Pharmacokinetic/pharmacodynamic modeling of combination-chemotherapy for lung cancer

Highlights

• Establishes a framework for evaluation of tumor response to combination chemotherapy.

• Couples PK–PD multi-compartment models with a model of vascularized tumor growth.

• Simulates tumor response to multiple drug regimens for non-small cell lung cancer.

• Combination of MTD and metronomic drug regimens may not offer improved response.

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.

Introduction

Non-small cell lung cancer (NSCLC) is a worldwide leading cause of death. About 85% of patients present with advanced (Stage IIIB or IV) disease, thus precluding curative surgery, while one-third of patients treated at early stages progress to unresectable advanced disease (Correale et al., 2006). Prognosis overall is poor, with 5-year survival rates being <50% for early and <5% for advanced disease, respectively Non-Small Cell Lung Cancer Survival Rates (2017). The recommendation for first-line chemotherapy for treating patients with advanced NSCLC is typically a two-drug (doublet) regimen, with cisplatin and gemcitabine being an established combination (Azzoli et al., 2009, Azzoli et al., 2011) that has shown significant reduction in overall mortality (Le Chevalier et al., 2005). Table 1 shows a sample of 21-day cycle regimens that have been evaluated for advanced disease, with response assessment after 1–2 cycles and then every 2–4 cycles. Cisplatin-based drug combinations are also employed as adjuvant chemotherapy for early (stage II/III) NSCLC following surgical resection, although the longer-term benefit is still debated (Artal Cortes et al., 2015, Tibaldi et al., 2009).

The molecular pharmacology of gemcitabine (2′,2;-difluoro 2′-deoxycytidine, dFdC) is complex. Deoxycytidine kinase intracellularly phosphorylates gemcitabine to gemcitabine monophosphate (dFdCMP), which is converted to the active metabolites gemcitabine diphosphate (dFdCDP) and triphosphate (dFdCTP) (Heinemann et al., 1988). Cytotoxic mechanisms include incorporation of dFdCTP into DNA, which terminates chain elongation (Huang et al., 1991), as well as inhibition of DNA polymerase (Gandhi and Plunkett, 1990). Drug activity is enhanced by dFdCDP hindering the synthesis of deoxyribonucleotides competing with dFdCTP as substrates for DNA incorporation (Baker et al., 1991, Heinemann et al., 1990). The metabolites inhibit cytidine triphosphate synthetase (CTP synthetase) and deoxycytidylate deaminase (dCMP deaminase) while enhancing gemcitabine phosphorylation by decreasing inhibition of deoxycytidine kinase (Xu and Plunkett, 1990). Consequently, the active metabolites self-potentiate their intracellular accumulation for extended availability to impair DNA synthesis and its repair (Heinemann et al., 1992). The drug is inactivated mainly by deoxycytidine deaminase (Heinemann et al., 1992), and the resulting deaminated metabolite (2′,2′-difluorodeoxyuridine, dFdU) in turn may modulate the rate of gemcitabine transport and intracellular phosphorylation via deoxycytidine kinase (Hodge et al., 2011). In the case of cisplatin (cis-diamminedichloroplatinum(II), CDDP), its chloride atoms are displaced by water molecules in the cell cytosol. The hydrolyzed product reacts with nucleophiles, such as nucleic acid nitrogen donor atoms and protein sulfhydryl groups. The product binds to the N7 reactive center on purine residues, which induces DNA damage including 1,2-intrastrand cross-links such as 1,2-intrastrand d(GpG) and 1,2-intrastrand d(ApG) adducts (Sinek et al., 2009). The high mobility group (HMG)-domain proteins HMG1 and human mitochondrial transcription factor can then specifically inhibit the DNA adduct repair by human excision nuclease (Huang et al., 1994).

Traditional chemotherapy targets single cancer cell populations with drug doses and administration frequencies determined by the maximum tolerated dose (MTD) (as illustrated by Table 1) to avoid lethal patient toxicity. However, a single-target MTD approach may be unable to target other components within the tumor system. A lung tumor is a complex multicellular tissue, and interactions between different cell types and their environment may become even more complex upon treatment. Components contributing to the tumor growth and treatment response include cancer and vascular endothelial cells, immune system and stromal cells, extracellular matrix, and the cellular microenvironment. Interactions within the tissue occur across a wide range of physical scales, from the molecular (nanometer) to the tissue (centimeter) scale. These components and their interactions can significantly affect cancer cell survival and eventually lead to the emergence of drug resistance.

