According to Doody, doctors who offer INVOcell can cut the number of office visits for one round of treatment from eight (for traditional IVF) to two or three, which is a big deal for patients in underserved areas, especially in the southeastern and southwestern United States, who often must drive several hours to reach fertility clinics. That means there’s less work for staff who administer blood draws and ultrasounds and play phone tag with patients with updates after each visit. “Patients take less medication, and we’ve gotten better at dosing and predicting how they will respond so we can do less monitoring,” says Doody, who is also the president of the Society for Assisted Reproductive Technology, the organization that reports fertility clinics’ data to the government. “We’re not trying to get 10 to 15 eggs like with regular IVF. We just need six to eight eggs to get one or two good embryos to transfer.” His rationale: More eggs aren’t always better, and doctors should aim for a handful of quality eggs, rather than the larger quantity typically generated during regular IVF.

And because the embryos are grown in the mother’s body, there’s no need for lab staff to run costly incubators with extensive security systems around the clock, which also brings down the price.

The fact that INVOcell preserves some of the mystery of baby-making was a big selling point for Brittney Koch-Dowell, since she and her wife are depending on help from science to conceive. (They each plan to take a turn carrying a baby.) “We’re already using donor sperm, so this helped it feel more real and natural,” says Koch-Dowell, 37, a restaurant manager from Elsberry, Missouri, who’s scheduled to undergo the procedure this month. “I get to be the incubator. My body and my heat are producing the child.”

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In some ways, the rationale behind INVOcell sounds so obvious. (“It’s like what’s old is new again,” quipped John Couvaras, a fertility doctor in Phoenix who’s helped four women conceive with the device.) Yet it took French embryologist Claude Ranoux nearly 30 years to fine-tune his invention, which has been available in Europe since 2008. Since the birth of the first “test-tube baby” in 1978, Ranoux had been fascinated by the idea of growing embryos inside the human body rather than in a petri dish. And he wasn’t impressed with the unreliable incubator at his workplace, the Cochin Hospital at Paris Descartes University. “I was forced to be an innovator because I had a bad machine,” says Ranoux.

So Ranoux rigged up a little portable incubator from plastic tubing. At first, he considered sewing it under the abdominal skin, but that would require two surgeries to implant and extract the device and risked causing an infection. Taping it under an armpit would provide a nice warm place, but he thought it would feel too uncomfortable over several days. He also considered securing it in the back of a patient’s mouth, but he didn’t want to risk shocking the embryos if she drank cold water or hot coffee. Besides, there was the chance she could accidentally swallow it.