Finding patterns helps us make sense of our world, break down complicated issues and predict how certain events might unfold. It also plays a critical role in understanding a complex biological issue: cancer.
Joshua Hiller, Ph.D., assistant professor of mathematics and computer science at Adelphi, recently completed two research reports in mathematical carcinogenesis, a field devoted to developing mathematical models for the way cancer develops in the body.
His reports have yielded surprising discoveries that could transform cancer treatment and prevention, and potentially save lives.
Three patterns
In his first report, “Characteristic Patterns of Cancer Incidence,” Dr. Hiller and his team analyzed 1,200 cancer studies published over 60 years across six continents to find common themes about how those cancers developed.
“We were trying to figure out exactly what a good mathematical model should look like,” Dr. Hiller said.
They discovered that most cancers fit into one of three patterns:
- The risk of getting cancer starts out low at birth and increases until age 75. This is known as a “power law.”
- The risk of getting cancer is high early on, but if it doesn’t appear by a certain age, usually around 20, then the risk is low, but gradually increases similar to a power law. This pattern commonly applies to childhood cancers and cancers caused by sexually transmitted diseases.
- The risk of cancer decreases in extreme old age, a fact that existing biological models can’t explain. Dr. Hiller and his team proposed that this happens because human tissue regenerates less as people age, so there are fewer opportunities for cancer to form.
With these insights, scientists could potentially develop new ways to help prevent, diagnose and treat cancer worldwide.
Probability findings
In the second study, “Asymptotic Relative Risk Results from a Simplified Armitage and Doll Model of Carcinogenesis,” Dr. Hiller and his team used mathematical models to figure out the probability of cancer appearing in two groups: former smokers and organ transplant recipients.
They unearthed two key findings:
- Former smokers are always at an increased risk of developing lung cancer. However, that increased risk decreases over time.
- Organ transplant recipients have an increased risk of developing all types of cancer. Unlike former smokers, their risk increases with time.
Based on these discoveries, Dr. Hiller and his team recommended specific methods of cancer screenings that doctors could implement.
“Clinicians should continue to monitor people who have stopped smoking, treating them as smokers for five more years or so,” Dr. Hiller said. “They can lower the amount of surveillance after that.” This is less costly and invasive than administering increased screenings indefinitely.
For transplant recipients, the team recommends increasing the frequency and range of surveillance over time, since their risk of developing all types of cancer increases. These checks for transplant recipients will be more costly and invasive than they are for former smokers—but they will also be most effective.
Bringing research home
Dr. Hiller’s research demonstrates the importance of mathematics in the field of cancer research. He hopes to share his methods with his Adelphi students by offering a course in mathematical oncology, which involves using math to study and treat tumors.
“Math gives you a way to connect medical data and biological theories,” Dr. Hiller said. “Through those translations, we can figure out how cancer is caused and hopefully figure out how to prevent it.”
» Learn more about Adelphi’s Department of Mathematics and Computer Science
