Mark Lundy says he has been a "guinea pig" in the justice system, with the use of "novel and junk science".
Two tiny spots of what is believed to be human brain tissue found on Lundy's shirt are the subject of a hearing in the Supreme Court in Wellington this morning.
Lundy is seeking leave to appeal to New Zealand's highest court over his convictions for murdering his wife and daughter.
His lawyer is arguing the Court of Appeal was wrong to uphold the convictions despite finding the evidence around the brain tissue was inadmissible.
Christine and Amber Lundy were found dead in their Palmerston North home in 2000, having been hacked to death, likely with an axe or tomahawk. The murder weapon was never found.
On the night of their murders Lundy was checked into a motel in Petone where he called an escort about 11.30pm.
It was fiercely contested during his first trial whether or not it was physically possible for Lundy to have travelled between Wellington and his family home in a time that would have allowed him to be in the house at the time of the murders.
Lundy was first convicted of their murders in 2002, and his first appeal attempt resulted in the court increasing the non-parole period of his life sentence to 20 years.
His conviction was quashed by the Privy Council in 2013, which ruled there were problems with the analysis of the brain tissue found on Lundy's shirt, as well as with the time of death.
In a 2015 retrial at the High Court in Wellington, Lundy was again convicted of the murders.
He appealed to the Court of Appeal last year, which found the evidence around the brain tissue should not have been presented to the jury, but decided to uphold the convictions anyway.
The Crown argued Christine Lundy's brain tissue was found on the polo shirt her husband wore on the night of the murders.
Tiny spots consistent with dried blood were also found on the shirt which were found to contain Amber's DNA.
At the heart of the defence appeal last year was that the jury at the 2015 retrial should never have heard the mRNA evidence, as the analysis was too new and unproven to be relied upon.
The mRNA evidence, which is similar to DNA evidence, was used to rule if the tissue on Lundy's shirt had a human or non-human source.
The Court of Appeal ruled the evidence was inadmissible, but believed Lundy would have been found guilty regardless.
In court this morning, lawyer Jonathan Eaton QC said Lundy referred to himself as being a "guinea pig through the justice system".
Eaton said the type of evidence had "never been used before, never been used again".
Crown lawyer Philip Morgan, QC, said the mRNA evidence was just one strand of the Crown case at trial.
He said if the tissue had been from an animal it would have had to be fresh to be able to be smeared into the fabric.
"There was really no suggestion that this was coming from cooking," he said.
"All of these issues were explored in enormous detail."
The use of the mRNA evidence was the subject of "thorough examination" in 2014 and in the months leading up to the trial.
"It's not as if [the defence] had to drop everything and run around at the last minute to sort this issue . . . with great respect, defence counsel used it very effectively to badger the Crown about how the Crown's sort of relying on unreliable science."
The court has reserved its decision.
Lundy is currently serving a sentence of life imprisonment with a minimum non-parole period of 20 years.