Interview with Professor Yang Kuang

Dr. Yang Kuang is a distinguished professor at Arizona State University in the School of Mathematical and Statistical Sciences. With over 200 published research papers, Dr. Kuang is a leading expert in mathematical biology and oncology. His innovative work in mathematical modeling sheds light on the complexities of cancer, particularly tumor growth and treatment dynamics. He is also the author of Introduction to Mathematical Oncology and the founder of the Journal of Mathematical Biosciences and Engineering.

Isaac

Hi, Dr. Kuang. Thank you so much for taking the time to speak with me today. For a lot of people, mathematical oncology can be challenging to understand. Could you explain briefly what it is and how it helps us better understand cancer and improve treatments for it?

Dr. Kuang

Yes, that’s a great question. I’m glad you asked it upfront. The definition of mathematical oncology that you have on your website is something I agree with, though if you dive deeper, you can see that, by definition, oncology is quite broad. From my perspective, though, any science really becomes powerful when it has predictive capabilities and can handle complexity. That’s where mathematical tools come in, not just computational tools. In current oncology practice, computational methods are often based on what others have already shown. They usually don’t start with real data, or they use synthetic data, which is something you probably encounter in other contexts as well.

The real challenge is the data. Data for oncology studies is incredibly hard to get and very expensive to obtain. Often, you can’t even access the data you need. Take the current hot topic of combining various treatments, for example. It’s not feasible to run clean trials for combined treatments, mainly because of the time, cost, and complexity involved. This is where mathematical models really shine. They can help simulate and predict the effects of different treatments, even when real data is limited. These models are incredibly effective and can provide precision in predictions, especially if you have enough data from single treatments.

That’s why I believe mathematical oncology is crucial for the future of cancer research, just like mathematical biology is essential for advancing biology as a whole. We’ve reached a point where we need to understand cancer as a science, and mathematics is the key to that understanding. Mathematics allows us to combine data in ways that can actually make sense of complex situations. When a model works, we know it because we can see it validated through real cases and experiments.

For students who pursue an undergraduate education in mathematics, they’ll eventually see how math can take medical data and transform it into classes or models that allow for better, more targeted treatments. Mathematics can help tailor treatments not just for broad patient groups, but for individual patients, which is where real precision medicine begins.

Isaac

It’s really fascinating to see how mathematics applies to cancer treatment. When I first learned about it, I found it so interesting.

Dr. Kuang

Yes, this is a huge topic. Let me clarify something important. We often say that biology is a science because it applies the principles of chemistry. If you look at the foundation of chemistry, it's built on laws and equations, like the equations that describe chemical reactions. In those reactions, you have components that interact and produce new components, and these interactions can be written as mathematical equations. This is what allows us to quantify and predict biological processes.

Because of this, biology is considered a science because we can apply these chemical principles to understand living systems. Similarly, medicine is the application of biology, so it also qualifies as a science. However, medicine becomes a true science only if we can apply these same principles, such as conservation laws from chemistry and physics. When we do that, we can turn medicine into a more mechanistic field, grounded in these laws. If we truly understand the science, we can build accurate mathematical models that explain what’s happening.

What I’m saying is that to make progress, you need to have deep knowledge. You can't just know a little bit of this and a little bit of that. It’s not enough to have a superficial understanding. Cancer research, in particular, is probably one of the last frontiers in human knowledge. When the "war on cancer" was declared in the early 1970s, over 50 years later, we still struggle to make significant progress. The reason is that we didn’t fully realize the complexity of the challenge. But I think we’re starting to make real progress now, although it’s still just the beginning.

Isaac

It’s interesting how all these areas tie together.

Dr. Kuang

Yes, absolutely. The more you understand your science, the better you’ll be able to work with mathematical models in oncology. It’s like any complex field—it’s all about applying fundamental principles to the problem at hand. Cancer, in particular, is one of the last frontiers for human endeavor in science, and while we’ve been fighting cancer for over 50 years, we’re still making progress. It’s slow, but it’s happening. It’s an ongoing process that will take time.

Isaac

That makes sense. You've been a major player in the field of mathematical oncology over the past few decades. How did you first become interested in this field?

Dr. Kuang

For me, this is actually a bit of an unusual path. I started out working on mathematical ecology about 40 years ago. Mathematical ecology is the foundation of mathematical bioscience, and in many ways, it shares a lot of the same principles. In ecology, the most important interactions we look at are competition, predation, and cooperation. These interactions can also be seen in tumor-immune responses, the competition between tumors, and how they all share the same environment. For instance, tumors require the same nutrients, like phosphorus and nitrogen, and that’s where the connection with ecology comes in.

