Math mimics hard-to-heal wounds

New model may lead to better treatments for chronic sores

A mathematical model may help clinicians speed the healing of persistent bedsores, diabetic ulcers and other types of chronic wounds, scientists report online September 21 in the Proceedings of the National Academy of Sciences.

BLOOD FOR THE WOUND A new mathematical model predicts ischemic, or blood-deprived, wounds take much longer to heal (upper curve) than nonischemic wounds (lower curve). C. Xue et al./PNAS

Chronic wounds are a serious public health problem, affecting 6.5 million people in the United States, says study coauthor Avner Friedman of Ohio State University in Columbus. These wounds linger, often because they don’t get enough blood flushing them with oxygen and other healing factors. Friedman and his colleagues’ new model is the first to predict the healing behavior of such blood-deprived — or ischemic — wounds, he says.

Mathematician John Dallon of Brigham Young University in Provo, Utah, says that the new model is the “start of something that could give valuable insight to the wound healing problem in the future.”

Friedman and his colleagues started by modeling a simple, flat wound at the skin’s surface. First the team developed equations to represent the springy, elastic tissue near the wound. Another set of equations predicted when and how healing factors enter the wound. Such factors include pathogen-busting white blood cells, capillary sprouts, blood-vessel–forming proteins and oxygen concentrations. By tweaking the amount of oxygen near the wound, researchers could model the healing of nonischemic and ischemic wounds.

The model’s simulations agreed with wound healing times found in experiments, the authors say. An eight-millimeter–wide wound under normal conditions is predicted to completely heal in about 13 days. But an ischemic wound would be only 25 percent healed after 20 days. The model also predicts that under low-oxygen conditions, fewer white blood cells can reach the wound.

The new model may help clinicians pinpoint better ways to treat wounds, Friedman says, for example by providing guidance about when oxygen and pressure therapies will be most effective.

Although the model includes many variables, others remain unexplored. “Of course, wound healing is extremely complex, and even in their model they have, out of necessity, ignored many things,” Dallon says.

Friedman and his colleagues would like to include in the model the behavior of genes, microRNAs and proteins known to speed along healing. The team would also like to model the tissue underneath the surface of the wound. These kinds of complexities are needed “to really make a big dent into this serious problem,” Friedman says. “Of course, we won’t cure wound healing with mathematics, but we can suggest ideas to biologists.”

Laura Sanders

Laura Sanders is the neuroscience writer. She holds a Ph.D. in molecular biology from the University of Southern California.

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