Paul made his first public comments since the incident on Sunday, tweeting that his wife "Kelley and I appreciate the overwhelming support after Friday's unfortunate event. Thank you for your thoughts and prayers."
Doug Stafford, Paul's chief of staff, said in a statement Sunday that the senator has five rib fractures, including three displaced fractures, meaning the bones are partly or completely cracked.
"This type of injury is caused by high velocity severe force. It is not clear exactly how soon he will return to work, as the pain is considerable as is the difficulty in getting around, including flying," Stafford said.
Paul has lung contusions, or bruises, caused by the broken ribs, Stafford said. He could not say whether one lung was bruised or both, but said Paul's recovery could last several months. Such fractures can cause other significant medical problems, including internal bleeding, damage to other organs or pneumonia.
The nature of the dispute between Paul and Boucher remained a mystery Sunday to locals who know both men as medical professionals based in this southwestern Kentucky town.
Paul is an ophthalmologist who has practiced in town since moving here with his wife in 1993. He continues to provide free medical care to low-income Kentucky residents on a regular basis throughout the year when the Senate is not in session.
Boucher is an anesthesiologist and the inventor of the Therm-a-Vest, a cloth vest partly filled with rice and secured with Velcro straps that is designed to help with back pain. He has worked at several local medical facilities through the years, according to public health records.
David Ciochetty, a doctor with Interventional Pain Specialists in Bowling Green, said in an interview Sunday that Boucher worked there as a "general pain medicine physician" for about a year and a half beginning in January 2010 before leaving.
Asked whether he knew what might cause Boucher to lash out, Ciochetty said, "The rest of Bowling Green would like to know that, too. I was quite surprised to see this in the news."
Ciochetty said Boucher used to work as an anesthesiologist at the hospital but "told people that he sustained a neck injury and could not continue his anesthesiology duties."
After Boucher left IPS, Ciochetty did not hear of him practicing anywhere else.
Paul had full staff privileges at the hospital when Boucher worked there, so Paul and Boucher "must have worked together at some point," Ciochetty said.
Boucher was released Saturday on $7,500 bond, according to county jail records. He is scheduled to appear in court Nov. 9.
A motive is not known, and there is no indication that the attack was political in nature.
Jeff Jones, a registered nurse who worked with Boucher at the Bowling Green Medical Center, described Boucher's politics as "liberal."
"He was active on social media and said some negative things about the Republican agenda," Jones said.
"I think it was unfortunate that they lived so close together," he added.
A Facebook page that appeared to be Boucher's included links to articles and memes critical of President Trump and a news article about a Montana Republican congressional candidate who attacked a reporter the day before winning his seat. The page said Boucher is a former Army pain-management specialist and graduated from the College of Osteopathic Medicine in Des Moines in 1984.
By late Saturday, the page had been overrun by other Facebook users criticizing Boucher for the alleged assault. On Sunday, the page appeared to be blocked from public view.
Jim Bullington, a former member of the city commission, knows both men. He said Sunday that Boucher is divorced and lives alone. Bullington described Boucher as a socialist.
"He's pretty much the opposite of Rand Paul in every way," Bullington said in an interview.
The neighbors had been known to have "heated discussions" about health care, Bullington said, adding that Boucher is an advocate of a national health system.
Paul, an outspoken libertarian, voted last summer against a Republican plan to repeal the Affordable Care Act, saying the plan didn't go far enough in repealing the 2010 health-care law.
Robert Porter, a friend of Paul's, said late Saturday that the senator was mowing his lawn moments before the attack.
Paul and Boucher live side by side along a small lake in Rivergreen, a close-knit gated community with large houses. On Sunday afternoon, nobody answered at Boucher's home. Next door at the Paul residence, four people were seen doing yard work. Other neighbors were out walking, enjoying the unseasonably warm weather.
The senator joins a growing list of lawmakers in both parties who have been attacked or threatened with violence this year. Congressional security officials have investigated thousands of general or specific threats against Democratic and Republican lawmakers.
The threats turned to violence during the summer when House Majority Whip Steve Scalise (R-La.) was nearly killed by a gunman who showed up at a congressional baseball practice in Alexandria, Va.
Paul, a member of the team, was on the field at the time of the shooting but was not hurt.
More recently, Rep. Frederica S. Wilson (D-Fla.) skipped several days of votes after threats were made against her after she sparred with Trump over the treatment of the widow of a U.S. soldier killed in Niger.
O'Keefe reported from Washington. Alice Crites, Caitlin Dewey and David Weigel contributed to this report.