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Mathematics eliminating guesswork from plastic surgery tissue transfer
Plastic surgeons are turning to mathematics to take the guesswork out of efforts to ensure that live tissue segments that are selected to restore damaged body parts will have enough blood and oxygen to survive the surgical transfer.
In the world's first published mathematical model of tissue transfer, mathematicians have shown that they can use differential equations to determine which tissue segments selected for transfer from one part of the body to another location on the same body will receive the level of oxygen required to sustain the tissue.
The most common tissue transfers are used to restore body parts destroyed by cancer and trauma. The researchers say reliable mathematical modeling of the blood supply and oxygen in tissue segments will not only reduce failures in reconstructive surgery, but will also improve understanding of conditions in which an adequate blood supply is a basic problem, such as heart disease, cancer and stroke.
To obtain tissue for reconstructive surgery, plastic surgeons cut away a segment of tissue, called a flap, that is fed by a single 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 within the flap intended for transfer.
Mathematicians working on the problem have set out to model that relationship. They have shown that under certain relationships between the size of the tissue flap and the diameter of the perforator vessel, the oxygen level in the flap will remain above 15 percent of the normal level, thus ensuring a successful flap transfer. If this relationship is not satisfied, the most distant tissue from the vessel will start to die something already observed by clinicians.