Kayla Edwards was the most recent to give birth.
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She was born without a uterus, which happens in about 1 out of every 4,500 girls.
Kayla and her husband moved from Washington state to Texas when they got into the transplant trials at Baylor.
But then it took 2 years, first with waiting for a donor, then with embryos that failed, before she was finally pregnant.
Two weeks ago, daughter Indy Pearl was born.
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Kayla says she hopes her story inspires others.
"Anyone just going through infertility, not losing hope. Struggle after struggle, mountain after mountain, just keep climbing, because your miracle will eventually come," she said.
Kayla plans to spend time enjoying her little miracle, but hopes to have another child in the coming years.
This is the 4th baby born to women who have had uterus transplants. Baylor Medical Center is taking 10 women into its trial.