An Introduction to Physical Oncology

How Mechanistic Mathematical Modeling Can Improve Cancer Therapy Outcomes

Vittorio Cristini, Eugene Koay, Zhihui Wang

• Publisher: Chapman and Hall/CRC
• Year: 2017
• eBook ISBN: 9781315356884
• Edition: 1
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

Physical oncology has the potential to revolutionize cancer research and treatment. The fundamental rationale behind this approach is that physical processes, such as transport mechanisms for drug molecules within tissue and forces exchanged by cancer cells with tissue, may play an equally important role as biological processes in influencing progression and treatment outcome.

This book introduces the emerging field of physical oncology to a general audience, with a focus on recent breakthroughs that help in the design and discovery of more effective cancer treatments. It describes how novel mathematical models of physical transport processes incorporate patient tissue and imaging data routinely produced in the clinic to predict the efficacy of many cancer treatment approaches, including chemotherapy and radiation therapy. By helping to identify which therapies would be most beneficial for an individual patient, and quantifying their effects prior to actual implementation in the clinic, physical oncology allows doctors to design treatment regimens customized to each patient's clinical needs, significantly altering the current clinical approach to cancer treatment and improving the outcomes for patients.

1What Should Be Modeled in CancerMilestones for Physical Models

With Alejandra C. Ventura and Sofia D. Merajver

The field of mathematical oncology is exploding, with increasing efforts directed at laying down the foundation for the phenomena of cancer development, growth, metastases, and response to therapies. This involves working at multiple space and time scales. The relative scarcity of data renders many parametrical models challenging and limits their robustness. Concepts from engineering and nonlinear systems can be applied to cell signaling in the cancer cell, yielding useful models. Here, we discuss the concepts of modularity, retroactivity, and pathway integration, and delineate some of the outstanding questions that we believe should be prioritized for modeling in cancer.

1.1Introduction

The first known documentation of the cancer disease is from Egyptian papyri written around 2000 BC. The cases described in the ancient texts were breast cancer, which, at the time, was treated surgically by cauterization with a hot object. Recognizing the enormous scientific and technical progress during the ensuing millennia, it is still true today that many cancers are controlled primarily by removal of the tumor mass, albeit by more exacting and humane methods. Indeed, to substantiate this assertion, we need not look further than modern early detection strategies in cancer. Current efforts at cancer screening are considered successful in general if the diagnosed cancer is small enough to be amenable to complete excision. With rare exceptions (such as lymphoma), solid tumors diagnosed at an “early” stage (~1 cm) are largely treated by surgery alone.

Let us consider for a moment the concept of “early” detection. This is a clinically useful empirical concept because randomized screening trials have shown that early detection of cancer improves survival, if appropriate treatments are available [12]. However, the concept of clinical early detection does not translate well at the tissue level of tumor development; an early-detected 1 cm human solid cancer contains ~109 cells (~1 g), with 1012 cells (~1 kg) being a lethal load of cancer in humans, 1000 times larger than the mass presumably detected early. Whereas we have made very substantial advances in the understanding of clonality, genetic alterations in individual cells, and the aberrant gene and protein expression patterns that occur in cancer, we still lack sufficient knowledge of the integration of signals that give rise to the abnormal behaviors that make untreated cancer a lethal disease. Additionally, there is a lack of effective therapies for eliminating cancer in an individual patient that are more efficacious when given alone than surgical removal of the primary tumor even with early tumor detection (at the scale of ~1 cm). Moreover, our knowledge deficit extends to a nearly complete lack of interventions (other than selective estrogen inhibitors, lifestyle, and avoidance of known carcinogens) that are effective even earlier in the path to clinical cancer, at the preclinical cancer stages or in primary prevention.

We define preclinical cancer stages as those detectable changes at the cellular and tissue levels (either by morphology, topology, protein expression, or other quantifiable readouts) that indicate dysregulation of signal integration that may predispose invasive cancer. Examples of different tissue conditions in this category include lobular carcinoma in situ (breast), atypical epithelial hyperplasia (any epithelial tissue), and atypical nevi (skin). As a result, in the United States cancer affects one in two men and one in three women in their lifetime, constituting a massive public health problem. The urgency to find new ways to understand the underlying mechanisms of cancer and to design entirely novel treatment is enormous.

