A statement on behalf of JT McNamara's family has revealed that the jockey is still "in an induced coma" at Frenchay Hospital.
The Irish amateur damaged the C3 and C4 vertebrae in a fall from Galaxy Rock during last week's Cheltenham Festival.
"JT McNamara remains stable in an induced coma in Frenchay Hospital, Bristol," read a statement from the Injured Jockeys Fund. "Further scans are planned and another statement will be issued as soon as there is more news.
"While visits to JT at the moment are not appropriate, JT's family are extremely grateful for all the kind messages and support."
The 37-year-old underwent a lengthy operation on Friday.