Positive mammograms typically result in a needle biopsy. Funding for the research has come from the Department of Defense, the National Science Foundation, the National Institutes of Health and the Whitaker Foundation. On that TV show, the doctor has a device that emits some form of radiation, scans it over a patient and receives the signal coming back. That's not so far from reality. The lifetime is the time it takes for these molecules to relax to a ground energy state, releasing fluorescent light in the process.
Lifetimes are typically a billionth or a trillionth of a second.
Based on the lifetime, the computer program generates an image that may, for example, show the metabolic state of the tissue, indicating disease is or isn't present, or map the chemical's concentration and distribution, indicating the boundaries of diseased tissue such as a tumor.