In a 2012 interview with The New York Times, she said that had she known about her dense tissue and the shortcomings of mammography, she would have requested ultrasound or M.R.I. scans, which are better than mammograms at finding tumors in dense breasts.

And if she had had those other tests, she believed, her cancer would have been found at an earlier stage, and she might not have even needed chemotherapy. Because the tumor was so large, she thought it must have been growing for four or five years.

She urged her doctors to begin telling women if they had dense breasts. But they told her that that was not part of the “standard protocol,” she said, and declined.

“We said, ‘Then we’re going to make you do it — this is life and death,’” Mr. Cappello said in an interview, referring to himself and his wife.

The couple learned that dense breasts are not rare: They occur in about 40 percent of women who have mammograms. The condition is more common in younger women, but some older women have it as well. It shows up only on mammograms and cannot be detected by touch.

The Cappellos approached state legislators and enlisted medical experts to help make their case. It took time, but in 2009 Connecticut became the first state to require that women be told if they had dense breasts and that insurance companies cover ultrasound scans for those women.

After that, Mr. Cappello said, women from around the country began to contact Dr. Cappello, asking how they could get similar laws passed in their states. She quit her state job and founded nonprofit education and advocacy groups, both called Are You Dense?