"Please do not tell the patient but that brainwave actually came to me in theatre," he jokes, and explains how four pairs of highly skilled hands simultaneously fashioned and merged a complete organ on a bed of ice. "This was a world first. No one had ever done this," he says, without a trace of hubris.

Read more: Call for review after doctors shelved dying man's liver transplant because donor had kidney cancer

Not for the first time, thinks Chan, top transplant centres around the world will follow Hong Kong's example.

"Hong Kong is a real leader in LLDT. Look, in simple football terms, we are not just Champions League; we are like Barcelona," says Chan, explaining that in the world of transplant surgery, standards are measured by survivability rates and Hong Kong's standards are exceptionally high.

An earlier example of Hong Kong ingenuity came in 1996, when local doctors performed the world's first adult-to-adult right lobe LLDT. The operation, which was widely condemned as being too risky for the donor because the right lobe is roughly two-thirds of the complete organ, has since been adopted as standard practice internationally.

Yet despite their surgical prowess, Chan and his colleagues are not in the mood to celebrate. Improvisation and ingenuity have proved to be a necessity for Hong Kong's transplant surgeons because there is an acute shortage of organs - hearts, kidneys and lungs, as well as livers - from deceased donors. Patients die every year as a consequence, and the recycling of precious organs has been elevated to an art form.

Last October, surgeons at QMH achieved a double world first when a liver originally transplanted 11 years previously was harvested from a deceased donor and given to a 37-year-old bodybuilder. Both patient and donor had Hepatitis B. In 2009, Chan had a 30-year-old female patient with a liver that was fully functional but produced proteins that caused acute limb numbness and weakness. It was an error of the metabolism but the liver could serve another person because it would be 20 years before they developed the same symptoms. The female patient was given a part of her husband's liver in an LLDT while Chan's team transplanted her old organ to a 60-year-old.

"This is an essential recycling," says Chan. "What is guaranteed is that if they don't have an operation, they would die."

Read more: ‘Please save my husband’s life’: Wife of dying Hong Kong man renews emotional appeal to find a liver donor

As of June 30, there were 94 people in Hong Kong desperately in need of a liver.

"Fifty per cent will die and only one in 10 of those admitted to the ICU [intensive-care unit] without a live donor option will survive," says Chan, who explains that even if a live donor is willing, they may not be suitable: parents may be too old or siblings too young or have severe health issues. Not all deceased donors are suitable, either. Last month, after it came to light that two patients had received organs from a donor who was found posthumously to have had kidney cancer, QMH patient Stephen Lee, 46, had his liver transplant - from the same donor - aborted mid-operation. The incident sparked debate on whether guidelines in Hong Kong should be relaxed; in the United States and Britain organ donations from cancer patients "under certain circumstances" are acceptable.

The acute lack of donors in Hong Kong is something that troubles surgeons like Chan in a personal way.

"When I was a young doctor, I regularly signed death certificates for candidates who never received a donation and it's very sad because, often, a family in the same hospital will have refused to allow the harvesting of a dead patient's organs," he says. "I saw this happen."

As of July 31, there were about 172,000 names on the Centralised Organ Donation Register in Hong Kong, which, out of a population of 7.24 million, is hardly impressive. According to irodat.org, there were only 39 deceased donors in Hong Kong last year, which equates to 5.4 per million of population.

The reluctance to sign up to donate organs after death is not uncommon in Asia. Donation rates in Taiwan are the highest in the region, at seven to eight per million of population, and Japan has about the worst, at 0.66 (according to 2013 data from irodat.org. By comparison, the rate is 35 in Spain - the highest in the world - and 20.4 in Britain.

In December, Beijing announced it was ceasing the controversial practice of harvesting organs from executed prisoners and a new policy document has been published for organ transplants. Despite official optimism, that could lead to a crisis; an estimated 95 per cent of donated organs came from convicts.

There are currently 1,894 Hongkongers waiting for a kidney transplant and all of them are buying time with dialysis treatment. At Queen Elizabeth Hospital (QEH), Dr Chak Wai-leung, a nephrology specialist and president of the Hong Kong Society of Transplantation, explains the difference between the two types of dialysis.

In haemodialysis, undertaken at hospital, blood is pumped out of the body to a machine that does the job of the kidneys - cleansing the blood - before being returned. This is normally undertaken two or three times a week and each session could take four hours. In peritoneal dialysis, two litres of cleansing fluid is poured by the patient into their own belly through a surgically inserted catheter. This is usually undertaken at home three or four times a day.

It is not easy to balance dialysis sessions with looking after a family or holding down a full-time job, and a patient's health gradually deteriorates. Holidays are usually impossible, as are sporting or athletic pursuits.

Read more: Chance of new liver snatched away from dying Hong Kong patient after donor's family refuse to let transplant go ahead

"Almost the only reason we do just 100 operations per year is the lack of organ donors," says Chak. "I am not completely sure but I would estimate at least 50 per cent of those 1,894 patients will die on the waiting list.

"[The situation] is much worse for heart, lung and liver patients, of course, because they have no treatment for their condition. For them it is organ transplant or death. In the last two years we have tried publicity, celebrity endorsement, education programmes in schools … We try everything but we still suffer from traditional Asian thinking."

