Optimized and Personalized Phlebotomy Schedules for Patients Suffering From Polycythemia Vera

Abstract

Polycythemia vera (PV) is a slow-growing type of blood cancer, where the production of red blood cells (RBCs) increase considerably. The principal treatment for targeting the symptoms of PV is bloodletting (phlebotomy) at regular intervals based on data derived from blood counts and physician assessments based on experience. Model-based decision support can help to identify optimal and individualized phlebotomy schedules to improve the treatment success and reduce the number of phlebotomies and thus negative side effects of the therapy. We present an extension of a simple compartment model of the production of RBCs in adults to capture patients suffering from PV. We analyze the model's properties to show the plausibility of its assumptions. We complement this with numerical results using exemplary PV patient data. The model is then used to simulate the dynamics of the disease and to compute optimal treatment plans. We discuss heuristics and solution approaches for different settings, which include constraints arising in real-world applications, where the scheduling of phlebotomies depends on appointments between patients and treating physicians. We expect that this research can support personalized clinical decisions in cases of PV.

Keywords: cancer; decision support; mixed-integer non-linear optimization; modeling; numerical simulation; optimal control; polycythemia vera; therapy scheduling.

Figure 1

Simplified schematic view of erythropoiesis. Certain cell stages over the age of the cell in days are displayed with a corresponding cell partition based on the model by Tetschke et al. (2018).

Figure 2

Graphical view on the general test setup including restrictions of the clinic in red. Phlebotomies are only allowed during times denoted in white.

Figure 3

Exemplary result for an optimal relaxed treatment schedule. The continuous control function u (blue) is zero, as long as the tHb-value (black) is below the upper bound (dashed, purple). As soon as the upper bound is reached, the control function increases exactly as much as necessary to keep the tHb-value at the upper bound.

Figure 4

Erythrocyte trajectories as a result of parameter estimation on three clinical data sets. The computed measurement values are given in red, and the healthy base value B is displayed in purple.

Figure 5

Erythrocyte trajectories of three exemplary patients using IP-Schedules and HC-Schedules. The upper threshold (red, dashed) and the end of the time horizon at T = 103 days (gray, dashed) are marked.

Figure 6

Duration of constraint violation d_viol over the difference in the number of treatments for each of the 140 test cases (blue). The purple dashed line shows a linear regression over all instances with n_diff ≥ 0.

Figure 7

Erythrocyte trajectories using DP-Schedules for both rounding approaches and HC-Schedules for three exemplary patients. X_3,up is shown as the red dashed line.