Optimized Treatment Schedules for Chronic Myeloid Leukemia

Estimating treatment sensitivity in synthetic and in vitro tumors using a random differential equation model

Resistance to treatment, which comes from the heterogeneity of cell types within tumors, is a leading cause of poor treatment outcomes in cancer patients. Previous mathematical work modeling cancer over time has neither emphasized the relationship between cell heterogeneity and treatment resistance nor depicted heterogeneity with sufficient nuance. To respond to the need to depict a wide range of resistance levels, we develop a random differential equation model of tumor growth. Random differential equations are differential equations in which the parameters are random variables. In the inverse problem, we aim to recover the sensitivity to treatment as a probability mass function. This allows us to observe what proportions of cells exist at different sensitivity levels. After validating the method with synthetic data, we apply it to monoclonal and mixture cell population data of isogenic Ba/F3 murine cell lines to uncover each tumor's levels of sensitivity to treatment as a probability mass function.

Using birth-death processes to infer tumor subpopulation structure from live-cell imaging drug screening data

Tumor heterogeneity is a complex and widely recognized trait that poses significant challenges in developing effective cancer therapies. In particular, many tumors harbor a variety of subpopulations with distinct therapeutic response characteristics. Characterizing this heterogeneity by determining the subpopulation structure within a tumor enables more precise and successful treatment strategies. In our prior work, we developed PhenoPop, a computational framework for unravelling the drug-response subpopulation structure within a tumor from bulk high-throughput drug screening data. However, the deterministic nature of the underlying models driving PhenoPop restricts the model fit and the information it can extract from the data. As an advancement, we propose a stochastic model based on the linear birth-death process to address this limitation. Our model can formulate a dynamic variance along the horizon of the experiment so that the model uses more information from the data to provide a more robust estimation. In addition, the newly proposed model can be readily adapted to situations where the experimental data exhibits a positive time correlation. We test our model on simulated data (in silico) and experimental data (in vitro), which supports our argument about its advantages.

Combination Chemotherapy Optimization with Discrete Dosing

Chemotherapy drug administration is a complex problem that often requires expensive clinical trials to evaluate potential regimens; one way to alleviate this burden and better inform future trials is to build reliable models for drug administration. This paper presents a mixed-integer program for combination chemotherapy (utilization of multiple drugs) optimization that incorporates various important operational constraints and, besides dose and concentration limits, controls treatment toxicity based on its effect on the count of white blood cells. To address the uncertainty of tumor heterogeneity, we also propose chance constraints that guarantee reaching an operable tumor size with a high probability in a neoadjuvant setting. We present analytical results pertinent to the accuracy of the model in representing biological processes of chemotherapy and establish its potential for clinical applications through a numerical study of breast cancer.

Phenotypic deconvolution in heterogeneous cancer cell populations using drug-screening data

Tumor heterogeneity is an important driver of treatment failure in cancer since therapies often select for drug-tolerant or drug-resistant cellular subpopulations that drive tumor growth and recurrence. Profiling the drug-response heterogeneity of tumor samples using traditional genomic deconvolution methods has yielded limited results, due in part to the imperfect mapping between genomic variation and functional characteristics. Here, we leverage mechanistic population modeling to develop a statistical framework for profiling phenotypic heterogeneity from standard drug-screen data on bulk tumor samples. This method, called PhenoPop, reliably identifies tumor subpopulations exhibiting differential drug responses and estimates their drug sensitivities and frequencies within the bulk population. We apply PhenoPop to synthetically generated cell populations, mixed cell-line experiments, and multiple myeloma patient samples and demonstrate how it can provide individualized predictions of tumor growth under candidate therapies. This methodology can also be applied to deconvolution problems in a variety of biological settings beyond cancer drug response.

An integrative systems biology approach to overcome venetoclax resistance in acute myeloid leukemia

The over-expression of the Bcl-2 protein is a common feature of many solid cancers and hematological malignancies, and it is typically associated with poor prognosis and resistance to chemotherapy. Bcl-2-specific inhibitors, such as venetoclax, have recently been approved for the treatment of chronic lymphocytic leukemia and small lymphocytic lymphoma, and they are showing promise in clinical trials as a targeted therapy for patients with relapsed or refractory acute myeloid leukemia (AML). However, successful treatment of AML with Bcl-2-specific inhibitors is often followed by the rapid development of drug resistance. An emerging paradigm for overcoming drug resistance in cancer treatment is through the targeting of mitochondrial energetics and metabolism. In AML in particular, it was recently observed that inhibition of mitochondrial translation via administration of the antibiotic tedizolid significantly affects mitochondrial bioenergetics, activating the integrated stress response (ISR) and subsequently sensitizing drug-resistant AML cells to venetoclax. Here we develop an integrative systems biology approach to acquire a deeper understanding of the molecular mechanisms behind this process, and in particular, of the specific role of the ISR in the commitment of cells to apoptosis. Our multi-scale mathematical model couples the ISR to the intrinsic apoptosis pathway in venetoclax-resistant AML cells, includes the metabolic effects of treatment, and integrates RNA, protein level, and cellular viability data. Using the mathematical model, we identify the dominant mechanisms by which ISR activation helps to overcome venetoclax resistance, and we study the temporal sequencing of combination treatment to determine the most efficient and robust combination treatment protocol.

