Mathematical Oncology Prediction of Drug Response in Breast Cancer Using Integrative Experimental/Computational Modeling

Nearly 30% of women with early-stage breast cancer develop recurrent disease attributed to resistance to systemic therapy. Prevailing models of chemotherapy failure describe three resistant phenotypes: cells with alterations in transmembrane drug transport, increased detoxification and repair pathways, and alterations leading to failure of apoptosis. Proliferative activity correlates with tumor sensitivity. Cell-cycle status, controlling proliferation, depends on local concentration of oxygen and nutrients. Although physiologic resistance due to diffusion gradients of these substances and drugs is a recognized phenomenon, it has been difficult to quantify its role with any accuracy that can be exploited clinically. We implement a mathematical model of tumor drug response that hypothesizes specific functional relationships linking tumor growth and regression to the underlying phenotype. Themodel incorporates the effects of local drug, oxygen, and nutrient concentrations within the three-dimensional tumor volume, and includes the experimentally observed resistant phenotypes of individual cells. We conclude that this integrative method, tightly coupling computational modeling with biological data, enhances the value of knowledge gained from current pharmacokinetic measurements, and, further, that such an approach could predict resistance based on specific tumor properties and thus improve treatment outcome. [Cancer Res 2009;69(10):OF1–9] Introduction We implement a novel quantitative approach that links growth and regression of a tumor mass to the underlying phenotype to study the effect of drug and nutrient delivery as mediators of physiologic resistance. It is well known that inefficient vascularization may prevent optimal transport of oxygen, nutrients, and therapeutics to cancer cells in solid tumors (1). As a result, the drug agentmust diffuse through the tumor volume to reach the entire tumor cell population, and there is mounting evidence to indicate that these diffusion gradients may significantly limit drug access (2–5). Both hypoxia and hypoglycemia contribute to physiologic resistance through various mechanisms, including induction of oxidative stress and a decrease in the number of proliferating cells (6–12). The myriad of stresses can lead to selection of cells that resist apoptotic conditions, thus adding to pathologic resistance in tumors (13). This evidence strongly suggests that the diffusion process alone can lead to the evolution of drug resistance in tumor cells that exceeds predictions based on individual cell phenotype (5). It has not been easy to quantify the resistance effects of diffusion gradients with any accuracy that can be exploited in a clinical setting. The different physical scales in a tumor spanning from the nanometer to the centimeter scale present a complex system that, to be better understood, could benefit from appropriate mathematical models and computer simulations in addition to laboratory and clinical observations. In particular, biocomputational modeling of tumor drug response has endeavored in the last two decades to address this need. Space limitations preclude a full description (see refs. 5, 14, 15, references therein). Doxorubicin cellular pharmacodynamics has been modeled; for example, ref. 16 presented a model providing good fits to in vitro cytotoxicity data. Drug transport was modeled in spheroids versus monolayers (17). A model capable of predicting intracellular doxorubicin accumulation that matched experimental observations was described in ref. 18. Different drug kinetic effects in vitro were compared in ref. 19, showing that a single drug infusion could be more effective than repeated short applications. Models using multiscale approaches [i.e., linking events at subcellular, cellular, and tumor scales (e.g., ref. 20); studying vascularized tumor treatment (e.g., ref. 21); and simulating nanoparticle effects (e.g., ref. 3)] have also been developed. Existing mathematical models are often limited to radially symmetrical tumor representations and not fully constrained through experimentally set parameters. Here, we use a multiscale computational model, extending a previous formulation of tumor growth founded in cancer biology Requests for reprints: Vittorio Cristini, School of Health Information Sciences, University of Texas Health Science Center, 7000 Fannin #600, Houston, TX 77030. Phone: 713-500-3965; Fax: 713-500-3929; E-mail: [email protected]. I2009 American Association for Cancer Research. doi:10.1158/0008-5472.CAN-08-3740 Major Findings By extracting mathematical model parameter values for drug and nutrient delivery from monolayer (onedimensional) experiments and using the functional relationships to compute drug delivery in MCF-7 spheroid (three-dimensional) experiments, we use the model to quantify the diffusion barrier effect, which alone can result in poor response to chemotherapy both from diminished drug delivery and from lack of nutrients required to maintain proliferative conditions. www.aacrjournals.org OF1 Cancer Res 2009; 69: (10). May 15, 2009 Research Article Published Online First on April 14, 2009 as 10.1158/0008-5472.CAN-08-3740 Research. on April 28, 2017. © 2009 American Association for Cancer cancerres.aacrjournals.org Downloaded from Published OnlineFirst April 14, 2009; DOI: 10.1158/0008-5472.CAN-08-3740