Ledzewicz receives NSF research grant to apply optimal control to problems in biomedicine

Mathematics professor Urzula Ledzewicz received a National Science Foundation grant to apply optimal control theory research to cancer and epidemiology Photo courtesy of Ledzewicz

It is possible tomathematically analyze ways to control cancer treatments and the spread of epidemics through optimal control theory, according to mathematics professor Urszula Ledzewicz.

Ledzewicz was recently awarded a National Science Foundation (NSF) research grant for her applications of optimal control theory (a specific field of applied mathematics) to problems arising in biomedicine.

The NSF grant is in collaboration with professor Heinz Schaettler from Washington University, with whom she has been working for several years.

In their research Ledzewicz and her collaborator will “try to shed some light and provide mathematical insights into this timely and relevant medical problem.”

The applications of optimal control they intend to pursue under the grant involve two main fields of study: cancer research and epidemiology.

Ledzewicz said objectives include finding out what combination ratio of cancer treatments affect cancer, and what combination ratios of vaccinations, treatment and sanitation efforts “minimize the number of infected individuals and also minimizes the cost of the whole procedure.”

Mathematics and statistics department chair Adam Weyhaupt said he believes Ledzewicz’ work is significant to the field of optimal control and will continue to benefit students.

“Dr. Ledzewicz is an internationally recognized scholar with a long history of attracting external support for her work.  This work, combined with her frequent work with graduate students, will continue to advance the field of optimal control and expand opportunities for our students.”

For the cancer treatment part of their grant, professors Ledzewicz and Schaettler intend to collaborate with the Center of Cancer System Biology of Tufts University School of Medicine.

The first topic will be a continuation of research done under five previous NSF grants. They will study mathematical models describing the dynamics of the interactions of various types of cancer treatments: chemotherapy or radiotherapy that targets the cancer cells, immunotherapy, which boosts the immune system, and anti-angiogenic therapy that stops tumors from growing their own blood vessels. In other words, through optimal control, they will analyze how effective various combinations of these therapies will be in fighting the disease.

Ledzewicz said this all leads to a mathematical structure that can be formulated and analyzed as a general optimal control problem.

According to Ledzewicz, problems and results of the analysis can apply to other fields in biomedicine like epidemiology.

“In epidemiology the dynamics describe the interaction between population of infected, susceptible and recovered individuals and the control represents various efforts to curtail epidemics like through vaccinations, treatment and even sanitation efforts,” Ledzewicz said.

Ledzewicz said they will also study metronomic chemotherapy, which is a way of administering chemotherapy at a lower dose (varying or constant) for more prolonged periods. She said it has been found to be very effective in several aspects.

“This kind of protocol not only kills cancer cells but has an anti-angiogenic effect and provides a boost to the immune system,” Ledzewicz said. “It’s like killing three birds with one stone.”

There is growing medical evidence that indicates that “more is not necessarily better” but properly calibrated biologically optimal dose (BOD) can lead to better outcomes Ledzewicz said.

She has had her research supported by NSF grants for nearly 25 years, but in the current time of tight federal budget Ledzewicz said she is “happy that the NSF decided to continue this support.”

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