Our body functions like an ecosystem. Mathematical ecology provides the foundation for understanding how these systems work. Ecology has been studied extensively, and many times, in a rigorous way—much more so than mathematical oncology. So, it’s easier to build on ecological models when applying them to cancer research. Russell Rockne, for example, used many ecological principles in his mathematical models.

For me, this approach felt natural because ecology itself has faced challenges in obtaining high-quality data. This is a similar issue to what we face in oncology. However, occasionally, we can get lucky and acquire good data. About 14 years ago, I was fortunate to obtain very high-quality data for prostate cancer, and around the same time, I also got access to a great dataset for glioblastoma multiforme (GBM). The researchers and clinicians in this field are exceptional—they read our work published in scientific journals like Biosciences and other publications. They saw how we applied ecological and bioscientific principles to create mathematical models that we could validate and use for predictions.

Making predictions about specific treatments for cancer patients is not an easy task. To do that, you need to rigorously validate your models. Unfortunately, many models in mathematical oncology don’t validate their predictions, and even if they do, they don't often make predictions about patient treatments. This is because it's very difficult. To create useful predictions, you need to keep assumptions minimal and carefully select the right parameters. By doing so, you can zoom in and focus on the most important aspects of the problem, which is essential for accurate modeling.

We need to recognize that progress in this field will be incremental. We can’t expect to solve cancer using mathematics in just a few years or even a few decades. It will take a lot of people, hard work, and time. But I believe that progress is coming, and it's happening slowly but surely.

Isaac

It's really interesting how understanding the minimum number of conditions is important, especially for things like prostate cancer or glioblastoma, and the tumor microenvironment. So, how do mathematical models help improve cancer treatments in real life, particularly in clinical settings?

Professor Kuang

This is a question I might give you two different answers.

The first answer depends a lot on the stage of the cancer. For patients diagnosed at a later stage, which is unfortunately the case for many, treatment often starts right away. However, there are many options for treatment. Treatments can be combined in different ways, and the order in which they are administered can also matter.

For example, many patients opt for surgery first and then follow up with chemotherapy. But others might prefer to start with chemotherapy first. This approach can sometimes help prevent metastasis by targeting the smaller cancer cells in the body before surgery. If you wait too long, the cancer could spread quickly once the body starts healing.

The timing of treatments is crucial. Some people may want to try chemotherapy first to stop the cancer from growing, while others, particularly older patients or those in weaker health, may be more conservative and prefer surgery first. This is because chemotherapy can be hard on the body, and sometimes complications can arise during treatment.

In some cases, this is where you need to think about which treatment sequence would be the best: surgery first, then chemotherapy, or chemotherapy first. You also need to consider the stage of the disease, your age, and overall health. Younger people may prefer chemotherapy first, while others may be more conservative, depending on their health status. If you opt for chemotherapy, the body may not be in the best condition and could develop complications quickly. So, it's really about balancing sequencing, dosage, and timing.

You might be surprised to know it's not simply 1 + 1 when combining two treatments. There can be a synergy. Some treatments allow you to reduce the dosage but still be effective. However, they can also counteract each other and lead to counterproductive results. It would be very useful if we had data for individual patients to make these decisions more informed. Unfortunately, getting such data is still a challenge, but mathematical models can help make sense of these combinations, providing important insights.

Ideally, we would have data for individual patients, so we could fine-tune treatments based on their specific needs. This is where mathematical models can make a significant impact. In the past 20 years, there have been many new treatments, but the question now is how to effectively combine them. There are so many possibilities, but mathematical modeling can help us navigate through these options and provide insights that may not be obvious at first glance.

Isaac

I read a recent paper by Dr. Rockne on oncolytic viruses and CAR-T cell therapy interactions, which explores similar concepts. 

Professor Kuang

Yes, exactly. The virus-based treatments look very promising. However, if we have more data, we also need to be cautious. The dosage is very important—these treatments can quickly become toxic. They can lose their effectiveness because the tumor can adapt and grow rapidly, so you need to know how long you can use these treatments. If not, what’s your contingency plan? So, I think having mathematical tools would be useful, but first, they need to be validated. At the very least, they could offer useful guidelines. Unfortunately, AI alone doesn’t help much here because modeling combined treatments is very complex. You can’t just use a single program for this. Maybe it can help you get started, but you’ll quickly find that it doesn’t fit the data very well. So, you really need to understand the science behind it. Having domain-specific knowledge is key. The good thing is, if we have many researchers, we can divide the tasks and work together.

