# Mathematics taking guesswork out of plastic surgery tissue transfer

##### July 14, 2009 by Emily Caldwell,

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 of 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 , 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.

"That guideline is based upon experience, trial and error. What we need is a more precise ability to determine what the necessary blood vessel size really is," said Michael Miller, professor of surgery and director of the division of at Ohio State University and a senior author of the research.

"I'm convinced that there is a relationship that's probably very predictive between the diameter and blood flow in the vessel and the ability of the piece of the tissue we're transferring to survive based on that."

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.

"This is still just a concept. But this initial system of five differential equations gives us a range between the flap size and the required diameter of the supporting artery that would ensure survival," said Avner Friedman, a senior author of the paper and a Distinguished University Professor at Ohio State.

The research appears this week 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.

"As time has gone on, we have learned that we don't have to take the muscle, but we can take a single blood vessel coming through the muscle and transfer the tissue on that vessel," Miller explained. "What we're finding is that the more we design flaps like this, the less reliable the tissue is becoming. The motivation to try to reduce injury to muscle is 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.

"The fact that there are thousands of capillaries makes it difficult to compute the oxygen levels, so we found a method of averaging. We 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," Friedman said.

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.

More work lies ahead to make the model truly useful in a surgical setting, Miller and Friedman agreed.

In live human tissue, the pattern of blood vessels and capillaries 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.

Friedman said he and colleagues 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 surgeon will take an image of a flap that will give 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," Friedman said.

Miller, a specialist in breast reconstruction, said the abdomen is 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.

"But theoretically, we can make flaps from anywhere on the body," he said. "The whole body is divided up on this vascular tree. So if you can isolate a flap of tissue on a blood supply, you can remove it and reattach it."

Source: The Ohio State University (news : web)

## Related Stories

#### Breast reconstruction advances fix distortions left by lumpectomy

April 23, 2008

Lumpectomy or breast conservation surgery is the most common type of breast cancer surgery currently performed. A benefit of the surgery is that only part of the breast is removed, but a drawback can be the resulting physical ...

#### Control of blood vessels a possible weapon against obesity

January 7, 2009

Mice exposed to low temperatures develop more blood vessels in their adipose tissue and metabolise body fat more quickly, according to a new study from Karolinska Institutet. Scientists now hope to learn how to control blood ...

#### From connective tissue to bones

April 30, 2009

Cartilage, bones and the internal walls of blood vessels can be created by using common connective tissue cells from human skin. Researchers in reconstructive plastic surgery at Linköping University have successfully manipulated ...

#### Fat Tissue Engineers Gather to Swap Notes on Repairing Human Tissue

October 23, 2006

Doctors, fat researchers and tissue engineers from around the world will trade techniques and their latest research findings to improve the use of human fat tissue in medical therapies like facial, breast, bone, vocal cord ...

#### Technique may help stem cells generate solid organs

March 2, 2009

Stem cells can thrive in segments of well-vascularized tissue temporarily removed from laboratory animals, say researchers at the Stanford University School of Medicine. Once the cells have nestled into the tissue's nooks ...

#### Photoacoustics useful in cancer research

December 5, 2008

(PhysOrg.com) -- Photoacoustics can be used to show the development of blood capillaries in and around a tumour. PhD student, Kiran Kumar Thumma, of the University of Twente (Netherlands) is the first to use the technology ...

## Recommended for you

#### Frog choruses inspire wireless sensor networks

January 21, 2019

If you've ever camped by a pond, you know frogs make a racket at night; but what you might not know is how functional and regulated their choruses really are. Frogs communicate with sound, and amid their ruckus is an internally ...

#### Researchers examine how musicians communicate non-verbally during performance

January 18, 2019

A team of researchers from McMaster University has discovered a new technique to examine how musicians intuitively coordinate with one another during a performance, silently predicting how each will express the music.

#### Study finds simple explanation for endurance of religion

January 17, 2019

Childcare can be expensive, stressful, and annoying to organise, but a University of Otago-led study has found it may also be behind religion's resilience.

#### Scientists confirm pair of skeletons are from same early hominin species

January 17, 2019

Separate skeletons suggested to be from different early hominin species are, in fact, from the same species, a team of anthropologists has concluded in a comprehensive analysis of remains first discovered a decade ago.

#### Study: Social media sways exercise motivation

January 17, 2019

It's January – a time when students are looking for that extra bit of oomph. For some, time spent on social media might provide the necessary inspiration to get up and exercising – but that time can come with consequences, ...

#### An ancient relative of humans shows a surprisingly modern trait

January 16, 2019

A relative of modern humans that lived at least 104,000 years ago in northern China showed evidence of dental growth and development very similar to that of people today, a new study found.