There has been a running controversy in circles that are committed to Jewish Law over “brain death.” Traditional sources require the heart and lungs to stop functioning. In olden days a mirror or a feather to the nose was the best they could do. Times have changed. Medical science has advanced and “brain death” has now been added to the halachic as well as the medical lexicon. It is of particular significance when it comes to transplants. Waiting until the heart finally runs down can be too late for some organs to be useful to others.
A great deal of halachic discussion has gone on ever since Rav Moshe Tendler, son-in-law of the late Rav Moshe Feinstein, and a qualified doctor as well as a halachic scholar, first suggested accepting brain death in principle. The fact that he affirmed he had his father-in-law’s agreement added weight to his position. There was a furor at the time, as there always is when anything new crops up in traditional circles; but over time more and more experts joined him.
Indeed the whole issue of transplants and organ or skin banks has been dealt with extensively in halacha, and given that new issues and refinements are emerging all the time, there is a massive amount of material readily available on the subject. But equally, opinion is still divided, largely because of the fear that doctors might rush to declare death prematurely when they want to get organs to recipients as quickly as possible. And there is still controversy over definitions. Still, the fact that there might be rogue doctors should not detract from the fact that brain death in principle is approved of by more real halachic authorities nowadays than not.
You might recall the tragic case of Yoni Jesner, a highly gifted young man cut down by a suicide terrorist in Israel some years ago. His courageous and religious family took advice from halachic experts and donated his organs, one of which saved the life of an Arab child. Around the Jewish world the issue of organ donation suddenly became a popular topic. More and more rabbanim encouraged Jews to carry donor cards, and specifically religious organizations sprouted to cover all religious reservations.