Math as Medicine

Math as Medicine

Using mathematical modeling, machine learning and more to detect cancer at its earliest stages

Dr. Cristian Tomasetti’s favorite uncle—the one his son is named after—died very quickly from his cancer.

“I took the train to Switzerland to visit him because they told me he was about to die,” Tomasetti (above left) recalls. “And I couldn’t believe it because I had talked to him just two months before and he looked absolutely fine.”

At the hospital, his aunt pointed him to his uncle’s room. There, he found four people in beds. 

“I looked at each one of them and I came out and said to her, ‘look, this is the wrong room, he’s not here.’ And my aunt told me, no, no, he is in there. I went back in and she told me which bed, and looking at him I then recognized him. He was a man in his 60’s yet he looked 90, and completely changed by the cancer.”

He pauses. “I will never forget for the rest of my life his expression which was—the very first instance I think was joy to see me—but that lasted a fraction of a second and then he was upset, upset that my aunt allowed me to see him like that.”

Almost every cancer researcher has a personal story like this, Tomasetti acknowledges, one that provides powerful motivation for the work that they do. But Tomasetti almost wasn’t a cancer researcher. 

Before Vesalius conducted the dissections that led to his groundbreaking Renaissance volume of human anatomy, our understanding of the human body was based on animal dissections – mainly of dogs and pigs – made by Galen, a second-century Greek physician. For example, most physicians used bloodletting on their patients based on the wrong understanding of the cardiovascular system, while others believed the uterus was made up of many small compartments rather than a single cavity. Before Robert Hooke glimpsed under a microscope the peculiar square compartments within a slice of cork, the notion of a “cell” was murky. And before the genomics revolution took hold in the early 2000s, scientists were blind to much of a cell’s contents and their impacts on human health.

It’s these great leaps forward that Tomasetti considers as he and his colleagues embark on what they believe is another revolution in medicine. But instead of a scalpel or a microscope, his unique team at Translational Genomics Research Institute (TGen), part of City of Hope, is wielding the tools of mathematics.

“The era of genomic medicine gives clinicians the ability to look at the human body in a more powerful, precise way. But what it brought with that are three billion letters per copy of DNA per cell,” he adds, “which looks like a big mess,” says Tomasetti, who leads TGen’s Division of Integrated Cancer Genomics and serves as the new Director of both the Center for Cancer Prevention and Early Detection and the Division of Mathematics for Cancer Evolution and Early Detection at City of Hope.

Given those daunting numbers compounded with millions of patients, math as medicine makes sense. The division brings together experts in mathematical modeling, statistics, artificial intelligence and machine learning, bioinformatics and genomic data. Working with their wet lab colleagues and physicians, Tomasetti’s team is tracing the path of cells from healthy to malignant, while looking for ways to detect cancer at its earliest stages and monitor its progression so that the best treatments can be delivered at the best moments.

As applied mathematicians, Tomasetti and colleagues like TGen’s research assistant professor Kamel Lahouel, Ph.D., (at right in the photo) are some of the first generation of researchers to use probabilistic tools to model the evolution of cancer and to predict cancer’s response to treatment. 

This work is changing our “model of reality” of how cancer evolves, Tomasetti says. “Twenty years ago, we didn’t have the data to build these models, or not to the degree that we can build them today. But now that we have information on the behavior of cells and their DNA, this model has become much more precise,” Lahouel adds.

Their findings are already having a significant impact, as a recent study led by Lahouel and Tomasetti demonstrates. The scientists showed that pieces of tumor DNA, circulating in the bloodstream, could help physicians decide whether follow-up chemotherapy would be right for their patients who have undergone surgery for stage II colon cancer.

The analysis helped identify patients who could benefit from further treatment, but it also helped certain patients avoid unnecessary chemotherapy--without affecting their survival. “So here is an example where sequencing data from a blood sample plus mathematics really made a big difference in physical and financial terms for the lives of these people, as half of the patients were spared chemotherapy” Tomasetti says.

The team hopes to uncover similar ways to monitor and personalize cancer treatment, but they are also gearing up for a major project to improve the early detection of cancer with a simple blood test.

“If there is a challenge that I want to succeed among our main goals … it’s really early detection, simply because it has a huge impact on society,” says Lahouel. “From the public health point of view, clearly it has the highest impact.”

When a cell sheds fragments of DNA into the bloodstream, the fragment can look different depending on whether it came from a cancer cell or a healthy cell, he explains. The researchers are now developing algorithms to detect and understand these differences, which could include the length of the fragments and the pattern of genetic “letters” at the end of each fragment, among other features.

In the next nine months, Tomasetti says, the team plans to screen 100,000 healthy people via a simple blood test to look for these cancer fragments that might show up long before a cancer diagnosis.

“The reason why cancer is such a terrible disease today is usually because it’s discovered late and then your options are not very good,” he explains. “But if we can have something like a blood test once a year that can find cancer at an early stage, it will drastically reduce cancer mortality.”

TGen and City of Hope’s outreach in southern California and Arizona make it a particularly attractive place to launch such a large project, Tomasetti notes. With a diverse pool of possible study participants that includes people from Black, Hispanic, Asian-American and Native communities in the region, the study’s findings will be more widely applicable.

The researchers are also working on ways to optimize the technology behind the test so that it will be less expensive than other genetic screening tools. “We are really at the forefront in this space, with a potential to disrupt the market, if we do this study,” Tomasetti says.

So what’s a mathematician like Tomasetti—or one like Lahouel—doing in a place like a cancer research institute?

Tomasetti, who came to the United States from Italy, had always thought he might do something with math. “It’s kind of in my blood, in my family,” he explained. “But in Italy it can be hard to do something with it beyond teaching high school.”

He thought he might go into financial or economics mathematics, and he began his Ph.D. studying probabilistic tools applied to chaos theory. But with two children and concerns about finding a job in “pure math,” he looked for applications and found cancer research.

“When I saw that I fell in love with it,” he recalls, “because I thought this is something where I can use the tools I like to work with and may be able one day to have a real impact on the health of people.”

Lahouel grew up being 100 percent sure he was going to be an astronomer working only on theoretical problems. By the time he met Tomasetti, he was working on the theoretical side of statistical learning but the cancer applications proved too intriguing to pass up.

“A lot of time you have great mathematicians who build sophisticated shiny models, and then find a real-life problem that fits their model. Here it’s completely different,” Lahouel says. “Most of the time we start building a model, think it’s great, and then find it rarely works the first time. You learn to adapt.”

Meanwhile, the field of cancer research is in the midst of its own adaptation, still adjusting to the idea of mathematicians like Tomasetti and Lahouel leading a transformation in how studies are conceived and carried out.

“For a long time, mathematicians were brought in as statisticians, usually not involved in the design of a study,” Tomasetti says. “But suddenly mathematicians start having a power and the ability to see things that many traditionally trained M.D.s might not.”

But he stresses that he and his colleagues “would be nowhere” without their collaborations with the clinicians and lab scientists. And Lahouel says working at TGen has given him “a lot of flexibility from the lab side.”

“We can participate in optimizing the experiments, and people are very open to including mathematical ideas in their lab work,” he says.

“I don’t know of another cancer center today that has a group of mathematicians of this size essentially all focused on working on cancer evolution and early detection,” Tomasetti adds. “I think we have built a little bit of a powerhouse at TGen and City of Hope. That’s unique, and I think this will pay back in terms of the difference we will make.”