A few years ago, concerns over these heart trials were voiced by a Norwegian professor, Harald Arnesen. He concluded in 2007 that they are not convincing and that one German team had achieved striking results only because the control group in its trial had done particularly badly. Prof Arnesen called for a moratorium on this kind of stem-cell therapy.

That still did not deter the clinicians. This January, another trial funded by the EU was announced the largest of all, with 3,000 heart-attack patients recruited from across Europe.

The idea behind the trials is straightforward. During a heart attack, a clogged blood vessel starves heart muscle of oxygen. Up to a billion heart muscle cells, called cardiomyocytes, can be damaged, and the body responds by replacing them with relatively inflexible scar tissue, which can lead to fatal heart failure. So why not implant stem cells that can grow into cardiomyocytes?

Stem cells, of course, come in many kinds: the embryonic variety have the potential to turn into all 200 cell types in the body. Adult stem cells, harvested from the patient, have a more limited repertoire: bone marrow stem cells generate blood cells, for example. So to claim, as was done in 2001, these bone marrow stem cells could turn into heart muscle was both surprising and exciting.

Analysis shows that, at best, the amount of blood pumped during a contraction of one heart chamber rose by 5 per cent after treatment. In a patient where heart efficiency has fallen to 30 per cent of normal, that could be significant but it is relatively meagre, none the less. And it turns out that this level of improvement results whatever the cells injected into the damaged muscle even if they have no prospect of forming cardiomyoctes.

Even the believers in the technique now agree that implanted cells exert a paracrine action, triggering a helpful inflammatory response or secreting chemicals that boost blood vessel formation. But were still waiting for convincing evidence that a patients lost heart muscle cells can be replaced.

Embryonic stem cells offer one route to that goal, though it is difficult to turn them into the right cell type reliably, and there are other risks, such as uncontrolled growths. Another option has come from work by Prof Richard Lee at the Harvard Stem Cell Institute, who has found that some adult stem cells can recruit other stem cells already in the heart to become cardiomyocytes.

Meanwhile, other fields of medicine that have seen more systematic research on stem cells are making real progress in using them for example, to treat Parkinsons, diabetes and macular degeneration. The lesson here is that, ultimately, it takes careful experiments, not belief, to make that huge leap from the laboratory to the hospital.

Roger Highfield is director of external affairs at the Science Museum Group

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Heart disease and stem-cell treatments: caught in a clinical stampede