Jasmine Foo

Optimization of dosing for EGFR-mutant non-small cell lung cancer with evolutionary cancer modeling.

Predictive models of EGFR-mutant tumor behavior point to alternative drug dosing strategies to prevent and treat acquired resistance. Harnessing Evolution to Improve Lung Cancer Therapy Like any organism under severe evolutionary pressure, a few select members of a cancer cell population acquire molecular changes that strengthen the clan’s chances of survival. Therapeutic drugs exert a powerful selective force on characteristically compliant cancer cells, as the common recurrence of drug-resistant cancers testifies. To learn how to better fight the potent forces of evolution, Chmielecki et al. examined the behavior of non–small cell lung cancer (NSCLC) before and after the cells acquire resistance to targeted therapy, which inevitably they do. The growth characteristics of these cells were consistent with patient tumor behavior, enabling construction of a mathematical model that predicted alternative therapeutic strategies to delay the development of drug-resistant cancer cells. The authors made paired isogenic cell lines that were sensitive and resistant to afatinib and erlotinib—drugs used to treat NSCLC that are directed against the epidermal growth factor receptor (EGFR) tyrosine kinase, which is activated in a subset of NSCLCs. To the authors’ surprise, the drug-resistant cells grew more slowly than their sensitive counterparts, and resistance was not maintained in the absence of selection. Multiple clinical observations corroborated these findings. For example, patients with resistant tumors showed a slow course of disease progression, and patients with acquired resistance have re-responded to tyrosine kinase inhibitor (TKI) therapy after a drug holiday. The authors then constructed an evolutionary mathematical model of tumor behavior based on the differential growth rates of TKI-sensitive and TKI-resistant cells in heterogeneous tumor cell populations. Understanding the growth dynamics of how tumors behave allowed the authors to calculate what would happen under different treatment regimes. Their models predicted that continuous administration of a low-dose EGFR TKI combined with high-dose pulses of an EGFR TKI should delay the onset of resistance. Subsequent cellular studies bore out this prediction. Modeling also indicated the wisdom of prolonging treatment with the EGFR TKI after the development of resistance to prevent fast overgrowth by the sensitive cells, a result also born out in vitro and in vivo. Ultimate proof will have to come from patients. Clinical trials based on these alternative dosing strategies will be the true test of the utility of evolutionary mathematical modeling in designing cancer treatments. If they prove beneficial, individual models based on the characteristics of diverse cancer cell types could offer clues for designing optimal treatment strategies. Non–small cell lung cancers (NSCLCs) that harbor mutations within the epidermal growth factor receptor (EGFR) gene are sensitive to the tyrosine kinase inhibitors (TKIs) gefitinib and erlotinib. Unfortunately, all patients treated with these drugs will acquire resistance, most commonly as a result of a secondary mutation within EGFR (T790M). Because both drugs were developed to target wild-type EGFR, we hypothesized that current dosing schedules were not optimized for mutant EGFR or to prevent resistance. To investigate this further, we developed isogenic TKI-sensitive and TKI-resistant pairs of cell lines that mimic the behavior of human tumors. We determined that the drug-sensitive and drug-resistant EGFR-mutant cells exhibited differential growth kinetics, with the drug-resistant cells showing slower growth. We incorporated these data into evolutionary mathematical cancer models with constraints derived from clinical data sets. This modeling predicted alternative therapeutic strategies that could prolong the clinical benefit of TKIs against EGFR-mutant NSCLCs by delaying the development of resistance.

The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications

Stochastic spectral methods are numerical techniques for approximating solutions to partial differential equations with random parameters. In this work, we present and examine the multi-element probabilistic collocation method (ME-PCM), which is a generalized form of the probabilistic collocation method. In the ME-PCM, the parametric space is discretized and a collocation/cubature grid is prescribed on each element. Both full and sparse tensor product grids based on Gauss and Clenshaw-Curtis quadrature rules are considered. We prove analytically and observe in numerical tests that as the parameter space mesh is refined, the convergence rate of the solution depends on the quadrature rule of each element only through its degree of exactness. In addition, the L^2 error of the tensor product interpolant is examined and an adaptivity algorithm is provided. Numerical examples demonstrating adaptive ME-PCM are shown, including low-regularity problems and long-time integration. We test the ME-PCM on two-dimensional Navier-Stokes examples and a stochastic diffusion problem with various random input distributions and up to 50 dimensions. While the convergence rate of ME-PCM deteriorates in 50 dimensions, the error in the mean and variance is two orders of magnitude lower than the error obtained with the Monte Carlo method using only a small number of samples (e.g., 100). The computational cost of ME-PCM is found to be favorable when compared to the cost of other methods including stochastic Galerkin, Monte Carlo and quasi-random sequence methods.

