Sometimes, just because they thought it couldn’t hurt, the Semperes would walk from the spot of the attack to their house in Medford, thinking they might establish a scent trail to guide Marisol home.

The Semperes, who are both 32, also did some old-school things, such as a flier campaign in the communities that surround the Fells. They made daily calls to police and animal control, and took long walks with friends through the Fells calling for Marisol.

They took out geo-targeted Facebook ads on the pages of those who live in the vicinity of the Fells and list dogs and hiking in their hobbies. They hired a $100-an-hour tracking dog and used GPS to create a 13-mile map of the route it took, following Marisol’s scent. (The map revealed, to their horror, that Marisol had crossed Interstate 93 several times, and basically circled back to where she’d disappeared.)

The Marisol campaign, as the Semperes call it, harnessed the social networking power of the Internet to create a search-and-rescue army. The couple created a blog, findmarisol.com , and a Twitter hashtag, #MarisolSearch, which got a boost when the best-selling author Susan Orlean tweeted it to her 91,000 followers.

The Semperes didn’t just meet at MIT; they met as students at the MIT Media Lab, a place that values, above all, unorthodox thinking about technology.

But they did not give up. Instead, they tried to reinvent the search for a lost dog.

“Then it got dark,’’ Anindita remembered. “It was horrible. Absolutely horrible. To leave felt like we were giving up.’’

Instinct said to go to their dog, so the Semperes went to the Fells, searched for hours, called Marisol’s name, and sang to her.

Andrew Sempere was at work when he got the call telling him his dog was missing. He’s a researcher at the IBM Center for Social Software, and he immediately called his wife, Anindita, whom he’d met when they were grad students at MIT.

That was Nov. 2. Toby is slowly recovering. Marisol — a 3-year-old, 20-pound copper-colored mutt — is still out there, and the search for her has become one of the most elaborate and high-tech ever mounted for a missing dog.

Toby, a normally timid golden retriever mix, stepped in for his little friend and took a beating, holding the pit bull off until its owner finally appeared and punched his dog off.

They had been out with their dog walker, six dogs having a playdate in the Middlesex Fells Reservation, when a pit bull charged out of the woods and lunged for Marisol.

In an instant, little Marisol was gone, and Toby, her buddy, was badly hurt.

In some ways, the campaign was a success. People around the world read the blog and tweeted about it; the comments section became a place for people to console the Semperes and share the happy endings to their own lost-dog stories.

The campaign led to regular calls from people who believed they had spotted Marisol. There were reported sightings all over the 2,000-acre Fells and its surrounding communities — but none of them brought Marisol home.

That’s because, the Semperes came to understand, most of what they’d been doing was all wrong.

They were leading a search-and-rescue operation for a pet. But, specialists told them, after a day, maybe less, Marisol had stopped thinking like a pet. And as hard as it was for the Semperes to believe, Marisol was not looking for them to rescue her.

To get her back, they’ve come to understand that they cannot go to her. They need to get her to come to them. And to do that, they will have to hunt her like a feral animal.

This moment of insight came more than a week after they’d launched their round-the-clock campaign. That’s when they talked to Karin TarQwyn, a Nebraska-based pet detective who is considered a leading specialist in the field.

Marisol, TarQwyn explained to them, is a “roaming dog.’’ TarQwyn says there are nine scenarios under which dogs go missing, and the roaming dog is the most difficult to catch.

Marisol’s primary instinct had become her own security, and that meant avoiding people, even her owners. All those people out there calling for her in the Fells had put her constantly on the move instead of settling down into a regular area.

In addition to her instincts, Marisol also had proven abilities. That’s because little Marisol is a “Sato,’’ a Puerto Rican street dog.

Three years ago, the Semperes went to Puerto Rico with some friends to volunteer at a Sato shelter. They weren’t really planning on getting a dog. There were 200 at the shelter, and, independently, the Semperes each fell in love with the same shy, timid, mischievous dog that looked a lot like a fox.

As Andrew was plotting how to broach the subject with his wife (who had never had a pet in her life), Anindita called to him from across the shelter, pointed at Marisol, and said: “That one! Let’s take her home.’’

All the shelter knew about Marisol was that she was about 7 months old, had been born and lived in an abandoned factory, had been pregnant with a litter that didn’t survive, and had scars on her muzzle and face that revealed she’d been in fights.