The police then cut out the stains from the shirt and took them to a Texas pathologist Dr Rodney Miller. He was also unable to positively identify the tissue under a microscope but conducted an immunohistochemical (IHC) procedure, from which he categorically stated the tissue was from the brain or spinal cord. The IHC procedure had never been used before in this manner.
At the original trial, the defence conceded the matter was brain tissue and the only issue was how it ended up on the shirt, possibly by accidental contamination during the police investigation.
One of the grounds of the Privy Council appeal was that the expert evidence given by Dr Miller, and others who relied on his opinion, was "fundamentally flawed" to the point that the trial was unfair.
Affidavits sworn by Professors Phillip Sheard, Helen Whitwell and Kevin Gatter - all experts in immunohistochemistry - concluded the tissue was poorly preserved and it was impossible to reach any conclusion as to the nature of the material.
They concluded the IHC procedure was an "uncontrolled experiment" which was incapable of producing a reliable outcome.
The Privy Council also heard evidence that IHC had been used "sparingly" worldwide to forensically identify tissue in criminal cases, with only one other example found.
The most startling "revelation" at the three-day hearing was the discovery of a previously undisclosed police document which Mr Hislop received from the Crown Law Office last week.
The document was written by the officer in charge of the murder case, Detective Sergeant Ross Grantham, asking a senior officer for funding to visit Dr Miller in the United States.
Dr James Pang, a pathologist for the police, thought it was brain tissue but said it was necessary for the evidence be reviewed by a neuropathologist Dr Heng Teoh.
However, Dr Teoh said the tissue was too degenerated to identify as brain tissue and Lundy should not be convicted on the strength of the cells on the slide he saw. Mr Grantham said this was why it was necessary to get Dr Miller's opinion.
However, the document was not disclosed to Lundy's lawyers before the trial, denying them a line of inquiry for the defence.
Were Christine and Amber Lundy killed around 7pm?
As well as the brain tissue evidence, the time of death was crucial to the prosecution case. Lundy had only a small window of opportunity to complete the 300km round trip from Petone to Palmerston North. Cellphone records show he was in Petone at 5.38pm and 8.28pm, so the murders had to be committed around 7pm for this to be even remotely possible. No one has been able to replicate the journey.
The appeal to the Privy Council has not mentioned the logic of whether Lundy could have made the trip to kill his wife and daughter in less than three hours.
But Mr Hislop described the science used to estimate the time of death as "without any scientific foundation whatsoever".
Dr Pang told the jury he estimated the time of death between 7 and 7.15 on the evening of August 29, 2000. This was based solely on the basis of examining the stomach contents of the murder victims - a full stomach containing potato chips and probably fish - and he noted the "distinctive" absence of the smell of gastric juices.
He did not take the temperatures of the bodies when they were found in the house, or examine them for rigor mortis. He also did not weigh the stomach contents.
Given the time of the purchase of the meals at McDonald's at 5.38pm and the journey time home, Dr Pang said the digestion process was in the early stages which led to his estimated time of death. His evidence was backed up at the trial by Professor Gilbert Barbezat, a consultant gastroenterologist, who was confident the murders happened within an hour of the last meal. Professor Barbezat had never done an autopsy but had seen more than 100 of them.
The defence case at trial was that the murders happened after 10.52pm, based on computer time evidence, and therefore Lundy had a "cast iron" alibi as he was with a prostitute a short time later at 11.36pm.
Mr Hislop presented to the Privy Council affidavits from several medical professionals, including Professor Bernard Knight, a world expert in forensic pathology, who reviewed the findings of the Crown experts. Ironically, Professor Knight was cited by Dr Pang during the trial.
Professor Knight said the use of stomach contents as an estimate of the time of death was "so unreliable as to be of little value" as there were several variables which make gastric contents almost useless as a way of determining the timing.
He particularly questioned Dr Pang's evidence that "absence of gastric smell" was an important factor. He considered this to be "utterly without foundation and little short of ludricrous" and had never heard of this suggestion.
Did Mark Lundy tamper with the family computer to create an alibi?
A "stumbling block" to the Crown case that Christine and Amber Lundy were killed around 7pm were records that showed the family computer was switched off at 10.52pm. If that was the case, then the killer could not have been Mark Lundy, as he was with a prostitute at his Petone motel at 11.36pm.
But a police computer expert told the jury there was evidence that the file registry in the computer was disordered, which suggested the time on the machine was tampered with.
Maarten Kleintjes demonstrated to the jury how it was possible to tamper with the computer and manipulate the "shut-down" time on the clock in a way that was undetectable - implying that the computer was shut down earlier than 10.52pm, which gave Lundy an alibi.
He also discounted the possibility that a computer virus could disorder the registry files saying it was "far fetched".
Mr Kleintjes said he did not know of such a virus, and found no sign of a virus on the Lundy computer.
However, a computer expert hired for the Privy Council appeal said there were several ways files could become disordered, including a virus.
Forensic examiner Michael Chappell discovered that the virus-checking program on the Lundy computer was out of date, and it was infected with a virus known as a KAK worm.
He traced it back to an infected email six weeks before the killings in August 2000.
What happens now?
The five members of the Privy Council, including NZ's most senior judge, Chief Justice Dame Sian Elias, will reserve their decision. There are several possible outcomes. The judges could reject Lundy's appeal, and he would continue to serve at least 20 years of his life sentence. Or, the Privy Council could quash his convictions and a new trial could be held, as happened in the David Bain case.
However, a third "middle ground" option was canvassed at the hearing. The Privy Council could send the case back to the Court of Appeal in New Zealand to determine the credibility of the conflicting scientific views on the "brain tissue" evidence. The Court of Appeal would then decide whether a new trial would be held.
