Mathematical Modeling in Optimizing Methotrexate-Based Chemotherapy.

Optimization of doses and administration schedules for anticancer drugs is crucial for effective and safe treatment. Since chemotherapy (CT) remains based predominately on empiric data, the creation of a mathematical model describing the complex interplay between dosing, tumor-response, agents' clearance, and toxicity, presents the opportunity to optimize treatment strategies of established but also new drugs. Primary central nervous system lymphoma (PCNSL) is a rare disease whose incidence is rising. Standard treatment of methotrexat (MTX) based CT has been approved in several studies. Here we report the most recent development of a real-life mathematical model describing the relationship between MTX serum levels and myelosuppression to optimize current treatment protocols.

We retrospectively analyzed 38 patients (pts) diagnosed and treated for PCNSL from 2005-2009. Pts <65 yrs of age were treated according to the high-dose MTX induction protocol (MTX 8g/m²/4hrs followed by leucovorin rescue), whereas treatment of pts >65 yrs of age followed the elderly protocol (MTX 3g/m²/4hrs followed by leucovorin rescue). Leukocyte and MTX serum levels were documented. We used an extended version of the mathematical model by Friberg et al. (J Clin Oncol 2002) as basis for our computations. The model was fitted to the data by using a least-squares-error approach.

First order elimination proves sufficient for describing the pharmacokinetics of MTX. The average elimination rate is 0.25 h^-1 with similar inter-patient and inter-therapy variation: the STD is 0.03 h^-1 among patients and 0.02 h^-1 among treatments. Similar analysis of all present parameters highlights the overall robustness of our approach.

Our model makes it possible to predict myelosuppression after treatment with MTX following leucovorin rescue based on clinical data. The parameters estimated are in accordance with those provided by Friberg et al. and thus confirm the model's general relevance. Extensions of the model describing tumor size reduction by MTX will be implemented to describe the complex interplay between MTX serum levels, clearance and anti-tumor effect. Additionally, mathematical optimal control theory methods will be employed to compute optimized schedules, i.e. doses and timing for the drugs that minimize tumor size and do not violate toxicity constraints such as leukocyte count.

No relevant conflicts of interest to declare.