“We use it for surgical planning,” said Dr. Frank Verstraete, a surgeon at the University of California, Davis, whose team has done dozens of lower-jaw reconstructions. “It saves us time in the actual operating room.”

3-D printing has also been used to make implants that replace damaged mandibles and leg bones, such as one placed in a young German shepherd with a limb deformity at Cornell in 2009.

But it has not entered mainstream use in surgery in small veterinary clinics. The costs associated with 3-D printed custom implants in surgery for disfigured or injured animals can be prohibitive. But some animals will not survive without such an implant.

That was the case with Patches, according to the team that worked on her.

Patches started to develop a small bump on her head several years ago, said Danielle Dymeck, a corrections officer in Pennsylvania who has raised the dog since she was 2 months old. The bump did not seem to bother Patches when she chased cows or frolicked with Ms. Dymeck’s grandchildren.

But it grew quickly, alarming the family. Their local veterinarian referred them to Cornell University, where Dr. Galina Hayes, an assistant professor, took on a leading role in the treatment in February.

Patches’s tumor soon became so large it “ran out of room on the top of her head,” Ms. Dymeck said. It started to invade the eye cavity and press inward onto the brain, Dr. Oblak said.

“It was like a big orange on her forehead,” she said.

[Like the Science Times page on Facebook. | Sign up for the Science Times newsletter.]