Optimal Therapy Scheduling Based on a Pair of Collaterally Sensitive Drugs
Preprint
- 2 October 2017
- preprint
- other
- Published by Cold Spring Harbor Laboratory
- p. 196824
- https://doi.org/10.1101/196824
Abstract
Despite major strides in the treatment of cancer, the development of drug resistance remains a major hurdle. One strategy which has been proposed to address this is the sequential application of drug therapies where resistance to one drug induces sensitivity to another drug, a concept called collateral sensitivity. The optimal timing of drug switching in these situations, however, remains unknown.To study this, we developed a dynamical model of sequential therapy on heterogeneous tumors comprised of resistant and sensitive cells. A pair of drugs (DrugA, DrugB) are utilized and are periodically switched during therapy. Assuming resistant cells to one drug are collaterally sensitive to the opposing drug, we classified cancer cells into two groups,ARandBR, each of which is a subpopulation of cells resistant to the indicated drug and concurrently sensitive to the other, and we subsequently explored the resulting population dynamics.Specifically, based on a system of ordinary differential equations forARandBR, we determined that the optimal treatment strategy consists of two stages: an initial stage in which a chosen effective drug is utilized until a specific time point,T, and a second stage in which drugs are switched repeatedly, during which each drug is used for a relative duration (i.e.fΔt-long forDrugAand (1 –f) Δt-long forDrugBwith 0 ≤f≤ 1 and Δt≥ 0). We prove that the optimal duration of the initial stage, in which the first drug is administered,T, is shorter than the period in which it remains effective in decreasing the total population, contrary to current clinical intuition.We further analyzed the relationship between population makeup, , and the effect of each drug. We determine a critical ratio, which we term , at which the two drugs are equally effective. As the first stage of the optimal strategy is applied, changes monotonically to and then, during the second stage, remains at thereafter.Beyond our analytic results, we explored an individual based stochastic model and presented the distribution of extinction times for the classes of solutions found. Taken together, our results suggest opportunities to improve therapy scheduling in clinical oncology.Keywords
Other Versions
- Published version: Version Bulletin of Mathematical Biology, 80, preprints
This publication has 35 references indexed in Scilit:
- Evolutionary dynamics of carcinogenesis and why targeted therapy does not workNature Reviews Cancer, 2012
- Intra-tumour heterogeneity: a looking glass for cancer?Nature Reviews Cancer, 2012
- Quantifying the Role of Angiogenesis in Malignant Progression of Gliomas: In Silico Modeling Integrates Imaging and HistologyCancer Research, 2011
- Phenotypic plasticity and epithelial‐mesenchymal transitions in cancer and normal stem cells?International Journal of Cancer, 2011
- The influence of toxicity constraints in models of chemotherapeutic protocol escalationMathematical Medicine and Biology, 2011
- The Worst Drug Rule Revisited: Mathematical Modeling of Cyclic Cancer TreatmentsBulletin of Mathematical Biology, 2010
- Drug resistance in cancer: Principles of emergence and preventionProceedings of the National Academy of Sciences of the United States of America, 2005
- The mathematical modelling of adjuvant chemotherapy scheduling: incorporating the effects of protocol rest phases and pharmacokineticsBulletin of Mathematical Biology, 2005
- A model for the resistance of tumor cells to cancer chemotherapeutic agentsMathematical Biosciences, 1983
- A general method for numerically simulating the stochastic time evolution of coupled chemical reactionsJournal of Computational Physics, 1976