NEW YORK — Sophia Wilansky, 21, a recent Williams College graduate who grew up in the Bronx, rested in a Minneapolis hospital bed, her father by her side, recovering from surgery to try to save her left hand and arm after an explosion at a pipeline protest in North Dakota this week.

“From an inch below the elbow, to an inch above her wrist, the muscle is blown off,’’ her father, Wayne Wilansky, said from the hospital, Hennepin County Medical Center. “The radius bone, a significant amount of it, is blown away. The arteries inside her arm are blown away. The median nerve is mostly blown away.’’

Her injury is the most serious to have been reported during months of increasingly acrimonious conflict over the 1,170-mile Dakota Access Pipeline, which Native American tribes, led by the Standing Rock Sioux, fear would pollute the Missouri River and harm sacred cultural lands and tribal burial grounds.

All the while, the protests have gone on, and the polarization between the police and protesters extended to their sharply differing explanations of how Wilansky was injured early Monday. Law enforcement accounts suggest that fellow protesters caused the explosion; the demonstrators insist that police are to blame.

Wayne Wilansky, who spoke by phone and checked details with his daughter as he did, said the explosion had taken place about 4 a.m. Monday, when most of the protesters were gathered around a bonfire near the foot of the bridge.

His daughter and a handful of others were farther up on the bridge, he said, “playing around,’’ using pieces of plastic and wood as sleds to skid across icy sections of the highway, when an officer began firing foam or plastic bullets at her and another person.

“She was backing away as they were shooting her,’’ Wayne Wilansky said, adding that someone from the police lines then threw a device, which he called a grenade, that hit her in the forearm and exploded.

But Lieutenant Tom Iverson of the North Dakota Highway Patrol offered a different version of the episode, which he said was being investigated by the North Dakota Bureau of Criminal Investigation and the federal Bureau of Alcohol, Tobacco, Firearms and Explosives.

At about the time of the explosion, Iverson said, officers fired sponge and beanbag rounds at three people who had shielded themselves behind a length of plywood near a burned vehicle on the bridge. The three were thought to be acting suspiciously and refused orders to emerge, he said.

Officers saw someone roll metal cylinders to the protesters by the burned vehicle, Iverson said, and then heard an explosion. Afterward, he said, several protesters ran up, pulled a woman from under the vehicle, and ran off. Three propane canisters were recovered from the vicinity of the explosion early Tuesday, he said.

Iverson said that officers have not used concussion or flash grenades at any time during the protest. Instead, officers have used tear gas, pepper spray canisters, and what are known as stinger balls, round grenadelike objects that spread tiny rubber pellets, to try to disperse protesters, he said.