A Mathematical Model of Breast Cancer Treatment with CMF and Doxorubicin

Modeling of Mouse Experiments Suggests that Optimal Anti-Hormonal Treatment for Breast Cancer is Diet-Dependent

Estrogen receptor positive breast cancer is frequently treated with anti-hormonal treatment such as aromatase inhibitors (AI). Interestingly, a high body mass index has been shown to have a negative impact on AI efficacy, most likely due to disturbances in steroid metabolism and adipokine production. Here, we propose a mathematical model based on a system of ordinary differential equations to investigate the effect of high-fat diet on tumor growth. We inform the model with data from mouse experiments, where the animals are fed with high-fat or control (normal) diet. By incorporating AI treatment with drug resistance into the model and by solving optimal control problems we found differential responses for control and high-fat diet. To the best of our knowledge, this is the first attempt to model optimal anti-hormonal treatment for breast cancer in the presence of drug resistance. Our results underline the importance of considering high-fat diet and obesity as factors influencing clinical outcomes during anti-hormonal therapies in breast cancer patients.

Mathematical Model of Triple-Negative Breast Cancer in Response to Combination Chemotherapies

Triple-negative breast cancer (TNBC) is a heterogenous disease that is defined by its lack of targetable receptors, thus limiting treatment options and resulting in higher rates of metastasis and recurrence. Combination chemotherapy treatments, which inhibit tumor cell proliferation and regeneration, are a major component of standard-of-care treatment of TNBC. In this manuscript, we build a coupled ordinary differential equation model of TNBC with compartments that represent tumor proliferation, necrosis, apoptosis, and immune response to computationally describe the biological tumor affect to a combination of chemotherapies, doxorubicin (DRB) and paclitaxel (PTX). This model is parameterized using longitudinal [18F]-fluorothymidine positron emission tomography (FLT-PET) imaging data which allows for a noninvasive molecular imaging approach to quantify the tumor proliferation and tumor volume measurements for two murine models of TNBC. Animal models include a human cell line xenograft model, MDA-MB-231, and a syngeneic 4T1 mammary carcinoma model. The mathematical models are parameterized and the percent necrosis at the end time point is predicted and validated using histological hematoxylin and eosin (H&E) data. Global Sobol' sensitivity analysis is conducted to further understand the role each parameter plays in the model's goodness of fit to the data. In both the MDA-MB-231 and the 4T1 tumor models, the designed mathematical model can accurately describe both tumor volume changes and final necrosis volume. This can give insight into the ordering, dosing, and timing of DRB and PTX treatment. More importantly, this model can also give insight into future novel combinations of therapies and how the immune system plays a role in therapeutic response to TNBC, due to its calibration to two types of TNBC murine models.

A Mathematical Model of Breast Tumor Progression Based on Immune Infiltration

Breast cancer is the most prominent type of cancer among women. Understanding the microenvironment of breast cancer and the interactions between cells and cytokines will lead to better treatment approaches for patients. In this study, we developed a data-driven mathematical model to investigate the dynamics of key cells and cytokines involved in breast cancer development. We used gene expression profiles of tumors to estimate the relative abundance of each immune cell and group patients based on their immune patterns. Dynamical results show the complex interplay between cells and molecules, and sensitivity analysis emphasizes the direct effects of macrophages and adipocytes on cancer cell growth. In addition, we observed the dual effect of IFN-γ on cancer proliferation, either through direct inhibition of cancer cells or by increasing the cytotoxicity of CD8+ T-cells.

Do we really understand how drug eluted from stents modulates arterial healing?

The advent of drug-eluting stents (DES) has revolutionised the treatment of coronary artery disease. These devices, coated with anti-proliferative drugs, are deployed into stenosed or occluded vessels, compressing the plaque to restore natural blood flow, whilst simultaneously combating the evolution of restenotic tissue. Since the development of the first stent, extensive research has investigated how further advancements in stent technology can improve patient outcome. Mathematical and computational modelling has featured heavily, with models focussing on structural mechanics, computational fluid dynamics, drug elution kinetics and subsequent binding within the arterial wall; often considered separately. Smooth Muscle Cell (SMC) proliferation and neointimal growth are key features of the healing process following stent deployment. However, models which depict the action of drug on these processes are lacking. In this article, we start by reviewing current models of cell growth, which predominantly emanate from cancer research, and available published data on SMC proliferation, before presenting a series of mathematical models of varying complexity to detail the action of drug on SMC growth in vitro. Our results highlight that, at least for Sodium Salicylate and Paclitaxel, the current state-of-the-art nonlinear saturable binding model is incapable of capturing the proliferative response of SMCs across a range of drug doses and exposure times. Our findings potentially have important implications on the interpretation of current computational models and their future use to optimise and control drug release from DES and drug-coated balloons.

Optimization of additive chemotherapy combinations for an in vitro cell cycle model with constant drug exposures

Proliferation of an in vitro population of cancer cells is described by a linear cell cycle model with n states, subject to provocation with m chemotherapeutic compounds. Minimization of a linear combination of constant drug exposures is considered, with stability of the system used as a constraint to ensure a stable or shrinking cell population. The main result concerns the identification of redundant compounds, and an explicit solution formula for the case where all exposures are nonzero. The orthogonal case, where each drug acts on a single and different stage of the cell cycle, leads to a version of the classic inequality between the arithmetic and geometric means. Moreover, it is shown how the general case can be solved by converting it to the orthogonal case using a linear invertible transformation. The results are illustrated with two examples corresponding to combination treatment with two and three compounds, respectively.

