Oncologists - and often also cancer patients who are involved in the decision making process - need to choose between different treatment alternatives, including different drugs and immune-boosters, scheduling of the treatments, and dosages. Issues like the balancing between positive (killing) impact on cancerous cells and negative (killing) impact on immune cells highlight the importance to understand the body as a complex dynamical system. I propose to use mathematical models and optimization to enlarge our understanding and come up with a patient-, cancer-, and time-dependent individualized DSS.
There are many different levels on which tumor growth and possible control targets can be modeled. Inherently this is a complex multi-scale problem. A mathematical model can be stochastic or deterministic, spatially resolved or not, continuous or agent-based. Also the level of detail may vary. For example, there may be good reasons to include circadian rhythms and the cell cycle. As a first step, we investigated the potential of timing for a variety of cancer models from the literature in [S2], compare also this page.
We showed that even for quite simplistic models that do not take pharmacokinetics or effects on the immune system into account, the timing of the drug (with a fixed overall amount over the time horizon) has a large impact and may be non-intuitive. We take this as an encouragement to concentrate our efforts on more accurate and reliable mathematical models with patient-specific model parameters.
In collaboration with the oncologists Thomas Fischer and Enrico Schalk in Magdeburg, we started to mathematically model the special case of acute myeloid leukemia (AML). We want to be able to reproduce the behavior of leukocytes and neutrophils during chemotherapy treatment. Of particular interest is the infection risk. Neutropenia is one of the most harmful side effects during leukemia treatment, since neutrophils are crucial in protecting patients against bacteria and fungi.