The operation on the back of the brain had been called impossible.

The occluded artery that had to be cleaned out was no larger around than a drinking straw. It was buried well beneath the skull and was surrounded by some of the body's most delicate nerves and brain structures. At most, only an inch and a half of its length could be reached, and no one knew whether that might do more harm than good.

But 14 months ago, Johns Hopkins neurosurgeon George S. Allen successfully did what surgeons had been calling impossible.

Operating on a 60-year-old Baltimore teaching nuns who had been having repeated attacks of dizziness and hallucinations -- tiny, temporary strokes that can presage a major and crippling one -- he first removed a 2-by-3-inch piece from the back of her skull.

Then, in a 10 1/2-hour operation, peering through an operating miscroscope and painstakingly wielding instruments like long needles, he lifted an offending chunk of yellowish cholesterol from that straw-like artery.

In medical parlance, he had successfully removed an atherosclerotic plaque that was preventing an adequate blood supply from reaching the brain.

This month, sure at last that his patient is well, he published his results in a neurosurgical journal.

And today Johns Hopkins Hospital introduced the patient: a healthy and vigorous-looking Sister Regina Marie Albert, a mathematics teacher at a Baltimore high school.

The cautious Allen told a new conference only that the operation had been a success so far, and "we do not know whether or not it will really prove safe and effective" and prevent strokes in other patients.

But a surgeon at a large Washington hospital, asked to comment, said: "Dr. Allen has done a very exciting thing. I see no theoretical reason why this operation should not be repeated now, and I predict it will be done at least by the hundreds."

In short, the operation could give medicine a new weapon against the common kind of brain damage known as stroke. nearly a half million Americans have strokes every year. Nearly 200,000 die annually of a stroke or its aftermath. And strokes cause a fifth of all senility in the elderly.

For her part, Allen's patient, a member of the School Sisters of Notre Dame, told today how she teaches regularly and takes daily walks and rides on an excercise cycle.

"The doctors had told me there was a great possibility that I would have a stroke," she said."I had seen many of our sisters who had had strokes, and they were really helpless.

"I would rather have died under the surgery than lived to be a vegetable or be dependent on other people."

Allen said he did not want to exaggerate the operation's importance. At most, he and his colleagues calculated, it might help about 2 1/2 percent of potential stroke victims; that is, those with a blockage in an accessible section of either of the two vertebral arteries at the back of the skull.

Another type of antistroke operation, surgery on one of the two carotid arteries that nourish the front of the brain, has been done since 1955. But blockages in the carotids commonly occur as they rise in the neck, and can be reached easily.

In either case, the event that signals a possible major stroke is a "TIA," or "transient ischemic attack," the kind of temporary blockages of blood flow that caused Sister Regina Marie's dizzy spells.