The latter was a throwback to the very dawn of the xenotransplant era itself – 1838, when Dr Richard Kissam, an ophthalmologist in New York, cut out the opaque cornea from a sensationally brave Irishman and replaced it with one from a six-month- old pig, attached with two stitches. Immediate results were encouraging. Within two weeks, though, the new cornea clouded over.

That was 67 years before the first human cornea transplant, performed by Dr Eduard Zirm on a labourer blinded in an accident. This time, as if by magic, the patient fully regained – and kept – his sight. But xenotransplant fans had not given up. In the same year, 1905, slices of rabbit kidney were implanted into a severely ill patient. Remarkably, the patient survived for 16 days.

It wasn’t until 1954 that the first major human organ transplant – of the kidneys – took place. But animal transplants had still not disappeared. In 1963, a patient survived for nine months after receiving chimpanzee kidneys. And in 1964, as Barnard closed in on his world first, Dr James Hardy performed the first chimpanzee-human heart transplant. (His patient lasted just two hours.)

Indeed, the apes which most resemble us remain the most suitable animal organ donors. “Non-human primates are the best,” says Reichart, “but, of course, there is a major ethical constraint. Some are endangered, and even if you discount that, they have long pregnancies, and have only one or two offspring.” Pigs, by contrast, have shorter pregnancies and produce around a dozen piglets.

And, of course, we already eat them: “I’m not saying there are no ethical barriers, but it’s easier.” Hence pigs have become the donor animal of choice, and the subject of decades of research, which only entrenches their use in future xenotransplantation study. Ultimately, however, animals may no longer be required, as technology matures that allows scientists to grow organs (or, indeed, meat) in the lab. At the Crick Institute in London, Dr Paola Bonfanti leads a team building a thymus, a mini-organ which is vital for the development of T-lymphocytes, which fight infections and cancerous cells. There are, she says, “intrinsic biological complexities” in building organs. Scaffolds are required on which to mount the vast numbers of cells required, and then there is the challenge of plugging them into the circulatory system to keep them alive.

“It’s hard for small organs,” she says. For larger organs – the heart, the lungs – it will be much harder still. The first step, she says, will be to build something big enough to replace at least part of the function of the failing organ.