Ledzewicz presents on optimal control in Allahabad, India

An SIUE professor travelled to Allahabad, India this past winter break to present her research on applications of mathematics to cancer treatments.  The presentation took place on December 31st, 2010.

Urszula Ledzewicz, distinguished research professor in mathematics and statistics, was invited as one of 15 plenary speakers to the “International Conference on Mathematics of Date” with all local expenses covered by the organizers. The conference was organized by Pushpa Publishing Company, an India based scientific publisher that issues about 30 journals in various branches of mathematics.

Prof. Ledzewicz  gave her talk on the first day of the conference and presented on overview of her research. The presentation was entitled “Challenges in Mathematical Modeling of Novel Cancer Treatments: An Optimal Control Approach.”

“It was an overview of how I see that optimal control can be applied to design protocols for cancer treatments,” said Ledzewicz.

She stated that her area of research is the application of the field of optimal control to mathematical models arising in biomedicine.  Optimal control is a theory that deals with the optimal selection of controlled processes and is widely used in engineering. In the context of biomedical applications, the aim is to find optimal treatment protocols.

“We try to answer the medical question of how to apply the drug to best shrink the tumor,” said Ledzewicz.

As Ledzewicz explained it, her research examines models created by a group of researchers from the Harvard School of Medicine.  The models are created by teams of researchers – biologists, M.D.’s, and mathematicians.  Ledzewicz explained that in the lab, researchers construct a model by estimating parameters based on experimental results from treatment of mice.

Mathematicians analyze models theoretically to understand the behavior of different classes of cells (cancer cells, healthy cells, immune system, … ) under various therapies. In this way, mathematicians are helping researchers discover how different drug treatments and therapies would best function in a patient, as well as helping in the planning stages of clinical trials.

“For example, there are two drugs.  Each of them can be given from zero dose to full dose.  And it can be given at chosen moments in time.  If you don’t have any mathematics behind this, your option is to shoot in the dark and try – vary the doses, vary the time you give it – and compare the outcome.  But then you are really experimenting on patients,” said Ledzewicz.  “Whereas, we create an abstract model and apply those drugs as an abstract function entering the model. And we see what would be the best way to do it.”

Ledzewicz presents at the University of Allahabad in Allahabad, India. photo courtesy of Ledzewicz.

The goal in designing such optimal protocols can vary according to Ledzewicz.  She stated that optimal may have a very different meaning depending on the researcher.

“For some models we analyze, optimal means that the tumor is as small as possible.  Somebody else will say… the tumor is as small as possible, but I also want the time to be short; I don’t like to take the drug forever.  For other models, it is also important that the vasculature of the tumor is pretty small so that the tumor doesn’t grow back or that the immune system does not get suppressed.”

Ledzewicz said the presentation went well.  She thoroughly enjoyed the trip and the university and the students were very hospitable and were genuinely interested in what she had to present.

“They really treated us like royalty from the moment we arrived until the moment we left,” said Ledzewicz

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