Mr Sturt said there were several reasons why he resigned.
He said he "really enjoyed" the issues health board members were allowed to comment publicly on, but struggled with the parts of the agenda that were discussed and decided confidentially.
Mr Sturt, a long-term anti-fluoride activist, also said from his perspective it had been an uphill battle to get his point across on issues such as water fluoridation.
Mr Shaw said he had no comment to make on Mr Sturt's resignation.
Mr Shaw said the health board was committed to improving the oral health of the Lakes community. He said its policy around fluoridation of public water supplies had been consistent for a number of years and was based on available evidence.
Mr Shaw said the upcoming election for the seven elected places on the board provided an opportunity for those committed to improving the health of the Lakes communities, who understood board processes and who had specific relevant skills and experience.