Abstract
Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic Science, there is no denying that mathematics continues to play an increasingly prominent role in cancer research. Mathematical Oncology—defined here simply as the use of mathematics in cancer research—complements and overlaps with a number of other fields that rely on mathematics as a core methodology. As a result, Mathematical Oncology has a broad scope, ranging from theoretical studies to clinical trials designed with mathematical models. This Roadmap differentiates Mathematical Oncology from related fields and demonstrates specific areas of focus within this unique field of research. The dominant theme of this Roadmap is the personalization of medicine through mathematics, modelling, and simulation. This is achieved through the use of patient-specific clinical data to: develop individualized screening strategies to detect cancer earlier; make predictions of response to therapy; design adaptive, patient-specific treatment plans to overcome therapy resistance; and establish domain-specific standards to share model predictions and to make models and simulations reproducible. The cover art for this Roadmap was chosen as an apt metaphor for the beautiful, strange, and evolving relationship between mathematics and cancer.
Highlights
Introduction to the2019 Mathematical Oncology RoadmapRussell C Rockne1 1 Department of Computational and Quantitative Medicine, Division of Mathematical Oncology, City of Hope National Medical Center, Duarte, CA 91010, United States of AmericaMathematical Oncology—defined here as the use of mathematics in cancer research —has gained momentum in recent years with the rapid accumulation of data and applications of mathematical methodologies
Each contribution is summarized here in the order it appears: Personalizing medicine by merging mechanistic and machine learning models The role of Mathematical Oncology in the future of precision or personalized medicine is demonstrated through patient-specific mathematical modelling, analysis of patient-specific clinical data, and patient-specific adaptive therapies
Hawkins-Daarud and Swanson highlight the potential and the challenges of merging these fields of mathematical modelling and machine learning with an application to primary brain cancers and clinical imaging data such as MRI
Summary
This is achieved primarily through the use of patient-specific clinical data In this Roadmap, mathematical approaches are used to: make individualized predictions of response to therapy; present data and simulation standards with the goal of creating reproducible models; and improve cancer screening to detect cancer earlier. Finley proposes a multiscale approach to modelling kinetics and time-varying heterogeneities that may arise in aberrant cell metabolism in cancer due to environmental fluctuations She proposes the use of patient-specific data and open source computational platforms that support data and model standards, with the ultimate goal of using these models to generate novel drug combinations and treatment strategies. In contrast to the theoretical considerations of Kaznatcheev et al, Krishnan et al demonstrate a practical method to experimentally estimate the parameters of an EGT model, with the goal of designing combination therapies that avoid therapeutic resistance but are even able to steer cancer evolution on a patient-specific basis. The authors hypothesize—and demonstrate—how EGT-driven therapies can be practically implemented in the clinic to overcome therapeutic resistance in cancer treatment
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