And nine years since his operation, the 57-year-old engineer from Gloucestershire in the UK has managed to help more than 40 people with similar conditions.
Andrew Ellis, a keen footballer, has benefited from Mr Golesworthy's inventiveness.
At just 27 years old, Mr Ellis said it was daunting to put himself through an experimental medical procedure experienced by so few, but he was glad he did.
Five years after his surgery, he remains fit and healthy and "feels like someone without a heart condition".
Mr Golesworthy is now calling on surgeons across Europe to start a trial and test his device against more conventional therapy.
Like Mr Ellis, Tal Golesworthy has Marfan syndrome - a disorder in which the body's connective tissues are faulty. These tissues normally act as scaffolding for the major organs, ensuring they are kept in shape and in place. But people with severe forms of the syndrome can have problems with their eyes, joints and particularly their hearts.
But he was "unimpressed" with the options available to him. Traditional surgery is lengthy and complex and includes replacing the stretched segment of the aorta with an artificial graft. Sometimes surgeons also have to put metal valves inside the heart to replace ones that are cut out.
But having metal in his heart would mean Mr Golesworthy would have to take blood-thinning medication for the rest of his life to ensure a smooth blood-flow. And this medication carries the risk of bleeding from even a minor fall.
As an active person and keen skier, this was a side effect Mr Golesworthy was unwilling to tolerate.
He says: "I didn't want to have to live my life in a cotton-wool cocoon and I thought I might be able to come up with something less intrusive and complex that didn't require a part of my heart to be taken away."
So he engineered himself a solution.
His thinking was straightforward.
He says: "If the hosepipe is bulging, I must get some insulation tape and wrap it round the outside of the hosepipe to stop it bulging.
"It's that crude and simple, and we have all done it in our gardens."
Persuading surgeons he might be able to improve upon their techniques was not easy. But he managed to convince Prof Tom Treasure, then at Guy's Hospital London, and Prof John Pepper, of the Royal Brompton Hospital, London, that they may be able to learn a thing or two from engineering techniques.
The process took a growing team three years to perfect. The result would be a personalised sleeve that is stitched snugly around the enlarged vessel, providing structural support and preventing it from growing any bigger.
The sleeve is made of a medical-grade mesh, using material that has been used to suture wounds for many years.
The team hypothesised that by putting the sleeve on the outside - rather than the inside - of the aorta, they would reduce the complexity of the surgery needed, there would be no need for anti-clotting drugs and there would be less time under the knife.
And four years on from its inception, they were ready for the next big step - Mr Golesworthy would be the first guinea pig for his device.
Although they had had several dry runs of the operation, he remembers it as the scariest day of his life.
He says: "I have spent my entire professional life project-managing various projects but of course this one was completely different. It was me that was going to be on the slab at the end of it."
The two-hour operation was carried out at the Royal Brompton Hospital. Nine years on, Mr Golesworthy's aorta has not grown in size.
"All of a sudden my aorta is now fixed, I began to breathe easy and sleep well and relax in a way that I hadn't done for years and years before," he says.
Mr Golesworthy says his motivation at the beginning of this project was entirely selfish, but the team has now been able to offer the tailor-made sleeves to more than 40 patients in London, the John Radcliffe Hospital, Oxford and the Leuven University Hospital in Belgium.
Andrew Ellis, who had his procedure at the Royal Brompton Hospital, London, knew cardiac surgery was on the cards for a long time.
His biological father had died with the condition in his early twenties so he was acutely aware of the risks of not having treatment. But like Mr Golesworthy, Mr Ellis wasn't keen on long and intrusive surgery or life-long medication.
He had the procedure using Mr Golewsorthy's device in 2007. Five years later, his latest scan showed his aorta had not grown in size.
"Tal's invention has taken away the looming threat of a major operation that was hanging over me for so long," he said.