Dean Doherty, 26, suffered spinal injuries five weeks ago after coming off his scrambler at a track in Magilligan.
He was subsequently airlifted to Belfast where he underwent surgery at the Royal Victoria Hospital. Earlier this week, he was transferred to Musgrave Park Hospital.
“We are hoping he will improve,” said Dean’s mother Christine.
“We haven’t stopped praying since but then you see other people in hospital and they’re worse than Dean and you think, ‘at least Dean can talk to us, at least he’s here’.
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“Things are much the same, but we hope over the next three weeks we’ll know more.”
The Doherty family say they have been overwhelmed with support since Dean’s accident and want to thank everyone for their support, including neighbours, Dean’s friends and Monsignor Bryan McCanny, for visiting Dean in hospital.
“I don’t think we would have got through this without them, to be honest,” said Christine.
“People have been so good. Dean is in the best hands and we hope we will know soon if he has a chance of being able to walk.
“You have to have hope.”
In the meantime, Causeway Coast and Glens Borough Council say their investigation into the incident is continuing.
A council spokesperson said the incident was not reported to them but they became aware of it through media reports.
“Council is currently investigating the circumstances of the accident and an inspection of the track has been carried out,” said a spokesperson.
It is understood council has also spoken to the owners of the facility and the landowner.
“The owners of the track have not been asked to carry out any interim actions while the investigation is pending, although council continues to work with the owners to ensure the activity is carried out as safely as possible,” added the spokesperson.