Minimizing metastatic risk in radiotherapy fractionation schedules

Optimizing multi-modal cancer treatment under 3D spatio-temporal tumor growth

In this paper we introduce a new mixed-integer linear programming (MIP) model that explicitly integrates the spread of cancer cells into a spatio-temporal reaction-diffusion (RD) model of cancer growth, while taking into account treatment effects. This linear but non-convex model appears to be the first of its kind by determining the optimal sequence of the typically prescribed cancer treatment methods-surgery (S), chemotherapy (C), and radiotherapy (R)-while minimizing the newly generated tumor cells for early-stage breast cancer in a unique three-dimensional (3D) spatio-temporal system. The quadratically-constrained cancer growth dynamics and treatment impact formulations are linearized by using linearization as well as approximation techniques. Under the supervision of medical oncologists and utilizing several literature resources for the parameter values, the effectiveness of treatment combinations for breast cancer specified with different sequences (i.e., SRC, SCR, CR, RC) are compared by tracking the number of cancer cells at the end of each treatment modality. Our results provide the optimal dosages for chemotherapy and radiation treatments, while minimizing the growth of new cancer cells.

Optimal treatment and stochastic modeling of heterogeneous tumors

In this work we review past articles that have mathematically studied cancer heterogeneity and the impact of this heterogeneity on the structure of optimal therapy. We look at past works on modeling how heterogeneous tumors respond to radiotherapy, and take a particularly close look at how the optimal radiotherapy schedule is modified by the presence of heterogeneity. In addition, we review past works on the study of optimal chemotherapy when dealing with heterogeneous tumors.

REVIEWERS

This article was reviewed by Thomas McDonald, David Axelrod, and Leonid Hanin.