At the time, Algar ordered a blood test to look for proof of the disease, but he knew it would take weeks to get the results, and this patient was too sick to wait. He decided to begin treating her before the results of the test came in. If she got better, he would know he had the right diagnosis.

The problem with treating an illness before it is confirmed through testing is that the patient can worsen while being treated for a disease she doesn’t have. And this patient was far too sick to risk wasting time. So Algar also sent off blood to look for H.I.V. or Lyme disease — two common infections known to cause unusual neurological symptoms. And he ordered another M.R.I. of the brain to look for signs of anything else he might have missed.

The patient began her treatment, and she seemed to get better at first. The double vision vanished; the coarse tremor that accompanied her every movement diminished; and her speech improved. But she was still vomiting four or five times a day, she was still losing weight and she still couldn’t walk. Even before the test came back negative (as it did several weeks later), it was clear that she didn’t have Guillain-Barré.

Now that his patient was back in the hospital, Algar went over her chart once more. Whatever it was, it wasn’t going to be one of the usual suspects. Could it be an unexpected type of infection? Algar sent off blood and spinal fluid looking for a dozen or so rare infections. Could it be an autoimmune disease like lupus? He ordered tests to look for these diseases.

He finally found something that he thought might be useful. Two months before her symptoms started, the patient had an operation. According to the hospital notes, she had a pelvic mass. It turned out to be a fibroid — a benign tumor of the uterus — but in the operating room, the surgeon noted a small irregularity on the surface of her left ovary. He biopsied the tissue, but the pathologist couldn’t see anything in the tiny sample. This additional history, however, provided Algar with another clue: some cancers trigger the immune system to create antibodies that target and destroy cancer cells. Sometimes, especially in cancers of the ovaries or breasts, these antibodies can attack cells in the brain as well, a phenomenon known as paraneoplastic syndrome. This injury to the brain can produce dizziness, double vision, vomiting and a severe loss of coordination.

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Algar quickly sent off the test to look for the antibodies. It took almost two weeks, but the result finally came back — positive. So the patient clearly had a cancer; the question was where. A CT scan of the chest, abdomen and pelvis did not reveal any sign of cancer. Algar was disappointed but not surprised: this paraneoplastic syndrome often shows up long before there are any other signs of disease. But what if the abnormality the surgeon saw on her ovary during her prior surgery was the first blush of cancer?

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If so, she should have her ovaries removed even though there was no sign of cancer. But would the patient be willing to take this risk? Her answer was an immediate yes. If there was even a small chance that an operation would bring an end to her four-month ordeal, it was a chance worth taking.

The surgery was scheduled for that week. Afterward, the surgeon visited the patient’s husband in the waiting room to break some bad news. He had seen no sign of cancer in the tissue he removed. Although the final answer would come from the pathologist, the surgeon was not optimistic. The patient’s husband fought back tears. He had watched his wife suffer for so long, and there still seemed to be no end in sight.

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The pathologist’s report came the next day. A nine-millimeter tumor was found in her left ovary. Seeing this, Algar felt a flood of relief. He had recommended the surgery on a hunch — a well-grounded hunch — but he had no way of knowing whether a tumor would be found.

It is strange to welcome a diagnosis of ovarian cancer, and yet Algar, the patient and her family knew it provided a long-needed answer. A second surgery found additional cancer in a lymph node and, once the patient awoke from this operation, the nausea and dizziness lessened significantly.

That was three years ago. Since then the patient has struggled to relearn the basics — how to walk, how to talk. But she doesn’t have ovarian cancer, and she’s slowly getting better. And for this patient and her family, that’s enough for now.