To take an extreme example, glioblastoma multiforme (GBM), a cancer that almost never metastasizes, is one of the most lethal cancers, in large part because aggressive surgery cannot be performed without unacceptable morbidity, and we lack effective ways to eradicate it in situ, even when extremely small. At the other end of the metastatic potential spectrum, we fail to achieve good survival rates in tumors such as inflammatory breast cancer (IBC), which is known to be intrinsically metastatic from its inception [13]. IBC is treated with multimodality therapy, including aggressive combination chemotherapy, rather than surgery up front. In spite of frequent complete clinical responses to initial chemotherapy, IBC is the most lethal form of breast cancer, with current five-year survival rates at only 45% [14,15]. These examples are meant to highlight the notion that deficits in current cancer therapy are pervasive and transcend whether or not a tumor is highly metastatic. We postulate that new breakthroughs in our understanding of cancer are needed to overcome these fundamental challenges. For the last century, formal scientific studies in the biomedical sciences have yielded large datasets and complex catalogs of observations and classifications. For many highly heterogeneous diseases, such as diabetes and cardiovascular diseases, this phenomenological approach has been extremely successful in finding cures, effective ways to control the symptoms, and good strategies for prevention. Cancer, possibly due to its enormous molecular and cellular complexity, is not as amenable to be conquered in this manner. We pose that a better approach is to understand how information is transferred within a cell and integrated across cells in tissues, particularly understanding the coding, decoding, transfer, and translation of information in cancer, insights that may likely be gained through modeling approaches.

1.2Cell Signaling

Despite half a century of detailed molecular signaling studies, there is no unified theory to account for transmission of signals in different cellular environments and to predict the manner in which such signals are integrated. Basic and translational research has focused predominantly on activation of a single signaling pathway using a specific ligand for a defined receptor, providing information only for the pathway in question, and typically focusing on a limited number of endpoints. A pathway-centric approach remains incomplete, however, because of the intricate cross talk among cell regulatory pathways [16]. Indeed, a given molecular component can be associated with or interact with multiple signaling, transcriptional regulation, metabolic, and cytoskeletal process pathways [17]. Pathways cannot properly be considered to operate in isolation, as an alteration of one pathway can lead directly (via protein–protein interactions) or indirectly (via transcriptional or translational influences) to changes in others. Cells receive multiple signaling inputs either simultaneously or sequentially, with each signal varying in intensity and duration. Given the dynamic profile of the signal, being itself a packet of information the cell must integrate, there is much to be done to understand the integration of all the possible types of interactions between pathways.

Given the enormity of the unknowns, what is necessary to begin unraveling the problem? Successful identification of transmembrane receptors, intracellular signaling proteins, and transcription factors that mediate the responses of cells to intra- and extracellular ligands has generated a wealth of information about the biochemistry of signal transduction [18]. It is important to note that most biochemical and molecular biology experiments tend to be biased toward ascertaining large static differences between the expression (or modification) of proteins or genes, rather than subtle steady-state differences or significant dynamical profiles. In this manner, our current thought in signaling is driven yet limited by those types of data. Moreover, accumulation of molecular detail does not automatically yield improved understanding of the ways in which signaling circuits process complementary and opposing inputs to control diverse physiological responses. For this, network-level perspectives are required [19]. When the number of species in the network is large, parameter estimation becomes very challenging [20]. A plausible, alternative approach is to depict the pathway as a collection of modules that are connected with each other through input–output properties. Another useful approach when parameter estimation is challenging is to exhaustively explore the parameter space.

1.2.1Parameter Space Exploration

A major goal for exploring the parameter space is to understand the uncertainty in a model’s output that derives from a lack of knowledge about the exact value for a parameter that is assumed to be constant under certain conditions throughout model analysis. It is then possible to make inferences on the contribution of individual parameters to specific components of the system steady-state or dynamical properties.

For a given mathematical model of a biological system or process, the properties that the model is required to reproduce are first mathematically defined. A sampling method will next be used to search for these properties throughout the parameter space. Model parameter values will undergo statistical analysis to test whether a particular parameter is biased toward a certain value (or certain range of values) for the model to produce the targeted dynamics or steady-state properties. After this is done for all parameters, the results can be compiled to identify recurrent parameter values and any patterns that may form.

As a commonly used sampling method, Latin hypercube sampling (LHS) uniformly samples the values of parameters on a logarithmic scale, defining a certain range of each group, for example, catalytic rate constants, Michaelis–Menten constants, and concentrations. LHS is a statistical method for generating a sample of plausible collections of parameter values from a multidimensional distribution. In the context of statistical sampling, a square grid containing sample positions is a Latin square if (and only if) there is only one sample in each row and each column. A Latin hypercube is the generalization of this concept to an arbitrary number of dimensions, where each sample is the only one in each ...

Table of contents

• Cover
• Half Title Page
• Series Page
• Published Titles
• Title Page
• Copyright Page
• Contents
• List of Figures
• List of Table
• Preface
• Acknowledgments
• Authors
• Contributors
• Definition of Technical Terms
• Chapter 1 What Should Be Modeled in CancerMilestones for Physical Models
• Chapter 2 Developing More Successful Cancer Treatments with Physical Oncology
• Chapter 3 Mathematical Pathology
• Chapter 4 Mathematical Modeling of Drug Response
• Chapter 5 Prediction of Chemotherapy Outcome in Patients
• Chapter 6 Clinical Management of Pancreatic Cancer
• Chapter 7 Application of Cancer Physics in the Clinic
• Chapter 8 Tumor Morphological Behavior and Treatment Outcome
• Chapter 9 Mechanistic Model of Tumor Response to Immunotherapy
• Chapter 10 Perspectives on Physical Oncology and Future Directions
• References
• Index