Dr. Sicinska used a quarter of a million dollars of Ludwig money for this project, buying mice without immune systems, which meant they could not reject human tumors, and housing them in a germ-free basement lab. She spent months learning to implant tumors in the mice and enlisted geneticists to study the implanted tumors, making sure they did not mutate beyond recognition.

She spends her days in the lab, using a miniature ultrasound machine to scan the mice, hairless creatures with prominent ears. Four types of sarcomas  cancers of fat, muscle or bone  are growing in them and look genetically identical to the tumors removed from patients.

Dr. Elias A. Zerhouni, former director of the National Institutes of Health, said he was not sure that a grant for the project would have been turned down. The N.I.H., he said, does finance research on mouse models for human cancer.

But Dr. Demetri said he did not apply “because we have lots of experience in what’s fundable.” His mouse work, he said, is exploratory, and he cannot predict what he will find or when. He certainly could not lay out a road map of what he would do and promise results in a few years.

Studies With a Different Goal

Researchers like Dr. Appelhans, who is studying weight control and tasty foods, do not expect to change the outlook for cancer patients anytime soon. But, they say, that does not mean their work is unimportant.

Dr. Appelhans will study 85 overweight or obese women, measuring how much the tastes and textures of food drive their eating. Then they will be given a weight loss diet and nutritional counseling. Dr. Appelhans will ask whether those who are most tempted by the tastes and textures also have the most trouble following the diet.

As for the grant to assess a Web-based program to improve food choices, it is predicated on studies indicating that what people eat in childhood and adolescence may have an impact on cancer risk in middle and old age, said the grant recipient, Karen Weber Cullen, associate professor of pediatrics at Baylor College of Medicine. Some studies have found that people who reported having eaten fruits and vegetables when they were younger and maintaining a healthy weight were less likely to have cancer.