DON'T EAT JUNK FOOD !!!

We have all heard this many times, but not everyone can resist the temptation! Fortunately for us, heart surgery is one of the successes of modern medicine. Blockages in arteries can sometimes be cleared, and, if not, surgeons can replace the artery by a length of artificial tube.

However, the down side is that the artificial tube can sometimes lead to the formation of a bubble, known as an aneurysm, in the artery. If the patient
also suffers from high blood pressure, then the pressure inside the bubble
may cause it to rupture, with serious consequences for the patient. Consequently heart surgeons are eager to learn more about aneurysms.

The growth of an aneurysm can be modelled mathematically. Dr Hart and Dr Shi in the Mathematics Department at the University of Queensland are doing just this. The aneurysm is modelled as a thin hemispherical bubble and the artificial artery as a cylinder as shown in the diagram above.

The tension, T, in the tissue that forms the bubble can be calculated using the equation T - pr/2, where p is the pressure of the blood and r the radius of the bubble. If the pressure, p increases so does the radius r. So that the tension, T, experiences a compound effect, which may cause the bubble to burst. Mathematical detail of this sort can give doctors an estimate of the risks from hypertension for patients with aneurysms.

What causes the bubble is a rather more complex problem. As the heart pumps blood along the artery, the pressure changes in a wave-like motion. When the pressure wave of the blood hits the artificial section there is a change in elasticity in the tube and some of the pressure is forced back towards the heart. This creates extra pressure and thus tension at the join. It is here near the join that the bubble forms.

Through complicated mathematics Drs Hart and Shi are seeking to understand the dynamics of the blood flow through the elastic walls of the arteries. Doctors can then use this knowledge to manufacture better artificial arteries.