Liam Whoriskey, 25, of Glenabbey Gardens in the city, denies murdering the three year old in 2017.
The toddler was found dead in his family home at Colmcille Court at 10 am on Sunday, September 1.
The waiter also denies two charges of child cruelty and one charge of failing to protect Kayden.
At Thursday’s hearing in Derry Crown Court, consultant neuropathologist Prof Al-Sarraj at London’s King’s College Hospital, told the jury of seven men and five women the fatal non-accidental brain injury was likely to have occurred between 19:00 on 16 September and 10:00 the following day.
The BBC reports the professor told the court the absence of a precise time of death was “most important in this case because it has restricted the number of options open to the court”.
The court has previously heard a post-mortem examination revealed Kayden had sustained multiple injuries and bruising.
There were at least 15 non-accidental bruises to the child’s scalp, which had been caused by blunt force trauma to the head.
The defendant had been babysitting the child and a five-month-old baby girl when their mother and his former fiancee, Erin McLaughlin, had stayed out overnight after socialising with family and friends.
Prof Al-Sarraj said the head injuries sustained by the child were either minor or mild injuries and the bruising of the child’s brain could have been caused by someone squeezing the boy’s head.
Under cross-examination by defence barrister Ciaran Mallon QC, Prof Al-Sarraj said he was not aware the child had displayed unusual behaviour on the evening before his death.
Mr Mallon said Kayden had gone to bed by himself, had not brought his toys to bed with him and did not play a countdown with his mother after she had put his bedtime milk bottle into the microwave.Asked if the unusual behavioural pattern could be an indication of the onset of swelling to the brain from an earlier injury, Prof Al-Sarraj said he agreed with that possibility.
He said in such circumstances a child would be confused, irritable and difficult to feed “in a manner typical of a child having sustained a head injury.”
On the opening day of the trial last week, prosecution counsel Peter Irvine QC said Kayden had died as a result of blunt force trauma injuries to the head.
He also had a fracture to one of his ribs.
On Wednesday, the assistant state pathologist for the North of Ireland, Dr Peter Ingram told the jury that in his opinion Kayden’s injuries was “non-accidental”.