Proefschrift

APPENDIX A. SUPPLEMENT TO CHAPTER 5 A.1 Objective Value Analysis Each of the ten treatment schedules are listed as rows. The top three are the non optimized schedules, the middle four are the intermittent schedules, and the bottom three are the optimized schedules labeled by the objective. The time to competitive release shown in Table 5.2 are included again here as the first column. The remaining three columns are the values of the objective functions: cumulative total tumor density (Volume), tumor variance (Variance), and cumulative T − density ( T − ). Entries highlighted in red indicate that the optimization algorithm successfully found the optimal control solution that minimized the objective. Calculating the value of the objective function, even when it is not being minimized, shows how the optimization of one objective affects the value of other potential objectives (i.e. how does minimizing the variance in tumor size influence the overall tumor size, and the variance in tumor size over time?). Of note, optimized treatment schedules that minimize the T − population tend to maximize total tumor volume, as the presence of T + and T P cells is the competition mechanism which controls the T − cell density. Treatment Schedule t CR Volume Variance T − No Treatment > 3000 5 . 607 × 10 7 1 . 607 × 10 7 1 . 121 × 10 − 4 SOC > 3000 8 . 312 × 10 5 1 . 752 × 10 4 21 . 855 20% SOC > 3000 4 . 4325 × 10 7 8 . 028 × 10 6 6 . 426 × 10 − 4 LFHA w/ Induction > 3000 6 . 736 × 10 6 1 . 297 × 10 6 4 . 395 LFHA w/o Induction > 3000 3 . 871 × 10 6 5 . 487 × 10 4 10 . 266 HFLA w/ Induction > 3000 4 . 003 × 10 7 6 . 867 × 10 6 0 . 001 HFLA w/o Induction > 3000 3 . 875 × 10 7 5 . 551 × 10 6 0 . 002 Volume > 3000 3 . 871 × 10 6 5 . 487 × 10 4 10 . 266 Variance > 3000 3 . 871 × 10 6 5 . 487 × 10 4 10 . 266 T − > 3000 4 . 071 × 10 7 2 . 215 × 10 7 4 . 681 × 10 − 4 Table A.1: Time to Competitive Release and Comparative Objectives for the “Best- Responder” Patient. A.2 Robustness Analysis of Jitter to Bang-Bang Treatment Schedules The N k possible combinations of bang-bang control are calculated where N = 25 possible control points and k = 5 to satisfy the constraint of 20% of the maximum tolerated dose. This results in 53130 possible bang-bang treatment schedules. The value of the objective function of interest is calculated for all 53130 bang-bang treatment schedules. This allows the likely minimum value of the objective for our pre-specified control structure and associated treatment schedule to be found. In all seven of nine applicable cases (minimizing tumor variance in the responder and non-responder patients is not bang-bang control) the constraint optimization was indeed approaching this likely minimum. 126