Charlie Gard's parents have begun the latest stage of their legal fight over treatment for their terminally ill baby.
A judge is further analysing issues at a hearing in the Family Division of the High Court in London.
Chris Gard and Connie Yates want Mr Justice Francis to rule that their 11-month-old son, who suffers from a rare genetic condition and has brain damage, should be allowed to undergo a therapy trial overseen by a specialist in New York.
Specialists at Great Ormond Street Hospital in London, where Charlie is being cared for, have said the therapy is experimental and will not help.
They say life support treatment should stop.
Charlie's parents, who are in their 30s and come from Bedfont, west London, have already lost battles in the High Court, Court of Appeal and Supreme Court in London.
They have also failed to persuade European Court of Human Rights judges to intervene.
But the couple say there is new evidence and want Mr Justice Francis, who in April ruled in favour of Great Ormond Street and said Charlie should be allowed to die with dignity, to carry out a fresh analysis of their case.
Mr Justice Francis considered the couple's new claims at preliminary hearings.
Last week, he suggested that the American specialist - Michio Hirano, a professor of neurology at Columbia University Medical Centre in New York - should travel to London to meet Great Ormond Street doctors and other clinicians.
Dr Hirano examined Charlie and discussed his case at Great Ormond Street on Monday and Tuesday.
Barrister Grant Armstrong, representing Charlie's parents, said Friday's hearing had been arranged so the judge could make case directions.
Mr Justice Francis is expected to analyse issues in more detail at another hearing on Monday.
Charlie's parents were in court.
Mr Armstrong said Charlie had undergone further scans in the last few days. He also said experts had discussed the case.
Mr Armstrong said Dr Hirano and Charlie's parents could give evidence at next week's hearing.
The judge said he would need to know what new material there is since he decided in April that life-support treatment should stop.
He said would also want to know what difference any new material would make.
Mr Armstrong said a range of opinions had been expressed at a medical experts' meeting earlier this week.
Mr Justice Francis said there had also been a "considerable amount of agreement".
He added that results from one scan were not yet available.
Mr Justice Francis urged anyone campaigning outside Great Ormond Street to be aware that other sick children were being treated at the hospital.