Mathematics plays an increasingly prominent role in cancer research, with applications ranging from theoretical studies to clinical trials designed using mathematical models. As such, mathematical oncology – defined as the use of mathematics in cancer research – has gained momentum in recent years with the rapid accumulation of clinical data and applications of mathematical methodologies.
The journal Physical Biology has now published The 2019 Mathematical Oncology Roadmap, a collection of 11 essays that provide a forward-looking view and demonstrate specific areas of focus within this unique field of research. Introducing the roadmap, Russell Rockne from City of Hope National Medical Center, explains that its dominant theme is the personalization of medicine through mathematics, modelling and simulation – achieved primarily through the use of patient-specific clinical data.
“The topics presented here are not intended to be exhaustive, but rather to feature emerging, high-impact areas that have the potential to shape the direction of mathematical oncology in the next five to 10 years,” Rockne explains.
Eleven essays
The collection begins with a demonstration of the role of mathematical oncology in personalizing medicine, via patient-specific modelling, analysis of patient-specific clinical data and patient-specific adaptive therapies. The next contribution emphasizes the importance of setting standards for data and mathematical models, to ensure interoperability and ultimately to develop useful tools for studying and treating cancer.
An essay on “tumour forecasting” examines the challenge of reproducing and predicting the spatiotemporal dynamics of tumour growth. This could be achieved using families of models where the optimal model(s) is selected and used to update patient-specific predictions over time. Another important challenge is improving the early detection of cancer. Here, the authors propose applying mathematical models of cancer to evaluate and predict the efficacy of screening strategies. The ultimate goal: to produce clinically actionable, personalized cancer screening recommendations.
The next three contributions examine the evolution of cancer. The authors discuss: mathematical modelling using large population sizes to simulate tumour evolution and predict the evolution of resistant cells; applying a single-cell view to examine cancer heterogeneity and evolution; and accurate representation of metabolism in cancer progression.
Mathematics can also be used to model patient-specific responses to radiation therapy. The authors of the next essay introduce the “proliferation-saturation index” and discuss challenges for the clinical adoption of this patient-specific predictive response index. This is followed by a look at evolutionary therapy, an entirely new pillar of cancer treatment in which treatment schedule and dose are mathematically designed to reduce the possibility of resistance.
The final two contributions in the collection examine how evolutionary therapy and treatment resistance can be modelled using evolutionary game theory, in which evolution is determined by selection or optimization of “fitness”. A fitness landscape is a mathematical concept that enables prediction and interpretation of the temporal process of evolution.
Future promise
The roadmap identifies three critical milestones along the path to mathematically designed cancer treatment: obtaining accurate, rigorous and reproducible predictions of cancer progression; avoiding and mitigating therapeutic resistance; and merging mechanistic knowledge-based mathematical models with machine learning.
Rockne notes that government agencies, such as the Federal Drug Administration (FDA) in the USA, have begun to recognize modelling and simulation as forms of valid scientific evidence in the review and approval process.
“With the support and adoption of regulatory agencies that recognize these methodologies, tumour forecasting, patient-specific adaptive therapies with the use of in silico treatment scenarios, virtual clinical trials, and mathematical modelling and simulation have the potential to accelerate our scientific progress in cancer research,” says Rockne. “[They] also have the potential to transform the way we detect and treat cancer in the clinic.”
