Mathematical oncology: Solving cancer’s most baffling puzzles

July 19, 2019 | by Maxine Nunes

Math equations
Why do targeted therapies succeed with some good candidates and not others? Is there a way to combat treatment resistance? How can we more accurately diagnose cancer and predict its course?
 
The answers to these and many other puzzling aspects of cancer care can be found in an area that might surprise you — math. Specifically, an exciting new front in the battle against cancer called mathematical oncology.
 
Using tools that range from the mathematical analysis of biopsies and imaging to the creation of computer models and simulations, mathematical oncologists are ushering in a new level of precision cancer care.
 
Russell Rockne, Ph.D.
The future of this emerging discipline has just been charted in The 2019 Mathematical Oncology Roadmap, a landmark paper published in June in Physical Biology. Russell Rockne, Ph.D., director of the Division of Mathematical Oncology at Beckman Research Institute of City of Hope and a recognized leader in the field, assembled this collection of essays with his colleagues at top cancer institutes in the United States and the United Kingdom.

A More Personalized Approach to Cancer Care

Mathematics may sound cold and conceptual, but the dominant theme of The Roadmap is quite the opposite — an approach to cancer care that is far more personal than ever before.
 
The goal is that every patient has their own individualized mathematical model so that we can optimize treatment for them,” said Rockne. “At a very simple level, we should be able to predict a patient’s cancer trajectory like we predict hurricanes.”
 
He explained the analogy this way. With hurricanes, we use satellite imagery, wind speed, ocean temperatures and other factors to predict how fast it will move, how strong the winds will be and where it will land. With cancer, mathematicians can study blood flow, genomic information and more to predict the course of the disease.

Each Patient — and Each Tumor — Is a Universe of Big Data

We usually think of Big Data as an enormous global collection of anonymous statistics and information — and that is certainly one resource that mathematical oncologists make use of. But a vast universe of data also exists within each individual.
 
“With City of Hope’s HopeSeq platform, we can now sequence the portions of a patient’s genome that are relevant to the cancer diagnosis — and these can contain millions or even billions of individual pairs of genomic information,” said Rockne. “Leveraging the bigness of this personalized data is what this work is about.”
 
There is also an enormous amount of information within each tumor that a biopsy alone cannot provide.
 
The biopsy is really just a very, very small piece of tissue from a very, very small portion of the tumor,” said Rockne. “It’s like taking five square blocks in Culver City and assuming that's a good representation of all of Los Angeles.”
 
Take, for example, a woman whose biopsy strongly indicates HER2-positive breast cancer. This should make her a good candidate for the standard-of-care treatment Herceptin. Many patients do respond well to it — but not all.
 
The reason can be difficult to pinpoint. The biopsy may not have caught other types of cancer in the tumor or accounted for new mutations. Or blood flow might not have been strong enough to carry medication to the tissue.
 
“Cancer cells are growing and developing vasculature and blood vessels that can be very chaotic and tortuous, and that causes a great deal of heterogeneity within the cancer,” said Rockne. “You can’t necessarily apply one rule, because each individual environment has different functional properties.”
 
Mathematical oncologists can take data from biopsies and scans, then use equations to predict where in a tumor the blood is flowing. They can also calculate how DNA mutations are likely to spread and what other types of cancer may exist in the tumor — predictions that are transforming the landscape of cancer care.

Mathematical Oncology at City of Hope

City of Hope is absolutely known as a leader in defining what mathematical oncology looks like. And what differentiates us from other mathematical oncology groups is that we have a really unique way of translating our scientific findings into the clinic,” said Rockne, who is currently involved in two clinical trials here.
 
One is a CAR T trial led by Behnam Badie, M.D., the Heritage Provider Network Professor in Gene Therapy, and Christine Brown, Ph.D., the Heritage Provider Network Professor in Immunotherapy. To be effective, CAR T has to elicit an immune response in the patient — but an active immune system and an active cancer can look very similar on an MRI. Rockne’s role is to solve the tricky problem of distinguishing between the two.
 
“What we’re doing,” he said, “is analyzing blood flow, perfusion and cell density to determine which patients are exhibiting an immune response and which are exhibiting a cancer response.”
 
Another City of Hope trial, led by Joanne Mortimer, M.D., the Baum Family Professor in Women's Cancers, was created expressly to study the effectiveness of mathematical oncology in predicting which patients will respond best to HER2 therapy.
 
One of the most interesting innovations at City of Hope is that Rockne, as a mathematical oncologist, is now a part of several multidisciplinary tumor boards, groups that create individual treatment plans for each patient.  
 
He is, he said, like the “weatherman” of the group.
 
“I can tell them, here's what the storm looks like, here's what the hurricane model is predicting,” he said, “and doctors are using that information to help them make more informed decisions.”
 
This integration of mathematical analysis and clinical practice is an exciting new inroad into more personal and precise cancer care at City of Hope.
 
****

Sign up to receive the latest updates on City of Hope news, medical breakthroughs, and prevention tips straight to your email inbox!

Back To Top

Search Blogs