Mathematical modeling predicts synergistic antitumor effects of combining a macrophage-based, hypoxia-targeted gene therapy with chemotherapy

Abstract

Tumor hypoxia is associated with low rates of cell proliferation and poor drug delivery, limiting the efficacy of many conventional therapies such as chemotherapy. Because many macrophages accumulate in hypoxic regions of tumors, one way to target tumor cells in these regions could be to use genetically engineered macrophages that express therapeutic genes when exposed to hypoxia. Systemic delivery of such therapeutic macrophages may also be enhanced by preloading them with nanomagnets and applying a magnetic field to the tumor site. Here, we use a new mathematical model to compare the effects of conventional cyclophosphamide therapy with those induced when macrophages are used to deliver hypoxia-inducible cytochrome P450 to locally activate cyclophosphamide. Our mathematical model describes the spatiotemporal dynamics of vascular tumor growth and treats cells as distinct entities. Model simulations predict that combining conventional and macrophage-based therapies would be synergistic, producing greater antitumor effects than the additive effects of each form of therapy. We find that timing is crucial in this combined approach with efficacy being greatest when the macrophage-based, hypoxia-targeted therapy is administered shortly before or concurrently with chemotherapy. Last, we show that therapy with genetically engineered macrophages is markedly enhanced by using the magnetic approach described above, and that this enhancement depends mainly on the strength of the applied field, rather than its direction. This insight may be important in the treatment of nonsuperficial tumors, where generating a specific orientation of a magnetic field may prove difficult. In conclusion, we demonstrate that mathematical modeling can be used to design and maximize the efficacy of combined therapeutic approaches in cancer.

Figure 1

Outline of macrophage-based cancer therapy and mathematical model framework. Key interactions are shown, in particular that tissue oxygen depends on the vascular layer, that VEGF drives angiogenesis and macrophage migration, that drug kills tumor cells, and that hypoxic macrophages activate prodrug under hypoxia. In addition, extravasation of macrophages loaded with magnetic nanoparticles is enhanced most strongly in vessels that are perpendicular to the direction of action of a magnetic field.

Figure 2

Typical simulation showing how a tumor responds to conventional chemotherapy with cyclophosphamide, via weekly boluses (Q_bolus=12) that start three weeks after tumor implantation. (A) The state of the simulated tissue before and two days after treatments at t=21, 28, 42 and 84 days, and the average rate of cell division, drug concentration and rate of cell-kill over each 2-day period. (B) The rate of cell division, average drug concentration and rate of cell-kill over days 21 to 100.

Figure 3

Typical simulation of macrophage therapy via a single bolus of engineered macrophages three weeks after tumor implantation, coincident with the first of 20 weekly boluses of the prodrug cyclophosphamide (P_bolus=250). (A) The state of the simulated tissue before and two days after treatments at t=21, 28, 35 and 84 days, and the average rate of cell division, drug concentration and rate of cell-kill over each 2-day period. (B) The average macrophage density, rate of cell division, drug concentration, and rate of cell-kill over days 12 to 100.

Figure 4

The response to therapy over time. (A) Conventional therapy, Q_bolus=12. Each bolus leads initially to tumor regression and then regrowth. (B) Engineered macrophages accumulate after injection on day 21. Weekly prodrug boluses (P_bolus=250) cause the tumor to shrink initially and then to regrow. (C) Engineered macrophages and conventional therapy (P_bolus=250, Q_bolus=12). In 10/10 simulations the tumor is eliminated and normal tissue recovers in 8/10 cases. (Colour version: Fig. S4 in supplement)

Figure 5

Dose-response data at 100 days for tumor growth with conventional and macrophage therapy. (A) Response to conventional therapy across a range of drug doses (Q_bolus). Half-maximal efficacy is reached at Q_bolus≈12. (B) Response to macrophage therapy across a range of prodrug doses (P_bolus). Half-maximal efficacy is reached at P_bolus≈250. (A,B) In both cases, drug/prodrug doses above the EC₅₀ can promote recovery of normal tissue, but if the dose is too large normal tissue is also damaged further. Bars represent mean values (n=10) and individual simulations are indicated by points. The point style indicates whether or not the tumor and/or normal cells persist at the end of each simulation (at 200 days).

Figure 6

(A) Series of curves showing dependence on the magnetic field of macrophage infiltration into a tumor, where the macrophages have been loaded with magnetic nanoparticles. Each curve is the mean of ten simulations. The macrophage fractions after five hours, without and with a magnetic field, are in agreement with experimental data in (5). (B) Cumulative macrophage extravasation at five hours, without a magnetic field, and with a magnetic field oriented in the x- and y-directions. The magnetic field increases the extravasation rate at specific vessels according to their orientation relative to the magnetic field. (C) The distribution of quiescent cancer cells, infiltrated macrophages, and the vascular network at five hours. The overall pattern of macrophage localisation is similar for both orientations of the field.

Figure 7

Summary data, showing the state at 100 days, for combination therapies starting three weeks after tumor implantation. (A) Comparison of conventional therapy (Q_bolus=11), macrophage therapy (P_bolus=120), magnetically enhanced macrophage therapy, and simultaneously delivered combinations. For combined conventional and macrophage therapy, the average reduction in tumor size is greater than would be expected from the sum of the individual effects. The results also illustrate the variability in response that can occur. (B) One combination (Q_bolus=120, Q_bolus=11), which gives tumor elimination in 6/10 cases, with various timing shifts of macrophage therapy relative to conventional therapy. “-1h” indicates macrophage therapy is 1 hour before conventional therapy, etc. Macrophage therapy 1h and 6h prior to conventional therapy gives a small advantage (tumor elimination in 7/10 cases). All other tested timing shifts give worse responses. (A,B) Bars represent mean values (n=10) and individual simulations are indicated by points. The point style indicates whether or not the tumor and/or normal cells persist at the end of each simulation (at 200 days).