This Friday, Donald Trump has an unusual appointment on his agenda. Before departing Washington for his Mar-a-Lago residence in Florida, he will make the 11km trip to Walter Reed National Military Medical Center in Bethesda just north of DC. The 45th president of the United States is due to undergo his first medical since assuming office.

Trump famously boasted about his “perfect” state of health in advance of his election to the White House. He was backed in this by his long-term doctor, Harold Bornstein, who penned a letter in December 2015 declaring: “If elected, Mr Trump, I can state unequivocally, will be the healthiest individual ever elected to the presidency.”

He was certainly the oldest, when he moved into the White House a year ago aged 70. (Ronald Reagan was 69 when he was elected president).

New stories about Trump’s eating habits – including reports in Michael Wolff’s book Fire and Fury: Inside the Trump White House, that he regularly eats cheeseburgers in bed as he watches his three TV screens – have prompted fresh concerns about the president’s health.

More significantly, his mental fitness for office has been under question following revelations in the book, prompting Trump to tackle the issue head-on in an extraordinary series of tweets on Saturday when he declared that he was a “very stable genius”.

Trump’s allegation that his former aide Steve Bannon had “lost his mind” was also seen by many as a description that was a touch too close to the bone, an unwitting sign, perhaps, of his own psychological weakness.

Brendan Boyle, a Democratic Congressman from Pennsylvania, is proposing new legislation – dubbed the Stable Genius Act – that would require all presidential candidates to undergo a mental health examination. “Before voting for the highest office in the land, Americans have a right to know whether an individual has the physical and mental fitness to serve as president,” he said.

‘Slurred words’ Jason Chaffetz, a departing Republican senator, also addressed the issues in a passionate speech to the Senate denouncing the president: “If you’re going to have your hands on the nuclear codes, you should probably know what kind of mental state you’re in.”

The White House announced last month that Trump was due to have a routine physical after some commentators believed he slurred words during a speech on the decision to recognise Jerusalem as the capital of Israel. White House press secretary Sarah Huckabee Sanders described the claims as “pretty ridiculous” and said a dry throat had been to blame.

Trump has a lot to feel good about as he faces the examination. He doesn’t smoke and doesn’t drink alcohol – he has said his brother’s death at 43 from alcoholism discouraged him from drinking.

But his eating habits and lack of exercise may cause alarm. His penchant for fast food is well known, while the New York Times reported last month that he drinks up to a dozen cans of Diet Coke a day. Apart from golf, the president appears to engage in little exercise. He sleeps minimal hours at night, and while he appears to have no problem with energy levels, his lack of sleep could have health implications.

He is not the only president with vices – Barack Obama famously struggled to quit smoking.

Whether the examination will include some kind of psychological element is unknown, and it is also not clear if he will be subject to neurological tests.

Similarly, the White House is not obliged to release details about the medical check, though Trump’s office has suggested that the White House doctor, Ronny Jackson, may give a “readout”.

In this regard the current president would not be unusual. John F Kennedy famously kept his chronic back pain and Addison’s disease from the public, while the extent of Franklin D Roosevelt’s condition – he used a wheelchair after contracting polio – was never fully known.