Patients who need a new liver are refusing to take live donor transplants from relatives because they believe it is too risky for their loved ones.
About one in 200 people die during the operation
Last year, Scotland became the first part of the UK to allow living adults to donate part of their liver, which is able to regenerate in the body.
However, researchers have found that no-one has yet taken up the option.
Many patients said they could not live with themselves if the operation resulted in the death of the donor.
Surgeons had anticipated that about five families would take up the option of a live transplant last year. That number had been expected to rise to 10 this year and 15 in the the forthcoming year.
The risk of death for the donor in live liver transplants is estimated to be between 0.5% and 1%, far higher than the risk of death in donating a kidney (0.03%).
In addition, the risk of complications arising from the operation is thought to be around 40-60%.
However the procedure, which involves removing a large chunk of the donor's liver, is relatively common in Japan, the US and some parts of Europe.
A group of researchers from Stirling University and the Royal Infirmary in Edinburgh questioned Scottish patients and potential donors who were suitable for a live liver transplant but had opted not to undergo it.
They found that the biggest problem was that patients did not want to put family members through a potentially dangerous operation.
In contrast, many potential donors did not appear to consider the risk involved, as they were too focused on helping their loved ones to survive.
Lesley McGregor, who will present the findings at a conference in Nottingham, said the results were an important step towards understanding the attitudes, concerns and risk perceptions of parents and their families to transplant operations.
She added: "The patients didn't want their loved ones to donate because they knew they would have to give up approximately two thirds of their healthy liver, with roughly a one in 200 chance of death.
"But the potential donors just wanted to help their ill relative, irrespective of the risk, which has the potential to cause significant tension within the family unit."
John Forsyth, a transplant consultant at Edinburgh Royal Infirmary, said he had assessed more than 40 people for suitability for the procedure since it was introduced in April 2006.
He said: "It hasn't gone ahead for a number of different reasons. It can be because of blood group incompatibility or because the recipient is too sick.
"But one of the reasons in about a quarter of the cases is that the potential recipient says 'I don't want my donor exposed to the risk of this procedure'."
Livers had previously only been taken from donors who were classed as brain stem dead. About 15 people die every year while waiting for a liver to become available.