Mathematics, modeling, and simulation to study cancer are topics covered in a new special series in JCO Clinical Cancer Informatics (JCO CCI). On April 24, JCO CCI published its fourth special collection of articles, “Mathematical Oncology,” which showcases the current state of the field and new applications for modeling and simulation, whether it’s translating patient-specific data into a treatment plan for personalized medicine; using game theory to optimize neoadjuvant combination therapies; or creating cell-based models that allow the analyzation of high-dimensional single-cell sequencing data.
In their introduction to the collection, Guest Editors Russell Rockne, PhD, and Jacob G. Scott, MD, DPhil, note the evolution of the field—which involves using mathematics, modeling, and simulation to study cancer—over the past few decades from theoretical work in mathematical oncology and biology, which provided a foundation for making predictions about cancer progression, to work that now uses real-world scenarios and data. “Mathematical models can now, more than ever, be directly applied to real scenarios and readily tested using large amounts of biological and clinical data,” they write. “In many ways, the era of big data has enabled an era of big theory to meet both the conceptual and practical challenges of analyzing and, to a limited extent, understanding, big data.”
The invited articles in the collection focus on three areas within the field of mathematics oncology, Dr. Rockne and Dr. Scott observe: “(1) Modeling the relationship between cancer therapy and the immune system; (2) optimizing personalized medicine through clinical imaging and predictive mathematical modeling; and (3) connecting individual cells to tumor behavior”:
- Immune System and Immunotherapies
- “Understanding the Dynamics of T-Cell Activation in Health and Disease Through the Lens of Computational Modeling,” which focuses on the use of ordinary differential equation-based mechanistic models to study T cell activation.
- “Immunologic Consequences of Sequencing Cancer Radiotherapy and Surgery,” which examines evidence suggesting that radiation therapy first followed by surgery could increase overall and disease-free survival for some cancer types and selected patients compared to surgery first before radiation.
- “The Immune Checkpoint Kick Start: Optimization of Neoadjuvant Combination Therapy Using Game Theory,” which examines the authors’ a mathematical model of the essential components of the preoperative endocrine prognostic index (PEPI) score to identify successful combination therapy regimens that minimize both tumor burden and metastatic potential, based on time-dependent trade-offs in the system.
- Personalized Medicine
- “Mechanism-Based Modeling of Tumor Growth and Treatment Response Constrained by Multiparametric Imaging Data,” which discusses imaging methods that utilize multiparametric imaging data to initialize and calibrate mechanistic models of tumor growth and response.
- “Quantifying Uncertainty and Robustness in a Biomathematical Model-Based Patient-Specific Response Metric for Glioblastoma,” which discusses the authors’ mathematical model for investigating the role of the DNA repair gene MGMT’s methylation in resistance to the standard chemotherapeutic agent temozolomide (TMZ) during the standard treatment regimen for glioblastoma multiforme (surgery, chemotherapy and radiation).
- “Blackboard to Bedside: A Mathematical Modeling Bottom-Up Approach Toward Personalized Cancer Treatments,” which presents a mathematical model for use with patient specific tumor-profiles to personalize cancer treatments and discusses the potential clinical benefits of mathematical tumor modelling.
- “Imaging-Genomic Study of Head and Neck Squamous Cell Carcinoma: Associations Between Radiomic Phenotypes and Genomic Mechanisms via Integration of The Cancer Genome Atlas and The Cancer Imaging Archive,” which presents an original study of the relationship between radiomic and genomic features in Head and Neck Squamous Cell Carcinoma aimed at discovering the imaging-genomics associations and exploring the potential of predicting tumor genomic alternations using radiomic features.
- Cell-Based Modeling
- “Glioblastoma Recurrence and the Role of O6-Methylguanine-DNA Methyltransferase Promoter Methylation,” which describes a mathematical model the authors developed to investigate the role of O6-methylguanine-DNA methyltransferase (MGMT) methylation in resistance to the chemotherapeutic agent temozolomide during the standard treatment regimen for glioblastoma multiforme
- “A Review of Cell-Based Computational Modeling in Cancer Biology,” which introduces the broad range of techniques available for cell-based computational modeling and illustrates these methods with examples drawn from cancer hypoxia, angiogenesis, invasion, stem cells, and immunosurveillance.
- “Leveraging Single-Cell RNA Sequencing Experiments to Model Intratumor Heterogeneity,” which proposes using a general diversity index to quantify intra-tumor heterogeneity—which can serve as defense against targeted drug therapy resistance—on multiple scales and relate it to disease evolution.
- “Stochastic Evolution of Pancreatic Cancer Metastases During Logistic Clonal Expansion,” which details the authors’ development of a stochastic evolutionary model of cancer progression that took into consideration alterations in metastasis-related genes and intercellular growth competition leading to density effects described by logistic growth.
The invited articles, from a multidisciplinary group of authors, showcase the way in which mathematics is playing an increasing role in oncology. As Dr. Rockne and Dr. Scott explain, “Mathematical oncology, which has historically been a sub-discipline of mathematics, has begun to migrate toward being a sub-discipline of oncology itself. Its practitioners, including the authors whose papers are highlighted herein, come from disparate fields, including engineering, physics, and computer science, yet all share the common goal of bringing their computational and theoretical tools to bear on the fight against cancer.”
This meeting of big data and clinical work is exactly the type of effort that JCO CCI is dedicated to sharing. The guest editors note that just as JCO CCI is focused on the intersection of informatics and the clinician with its focus on research into the “tools, knowledge, and infrastructure required to translate vast amounts of data into the clinic and improve our treatment and understanding of cancer,” so, too, is the field of mathematical oncology. This discipline “has served as a bridge between the data, the biologist, and the practicing clinician,” they state. “In this way, knowledge-based predictive mathematical modeling is used to fill in gaps in sparse data; guide and train machine learning algorithms; provide actionable interpretations of complex data sets; and make predictions of cancer progression and response to therapy on a patient-specific basis.”
Read the full collection of articles.
View an infographic that illustrates the definition of mathematical oncology.