Simulation of tumor-induced angiogenesis and its response to anti-angiogenic drug treatment: mode of drug delivery and clearance rate dependencies

Tumor cells secrete diffusible substances collectively called tumor angiogenic factors (TAFs), most notably vascular endothelial growth factor (VEGF) and basic fibroblast growth factor (bFGF), which in turn stimulate endothelial cell migration and thus angiogenesis, or new blood vessel formation. Anti-angiogenic drugs for cancer treatment are receiving much attention, with endostatin identified as one of the potent inhibitors. Although the mechanisms of action of endostatin are yet to be fully elucidated, there is evidence that bFGF and endostatin may bind competitively to heparan sulfate proteoglycan receptors on endothelial cells, or endostatin may otherwise downregulate bFGF or VEGF and its receptors, putatively inhibiting cell proliferation. To test these and other hypotheses of inhibitory action that can be similarly formulated, for other TAF inhibitors as well as endostatin, we have developed a mathematical model of extratumoral angiogenesis in cancer in response to specific anti-angiogenic drug treatment. It is built on previous work, a modification and augmentation of published models, and is expressed as four nonlinear partial differential equations, with specific terms for endothelial cell proliferation, degradation, and endostatin-TAF inhibition, and a stochastic, discretized version of this model to represent vessel growth. Our extended model reproduces the simulated kinetics of angiogenesis in a mouse tumor model reported earlier. We assessed the anti-angiogenic kinetic behavior of our extended model by simulating dynamic responses to exogenous endostatin treatment in the same mouse model, using four dosage regimens, two of these reported for in vivo pre-clinical or clinical studies, and two 10 times greater: daily single bolus injections of 20 mg/kg per day and 200 mg/kg per day, and constant infusions of 20 mg/kg per day and 200 mg/kg per day, each for 20 simulated days. We also explored the effects of drug clearance, over an eightfold range of clearance rates that include scaled clearances for endostatin, a sister-drug angiostatin, or similar drugs with clearances in this range. Predictively, our simulation results suggest ineffectiveness of the bolus injection protocols, consistent with in vivo data with angiostatin treatment, whereas simulated constant infusion of endostatin in the mouse model effectively suppresses angiogenesis after only 3 days of treatment, at the lowest dose, over a wide range of drug clearance rates.