracellular matrix; these can be included when quantification of binding sites and the kinetics become available. Bevacizumab has also been reported to alter the VEGF-dependent microvascular permeability to soluble molecules (20 (link)). As a first approximation, we assume that the geometry of each tissue and the capillary density remain constant in the course of our simulations, i.e., we do not include tissue remodeling after the injection of the anti-VEGF agent. Although it may be important, the inclusion of tissue remodeling would take the model beyond the scope of this study but could be of interest for further studies. This model does not include VEGF receptors on the luminal side of endothelial cells that have not been experimentally characterized, but we have recently shown how such expression would alter the VEGF distribution (21 (link)).
Note that the simulations are not aimed at representing a particular type or stage of cancer, recognizing that VEGF-neutralizing agents may be administered in cases of both metastatic and primary tumors. Thus, in the model the tumor compartment can represent either an aggregate volume of metastases or a primary tumor. Due to the wide range of possibilities that could be represented for different types and stages of cancer, we adopt the parameters for this compartment from our previous study (16 (link)) and conduct a sensitivity study to ascertain that our qualitative conclusions are not dependent on the choice of parameters.
For each simulation, the system was first equilibrated at a baseline for a cancer patient with tumor before the injection of the VEGF-neutralizing agent. At time zero, intravenous infusion of the anti-VEGF agent begins and delivery to the blood compartment continues as a slow infusion for 90 minutes. We considered two treatment regimens: a single-dose treatment of 10 mg/kg or 10 consecutive daily doses of 1 mg/kg (metronomic therapy).
The parameters and their assigned numerical values are summarized inSupplement 3 . The equations governing the three-compartment VEGF transport system have been described in our previous papers (16 (link), 21 (link)) and can be found in Supplement 1 . We have also added equations to describe the interactions and inter-compartmental transport of the anti-VEGF molecule (Equations (S.30) to (S.38)).
Experiments have shown that bevacizumab may have multimeric binding to VEGF (9 (link), 18 (link)) and can bind to extracellular matrix-sequestered VEGF (19 (link)). For simplicity purposes, we limit our model to monomeric binding to VEGF and neglect binding to VEGF sequestered by the extracellular matrix; these can be included when quantification of binding sites and the kinetics become available. Bevacizumab has also been reported to alter the VEGF-dependent microvascular permeability to soluble molecules (20 (link)). As a first approximation, we assume that the geometry of each tissue and the capillary density remain constant in the course of our simulations, i.e., we do not include tissue remodeling after the injection of the anti-VEGF agent. Although it may be important, the inclusion of tissue remodeling would take the model beyond the scope of this study but could be of interest for further studies. This model does not include VEGF receptors on the luminal side of endothelial cells that have not been experimentally characterized, but we have recently shown how such expression would alter the VEGF distribution (21 (link)).
Note that the simulations are not aimed at representing a particular type or stage of cancer, recognizing that VEGF-neutralizing agents may be administered in cases of both metastatic and primary tumors. Thus, in the model the tumor compartment can represent either an aggregate volume of metastases or a primary tumor. Due to the wide range of possibilities that could be represented for different types and stages of cancer, we adopt the parameters for this compartment from our previous study (16 (link)) and conduct a sensitivity study to ascertain that our qualitative conclusions are not dependent on the choice of parameters.
For each simulation, the system was first equilibrated at a baseline for a cancer patient with tumor before the injection of the VEGF-neutralizing agent. At time zero, intravenous infusion of the anti-VEGF agent begins and delivery to the blood compartment continues as a slow infusion for 90 minutes. We considered two treatment regimens: a single-dose treatment of 10 mg/kg or 10 consecutive daily doses of 1 mg/kg (metronomic therapy).
The parameters and their assigned numerical values are summarized in