Story highlights The first three patients have had the transplanted uterus removed

A Swedish surgical team worked alongside Baylor doctors

(CNN) A team of surgeons at Baylor University Medical Center announced Wednesday they have performed the first living donor uterus transplants in the United States.

The hospital said in a statement the experimental procedure was performed four times between September 14-22.

The procedure was unsuccessful for the first three patients, however, and the transplanted organ was removed because there was not adequate blood flow to it. According to the hospital, those three patients are recovering well.

The fourth patient seems to be on a better path to success. "Her tests are showing good blood flow to the uterus. There are also no signs of rejection or infection at this time," the statement said.

"We are cautiously optimistic that she could ultimately become the first uterine transplant recipient in the US to make it to the milestone of uterine functionality."

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