Gardaí investigating the murder of Ashling Murphy are checking the DNA of a suspect in hospital against samples taken from the crime scene in Offaly.
Detectives are still waiting to question the man, who is being treated for a number of injuries, in connection with the teacher's death.
The Grand Canal in Tullamore where the 23 year-old was attacked last Wednesday while out jogging is also being searched for any weapon which might have been used. Garda divers are combing the waterway.
Kevin Doyle, head of news with Independent News and Media, says significant progress is being made in the investigation;
"A number of searches have taken place, a house in Dublin and a house in a village just outside Tullamore. They have gathered a lot more DNA evidence from the scene."