Multi-element probabilistic collocation method in high dimensions

We combine multi-element polynomial chaos with analysis of variance (ANOVA) functional decomposition to enhance the convergence rate of polynomial chaos in high dimensions and in problems with low stochastic regularity. Specifically, we employ the multi-element probabilistic collocation method MEPCM [1] and so we refer to the new method as MEPCM-A. We investigate the dependence of the convergence of MEPCM-A on two decomposition parameters, the polynomial order @m and the effective dimension @n, with @n@?N, and N the nominal dimension. Numerical tests for multi-dimensional integration and for stochastic elliptic problems suggest that @n>=@m for monotonic convergence of the method. We also employ MEPCM-A to obtain error bars for the piezometric head at the Hanford nuclear waste site under stochastic hydraulic conductivity conditions. Finally, we compare the cost of MEPCM-A against Monte Carlo in several hundred dimensions, and we find MEPCM-A to be more efficient for up to 600 dimensions for a specific multi-dimensional integration problem involving a discontinuous function.

Evolution of acquired resistance to anti-cancer therapy

Acquired drug resistance is a major limitation for the successful treatment of cancer. Resistance can emerge due to a variety of reasons including host environmental factors as well as genetic or epigenetic alterations in the cancer cells. Evolutionary theory has contributed to the understanding of the dynamics of resistance mutations in a cancer cell population, the risk of resistance pre-existing before the initiation of therapy, the composition of drug cocktails necessary to prevent the emergence of resistance, and optimum drug administration schedules for patient populations at risk of evolving acquired resistance. Here we review recent advances towards elucidating the evolutionary dynamics of acquired drug resistance and outline how evolutionary thinking can contribute to outstanding questions in the field.

Intratumor Heterogeneity in Evolutionary Models of Tumor Progression

With rare exceptions, human tumors arise from single cells that have accumulated the necessary number and types of heritable alterations. Each such cell leads to dysregulated growth and eventually the formation of a tumor. Despite their monoclonal origin, at the time of diagnosis most tumors show a striking amount of intratumor heterogeneity in all measurable phenotypes; such heterogeneity has implications for diagnosis, treatment efficacy, and the identification of drug targets. An understanding of the extent and evolution of intratumor heterogeneity is therefore of direct clinical importance. In this article, we investigate the evolutionary dynamics of heterogeneity arising during exponential expansion of a tumor cell population, in which heritable alterations confer random fitness changes to cells. We obtain analytical estimates for the extent of heterogeneity and quantify the effects of system parameters on this tumor trait. Our work contributes to a mathematical understanding of intratumor heterogeneity and is also applicable to organisms like bacteria, agricultural pests, and other microbes.

Evolution of Resistance to Targeted Anti-Cancer Therapies during Continuous and Pulsed Administration Strategies

The discovery of small molecules targeted to specific oncogenic pathways has revolutionized anti-cancer therapy. However, such therapy often fails due to the evolution of acquired resistance. One long-standing question in clinical cancer research is the identification of optimum therapeutic administration strategies so that the risk of resistance is minimized. In this paper, we investigate optimal drug dosing schedules to prevent, or at least delay, the emergence of resistance. We design and analyze a stochastic mathematical model describing the evolutionary dynamics of a tumor cell population during therapy. We consider drug resistance emerging due to a single (epi)genetic alteration and calculate the probability of resistance arising during specific dosing strategies. We then optimize treatment protocols such that the risk of resistance is minimal while considering drug toxicity and side effects as constraints. Our methodology can be used to identify optimum drug administration schedules to avoid resistance conferred by one (epi)genetic alteration for any cancer and treatment type.

Effects of Pharmacokinetic Processes and Varied Dosing Schedules on the Dynamics of Acquired Resistance to Erlotinib in EGFR-Mutant Lung Cancer

Introduction: Erlotinib (Tarceva) is an epidermal growth factor receptor (EGFR) tyrosine kinase inhibitor, which effectively targets EGFR-mutant driven non–small-cell lung cancer. However, the evolution of acquired resistance because of a second-site mutation (T790M) within EGFR remains an obstacle to successful treatment. Methods: We used mathematical modeling and available clinical trial data to predict how different pharmacokinetic parameters (fast versus slow metabolism) and dosing schedules (low dose versus high dose; missed doses with and without make-up doses) might affect the evolution of T790M-mediated resistance in mixed populations of tumor cells. Results: We found that high-dose pulses with low-dose continuous therapy impede the development of resistance to the maximum extent, both pre- and post-emergence of resistance. The probability of resistance is greater in fast versus slow drug metabolizers, suggesting a potential mechanism, unappreciated to date, influencing acquired resistance in patients. In case of required dose modifications because of toxicity, little difference is observed in terms of efficacy and resistance dynamics between the standard daily dose (150 mg/d) and 150 mg/d alternating with 100 mg/d. Missed doses are expected to lead to resistance faster, even if make-up doses are attempted. Conclusions: For existing and new kinase inhibitors, this novel framework can be used to rationally and rapidly design optimal dosing strategies to minimize the development of acquired resistance.

