The majority of cancer-related fatalities are due to metastatic disease. Chemotherapeutic agents are administered along with radiation in chemoradiotherapy (CRT) to control the primary tumor and systemic disease such as metastasis. This work introduces a mathematical model of CRT treatment scheduling to obtain optimal drug and radiation protocols with the objective of minimizing metastatic cancer cell populations at multiple potential sites while maintaining a desired level of control on the primary tumor. Dynamic programming framework is used to determine the optimal radiotherapy fractionation regimen and the drug administration schedule. We design efficient DP data structures and use structural properties of the optimal solution to reduce the complexity of the resulting DP algorithm. We derive closed-form expressions for optimal chemotherapy schedules in special cases. The results suggest that if there is only an additive and spatial cooperation between the chemotherapeutic drug and radiation with no interaction between them, then radiation and drug administration schedules can be decoupled. In that case, regardless of the chemo- and radio sensitivity parameters, the optimal radiotherapy schedule follows a hypofractionated scheme. However, the structure of the optimal chemotherapy schedule depends on model parameters such as chemotherapy-induced cell kill at primary and metastatic sites, as well as the ability of primary tumor cells to initiate successful metastasis at different body sites. In contrast, an interactive cooperation between the drug and radiation leads to optimal split-course concurrent CRT regimens. Additionally, under dynamic radio sensitivity parameters due to the reoxygenation effect during therapy, we observe that it is optimal to immediately start the chemotherapy and administer a few large radiation fractions at the beginning of the therapy, while scheduling smaller fractions in later sessions. We quantify the trade-off between the new and traditional objectives of minimizing the metastatic population size and maximizing the primary tumor control probability, respectively, for a cervical cancer case. The trade-off information indicates the potential for significant reduction in the metastatic population with minimal loss in the primary tumor control.
Bibliographical noteFunding Information:
The first author thanks the National Science Foundation (NSF) for their support [Grant CMMI-1362236]. The second author thanks NSF for their support [Grant CMMI-1662819]. The fourth author thanks NSF for their support [Grants CMMI-1362236 and CMMI-1552764].
History: Accepted by Allen Holder, Area Editor for Applications in Biology, Medicine, and Health Care. Funding:The first author thanks the National Science Foundation (NSF) for their support [Grant CMMI-1362236]. The second author thanks NSF for their support [Grant CMMI-1662819]. The fourth author thanks NSF for their support [Grants CMMI-1362236 and CMMI-1552764]. SupplementalMaterial: The online supplement is available at https://doi.org/10.1287/ĳoc.2017.0778.
- Dynamic programming
- Metastatic disease
- Optimal fractionation