Most DHB funding is allocated using a population-based tool which is partly determined by the weighting given certain factors, such as the number of elderly people a DHB looks after.
Southern DHB received significantly lower per capita funding than many other DHBs, Prof Gauld believed.
Figures released by the Ministry of Health show South Canterbury receives $2684 per head of population compared with Southern's $2255.
The national average is $2300, with the highest rate going to the West Coast District Health Board on $2889, followed by Tairawhiti ($2854) and Whanganui ($2848).
Prof Gauld said if Southern DHB received the same level of funding as South Canterbury, the board would be in surplus.
It was hard to work out how the highly complex funding formula worked.
"The population-based formula is a rough-cut tool. It's a mystery. It's impossible to get to the bottom of how it is [worked out]," Prof Gauld said.
He questioned the strength of data used to make calculations.
"A lot of the weightings are based on historical data.
"The data [is] ... not always consistent in terms of the year they are drawn from."
It was unclear how the issue of "rurality" - the rural population - was factored in to the formula.
"The Government doesn't make enough information available about how the [population-based funding] works and why it is that different regions receive quite different levels of funding."
Prof Gauld was supervising a postgraduate student studying how the Ministry of Health allocated health dollars using the formula.
The stress of working under insufficient funding could create the negative culture revealed in this month's National Health Board systems review of Dunedin Hospital.
In response to a series of questions on Prof Gauld's comments, the leader of the National Health Board team which carried out the Dunedin Hospital assessment, Jill Lane, repeated earlier statements that the DHB received significant funding and a lack of funding was not considered by the team to be a barrier.
"The team identified long-standing issues with the DHB's culture and systems as the real issues which need to be addressed for improvements to be made at Dunedin Hospital."Southern DHB funding and finance general manager Robert Mackway-Jones said the board's main point of contention was whether it was funded sufficiently for its rural population. Its next review for rural funding was 2013-14.
Mr Mackway-Jones would be keen to see this review happen sooner.
Population-based funding accounted for 87% of Southern DHB's funding.
The DHB looked forward to the result of the Otago University research into the funding model, he said.
A Ministry of Health spokeswoman advised that the reason South Canterbury received more funding than Southern was because of its older population.
Because it was a smaller district health board, it also received a higher amount of rural adjuster, the spokeswoman said.
Auckland received the lowest amount per head of population at $2032 because it had a younger population and received little in the way of a rural adjuster.
Factors taken into account in setting the rate include populations' age, gender, ethnicity, unmet need, rurality and deprivation. The number of eligible overseas visitors a district health board has to treat also comes into the calculation.
