Mathematics Enabling Successful Plastic Surgery Tissue Transfer
Posted Jul 21 2009 12:02am
Science Daily recently reports that 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.
Mathematicians, in the world’s first published mathematical model of tissue transfer, 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, aplastic surgeon Phoenixexperts explain, cuts 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 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 and specialists inplastic surgery Phoenixsources say.
The research appears the week of July 13 in the online early edition of the Proceedings of the National Academy of Sciences. The routine use of a patient’s own tissue from the lower abdominal wall to restore deformities on the chest dates to 1982. In the early days of full removal and transfer of tissue, surgeons took muscle along with skin and fat, resulting in loss of strength where the muscle was removed. With chest deformities andbreast augmentation Phoenixsurgeons quote the researchers as saying that as time has gone on, they have learned that they don’t have to take the muscle, but can take a single blood vessel coming through the muscle and transfer the tissue on that vessel. What they found was that the more they designed flaps like this, the less reliable the tissue became. The motivation to try to reduce injury to muscle was leading to an increase in problems with part of the flap failing because it doesn’t have enough blood.
Miller asked Friedman, founding director of Ohio State’s Mathematical Biosciences Institute, to work on a model that could add more predictability to tissue transfer.
To create the initial model, Friedman and colleagues needed to determine a number of values: the level of oxygen in the tissue, which comes from tiny capillaries spaced just microns apart; the rate of exchange of oxygen from vessels to tissue; and the pressure under which the blood is flowing in those vessels.
Because there are thousands of capillaries that make it difficult to compute the oxygen levels, the researchers found a method of averaging. They average the oxygen concentration in the capillaries, think of capillaries as being uniformly spread all over, and look at the transport of oxygen from vessels into tissue. The model’s outcomes exploited clinical observations, in that if the oxygen pressure fell below 15 percent during the few days following the tissue transfer, fat tissue on the outer edges of the flap would start to die. When that happens on actual surgical cases, doctors must replace the dead tissue, and sometimes have to redo the entire operation.
The pattern of blood vessels and capillaries in live human tissue is not uniformly spread throughout the flap. In many cases, there is a gap in the presence of branching vessels at the point at which the feeder artery and vein enter the fat and divide. And to add accuracy to the parameters used in the equations, the researchers agree that animal studies of tissue transfer are needed to make the model more reliable.
Imaging technology is also expected to factor into the future of reconstructive surgery. Surgeons currently use three-dimensional CT scans to image a potential flap and the perforator vessels that are feeding that flap. But the imaging available to date can’t display the entire vasculature of a flap. The researchers hope to provide surgeons with software that could be combined with advanced imaging to supply more reliable information about the likely survival of a tissue flap. The image of the flap will give the surgeon an idea of the distribution of vessels. Then the surgeon will use the software to determine that with this given vasculature, a specific size of tissue can be cut. According to specialists intummy tuck Phoenixsurgeons often go to the abdomen as a common source for tissue to be transferred because it contains a lot of tissue in a location that allows the resulting scar to be hidden by clothing. Theoretically, surgeons can make flaps from anywhere on the body; the whole body is divided up on a vascular tree. If you can isolate a flap of tissue on a blood supply, you can remove it and reattach it. This research was supported by the National Science Foundation. For more information on these developments in tissue transfer technology, contact your local plastic surgeons.