Understanding Cancer with Math: Interview with Dr. Russell Rockne

Dr. Russell Rockne

Dr. Russell Rockne is an Associate Professor at City of Hope National Medical Center. He leads the Division of Mathematical Oncology and works on projects that use math and computer models to improve cancer treatment. Dr. Rockne has a Ph.D. in Applied Mathematics from the University of Washington, and his research focuses on combining math and biology to understand how cancer grows and responds to treatment. He integrates machine learning with mechanistic modeling to develop patient-specific predictive models, contributing to the advancement of personalized medicine.

Isaac Jung:

Hi, Doctor Rockne. Thank you for agreeing to have this interview with me. How would you explain mathematical oncology to students who are just discovering it?

Dr. Russell Rockne:

Mathematical oncology is kind of what it sounds like; it uses mathematics to study cancer. There are a lot of different ways we can use mathematics to study cancer, but the way I do it is by building mathematical models. These models predict how cancer is going to grow or respond to therapy. You can think of a mathematical model like the concept of gravity.

For example, if you throw a football, you can predict where it is going to go based on its initial position and velocity because we understand projectile motion and gravity. The mathematical representation of gravity is a mathematical model, and it is sufficiently precise that we can not only predict where the football is going to go, but we can also send satellites into space and land rovers on Mars. So, mathematical oncology is about writing the equations and mathematical models for how cancers grow and respond to therapy so that we can help patients have better responses to their treatment.

Isaac Jung:

What led you to pursue a career in mathematical oncology?

Dr. Russell Rockne:

It's kind of a long story that I'll make short for the purposes of this interview. I want to start by saying that I would never have predicted when I was your age or in high school, or even at the beginning of college, that I would be doing what I'm doing now. I got into mathematical oncology because when I went to graduate school to do my Ph.D. in applied mathematics at the University of Washington in Seattle, I found out that you got your tuition paid if you did research. I looked around for research labs that were hiring, and Kristen Swanson, who was my Ph.D. advisor and is considered one of the leaders and founders of the field of mathematical oncology, was looking for students.

I did my Ph.D. research with her, developing mathematical models for brain tumor response to radiation therapy, and the rest really is history because I really enjoyed it. I found a lot of satisfaction in it. It's a very impactful contribution to society, and I felt like I was using my math talents for good, so to speak. After I finished my Ph.D., I continued to do research and went to Northwestern University in Chicago as a postdoc. Then I came to City of Hope as a faculty member, and I've been doing mathematical oncology research at City of Hope since 2015.

Isaac Jung:

Could you speak a little bit about how math is important to cancer research, such as in the brain tumor models, and provide one example of how it could be applied?

Dr. Russell Rockne:

Math is becoming more and more important in every aspect of science, but particularly in cancer research right now, and that's for a lot of reasons. One reason is because of the data. The data that we're collecting is so complicated and is in such high quantities that really, without math, you can't understand the data.

A perfect example of this is how we think about DNA mutations or anything related to DNA sequencing or genomics data. In general, it’s impossible to understand it in its absolute sense. If you think about a Rubik's Cube, what makes it hard is that it's three-dimensional, and each face has a color, so it's really kind of like four dimensions. You have three axes (X, Y, and Z) plus the color. That makes it a very difficult puzzle because you have to move things around in 3D while keeping track of the color.

Your genome, however, is like 8 billion dimensions if you think about base pairs as dimensions. If you say it’s just about genes that produce proteins and how cells function, then it’s about 20,000 dimensions. Trying to solve a 20,000-dimensional Rubik's Cube is how you can think about how your cells and DNA evolve over time. It’s extremely complicated, and that’s why you need math to help understand it. By using mathematical models to predict cancer progression and responses to therapy, you don't have to track every single gene and every single protein in the cell. In fact, I would argue that it's not even really possible to do that. The prediction of how a patient is going to respond or not all comes down to math. Whether it's a model for cancer growth or a machine learning approach to analyze all the data, all these methods to make predictions about patient outcomes revolve around math. Math plays a really, really important part in all of science right now, but particularly in cancer research.