Eradication of Chronic Myeloid Leukemia Stem Cells: A Novel Mathematical Model Predicts No Therapeutic Benefit of Adding G-CSF to Imatinib

Imatinib mesylate induces complete cytogenetic responses in patients with chronic myeloid leukemia (CML), yet many patients have detectable BCR-ABL transcripts in peripheral blood even after prolonged therapy. Bone marrow studies have shown that this residual disease resides within the stem cell compartment. Quiescence of leukemic stem cells has been suggested as a mechanism conferring insensitivity to imatinib, and exposure to the Granulocyte-Colony Stimulating Factor (G-CSF), together with imatinib, has led to a significant reduction in leukemic stem cells in vitro. In this paper, we design a novel mathematical model of stem cell quiescence to investigate the treatment response to imatinib and G-CSF. We find that the addition of G-CSF to an imatinib treatment protocol leads to observable effects only if the majority of leukemic stem cells are quiescent; otherwise it does not modulate the leukemic cell burden. The latter scenario is in agreement with clinical findings in a pilot study administering imatinib continuously or intermittently, with or without G-CSF (GIMI trial). Furthermore, our model predicts that the addition of G-CSF leads to a higher risk of resistance since it increases the production of cycling leukemic stem cells. Although the pilot study did not include enough patients to draw any conclusion with statistical significance, there were more cases of progression in the experimental arms as compared to continuous imatinib. Our results suggest that the additional use of G-CSF may be detrimental to patients in the clinic.

Evolution of resistance to anti-cancer therapy during general dosing schedules

Anti-cancer drugs targeted to specific oncogenic pathways have shown promising therapeutic results in the past few years; however, drug resistance remains an important obstacle for these therapies. Resistance to these drugs can emerge due to a variety of reasons including genetic or epigenetic changes which alter the binding site of the drug target, cellular metabolism or export mechanisms. Obtaining a better understanding of the evolution of resistant populations during therapy may enable the design of more effective therapeutic regimens which prevent or delay progression of disease due to resistance. In this paper, we use stochastic mathematical models to study the evolutionary dynamics of resistance under time-varying dosing schedules and pharmacokinetic effects. The populations of sensitive and resistant cells are modeled as multi-type non-homogeneous birth-death processes in which the drug concentration affects the birth and death rates of both the sensitive and resistant cell populations in continuous time. This flexible model allows us to consider the effects of generalized treatment strategies as well as detailed pharmacokinetic phenomena such as drug elimination and accumulation over multiple doses. We develop estimates for the probability of developing resistance and moments of the size of the resistant cell population. With these estimates, we optimize treatment schedules over a subspace of tolerated schedules to minimize the risk of disease progression due to resistance as well as locate ideal schedules for controlling the population size of resistant clones in situations where resistance is inevitable. Our methodology can be used to describe dynamics of resistance arising due to a single (epi)genetic alteration in any tumor type.

Evolutionary modeling of combination treatment strategies to overcome resistance to tyrosine kinase inhibitors in non-small cell lung cancer

Many initially successful anticancer therapies lose effectiveness over time, and eventually, cancer cells acquire resistance to the therapy. Acquired resistance remains a major obstacle to improving remission rates and achieving prolonged disease-free survival. Consequently, novel approaches to overcome or prevent resistance are of significant clinical importance. There has been considerable interest in treating non-small cell lung cancer (NSCLC) with combinations of EGFR-targeted therapeutics (e.g., erlotinib) and cytotoxic therapeutics (e.g., paclitaxel); however, acquired resistance to erlotinib, driven by a variety of mechanisms, remains an obstacle to treatment success. In about 50% of cases, resistance is due to a T790M point mutation in EGFR, and T790M-containing cells ultimately dominate the tumor composition and lead to tumor regrowth. We employed a combined experimental and mathematical modeling-based approach to identify treatment strategies that impede the outgrowth of primary T790M-mediated resistance in NSCLC populations. Our mathematical model predicts the population dynamics of mixtures of sensitive and resistant cells, thereby describing how the tumor composition, initial fraction of resistant cells, and degree of selective pressure influence the time until progression of disease. Model development relied upon quantitative experimental measurements of cell proliferation and death using a novel microscopy approach. Using this approach, we systematically explored the space of combination treatment strategies and demonstrated that optimally timed sequential strategies yielded large improvements in survival outcome relative to monotherapies at the same concentrations. Our investigations revealed regions of the treatment space in which low-dose sequential combination strategies, after preclinical validation, may lead to a tumor reduction and improved survival outcome for patients with T790M-mediated resistance.