Optimization of Dose Schedules for Chemotherapy of Early Colon Cancer Determined by High-Performance Computer Simulations

Abstract

Cancer chemotherapy dose schedules are conventionally applied intermittently, with dose duration of the order of hours, intervals between doses of days or weeks, and cycles repeated for weeks. The large number of possible combinations of values of duration, interval, and lethality has been an impediment to empirically determine the optimal set of treatment conditions. The purpose of this project was to determine the set of parameters for duration, interval, and lethality that would be most effective for treating early colon cancer. An agent-based computer model that simulated cell proliferation kinetics in normal human colon crypts was calibrated with measurements of human biopsy specimens. Mutant cells were simulated as proliferating and forming an adenoma, or dying if treated with cytotoxic chemotherapy. Using a high-performance computer, a total of 28 800 different parameter sets of duration, interval, and lethality were simulated. The effect of each parameter set on the stability of colon crypts, the time to cure a crypt of mutant cells, and the accumulated dose was determined. Of the 28 800 parameter sets, 434 parameter sets were effective in curing the crypts of mutant cells before they could form an adenoma and allowed the crypt normal cell dynamics to recover to pretreatment levels. A group of 14 similar parameter sets produced a minimal time to cure mutant cells. A different group of nine similar parameter sets produced the least accumulated dose. These parameter sets may be considered as candidate dose schedules to guide clinical trials for early colon cancer.

Keywords: agent-based model; chemotherapy; colon cancer; computer simulation; dose schedules; high-performance computer; mutants.

Figure 1.

Distributions of average time to cure and sum dose of chemotherapy. (A): time, in simulation steps, to cure mutants versus the rank of each of 434 dose schedule parameter sets. (B): sum of lethal doses to cure mutants versus the rank of the each of the 434 dose schedule parameter sets. Points are color-coded according to the average time of 50 simulations that it takes to cure mutants, see Figure 3. (C): comparison of the ranks of parameter sets for the sum of doses and the ranks of the parameter sets for the time to cure. The ranks are not highly correlated (R² = 0.45).

Figure 2.

Time to cure and accumulated dose for different dose schedules. (A) and (B): dose schedules for the shortest time to cure (two time-steps), and the slowest time to cure (263 time-steps), with the indicated parameter set of duration, interval, and lethality. The red arrows indicate the average times to cure for 50 simulations. (C) and (D): example of one of 50 simulations of the kinetics of the proportion of mutants per crypt for the dose schedules shown in (A) and (B), respectively. (E) and (F): total dose accumulation as a function of time-steps for the dose schedules shown in (A) and (B), respectively. The average total dose at the time of cure is indicated by the red line.

Figure 3.

Dose schedule parameter sets that cure mutants when chemotherapy is started at different times. Each point represents a dose schedule parameter set that yield a 100% mutant cure rate and 0% crypt mortality rate when tested over 50 stochastic replicates. The duration of chemotherapy (in simulation time-steps) is represented on the x-axis; the interval between doses (in simulation time-steps) is represented on the y-axis; cytotoxic lethality factor is represented on the z-axis. Points are color-coded based on the average time to cure a crypt of mutant cells, with red representing a treatment schedule that quickly eliminates the mutant cells and dark blue representing a treatment which takes longer to eliminate mutant cells. (A): successful parameter sets for chemotherapy that is initiated when mutant cells make up 20% of the total crypt population; (B): successful parameter sets for chemotherapy that is initiated when mutant cells make up 40% of the total crypt population. (C): comparison of parameter sets in A and B. Points shaded in red are those which are unique to the set of simulations that initiate chemotherapy when mutant cells compose 20% of the crypt; points shaded in blue are those which are unique to the set of simulations that initiate chemotherapy when mutant cells compose 40% of the crypt; points shaded in green are those which are shared between the set of simulations that initiate chemotherapy when mutant cells compose 20% of the crypt and the set of simulations that initiate chemotherapy when mutant cells compose 40% of the crypt.