It was revealed Chris Gard and Connie Yates lost a skirmish over their terminally ill son's treatment, following a court hearing conducted via email.
The pair, from Bedfont , had agreed "in principle" to further "imaging" being carried out on the 11-month-old boy's brain prior to medical experts meeting in London during Monday and Tuesday (July 17 and 18).
But the couple said an electroencephalogram (EEG) should be carried out for no longer than 30 minutes, whereas Great Ormond Street Hospital specialists said it would have to last at least four hours in order to generate useful data.
The judge overseeing the battle released a written order he made on Saturday (July 15) after analysing lawyers' rival emailed arguments.
Mr Justice Francis said the latest "out-of-hours" dispute between the couple and doctors caring for Charlie centred on a new brain scan - and ruled in favour of Great Ormond Street doctors.
He said the scan should "be of such duration" as treating clinicians "may advise".
Charlie's parents want Mr Justice Francis to rule that their 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.
Great Ormond Street specialists say the therapy is experimental and will not help.
They say life support treatment should stop.
Charlie's parents 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 has considered the couple's latest claims at preliminary hearings in the Family Division of the High Court in London.
Last week, Mr Justice Francis suggested that the American specialist - Michio Hirano, a professor of neurology at the Columbia University Medical Centre in New York - should travel to London to meet Great Ormond Street doctors and other clinicians.
Dr Hirano has examined Charlie and discussed his case while visiting Great Ormond Street on Monday and Tuesday.
Mr Justice Francis is due to oversee further court hearings in the next few days.
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