In the best-case scenario, Barbaro would have recovered from his catastrophic injuries, spent his days on a farm and perhaps even produced little Barbaros.

When the Kentucky Derby winner was euthanized Monday after complications from his gruesome breakdown at last May’s Preakness, it led to a natural question: Was any sperm taken from the colt?

It wasn’t, said Barbaro’s doctor and co-owner.

“We don’t even know if he was potent,” co-owner Gretchen Jackson said Wednesday. “It would be great to have his babies, but it won’t happen.”

Dean Richardson, chief surgeon at the University of Pennsylvania’s New Bolton Center in Kennett Square, Pa., said future fertility would have been a bonus, but “we only were interested in saving his life.”

Anyway, established rules require that thoroughbreds breed naturally with mares.

Barbaro’s lineage survives with his siblings.

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A full brother to Barbaro is a yearling at Mill Ridge Farm in Lexington, Ky., and his mother, La Ville Rouge, is in foal again to Barbaro’s sire, Dynaformer. The foal is due in April.

Bayne Welker, director of sale at Mill Ridge, said Wednesday another La Ville Rouge-Dynaformer mating is scheduled for later in the spring.

But for the Jacksons, there’s no replacing Barbaro.

A final resting place for Barbaro’s ashes has not been determined.

It could be the Kentucky Derby Museum, just a few hundred yards from the scene of his greatest triumph in the 2006 Derby at Churchill Downs in Louisville, Ky. Or it could be in the bluegrass of Lexington, Ky., at the 1,200-acre Kentucky Horse Park.

Video: barbaro death TODAY Hero horse Barbaro loses gallant battle Jan. 30: Kentucky Derby champion Barbaro is euthanized, ending an eight-month struggle since the colt broke down at last year’s Preakness Stakes. NBC's Peter Alexander reports. MSNBC-TV talks with columnist Celizic Doctor: Barbaro’s death 'very difficult'

Barbaro’s final home might even form the basis of a regional racing museum in Pennsylvania, the home of several top horses the past few years, including 2004 Derby and Preakness winner Smarty Jones and 2005 Preakness and Belmont winner Afleet Alex.

“Right now, it’s a concept, and we want to look at that before we decide where Barbaro goes,” Jackson said. “We’re hoping some of the other owners of horses from the area who have done well will be interested as well.”

Count in Pat Chapman, co-owner of Smarty Jones and a longtime friend of Gretchen and Roy Jackson.

“I would throw my support behind them in anything they would want to try,” she said. “I’d love to be part of it.”