Outside the office of Professor Anna Dominiczak at the University of Glasgow, there is a wall covered with pictures of men, regius professors of medicine going back to 1637.

There are some severe-looking old coves among them. What would they make of Dominiczak's appointment as the first woman in the post? A few look like they'd need their smelling salts.

Dominiczak smiles benignly but not too reverently up at them before ushering me into her office with its huge glass window onto University Avenue. We get talking straight away about gender differences at work and the professor comments chattily on men's greater capacity than women to push themselves forward.

Surely she must be an exception, though? A world-leading expert on cardiovascular medicine whose research has focused on identifying genetic factors which may predispose people to heart disease, hypertension and stroke, she is one of the country's most eminent scientists and was founding head of the Glasgow Cardiovascular Research Centre. She is the first ever boss of the new College of Medical, Veterinary and Life Sciences at Glasgow University with a £200 million annual turnover and 2000 staff, and somehow manages this alongside being president of the European Society of Hypertension and editor-in-chief of the world's top medical journal on high blood pressure. This the mother-of-one has achieved having been a newcomer to the Scottish medical establishment when she arrived from Poland in 1982. Presumably she has a natural flair for promoting herself? She shakes her head. "No, I have to practise," she confirms, in her accented English, and laughs. "But I think as you get older, you get better at it. You care less."

Svelte, petite and stylishly dressed, her chic blonde bob makes me think of tough Vogue supremo Anna Wintour - until she smiles, that is, which is nearly all the time. It is easy to stereotype women who reach the top of male-dominated professions, but if I was expecting steely detachment, I don't find it. Dominiczak is friendly and self-deprecating without doing herself down. Asked about her success, she has a straightforward answer: "It's just about working a little harder than the man or woman next door," she shrugs. "Also not taking no for an answer. In order to make it in biomedical academia, you really need big grant funding, but people tell you no. Maybe in some way you have to have the right type of character that you just don't give up. But the main ingredient is not the quality of the brain but the hard work."

She typically works from 8.30am until 7pm, then goes home to walk the dog and works some more. "Hmmn, yeh, I have slightly workaholic tendencies," she admits. A lot of people would be frazzled by that, I comment. "No no, I am not stressed, I enjoy it immensely," she says with feeling. "It's fun, it's fun."

Has she ever experienced sexism? "Yes and no," she says, picking her words carefully. Looking back, she can recall occasions when being a woman influenced how she was treated. There was the time in 1983 when she told a professor of medicine she wanted a career in medical academia and he suggested she went home and had babies; then there was the experience of having her contribution in meetings ignored only for a man to say exactly the same thing five minutes later and be praised for his fantastic idea. Still, she talks of this without rancour. That was then; things are different now: "Certainly in my college of medicine, vet medicine and life sciences, it never happens. Never happens."

Dominiczak's latest role as head of college is "the best job I've ever had", she declares, because having so much diverse expertise under one management structure allows for exciting new multidisciplinary collaborations. It also means she is overseeing for the university the building of state-of-the-art facilities at the new South Glasgow Hospital. It will have 1000 beds, making it the biggest acute hospital complex in the UK and probably Europe, and will incorporate a teaching and learning centre, built jointly by Glasgow University and NHS Greater Glasgow & Clyde. This will include a cutting edge stratified medicine centre. The aim is to use techniques such as studying patients' genetic make-up to "stratify" them into groups, allowing for drugs to be personalised for individuals from the start. The centre will bring in industry expertise with two companies already signed up - Life Technologies and Aridhia. It is a collaboration between all four Scottish medical schools under the umbrella Health Science Scotland, NHS Scotland and industry partners; Glasgow City Council contributed £1.5m. For stratified medicine to work, patients have to be diagnosed even better than usual, so the hospital will also have a clinical research facility with very high level MRI and CT scanners.

Perhaps it is no wonder she regards coming to Scotland as "the best thing we've ever done".

The "we" refers to herself and husband Marek, honorary professor at the university and consultant clinical biochemist with NHS GGC. The couple met at school in Gdansk and have been married more than 30 years. It was Marek who persuaded Dominiczak to leave Poland, first briefly for Malta and then Scotland. "For me, this was a wonderful opportunity," she says. "I think that without Marek I would have stayed and had precisely the same life as my parents did. Glasgow's been a wonderful place for me."

Dominiczak was the only child of two doctors, both professors of medicine. It was more usual then to have eminent female doctors in Poland than in the UK because so many young Polish men had been killed in the war. "In my medical school in Gdansk there were a number of women professors including in surgery so when I came to Glasgow I was flabbergasted because there weren't any. I think it helped me because I just didn't accept that that wasn't a thing you do."

The Poland she grew up in was a Communist-run satellite of the Soviet Union and the population faced certain privations. "There were periods where there was nothing to buy in the shops," she recalls. "If I wanted to go abroad as a young student - I went for exchange of students to Sweden - in order to get the passport I had to queue from 3am, at the local police station, because my passport wasn't in my desk at home; it could be given to me or not. I remember from my school days walking home from the shipyard during the first strike - my secondary school was at the shipyard gates - and there were all these tanks coming, and soldiers. But between all that there was normal life."

The Gdansk shipyards were famously the centre for the Solidarity movement, led by Lech Walesa, which emerged in 1980 and eventually brought about the end of communist rule. Dominiczak left in 1981, but remembers those heady early days. "I had just qualified and the entire academic hospital, everyone, including me, was a member of Solidarity, so it was very uplifting.

"If you were a politician, it was great; if you were a journalist, it was wonderful all this change. It was just difficult for a young person who wanted an academic career."

She does not return as often as she would like - her mother is still there - but she and her husband speak Polish at home. She is amused to hear Poles on Glasgow streets. "Some of them swear terribly," she laughs. "They think nobody understands."

Leisure time is in short supply, but her treat is visiting Taylor Ferguson hair salon and her main exercise is walking her cocker spaniel Chuck. Though originally bought for her son Peter, 28, now a political correspondent for The Daily Telegraph, she has been in sole charge of Chuck for many years.

Dominiczak does not seem to mind the lack of free time. She says that stratified medicine will "revolutionise the way the world practises medicine" and looks forward to being part of it.