Previous work has shown that a regimen of drugs that under an MTD approach would typically trigger resistance in lung cancer may actually be therapeutically effective when administered metronomically (Francia et al., 2012, Pratt et al., 2013). Metronomic chemotherapy was originally developed to affect vascular endothelial cells through doses lower than MTD (Klement et al., 2000). The combination of low-dose metronomic chemotherapies simultaneously targeted to multiple cancer tissue components, such as tumor cells and vascular endothelial cells, has been shown to deliver treatment with lower systemic toxicity while avoiding the emergence of drug resistance (Bertolini et al., 2003, Stolting et al., 2004). In addition to anti-angiogenesis, metronomic chemotherapy for certain drugs has been shown to stimulate immune-suppressive immunity (Lutsiak et al., 2005), induce cancer dormancy (Bahl and Bakhshi, 2012), and promote cancer cell senescence (Ewald et al., 2010).

The large number of combinational protocols specifying the targeting of multiple tumor cell populations and their microenvironment by chemotherapeutic agents in concomitant or sequential administration may preclude determination of potential clinical options solely through empirical determination. This assessment would benefit from methods and principles typically used in systems analysis. In Traina et al. (2010), a mathematical method was derived from the Gompertz (1825) equation to define a drug dosing schedule in xenograft models based upon maximal efficacy instead of maximal tolerable toxicity. The method, inspired by Norton–Simon modeling (Norton et al., 1976), was applied to the design and analysis of preclinical data to forecast the dosing schedule. In Hadjiandreou and Mitsis (2014) the effects of drugs on tumor progression in mice were modeled using a Gompertz-type growth law, and optimal therapeutic patterns were explored. The in vivo response of pancreatic tumors treated with gemcitabine was simulated in Lee et al. (2013) and of Non-Hodgkin's lymphoma treated with doxorubicin in Frieboes et al. (2015). The combination of gemcitabine with non-invasive radio frequency radiation to treat pancreatic cancer has also been modeled (Ware et al., 2017). MTD and metronomic regimens were compared in André et al. (2013) with a theoretical tumor model evaluated in a radially-symmetric configuration, while chemotherapy protocols obtained with the methods of optimal control were reviewed in Ledzewicz and Schättler (2014). Recently, the usefulness of mathematical modeling in designing drug regimens was reviewed in Barbolosi et al. (2016), and modeling results specific to metronomic chemotherapy were evaluated in Ledzewicz and Schattler (2017). Mathematical modeling has also lent support to the concept of designing different chemotherapeutic schedules for tumors with different growth rates (West and Newton, 2017). In particular, low-dose, high-density metronomic strategies were predicted to outperform MTD therapy, especially for fast growing tumors. The modeling work to date highlights the critical need to further elucidate the relative performance of single and multi-drug regimens, metronomic and MTD strategies, and their combinations. In this study, we integrate mathematical modeling of vascularized tumor tissue with drug-specific pharmacokinetic components to evaluate response to multiple drug regimens, providing the capability to assess MTD as well as metronomic drug administration. Thus, this work represents an initial step towards the development of a comprehensive virtual system to more efficiently evaluate patient tumor-specific pharmacokinetics (PK) and pharmacodynamics (PD).

Previous work by Sinek et al. (2009) computationally evaluated intracellular pharmacokinetics and pharmacodynamics of two common chemotherapeutic drugs, cisplatin and doxorubicin in a vascularized tumor model incorporating morphological and vascular structural heterogeneity along with PK determinants simulating P-glycoprotein (Pgp) efflux and tumor tissue density. This work established a multi-compartment PK–PD model rigorously calibrated from published experimental data to simulate systemic drug bolus administration in heterogeneous tumor tissue, showing that the associated intratumoral nutrient and drug distribution may significantly hinder therapeutic efficacy. Battaglia and Parker (2011) developed a detailed intracellular mathematical model describing the pharmacokinetics of gemcitabine and linked it to a systemic plasma gemcitabine PK model. A simplified cell-cycle model was used for pharmacodynamic effect, with predictions based on PK parameter values calibrated from clinical data. The kinetic properties of gemcitabine triphosphate were estimated from previously published in vitro data. The detailed intracellular model coupled with the systemic PK model and the cell-cycle model was simulated to predict gemcitabine triphosphate concentrations in the plasma and intracellular compartments.

We build upon these PK models to simulate multiple chemotherapy for lung cancer, coupling PK–PD intracellular multi-compartment models with a vascularized tumor growth model (Macklin et al., 2009, van de Ven et al., 2012, Wu et al., 2013). Based on dosages used clinically, we illustrate the system's capability by simulating four hypothetical treatment scenarios combining MTD and metronomic approaches as described in Table 2. The drugs are administered to a representative lesion ∼750 µm in diameter, and the effects are measured for 15 days post treatment initiation.