Proefschrift

(a) Stable points for Matrix 2 with α 32 = 1 . 0. (b) Stable points for Matrix 2 with α 32 = 1 . 1 (c) Stable points for Matrix 2 with α 32 = 2 . 0 (d) Stable points for Matrix 2 with α 32 = 5 . 0 Figure B.1: Stable points for various values of α in Matrix 2. (a) Stable points for Matrix 2 with α 32 = 1 . 0. (b) Stable points for Matrix 2 with α 32 = 1 . 1 (c) Stable points for Matrix 2 with α 32 = 2 . 0. (d) Stable points for Matrix 2 with α 32 = 5 . 0. Figure B.1 shows that increasing the value of α 32 shifts the stable points. The values of the competition coefficients being less than or equal to one require high cell densities to elicit a strong competition between cell types, specifically the T − cells, which makes all stable points have total volumes above the patient viability constraint. As α 32 increases, the stable points shift, allowing the same dose of abiraterone to maintain lower levels of T − , along with some stability points where T − is excluded. The case where α 32 = 2 . 0 is the matrix discussed in detail in Chapter 6. We chose α 32 = 2 . 0, because it 1) allows for stability points within the patient viability constraint and 2) did not eliminate T − from all stability points (like that seen with α 32 = 5 . 0). In this way, we could analyze a case where the resistant T − cells are still present in the tumor, which would be expected clinically. Obviously, the exact value of any of the competition coefficients will affect the behavior and stability of this model. Experimental work to identify the exact, or at least probable, values of these coefficients will greatly improve the validity of the model predictions. The work provided here assumes that there is a heterogeneous stable point of any kind within the patient tumor burden. There are many ways to achieve this, and we will show a few examples beyond that shown in the main text here. Until experimental work is provided, the values chosen here provide a starting point for further analysis. For Matrix 5, increasing the value of α 32 = 2 . 0 introduced a region of stable points that include only T + and T P cells shown in Figure B.2. 139