A couple who want to take their sick baby son to the United States for treatment have begun the first round of a fight in the Supreme Court.
Chris Gard and Connie Yates want 10-month-old Charlie Gard, who suffers from a rare genetic condition and has brain damage, to undergo a therapy trial.
Specialists at Great Ormond Street Hospital in London, where Charlie is being cared for, say therapy proposed by a doctor in America is experimental and will not help.
They say life support treatment should stop.
A High Court judge in April ruled against a journey to the US and in favour of Great Ormond Street doctors.
Mr Justice Francis concluded that life support treatment should end and said Charlie should be allowed to die with dignity.
Three Court of Appeal judges upheld that ruling in May.
A panel of three Supreme Court justices have begun analysing the couple's claims at a hearing in London.
Justices are considering preliminary arguments before deciding whether to give the go-ahead for a full appeal hearing.
Doctors at Great Ormond Street are continuing to provide treatment pending decisions by Supreme Court justices.
Mr Justice Francis had made a ruling on April 11 after a trial in the Family Division of the High Court in London.
He heard that Charlie, who was born on August 4 last year, had a form of mitochondrial disease, a condition which causes progressive muscle weakness and brain damage.
Specialists in the US have offered a therapy called nucleoside.
Charlie's parents, who are in their 30s and come from Bedfont, west London, have appealed for money on a GoFundMe page to cover doctors' bills in the US.
They reached a £1.2 million target before the High Court trial.
People are continuing to donate and the fund has now topped £1.3 million.
Mr Justice Francis said Great Ormond Street doctors had considered the experimental treatment, but decided it would not help Charlie.
He said the case had never been ''about money''.
Lawyers representing Charlie's parents say parents should be free to make decisions about their children's treatment unless any proposed treatment poses a risk of significant harm.
Richard Gordon QC, who leads the couple's legal team, said the case had implications for others.
"(Charlie's) parents have made a decision, it's not a wish, it's a decision, to try to keep all options open and retain life for their child," he said.
"We say Charlie is being deprived of his liberty at Great Ormond Street Hospital."
He said the couple were "model parents".
"They would not wish to do anything that would cause Charlie harm," he added.
"The state is not entitled to cause a child's life to be extinguished."
Charlie's parents have indicated that they will ask the European Court of Human Rights in Strasbourg to consider the case if Supreme Court justices rule against them.
Lady Hale, the Deputy President of the Supreme Court and the most senior justice on the panel, said the case was "very, very serious".
Justices were told that without treatment Charlie's life expectancy was measured in months.
Mr Gordon said the case was "so important" yet there was "so little time".
Mr Gard sat next to Ms Yates during the hearing and clutched a toy monkey belonging to Charlie.
Katie Gollop QC, who led Great Ormond Street's legal team, said the case was "sad" but not "exceptional".
She said the couple seemed to be suggesting that "parents always know best".
But she said the paramount interest in such cases was the welfare of the child.
Ms Gollop said the case was "particularly sad" and "particularly difficult for all those who care about Charlie".
But she said there were children who had illnesses which could not be cured.
She said in such cases parents did not want to look back and think something else could have been tried and sometimes became embroiled in disagreements with doctors.
Ms Gollop said Great Ormond Street specialists had tried to work with the couple, had "listened intently" to them and sought a number of second opinions from doctors at other hospitals.
"Fundamentally the parents don't accept the facts," said Ms Gollop. "They don't accept that nucleoside therapy will be futile."
Ms Gollop said Charlie could not could see, hear, move, cry or swallow.
She added: "He is on a machine which causes his lungs to move up and down because his lungs cannot go up and down."
Ms Gollop said Charlie's condition "affords him no benefit".
She said some doctors thought that Charlie felt pain and some thought he did not.
Barrister Victoria Butler-Cole, who is instructed by a guardian appointed to independently represent Charlie's interests, said a trip to the US was not in Charlie's best interests and said life-support treatment should stop.
Justices retired after hearing legal argument from all sides and said they hoped to give a decision later in the afternoon.