Mr Baum regularly takes medical students on tours of the National Gallery to study the physiognomy and features of many of the paintings' subjects.
During one of his "National Gallery ward tours" he handed Cook the task of proving his Paget's disease theory.
"He did the most meticulous research, I gave him top marks. It was a beautiful piece of work, utterly convincing," said the professor.
Mr Baum believes the sitter would have been "a very powerful woman and may even have been a real duchess".
He added: "I reckon the artist was paid a princely sum to do it, because who is going to buy a painting like that? Artists had to make a living. I think the painting is probably quite a close likeness."
It had long been thought that Massys' painting of 1513 was a copy of a 1490 work by Leonardo Da Vinci. Previous experts have noted how similar it is to two Leonardesque drawings which were supposed to reflect a lost original by Leonardo.
But research by the National Gallery suggests the opposite. Susan Foister, curator of the National Gallery's exhibition Renaissance Faces: Van Eyck to Titian, which opens next Wednesday, said: "We can now say with confidence that Leonardo - or, at least, one of his followers - copied Massys' wonderful painting, not the other way around. This is a very exciting discovery."
The curator said the gallery had discovered that Massys made amendments as he went along, suggesting he was making a study from close quarters.
She added: "It was always assumed that a lesser-known northern European artist would have copied Leonardo, and it has not really been thought that it could have been the other way round."
She added that both artists were interested in ugliness and exchanged drawings, "but credit for this masterful work belongs to Massys".
The portrait, which inspired illustrations for Lewis Carroll's Alice's Adventures in Wonderland, will be part of the Renaissance Faces exhibition.
Mr Baum said: "You either love it or you hate it and I love it, it's part of the background of London, part of London's iconography."
Paget's disease is named after Sir James Paget, the British surgeon who first described it in the late 19th century, and more commonly affects the lower body such as the pelvis and femur.