The preference for many in this part of the world is to die with one's organs intact rather than offer new life to a stranger.

the second floor of the nurse's quarters at QEH, May Pong Mei-lan takes an urgent call from the neurosurgery ward. She is being tipped off about a potential donor and, as the hospital's organ donation coordinator, it is Pong's job to liaise with medical staff and family members of the deceased. She needs to call on her many years of experience as a senior nurse in the ICU and at the dialysis centre to counsel grieving relatives. She describes why it can be so difficult to source organs.

"In Hong Kong, we use only brain-dead donors … [and] not enough people die of brain death," says Pong. The only liver donors permitted in Hong Kong are family members.

In brain death, a patient's heart is still beating as they breathe with the aid of a ventilator. According to Chak, most deaths in Hong Kong are cardiac, not brain, deaths. Brain death donation offers a much better chance of success to the recipient but donation after cardiac death is now being practised in the United States and many European countries.

Read more: Hong Kong housewife who gave two-thirds of her liver to husband urges others to help a dying patient

"This is one of the ways to solve the organ shortage but it needs expertise and extra resources," says Chak.

"The second issue is consent," says Pong. With a ventilator, "it can look like their loved one is just sleeping so some families find this very tough".

"Some families do not understand or accept the concept of brain death," says Chak. "They want to wait for a miracle but there is never any miracle."

Pong estimates that about half of the families she counsels are sympathetic and want to help others but points out that if a potential donor has not registered as such, the decision can be an agonising one for relatives.

"Many families worry they are being asked to make a big decision at a time of distress," says Pong. "Sometimes there is disagreement between family members; sometimes these arguments last for days." After 24 hours, it is too late for the organs to be of any use.

Pong admits she often feels helpless knowing that just a few corridors away from the heated deliberations, in another ward, a patient waiting for an organ may be desperate to live.

"I maintain my professional approach even though I feel upset and frustrated if the family says no. One donor can save many lives but I must always respect their choice and I will continue to care and provide counselling even after they have refused," she says. "If I had a magic wand, I would increase the consent rate to 100 per cent."

On the wall of Pong's office is a framed picture of a smiling young woman, Annie Kwok Wing-yee, who was among the 50 per cent who see out their days on a waiting list.

Kwok's sister, Amy, explains that her older sibling was only 20 years old when she was diagnosed with acute renal failure. She had to start dialysis while looking after her baby daughter. After some years, she received a live organ transplant from her father, which gave her a decade of high-quality life, during which she had a second daughter. Then the donated organ failed and Kwok was compelled to return to the waiting list. She endured haemodialysis treatment while caring for her daughters and working as a medical secretary at a doctors' surgery. She also found time to volunteer for the hospital's organ-donation appeal, manning information booths and talking to schoolchildren about overcoming adversity.

Kwok knew that her time was running out but remained cheerful and positive, says her sister. By the time a suitable deceased donor was identified, Kwok's condition had worsened so much that she was not well enough to undergo the surgery. Kwok died on September 16 last year, at the age of 41, simply because of a lack of donors.

Tommy Tsang Wai-on was luckier. Fourteen years ago, he managed a tutoring centre, played volleyball and, even though he was only 21, was making plans with his girlfriend for their future. Then he went to the doctor with a bout of diarrhoea and vomiting and was diagnosed with acute renal failure.

"It was just a white out," he says. "I could see no future at all."

He had to stop working, the tutoring centre closed and, for months, he was more or less confined to his apartment, undergoing peritoneal dialysis four times a day. In 2004, his mother was approved as a live donor, even though she was nearly 60 years old.

Twenty months ago, Tsang and his wife (the former girlfriend) had a daughter called Melody and they are now expecting a second child. He is planning to set up a dog grooming and training business and has high hopes for the future. His mother is also fine.

"Without that kidney I would not have been reborn and be able to have a marriage and children and a real future," says Tsang. Nevertheless, "if there are more donors there will be less pressure and risk on family members, trying to save their loved ones".

For Harry Cha Hoi-kit, it was a huge shock when his grandmother, Tsang Mei-king, died of a stroke last year.

"At the hospital everyone was crying," Harry, a high school student, remembers. "I wanted to approve the donation [of her organs] so my grandmother could help other people have a healthy life."

Consent for donation was given in time and Harry has honoured his grandmother by volunteering at QEH to persuade others to pledge their organs.

"I meet many recipients through my volunteering work and I like to think one of them may have benefited from [his grandmother]," he says.

Pong reports that volunteers such as Harry have managed to sign up 1,000 donors over the past few months but they have had to engage with more than 10,000 people to achieve that: a low conversion rate considering much of the work is undertaken within the grounds of the hospital.

Volunteers report that they must overcome many myths about organ donation. One is that critical medical treatment may be withdrawn from those known to be registered donors. A popular superstition suggests that it's unlucky or tempting fate to sign up for organ donation. People quote religious objections but, as Chan points out, he is not aware of any religion that objects to saving the lives of others.

Volunteers also say that some people think they may be too old to register for organ donation, others think they are too young. Many claim they do not even know that a donation scheme exists.

While committed volunteers work to increase the number of registered donors and Hong Kong's surgeons perform miracles with live organ transplants and advanced organ recycling, many valuable organs are cremated with their corpses, meaning the last hope of many, often young sufferers, sentenced to death by the arbitrary hand of fate, literally go up in smoke.

It takes about three minutes to register as an organ donor online yet at least half of the 2,029 Hongkongers currently hoping for a kidney, liver, heart (29) or lung (12) will die needlessly because of myths and pseudo-religious superstition, or because the citizens of Asia's world city are just too busy.