Isaac

In your research, one important aspect of tumors is their chemical heterogeneity. How does this variability impact treatment modeling, and how do you balance the complexity of real biological data with the simplifications needed in mathematical models?

Professor Kuang

When you mention heterogeneity, you’re likely referring to partial differential (PD) models most of the time. But of course, this can also apply to other models. It all depends on how you classify heterogeneity—whether it’s in terms of groups or, often, individual cells. These cells can mix, so in many models, people make the mistake of thinking they can treat them as separate groups.

Many early models, such as those by Dr. Kristen Swanson and Russell Rockne, started with the Fisher model, but this model doesn’t distinguish between proliferating cells, quiescent cells, or dead cells. In reality, 80-90% of the cells are actually quiescent. It’s only the first 20 layers of cancer cells that can actively grow. Later, they develop their own blood supply. But as the tumor grows, the pressure can crush blood vessels and cause leakage. So, there are many challenges when it comes to building models that can account for these dynamics.

Fortunately, there have been improvements in existing models. For example, Professor Trachette Jackson from the University of Michigan, a former student of ours, has done exceptional work. She works with people who can provide high-quality data and enough time to test hypotheses, which is crucial for cancer research. She’s also well-funded, and right now she serves as the Vice President for Research Services at the University of Michigan. She would be a great person to talk to.

Something I wanted to mention earlier, related to your previous question, is that for older patients diagnosed with cancer, if they don’t show symptoms, it’s often a good idea to give them time to evaluate treatment options. It’s important not to rush into decisions. For example, in melanoma, up to 70% of the tumor can consist of immune cells. This means that the immune system is already working against the cancer, which is why melanoma can progress very slowly. If treatment is rushed, it can often harm the patient. For instance, if you surgically remove the tumor, you’re also removing the immune cells that were fighting it. Or, if you use radiotherapy, you could be diminishing the immune response, making the situation worse.

So, the existing treatments—such as surgery or radiotherapy—are helpful, but they also have limitations. Immunotherapies like CAR T-cells or PD-1 inhibitors are promising, but they only work if you have the right data for the individual patient. It’s crucial to get the correct data for each patient, as an overdose of these therapies can lead to counterproductive results. It’s a complicated issue. However, with the right time and data, personalized medicine can really help, and that’s where mathematical models can make a difference.

Now, some people suggest using population data to inform decisions. While this can be useful for some general insights, once you average the data, you lose the individual nuances. For example, with glioblastoma (GBM), if you average the treatment results from a large group of patients, you might find that the treatment works for some but not for others. This population-level approach can sometimes lead to misleading conclusions. That’s why, while population data is important for modeling, it’s the individual data that truly enables personalized treatment plans.

What my group is trying to do is use individual patient data to personalize treatments. For instance, if we can obtain detailed data on a patient’s cancer, such as growth rates or death rates, we can use this information to tailor the treatment specifically for them.

However, this is not easy. We use PDEs (partial differential equations), which are nonlinear and can be difficult to analyze. Many people working with these models focus mainly on computation, but they don’t always understand the underlying mathematical theory. Computation is very important—it’s a necessary first step—but to really understand the model, you need a deep mathematical understanding.

In the past, people used to say "a picture is worth a thousand words," but now, a thousand pictures might not convey the message if you don’t have a solid understanding of the data. For example, in cancer research, we know that tumors smaller than 1mm often don’t show up in scans, because at that stage, the cells are mainly focused on survival. But once they reach a larger size, they become visible in clinical images.

In fact, the speed at which a tumor grows can be mathematically computed, not just through computational methods but with analytic formulas. We can use a technique called traveling wave solutions, which is commonly used to model tumor growth and spread.

Isaac

So, in your research, you've highlighted the importance of chemical heterogeneity in tumors. How does this variability affect treatment modeling, and how do you manage the complexity of real biological data while simplifying it for models?

Professor Kuang

When you refer to heterogeneity, you're probably thinking of PD (partial differential) models, but of course, heterogeneity can be understood in many different ways. Models vary in how they classify heterogeneity, often grouping different tumor cells, but in reality, these cells intermingle. Many early models, like those by Dr. Kristen Swanson and Russell Rockne, used the Fisher model, but it didn’t distinguish between proliferating cells, quiescent cells, and dead cells. In reality, a large percentage of tumor cells are quiescent or dying, and only the top 1-2 layers of cells actively proliferate.