Isaac Jung:

Could you speak a bit about some of the bigger challenges in creating mathematical models, such as how you go from all the variables in the cell to focus on the most important ones?

Dr. Russell Rockne:

This is a really fascinating, fun, and challenging part of what I do in cancer research and in science in general right now. The way that mathematical modeling works is that you take some observations and try to encapsulate those observations in equations. To make a slight variation on my previous example, think about how we shifted from an Earth-centric view of the solar system to a sun-centric view.

It all revolved around observations of planetary motion. We understood that there were things like orbits, as we saw the moon in certain phases and in certain places in the sky, and different planets in the solar system. We observed them at different places in the sky at different times. What you can do is write down equations that represent that process and then compare those equations with the data. If you have a model, it has to agree with the data, assuming your data is correct.

Once you have some equations that you can compare with the data, the next step is to ask if it makes a meaningful prediction. Can my equations explain something that I didn't already observe? Or if I take some of the observations out, can it explain something that had been taken out? That’s part of the model validation process.

Building the model, validating the model, and then using the model to predict something are all fundamental steps of how you do mathematical modeling. A very interesting recent advance in this field is now using machine learning to effectively use the data to discover the equations. This turns the whole process I just described on its head, which is how all of science was done effectively for all of human existence. Now we can ask if we have enough data, can we use the data to actually recover what the equations must be? This field is known as model discovery, and there are a number of different approaches to it.

If you take all the planetary trajectories over time, you can use these model discovery approaches to figure out what the equation of gravity is. Before, you had to be someone like Einstein, Newton, or Galileo to write down these equations. If you understand what you're observing and you understand the math well enough, you can write down the right equations. This makes an enormous contribution to science.

All the most famous scientists you can probably think of, like Newton, Einstein, and Dirac, are well known for their science for lots of reasons, but principally because they figured out the right equation for the right problem. We're getting to a point now in machine learning and artificial intelligence where, if we have the right data and enough of it, we can start to figure out what the equations of life, biology, and cancer are, rather than having to guess, which is what we've done for all of human existence until recently.

That is what makes Einstein famous. He not only knew a lot of physics and math, but he figured it out through very sophisticated guessing. It turns out he was right, and for over 100 years, he has been continually proven correct. He had an extremely good guess, and that is what makes him who he is. If we can now remove the element of guessing and the need to figure it out ourselves, we can reach an advanced point in science where we can assign equations and mathematical models to almost any process we can characterize through data. That is an amazing thing.

To summarize your question about the pieces and steps involved in creating a model: Building the model, validating it with data, and then using the model to predict—going back through that loop—is always at the heart of scientific discovery. The new wrinkle on that process is removing the step of writing down the model by someone who is just extremely lucky or extremely smart and accelerating that part of model building through model discovery from the data. But it still involves making observations, writing down a mathematical representation, comparing it with the data, validating it, and repeating that process, which is the core of what we do in science.

Isaac Jung:

How do you think this new method of model building will affect the ability to develop cancer treatments in the next 5 to 10 years?

Dr. Russell Rockne:

I think it will revolutionize it. Machine learning and artificial intelligence have already revolutionized many fields, and this will be no different. We know that AI has flaws; it can hallucinate and tell us things that are just plain wrong. It also has a very difficult time reasoning through basic problems. But it’s also true that AI, large language models, and other highly complex learning models can help us learn at a faster rate than we could before.

The model discovery advance helps us continue to do what we have always done in cancer research but much faster. I think we’ll identify better drugs, more effective drugs, and patients who are responding to treatments sooner. We’ll be able to tailor treatments to patients more efficiently and precisely, ultimately allowing us to detect, diagnose, and treat cancers with more precision and efficiency.