Police have spoken to more than 20 people in relation to NHS Tayside brain surgeon Sam Eljamel.
It follows a BBC Disclosure documentary that revealed allegations Mr Eljamel had harmed dozens of patients.
Police Scotland said it was a complex investigation that would take time.
Separately, new figures seen by the BBC show the health board paid out more than £3m on settling cases against its neurosurgery department in just five years.
A Freedom of Information request found NHS Tayside paid out £3,163,716 for just five cases against its neurosurgery department as a whole, between 2012 and 2017.
The health board said each case was investigated thoroughly and in a small number compensation was paid.
Mr Eljamel was the head of the neurosurgery department in Ninewells Hospital in Dundee – one of just four specialist centres in Scotland.
He was suspended in December 2013 and retired soon after.
The BBC Disclosure investigation found the health board did not have effective systems in place to pick up on recurrent mistakes prior to 2013.
It saw evidence dozens of people claimed to have been harmed by Mr Eljamel.