Bio-algorithms for the modeling and simulation of cancer cells and the immune response

There have been significant developments in clinical, experimental, and theoretical approaches to understand the biomechanics of tumor cells and immune cells. Cytotoxic T lymphocytes (CTLs) are regarded as a major antitumor mechanism of immune cells. Mathematical modeling of tumor growth is an important and useful tool to observe and understand clinical phenomena analytically. This work develops a novel two-variable mathematical model to describe the interaction of tumor cells and CTLs. The designed model is providing an integrated framework to investigate the complexity of tumor progression and answer clinical questions that cannot always be reached with experimental tools. The parameters of the model are estimated from experimental study and stability analysis of the model is performed through nullclines. A global sensitivity analysis is also performed to check the uncertainty of the parameters. The results of numerical simulations of the model support the importance of the CTLs and demonstrate that CTLs can eliminate small tumors. The proposed model provides efficacious information to study and demonstrate the complex dynamics of breast cancer.

Crosstalk between HER2 and PD-1/PD-L1 in Breast Cancer: From Clinical Applications to Mathematical Models

Breast cancer is one of the major causes of mortality in women worldwide. The most aggressive breast cancer subtypes are human epidermal growth factor receptor-positive (HER2+) and triple-negative breast cancers. Therapies targeting HER2 receptors have significantly improved HER2+ breast cancer patient outcomes. However, several recent studies have pointed out the deficiency of existing treatment protocols in combatting disease relapse and improving response rates to treatment. Overriding the inherent actions of the immune system to detect and annihilate cancer via the immune checkpoint pathways is one of the important hallmarks of cancer. Thus, restoration of these pathways by various means of immunomodulation has shown beneficial effects in the management of various types of cancers, including breast. We herein review the recent progress in the management of HER2+ breast cancer via HER2-targeted therapies, and its association with the programmed death receptor-1 (PD-1)/programmed death ligand-1 (PD-L1) axis. In order to link research in the areas of medicine and mathematics and point out specific opportunities for providing efficient theoretical analysis related to HER2+ breast cancer management, we also review mathematical models pertaining to the dynamics of HER2+ breast cancer and immune checkpoint inhibitors.

Mathematical models of breast and ovarian cancers

Women constitute the majority of the aging United States (US) population, and this has substantial implications on cancer population patterns and management practices. Breast cancer is the most common women's malignancy, while ovarian cancer is the most fatal gynecological malignancy in the US. In this review, we focus on these subsets of women's cancers, seen more commonly in postmenopausal and elderly women. In order to systematically investigate the complexity of cancer progression and response to treatment in breast and ovarian malignancies, we assert that integrated mathematical modeling frameworks viewed from a systems biology perspective are needed. Such integrated frameworks could offer innovative contributions to the clinical women's cancers community, as answers to clinical questions cannot always be reached with contemporary clinical and experimental tools. Here, we recapitulate clinically known data regarding the progression and treatment of the breast and ovarian cancers. We compare and contrast the two malignancies whenever possible in order to emphasize areas where substantial contributions could be made by clinically inspired and validated mathematical modeling. We show how current paradigms in the mathematical oncology community focusing on the two malignancies do not make comprehensive use of, nor substantially reflect existing clinical data, and we highlight the modeling areas in most critical need of clinical data integration. We emphasize that the primary goal of any mathematical study of women's cancers should be to address clinically relevant questions. WIREs Syst Biol Med 2016, 8:337-362. doi: 10.1002/wsbm.1343 For further resources related to this article, please visit the WIREs website.

Understanding Drug Resistance in Breast Cancer with Mathematical Oncology

Chemotherapy is mainstay of treatment for the majority of patients with breast cancer, but results in only 26% of patients with distant metastasis living 5 years past treatment in the United States, largely due to drug resistance. The complexity of drug resistance calls for an integrated approach of mathematical modeling and experimental investigation to develop quantitative tools that reveal insights into drug resistance mechanisms, predict chemotherapy efficacy, and identify novel treatment approaches. This paper reviews recent modeling work for understanding cancer drug resistance through the use of computer simulations of molecular signaling networks and cancerous tissues, with a particular focus on breast cancer. These mathematical models are developed by drawing on current advances in molecular biology, physical characterization of tumors, and emerging drug delivery methods (e.g., nanotherapeutics). We focus our discussion on representative modeling works that have provided quantitative insight into chemotherapy resistance in breast cancer and how drug resistance can be overcome or minimized to optimize chemotherapy treatment. We also discuss future directions of mathematical modeling in understanding drug resistance.

The dynamics of drug resistance: a mathematical perspective

Resistance to chemotherapy is a key impediment to successful cancer treatment that has been intensively studied for the last three decades. Several central mechanisms have been identified as contributing to the resistance. In the case of multidrug resistance (MDR), the cell becomes resistant to a variety of structurally and mechanistically unrelated drugs in addition to the drug initially administered. Mathematical models of drug resistance have dealt with many of the known aspects of this field, such as pharmacologic sanctuary and location/diffusion resistance, intrinsic resistance, induced resistance and acquired resistance. In addition, there are mathematical models that take into account the kinetic/phase resistance, and models that investigate intracellular mechanisms based on specific biological functions (such as ABC transporters, apoptosis and repair mechanisms). This review covers aspects of MDR that have been mathematically studied, and explains how, from a methodological perspective, mathematics can be used to study drug resistance. We discuss quantitative approaches of mathematical analysis, and demonstrate how mathematics can be used in combination with other experimental and clinical tools. We emphasize the potential benefits of integrating analytical and mathematical methods into future clinical and experimental studies of drug resistance.