When Catherine Smith's daughter Ella was born prematurely at 28 weeks, she feared the worst would happen.
Ella weighed just 1lb 10oz (737g) and was about the size of an adult's hand. For weeks she was kept in an incubator.
Catherine, the daughter of ex-Labour leader John Smith, said she knew little about premature babies at the time.
"I didn't really think there was that much chance of survival," she told the BBC.
But Ella survived - thanks to a research centre set up by former prime minister Gordon Brown and his wife Sarah after the couple's 10-day-old baby, Jennifer, died in 2002.
Following the death, the Browns founded the charity PiggyBankKids - now known as TheirWorld - in memory of their daughter.
And in 2004, the charity established the Jennifer Brown Research Laboratory (JBRL) at the University of Edinburgh.
The JBRL looked at ways to help premature babies thrive, including research into how much oxygen should be given to babies in incubators.
It was this research that was to prove absolutely crucial to the survival of Ella 15 years later.
Catherine's father had been one of Mr Brown's closest political allies.
She became aware of the link between the Browns' charity and her own daughter after Ella started to pull through.Image caption The Browns with their children John and James Fraser in 2006
"I thought I could donate to their research lab - because I knew they'd set up a research lab in Jennifer's name," said Catherine.
"I went on the website to try to make a donation, and I read a little, and I realised that some of the work they had done had impacted directly on the care that Ella was getting - and that was just incredibly moving."
Work done by scientists at the JBRL established that giving a premature baby too much or too little oxygen could seriously damage its chances of survival.
"By the time Ella was getting care this change had made its way into clinical practice and it was one of the things we were very aware of because the machine that was monitoring oxygen was constantly going off," said Catherine, from Dundee.
"If the oxygen went too high or too low an alarm sounded and that would happen many times in an hour. It was so obviously being monitored very strictly and very closely.
"That was as a result to the work done in Jennifer's name. I really think it made a difference. I personally believe it had a direct impact on her survival and it is humbling."
Speaking to the Daily Record, she added: "What Gordon and Sarah have done is the most extraordinary gift. They've given us our daughter."Image caption Ella is now two years old
Sarah, 53, told the newspaper that it was "uplifting" to learn that the research was helping other babies survive.
She said: "You don't wish this on anyone, and you certainly don't wish it on yourself, but I look for the good I can do, and ensure we contribute to a body of knowledge so more mysteries are unlocked and there are more possibilities for happy outcomes.
"It's very uplifting to know somebody has gone home with their baby thanks to the work of the lab created in Jennifer's memory.
"And this translates itself through to many other families who've also been able to take their babies home. To know if you can do good for one person it's enough. But if it can go beyond that then it's even better.
"And having a personal connection - as we do with Catherine and her family - to someone where the outcome has changed, is wonderful."
Ella is now two years old and is in "absolutely brilliant" health, Catherine said.
She said she had had an "emotional lunch" with Sarah after writing to the Browns to tell them about Ella - though she admitted it had been difficult at first as their experiences had been so different.
But she told the BBC that Sarah had insisted she should not feel guilty.
"Sarah said to me absolutely straight: 'Don't be ridiculous. What's the point of the lab, what's the point of all the work we've done in Jennifer's name if it isn't for an Ella?'"