Proefschrift

APPENDIX B. SUPPLEMENT TO CHAPTER 6 Figure B.12: Two-dimensional projections of state dynamics from FBS for Matrix 2 to the three-species equilibrium. Projections of the state trajectories from 100 random initial states x ( t 0 ) to x ∗ with Λ ∗ ( · ) found by FBS to the three species equilibrium. ( x T + , x T P )- space in the left panel, ( x T + , x T − )-space in the center panel, and ( x T P , x T − )-space in the right panel. Paths highlighted in red breach the patient viability constraint before reaching the equilibrium point. B.5 Comparison of Titration Protocols for One Patient under Matrix 2 Figure B.13 shows the population dynamics of the simulated patients under the four titration protocols. The patient’s incoming tumor volume is 5924.83. Panel (a) attempts to stabilize at V a with the initial dose as Λ( t 0 ) = 1. The high initial doses cause the volume to drop below V a and in response the dose is titrated down quite quickly. Unfortunately, due to the high initial doses the underlying tumor composition includes a high proportion of T − cells and stabilization is lost once these cells outgrow the T P population. Panel (b) attempts to instead stabilize at V b with the same initial dose of Λ( t 0 ) = 1. The same initial dynamics are observed but because the stabilization volume is allowed to be larger than that in panel (a), the T P population increases enough to out-compete the T − population. Furthermore, a T + population is sustained by the large T P population and stabilization is achieved. In panel (c), the target volume is again V a but the initial dose is now changed to Λ( t 0 ) = 0. The dosage is only increased as the T P and T + cells begin to grow, but the competitive release of T − cells is avoided because no high doses of abiraterone were given. The underlying dynamics show that eventually the T − cells will take over the tumor population but the total tumor volume does not exceed the patient viability constraint during the simulation. If instead we use V b , panel (d), the presence of the large T P and T + population out-compete the T − population and stabilization is achieved. 146