Mathematical Models Can Help Us Understand — and Possibly Treat — Complex Diseases 

A rare but painful disorder can make it difficult for people to swallow food. The symptoms include weight loss and chest pain after eating. Scientists are working to better understand this condition, known as corkscrew esophagus, in hopes of finding more treatment or prevention options. 

We are working to contribute to that effort with an approach you may not associate with medical research. It involves math, physics and computer modeling. 

First, it’s helpful to understand how the esophagus works. When a person swallows food, the esophagus muscles contract in a coordinated manner to move the food to the stomach and digestive system.       

In a patient with a corkscrew esophagus, their esophagus has an unusual, spiral shape (hence the name).   Doctors have told us that atypical muscle contractions when swallowing are an important factor in how the corkscrew shape forms. The corkscrew is more visible when someone with this condition is swallowing. When their muscles are relaxed, the esophagus returns to a typical cylindrical shape. 

So, in our labs at NIST and Northwestern University, we’re making a computer model of the human esophagus and measuring minute details of it to see what we can learn about the esophagus and the muscles that move food to the stomach. 

Measuring the Esophagus … on a Computer 

This computer model is a complex undertaking because human bodies are incredibly complicated. According to current estimates, there are 30 trillion cells in the body! Keeping track of all of these cells and their movements is far too challenging for any person or computer (at least so far).     

Body organs have interesting responses to stimuli, so we have to consider that as we try to model them. In high school physics, you model concepts with billiard balls and assume their shapes don’t change as you demonstrate a physical law, such as momentum. But in our bodies, geometry is part of physics. Our skin wrinkles, our brains have crinkles, and our hands can make different shapes. 

So, not all of the rules of traditional physics apply to our bodies the same way they do for inanimate objects. For example, you may remember Newton’s laws of motion. A key law is that objects at rest remain at rest, and objects in motion remain in motion — unless they are acted upon. 

Body parts move, even without being acted upon by a force, seemingly in contradiction to this law. Human hearts, for example, beat automatically without any force making that happen. Our cells also grow, move and divide on their own. 

With all those factors in mind, we started with a basic model of the esophagus that looks a bit like an elastic cylinder. 

When we swallow, pressure increases as our muscles contract to push food toward the stomach. Abnormally high pressure in this process is linked to esophageal tissue damage. This contributes to conditions such as corkscrew esophagus. 

Measuring esophageal pressure in patients directly would be invasive, so computer models provide a safer, more practical alternative. We use simulations to measure pressure and its impact on tissues, so we can help identify pressure thresholds that may lead to esophageal diseases. 

Seeing the Impacts of the Research: Xinyi’s Story

My undergraduate degree was in physics and math. Now, I’m a fifth-year Ph.D. candidate at Northwestern University, where I study engineering sciences and applied math in Professor Neelesh A. Patankar’s research group. 

One of Professor Patankar’s research projects focuses on how food moves through the esophagus. We’re working with gastroenterologists at Northwestern University’s Feinberg School of Medicine to better understand the esophagus’s motion during swallowing. The overall goal is to help identify fundamental causes of esophageal conditions.  

Last summer, I completed an internship with NIST researcher Leroy Jia. Leroy’s interest in mathematical modeling complements my own interest in the mechanical aspects of this medical condition. 

This research is personal to me because my dad has a medical condition that makes swallowing difficult. So, I’m observing in my own family how our work can impact people. Being able to use mathematical skills to help solve a problem makes me feel very accomplished, especially when it may benefit someone in my family.

Solving Problems With Math (Problems): Leroy’s Story

Similar to Xinyi, I also studied physics and math at the undergraduate level, and I got my Ph.D. in applied math. When I was a Ph.D. student at Brown University, I realized I was more interested in the physical applications of math. I wanted to see how it could be applied to real-world problems. 

I had two advisers — one in physics and one in engineering. I spent a lot of time in both departments working with people of different backgrounds. I’ve always loved interdisciplinary research because it allows me to gain different perspectives on many types of problems. 

When Xinyi approached me about this internship, I had not heard of this particular medical condition, but I thought the equations seemed fascinating. I thought it was an interesting and deep mathematical problem to work on, with practical applications that could help people. As a mathematician, I have spent much of my career working more in the theoretical realm, so working on this project and knowing the positive impact we may have has been very gratifying. 

I love being a mathematician because of the elegance of mathematics. Our equations can be difficult. But logically, when you explain the results, the ideas are actually quite simple. 

For example, when small changes trigger an outsized effect, that’s an example of the scientific concept of instability. While predicting when an esophagus turns into a corkscrew is hard, the ideas behind it are basic — figure out what the most important effects are and how they conspire to create instability in the esophagus.

When you do mathematical modeling well, you get a correct understanding of what’s going on. This is the case whether you’re modeling a facet of the human body, the patterns of the weather or the motions of the planets. You can back up your conclusions with numbers and interpret the findings.

Using Computer Models and Math to Improve Our Health

There is currently no definitive cure for corkscrew esophagus. Doctors mostly focus on alleviating symptoms rather than addressing the underlying cause of the condition. A better understanding of the physics behind why this condition occurs may help scientists develop more targeted, effective treatments for these patients. This could include possibly a medical device or engineered tissues to help people swallow. 

We’re also hoping to address a broader scientific and medical challenge — how subtle changes in the behavior of our tissues can lead to dramatic and damaging changes in parts of the body. We want to gain greater insight into other ways in which instability can affect our health. If we can uncover broadly applicable principles of instability, we could learn about many biological challenges, including certain blood vessel diseases. 

Ultimately, this research is about more than just solving a medical puzzle. It bridges the gap between theoretical modeling and real-world patient applications. We hope it will offer a pathway to alleviate suffering and expand our understanding of how complex systems work in the human body.