In this work, we develop a multi-scale systems biology approach to study the mechanisms by which the integrated stress response (ISR) activation helps to overcome venetoclax resistance in acute myeloid leukemia (AML). The multi-scale model enables the integration of RNA-level, protein-level, and cellular viability and proliferation data. The model developed in this work can predict several important features of the resistant AML cell lines that are consistent with experimental data. Further, our integrative systems biology approach led to the determination of the optimal combination treatment protocol.

Optimization of Cancer Treatment in the Frequency Domain

Thorough exploration of alternative dosing frequencies is often not performed in conventional pharmacometrics approaches. Quantitative systems pharmacology (QSP) can provide novel insights into optimal dosing regimen and drug behaviors which could add a new dimension to the design of novel treatments. However, methods for such an approach are currently lacking. Recently, we illustrated the utility of frequency-domain response analysis (FdRA), an analytical method used in control engineering, using several generic pharmacokinetic-pharmacodynamic case studies. While FdRA is not applicable to models harboring ever increasing variables such as those describing tumor growth, studying such models in the frequency domain provides valuable insight into optimal dosing frequencies. Through the analysis of three distinct tumor growth models (cell cycle-specific, metronomic, and acquired resistance), we demonstrate the application of a simulation-based analysis in the frequency domain to optimize cancer treatments. We study the response of tumor growth to dosing frequencies while simultaneously examining treatment safety, and found for all three models that above a certain dosing frequency, tumor size is insensitive to an increase in dosing frequency, e.g., for the cell cycle-specific model, one dose per 3 days, and an hourly dose yield the same reduction of tumor size to 3% of the initial size after 1 year of treatment. Additionally, we explore the effect of drug elimination rate changes on the tumor growth response. In summary, we show that the frequency-domain view of three models of tumor growth dynamics can help in optimizing drug dosing regimen to improve treatment success.

Optimal dynamic control approach in a multi-objective therapeutic scenario: Application to drug delivery in the treatment of prostate cancer

Numerous problems encountered in computational biology can be formulated as optimization problems. In this context, optimization of drug release characteristics or dosing schedules for anticancer agents has become a prominent area not only for the development of new drugs, but also for established drugs. However, in complex systems, optimization of drug exposure is not a trivial task and cannot be efficiently addressed through trial-error simulation exercises. Finding a solution to those problems is a challenging task which requires more advanced strategies like optimal control theory. In this work, we perform an optimal control analysis on a previously developed computational model for the testosterone effects of triptorelin in prostate cancer patients with the goal of finding optimal drug-release characteristics. We demonstrate how numerical control optimization of non-linear models can be used to find better therapeutic approaches in order to improve the final outcome of the patients.

A Robust Optimization Approach to Cancer Treatment under Toxicity Uncertainty

The design of optimal protocols plays an important role in cancer treatment. However, in clinical applications, the outcomes under the optimal protocols are sensitive to variations of parameter settings such as drug effects and the attributes of age, weight, and health conditions in human subjects. One approach to overcoming this challenge is to formulate the problem of finding an optimal treatment protocol as a robust optimization problem (ROP) that takes parameter uncertainty into account. In this chapter, we describe a method to model toxicity uncertainty. We then apply a mixed integer ROP to derive the optimal protocols that minimize the cumulative tumor size. While our method may be applied to other cancers, in this work we focus on the treatment of chronic myeloid leukemia (CML) with tyrosine kinase inhibitors (TKI). For simplicity, we focus on one particular mode of toxicity arising from TKI therapy, low blood cell counts, in particular low absolute neutrophil count (ANC). We develop optimization methods for locating optimal treatment protocols assuming that the rate of decrease of ANC varies within a given interval. We further investigated the relationship between parameter uncertainty and optimal protocols. Our results suggest that the dosing schedule can significantly reduce tumor size without recurrence in 360 weeks while insuring that toxicity constraints are satisfied for all realizations of uncertain parameters.