By the Numbers

Mathematics taking guesswork out of tissue transfer

Plastic surgeons at The Ohio State University are turning to mathematics to ensure that live tissue selected to restore damaged body parts has enough blood and oxygen to survive the surgical transfer.

In the world’s first published mathematical model of tissue transfer, mathematicians have used differential equations to determine which tissue segments selected for transfer from one part of the body to another will receive enough oxygen to survive.

The most common transfers are used to restore body parts destroyed by cancer and trauma. Researchers say reliable mathematical modeling of the blood supply and oxygen in tissue segments will reduce failures in reconstructive surgery.

To obtain tissue for reconstructive surgery, surgeons cut away a tissue flap fed by a set of perforator vessels – an artery and vein that travel through underlying muscle to support skin and fat. Surgeons generally agree that vessels at least 1.5 millimeters in diameter are required to sustain oxygen flow in the flap.

“That guideline is based on experience, trial and error. We need a more precise ability to determine the necessary blood vessel size,” says Michael Miller, MD, professor of Surgery OSUCCC – James and director of the Division of Plastic Surgery at Ohio State. “I’m convinced there’s a relationship that’s probably very predictive between diameter and blood flow in the vessel and the ability of the tissue to survive based on that.”

The mathematicians have shown that, under certain relationships between flap size and perforator vessel diameter, the oxygen level in the flap remains above 15 percent of normal, ensuring a successful transfer.

“This is still just a concept, but this initial system of five differential equations gives us a range between flap size and the required diameter of the supporting artery that would ensure survival,” says Avner Friedman, PhD, a Distinguished University Professor of Mathematical and Physical Sciences at Ohio State.

Published in the July 21, 2009 issue of the Proceedings of the National Academy of Sciences.

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