This is a significant simplification in many models because the tumor has its own unique challenges, such as blood supply and pressure buildup from rapidly growing cells, which can crush blood vessels and make them leaky. So, while we have a lot of theoretical models, there’s room for improvement, especially as we try to account for tumor complexity in a more realistic way.

One of the key challenges is ensuring that we get accurate data and feedback to make models more accurate. I highly recommend contacting Professor Tracy Jackson from the University of Michigan. She’s doing some great work on cancer modeling, and she’s very experienced in working with real-world data. She has access to the right resources and time to develop and test hypotheses.

On a related note, if you are older and have been diagnosed with cancer but don't have significant symptoms yet, you may be given time to consider your treatment options rather than rushing into immediate treatment. For example, with melanoma, up to 70% of the tumor may actually be immune cells, so the immune system is doing much of the work. Tumors like this can progress slowly, and rushing into treatment, like surgery or radiotherapy, might remove those immune cells, which are essential for slowing tumor growth.

It’s also important to note that the use of checkpoint inhibitors like PD-1 or CAR-T cells is promising, but they need to be used carefully. They can be very effective, but only when data is used correctly, especially for individual patients. Overdosing can be counterproductive.

Many existing treatments are more like a "slash and burn" approach, where everything is attacked in hopes of getting rid of the cancer. But individualized approaches with the right data can provide much better outcomes. Using population-level data can be helpful, but you must be careful. If you rely on averages, like in GBM (glioblastoma multiforme), you could miss the nuances. Everyone is different, and the average doesn't always provide the best insight for treatment.The key takeaway is that individualized data is essential. With the right information, we can fine-tune treatments and provide better outcomes for each patient. In my group, we're trying to individualize treatment and improve the decision-making process. Having access to this data is what will make a real difference in cancer treatment.

MRI or CT scan can help personalize the treatment for an individual patient's cancer. The rates, death rate, or changes in cancer progression can be personalized for each patient, right? This is what we need—individualized medicine. But it's not easy because we use PDE models, and these PDEs are nonlinear PDEs. Most people don't have exposure to these, even those using any model, but they don't really understand or do mathematical analysis; they just rely on computation. Computation is important, but it's just the first step. It allows you to see what the model shows. But to truly understand the model, you need to have a mathematical understanding of it, and that's very different. We used to say one picture was worth a thousand words, but now it's clear that a thousand pictures may not match one solid understanding. If you have the right understanding, you know there's a critical size below which you're not going to see anything. For instance, we can't detect cancer smaller than 1mm in size. Below that size, the tumor is fighting for survival. It’s just trying to control its own growth. But once it reaches a certain size, we may be able to detect it, and it will also appear clinically or in imaging. How fast the cancer grows can be computed mathematically, not just through computational methods, but through an analytic formula. We can use what we call traveling wave solutions, which are very common in the context of tumor growth and spread.

Isaac

I've been talking to many people, and everyone tells me that you can't assume the average is the same as an individual in this context.

Professor Kuang

Exactly, like with blood pressure, for example. I think a lot of confusion comes from the way we talk about things in medicine.

For instance, when we say "normal" blood pressure, it often has a specific statistical meaning. It refers to the normal distribution of pressures, but in medicine, "normal" means the level of health that we consider ideal.

But we don’t always have the right data. It’s very challenging to practice medicine because it’s difficult to get good, quality data. If you're not careful with the data collection protocols, you can end up misinterpreting the data.

You need to understand how the data was collected to properly interpret it. Knowing the structure of the data and being able to distinguish between good and bad data is crucial. If you just use whatever data comes your way, there’s a high chance you're working with poor-quality data. And as the saying goes, "garbage in, garbage out." If you use bad data, your model will likely produce misleading results.

Isaac

That’s a good point. I’d like to pivot into your book Introduction to Mathematical Oncology. You discuss various mathematical models in the book. Could you share one example of a model that is particularly important to cancer research?

Professor Kuang

This might surprise you. If you look at many cancer models, people often think of the simplest models. These models, while simple, are actually very effective because they have just two parameters, and they fit the data well. The reason they work is that these parameters are measurable and depend on specific conditions. However, that simplicity can also be a limitation.

What I would argue for is what we call the two-equation Lotka-Volterra model, which we discuss in Chapter 6 of the book. The first few sections of this chapter cover it. This model is very important because it addresses resource competition. For example, the growth of cancer cells is influenced by many factors, but one of the most important observations is that growth is often limited by resources such as space or nutrients like nitrogen.

