Texas Tech University mathematicians Casey Mills, a doctoral candidate, and associate professor of mathematics, Raegan Higgins, are using a mathematical approach to modeling the treatment of prostate cancer. After being diagnosed with prostate cancer, patients typically undergo intermittent androgen deprivation therapy prior to starting radiation or when surgery or radiation are not an option. Mills says that these patients undergo cancer treatment for a few months, then go without treatment for a few months.
“They alternate between periods of on-treatment and off-treatment, and those periods last several months,” Mills said. “We’ve created a new approach using something called time scales, which are able to combine discrete and continuous time very well.” A discrete variable is countable in a finite amount of time, but a continuous variable will continue on forever. “Most clinical models currently use strictly continuous time frames”, Mills said. Because of the change between on-and-off-treatment intervals, she and her advisor wanted to see if it was possible to combine the continuous and discrete to create a new model.
“What we’re doing introduces the fact that you can model both the continuous time and discrete time. We want to more realistically reflect the break of switching from on-treatment to off-treatment to on-treatment to off-treatment, without just assuming that it’s always continuous time,” Higgins said. “The benefit of this intermittent therapy is it gives patients a better quality of life. They’re not getting so much treatment at once. The doctors can see if the treatment is working and adjust accordingly.”
In using data from six patients whose treatment intervals best fit their mathematical formulas, the Texas Tech mathematicians said they accomplished their goal of building a solid foundational model. “Right now, we have a very, very novel model, and it will require more building and collaboration with biologists to increase its chances of being used in a clinical setting”, Mills said.