Cancer is a highly heterogeneous disease, exhibiting spatial and temporal variations that pose challenges for designing robust therapies. Here, we propose the VEPART (Virtual Expansion of Populations for Analyzing Robustness of Therapies) technique as a platform that integrates experimental data, mathematical modeling, and statistical analyses for identifying robust optimal treatment protocols. VEPART begins with time course experimental data for a sample population, and a mathematical model fit to aggregate data from that sample population. Using nonparametric statistics, the sample population is amplified and used to create a large number of virtual populations. At the final step of VEPART, robustness is assessed by identifying and analyzing the optimal therapy (perhaps restricted to a set of clinically realizable protocols) across each virtual population. As proof of concept, we have applied the VEPART method to study the robustness of treatment response in a mouse model of melanoma subject to treatment with immunostimulatory oncolytic viruses and dendritic cell vaccines. Our analysis (i) showed that every scheduling variant of the experimentally used treatment protocol is fragile (nonrobust) and (ii) discovered an alternative region of dosing space (lower oncolytic virus dose, higher dendritic cell dose) for which a robust optimal protocol exists.

Oncolytic viruses (OVs) are used to treat cancer, as they selectively replicate inside of and lyse tumor cells. The efficacy of this process is limited and new OVs are being designed to mediate tumor cell release of cytokines and co-stimulatory molecules, which attract cytotoxic T cells to target tumor cells, thus increasing the tumor-killing effects of OVs. To further promote treatment efficacy, OVs can be combined with other treatments, such as was done by Huang et al., who showed that combining OV injections with dendritic cell (DC) injections was a more effective treatment than either treatment alone. To further investigate this combination, we built a mathematical model consisting of a system of ordinary differential equations and fit the model to the hierarchical data provided from Huang et al. We used the model to determine the effect of varying doses of OV and DC injections and to test alternative treatment strategies. We found that the DC dose given in Huang et al. was near a bifurcation point and that a slightly larger dose could cause complete eradication of the tumor. Further, the model results suggest that it is more effective to treat a tumor with immunostimulatory oncolytic viruses first and then follow-up with a sequence of DCs than to alternate OV and DC injections. This protocol, which was not considered in the experiments of Huang et al., allows the infection to initially thrive before the immune response is enhanced. Taken together, our work shows how the ordering, temporal spacing, and dosage of OV and DC can be chosen to maximize efficacy and to potentially eliminate tumors altogether.

Mathematical modeling techniques have been widely employed to understand how cancer grows, and, more recently, such approaches have been used to understand how cancer can be controlled. In this manuscript, a previously validated hybrid cellular automaton model of tumor growth in a vascularized environment is used to study the antitumor activity of several vascular‐targeting compounds of known efficacy. In particular, this model is used to test the antitumor activity of a clinically used angiogenesis inhibitor (both in isolation, and with a cytotoxic chemotherapeutic) and a vascular disrupting agent currently undergoing clinical trial testing. I demonstrate that the mathematical model can make predictions in agreement with preclinical/clinical data and can also be used to gain more insight into these treatment protocols. The results presented herein suggest that vascular‐targeting agents, as currently administered, cannot lead to cancer eradication, although a highly efficacious agent may lead to long‐term cancer control.

While chemoresistance in primary tumors is well-studied, much less is known about the influence of systemic chemotherapy on the development of drug resistance at metastatic sites. In this work, we use a hybrid spatial model of tumor response to a DNA damaging drug to study how the development of chemoresistance in micrometastases depends on the drug dosing schedule. We separately consider cell populations that harbor pre-existing resistance to the drug, and those that acquire resistance during the course of treatment. For each of these independent scenarios, we consider one hypothetical cell line that is responsive to metronomic chemotherapy, and another that with high probability cannot be eradicated by a metronomic protocol. Motivated by experimental work on ovarian cancer xenografts, we consider all possible combinations of a one week treatment protocol, repeated for three weeks, and constrained by the total weekly drug dose. Simulations reveal a small number of fractionated-dose protocols that are at least as effective as metronomic therapy in eradicating micrometastases with acquired resistance (weak or strong), while also being at least as effective on those that harbor weakly pre-existing resistant cells. Given the responsiveness of very different theoretical cell lines to these few fractionated-dose protocols, these may represent more effective ways to schedule chemotherapy with the goal of limiting metastatic tumor progression.