If you limit space or nutrients, the tumor can’t grow as fast, or in some cases, it may not grow at all. Identifying the limiting factor—whether it’s space or nutrients—can lead to accurate predictions of tumor growth, which is where the two-equation model is valuable. Unlike other models, like the logistic equation, this model is more precise because it only has two parameters, and these parameters can be measured.

The logistic equation, which many people use, is problematic because it estimates growth rate based on an unknown carrying capacity. But with the two-equation model, you can isolate the limiting factor and predict growth more accurately.

While tests like chemotherapy or radiation can influence tumor growth, the model also accounts for factors like nutrient limitations or tumor cell predation, which affect the overall growth rate. And since the division of cancer cells follows the same principles, this model provides a solid foundation for building more complex models.

In summary, the two-equation model is fundamental and simple, and from there, you can expand and refine your models. By starting with the right foundation, you're more likely to make accurate predictions in cancer research.

Isaac

We have about 10 minutes left, so I'd like to ask: are there any mathematical or computational skills you would recommend students learn, like Python or MATLAB?

Professor Kuang

Yes, these are all important, but I wouldn't worry too much. You'll pick them up quickly. You don't need to know everything at the beginning. Even compared to five years ago, nearly everything you want to model is available online. If you read a paper, you can often download the program directly from the author or from certain websites, and you can quickly understand it.

That said, the real bottleneck is always data. Understanding how to evaluate data is crucial, and for that, you’ll need domain-specific knowledge. But in terms of mathematics, I think nonlinear dynamics would be a good place to start because we have to understand the complexity of biological systems. Many of these systems are not built in a linear way.

Conservation laws apply in many settings—space, nutrients, energy, and even momentum, depending on how you look at it. Each equation in a model can often be thought of as a conservation law. Understanding these conservation laws will help you understand the dynamics of your model.

Unfortunately, this usually isn’t something you can fully grasp until graduate level studies. But there's a shortcut: you can still explore and appreciate concepts like bifurcation analysis or bifurcation diagrams. These tools allow you to understand your model dynamics, especially when you're testing various parameters. They give you insight into what nonlinear dynamics might appear at different values.

Isaac

So, for a high school student interested in mathematical oncology, are there any specific undergraduate majors that would be especially helpful for this field?

Professor Kuang

Actually, I think starting with mathematics is a great idea. If you focus on math, you'll quickly see how everything connects. If you don't have a strong math background, it will be harder to make those connections. A solid understanding of mathematics, along with some physics, is very helpful. Physics is a good foundation, and if you understand math well, physics becomes easier.

In addition, you'll need to study advanced calculus, which will allow you to prove the mathematical principles you're using in your models. It also helps you understand why certain methods work, or why certain solutions converge.

Advanced calculus will help you think rigorously. With that type of thinking, you’ll be able to challenge the status quo, especially in medicine, where almost everything is wrong or incomplete. The medical field is complicated, and models have limitations because of the complexity of biological systems. For example, prostate cancer can mutate in four major ways, and these mutations happen rapidly—up to 1% every minute. So, the evolution of cells follows nonlinear dynamics, and understanding that is key to working with mathematical models in oncology.

Isaac

What’s the most exciting breakthrough you hope to see in mathematical oncology in the next 5 to 10 years?

Professor Kuang

One exciting breakthrough would be using patient data more effectively. Right now, we collect treatment data for individuals, but we don’t always have a successful model for combining all of this data. I think a major breakthrough would be utilizing both treatment and imaging data—especially sequential high-quality images. If we can classify patients based on factors like stage, sex, age, and even genetic ratios, we could increase the resolution of our analyses and model predictions.

With the right data and treatments, we could find the most effective combination therapies for cancer. It would require having access to national databases and allowing researchers to use them for better model development. If we can achieve this, it would drastically improve how we model and treat cancer.

Isaac

It sounds like it would really enhance the effectiveness of mathematical modeling in oncology.

Professor Kuang

I completely agree.

Isaac

Thank you so much for speaking with me today. One last question: if you could give one piece of advice to young students interested in mathematical modeling, what would it be?

Professor Kuang

I would say, be patient. Progress will be slow at first, but I believe that mathematical modeling can provide lasting value to the community. Look at the decades-long war on cancer—the progress has been minimal. Any improvement on that should be worth pursuing, and mathematics can accelerate that progress.

So, be patient and focus on building a solid foundation before making contributions. You can always join a research project to contribute quickly, but don’t expect instant breakthroughs. The problems in this field are vast and complex, and it’s a long-term endeavor.

Isaac

That’s great advice. Thank you so much for speaking with me today.

Professor Kuang

Thank you for the invitation.