Pharmacokinetic/pharmacodynamic modeling of combination-chemotherapy for lung cancer

Abstract

Chemotherapy for non-small cell lung cancer (NSCLC) typically involves a doublet regimen for a number of cycles. For any particular patient, a course of treatment is usually chosen from a large number of combinational protocols with drugs in concomitant or sequential administration. In spite of newer drugs and protocols, half of patients with early disease will live less than five years and 95% of those with advanced disease survive for less than one year. Here, we apply mathematical modeling to simulate tumor response to multiple drug regimens, with the capability to assess maximum tolerated dose (MTD) as well as metronomic drug administration. We couple pharmacokinetic-pharmacodynamic intracellular multi-compartment models with a model of vascularized tumor growth, setting input parameters from in vitro data, and using the models to project potential response in vivo. This represents an initial step towards the development of a comprehensive virtual system to evaluate tumor response to combinatorial drug regimens, with the goal to more efficiently identify optimal course of treatment with patient tumor-specific data. We evaluate cisplatin and gemcitabine with clinically-relevant dosages, and simulate four treatment NSCLC scenarios combining MTD and metronomic therapy. This work thus establishes a framework for systematic evaluation of tumor response to combination chemotherapy. The results with the chosen parameter set indicate that although a metronomic regimen may provide advantage over MTD, the combination of these regimens may not necessarily offer improved response. Future model evaluation of chemotherapy possibilities may help to assess their potential value to obtain sustained NSCLC regression for particular patients, with the ultimate goal of optimizing multiple-drug chemotherapy regimens in clinical practice.

Keywords: Combination chemotherapy; Gemcitabine and cisplatin; Lung cancer; Mathematical modeling and computational simulation; Pharmacokinetics and pharmacodynamics.

Figure 1

Simulated NSCLC tumor prior to treatment. (A) Lesion (center) is shown with surrounding capillaries (brown lines). Red: Viable (proliferating) tissue; blue: hypoxic (quiescent) tissue; brown: necrotic (dead) tissue. Existing capillary grid is denoted by regularly spaced lines, with vessels induced by angiogenesis, irregularly growing towards the tumor, attracted by angiogenic stimuli diffusing from the hypoxic regions. Host tissue (not shown) surrounds the lesion. (B) Pressure profile (non-dimensional values) corresponding to the growing tumor lesion, with highest values (red) in the proliferating ring and lowest values (blue) in the host. (C) Oxygen concentration profile (maximum value normalized by the concentration in vasculature) is determined by diffusion from the vasculature into the hypoxic and necrotic tumor regions. Bar, 250 μm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Figure 2

Case 1 (standard CDDP and dFdC) on day 1 of treatment immediately after drug injection. The drug concentrations are shown for the extracellular (μM), intracellular (fMoles/cell), and DNA-bound (fMoles/cell) compartments as defined at this timepoint by the corresponding pharmacokinetic equations.

Figure 3

Case 1 (standard CDDP and dFdC) after 7 days post treatment initiation. The drug concentrations are shown for the extracellular (μM), intracellular (fMoles/cell), and DNA-bound (fMoles/cell) compartments as defined at this timepoint by the corresponding pharmacokinetic equations. While the proliferation region has shrunk compared to day 1, the overall tumor is larger. The dFdC extracellular concentration reflects the second dose at this timepoint.

Figure 4

Case 4 (metronomic CDDP and dFdC) on day 1 of treatment immediately after drug injection. The drug concentrations are shown for the extracellular (μM), intracellular (fMoles/cell), and DNA-bound (fMoles/cell) compartments as defined at this timepoint by the corresponding pharmacokinetic equations.

Figure 5

Case 4 (metronomic CDDP and dFdC) after 7 days post treatment initiation. The drug concentrations are shown for the extracellular (μM), intracellular (fMoles/cell), and DNA-bound (fMoles/cell) compartments as defined at this timepoint by the corresponding pharmacokinetic equations. While the proliferation region is comparable to day 1, the overall tumor is smaller. The dFdC extracellular concentration reflects the second dose at this timepoint.

Figure 6

Average concentrations of CDDP (left column) and dFdC (right column) over 7 hours following treatment initiation for Cases 1 (top row) and 4 (bottom row). Values are shown for the extracellular (μM), intracellular (fMoles/cell), DNA-Bound (fMoles/cell), and intracellularly-activated (IC-Activated, specific to dFdC) (fMoles/cell) compartments. Note that Cases 2 and 3 combine these same concentrations, as specified in Table 6.

Figure 7

Time evolution of the tumor radius as a fraction of initial size for each treatment scenario.

Figure 8

Tumor radius as a fraction of untreated control for Cases 1 through 4.