Mathematical optimisation of the cisplatin plus etoposide combination for managing extensive-stage small-cell lung cancer patients.

BACKGROUND: Small-cell lung cancer (SCLC) represents one of the most aggressive forms of lung cancer. Despite the fair sensitivity of SCLC to chemotherapy and radiotherapy, the current standard treatment regimens have modest survival rates and are associated with potential life-threatening adverse events. Therefore, research into new optimised regimens that increase drug efficacy while respecting toxicity constraints is of primary importance. METHODS: A PK/PD model for the combination of cisplatin and etoposide to treat extensive-stage SCLC patients was generated. The model takes into consideration both the efficacy of the drugs and their haematological toxicity. Using optimisation techniques, the model can be used to propose new regimens. RESULTS: Three new regimens with varying timing for combining cisplatin and etoposide have been generated that respect haematological toxicity constraints and achieve better or similar tumour regression. The proposed regimens are: (1) Protocol OP1: etoposide 80 mg m-2 over 1 h D1, followed by a long infusion 12 h later (over 3 days) of 160 mg m-2 plus cisplatin 80 mg m-2 over 1 h D1, D1-D1 21 days; (2) Protocol OP2: etoposide 80 mg m-2 over 1 h D1, followed by a long infusion 12 h later (over 4 days) of 300 mg m-2 plus cisplatin 100 mg m-2 over 1 h D1, D1-D1 21 days; and (3) Protocol OP3: etoposide 40 mg m-2 over 1 h, followed by a long infusion 6 h later (3 days) of 105 mg m-2 plus cisplatin 50 mg m-2 over 1 h, D1-D1 14 days. CONCLUSIONS: Mathematical modelling can help optimise the design of new cisplatin plus etoposide regimens for managing extensive-stage SCLC patients.

Modeling circadian clock-cell cycle interaction effects on cell population growth rates.

The circadian clock and the cell cycle are two tightly coupled oscillators. Recent analytical studies have shown counter-intuitive effects of circadian gating of the cell cycle on growth rates of proliferating cells which cannot be explained by a molecular model or a population model alone. In this work, we present a combined molecular-population model that studies how coupling the circadian clock to the cell cycle, through the protein WEE1, affects a proliferating cell population. We show that the cell cycle can entrain to the circadian clock with different rational period ratios and characterize multiple domains of entrainment. We show that coupling increases the growth rate for autonomous periods of the cell cycle around 24 h and above 48 h. We study the effect of mutation of circadian genes on the growth rate of cells and show that disruption of the circadian clock can lead to abnormal proliferation. Particularly, we show that Cry 1, Cry 2 mutations decrease the growth rate of cells, Per 2 mutation enhances it and Bmal 1 knockout increases it for autonomous periods of the cell cycle less than 21 h and decreases it elsewhere. Combining a molecular model to a population model offers new insight on the influence of the circadian clock on the growth of a cell population. This can help chronotherapy which takes benefits of physiological rhythms to improve anti-cancer efficacy and tolerance to drugs by administering treatments at a specific time of the day.