Tatyana discovered many more infants had died at the hospital in similarly odd circumstances. And after intensive lobbying, the authorities eventually agreed to have the tiny bodies of around 30 babies exhumed and examined.
Tatyana showed me the video she had been allowed to record of the post-mortem examinations that followed. The gruesome film shows the carcasses of babies, some of whom were full-term, with their organs and brains missing. Neurones in infants' brain are a rich source of stem cells.
Another body shown in the video is so badly dismembered it has to be put together piece by piece, like a jigsaw. Dismemberment is not standard autopsy practice and could, according to experts, indicate stem cells were harvested from bone marrow.
The post-mortem examination conclusions were profoundly disturbing. But Tatyana is now living in fear that the authorities are trying to silence her.
Her 20-year-old son went missing in October in mysterious circumstances, and she fears he may have been killed in revenge for her campaign to uncover the truth.
The Ukrainian authorities deny any conspiracy and refute claims that there is a trade in stem cells taken from stolen babies.
However, alarmed by the whole stem cell issue, the Council Of Europe is now carrying out its own investigation into the Ukrainian mothers' claims.
The Council's interim report talks of a "culture of trafficking of children snatched at birth and a wall of silence from hospital staff upwards over their fate".
As part of the second stage of the inquiry, the council will no doubt want to talk in detail to staff at Maternity Hospital Number Six. But whether they will get any answers is another matter - as I discovered when I tried to speak to the hospital authorities myself.
It was a grim scene. As I waited for hours at Maternity Hospital Number Six, heavily pregnant women in maternity smocks wandered past me in its dark corridors, along with the occasional elderly midwife.
Paint was peeling off the walls and there was a strong smell of antiseptic. Eventually, I was granted five minutes with the chief doctor, Larysa Nazarenko.
She was visibly uncomfortable as I set up my camera - her eyelids blinking rapidly as she stood behind her desk. "The children are not lost," she told me. "They are not stolen - that's just somebody else's illusion."
Who, she asked, had put these ideas in this young mother's head?
"It's about money," I said, "about stem cells. About Westerners paying a lot of money for stem cells from babies. And claims that cells from their brains are taken for treatment by various organisations."
"There is no such therapy," she said. "No work in this hospital is connected with the use of cells. This is the wrong address. I deny everything." Then I was ordered to leave.
Dr Nazarenko may have to spare more time to speak to Council Of Europe officials in February, when they will return to Kharkiv to continue their investigation.
The wall of silence is crumbling. And it may yet reveal a very ugly side to the global beauty business.