Optimization of vascular-targeting drugs in a computational model of tumor growth

A biophysical tool is introduced that seeks to provide a theoretical basis for helping drug design teams assess the most promising drug targets and design optimal treatment strategies. The tool is grounded in a previously validated computational model of the feedback that occurs between a growing tumor and the evolving vasculature. In this paper, the model is particularly used to explore the therapeutic effectiveness of two drugs that target the tumor vasculature: angiogenesis inhibitors (AIs) and vascular disrupting agents (VDAs). Using sensitivity analyses, the impact of VDA dosing parameters is explored, as is the effects of administering a VDA with an AI. Further, a stochastic optimization scheme is utilized to identify an optimal dosing schedule for treatment with an AI and a chemotherapeutic. The treatment regimen identified can successfully halt simulated tumor growth, even after the cessation of therapy.

Figure 1

Summary of the HCA model used in this paper to test the efficacy of several vascular-targeting treatment strategies. Viable nonmalignant cells are white, nonproliferative/hypoxic tumor cells are yellow (light gray in black and white), and proliferative tumor cells are blue (dark gray in black and white).

Figure 2

Schematic representation of the system of PDEs detailed in Eqs. (A1, A2, A3, A4, A5, A6, A7, A8), showing the interactions between growth factors, receptors, ligand-receptor complexes, and cell types. The ligand VEGF is denoted by $V$, Ang-1 by $A1$, and Ang-2 by $A2$. Curved arrows indicate the cell type that produced the referenced protein (for instance, hypoxic cells produce VEGF and Ang-2, whereas ECs produce Ang-1 and Ang-2), and straight arrows indicate the physiological response to ligand-receptor binding (for instance, VEGF binding to VEGFR-2 induces angiogenesis). Notice how VEGF and Ang-2 diffuse in the extracellular space, whereas Ang-1 only acts locally.

Figure 3

Average active tumor area for four VDA dosing strategies (with $T_3=0.6$): daily administration, weekly administration, administration once every 3 weeks, administration once every 5 weeks. Tumor growth is compared to the case where no treatment is administered.

Figure 4

Average area of active tumor region compared for four different scenarios: no therapy is administered, AI administration only, VDA administration only, and an AI coupled with a VDA.

Figure 5

Sensitivity analysis of the AI plus VDA treatment regimen. In (a) the AI parameter is $T_1=10$, in (b) the AI parameter is $T_1=100$, and in (c) the AI parameter is $T_1=1000$, with the VDA taking on a range of values in each case.

Figure 6

Simulated annealing results. (a) Change in the treatment parameters ${\lambda }_{AI}$, ${\lambda }_{AIC}$, and ${\lambda }_C$ as a function of accepted annealing step $\overline{k}$. $\overline{k}=N$ represents the $N\text{th}$ accepted parameter set. (b) Change in the average number of active cells remaining after 8 weeks of treatment as a function of accepted annealing step $\overline{k}$.

Figure 7

Optimal treatment strategy. (a) Comparing the efficacy of the proposed optimal treatment strategy to the simultaneous administration of an AI and a chemotherapeutic [5]. (b) Response of active tumor area to cessation of therapy. The average time of therapy cessation is denoted by a dashed black vertical line.