A doctoral thesis at NMBU could make it easier to develop software for medical use.
Ole Løseth Elvetun has studied an optimisation problem within medical research that can be used to prevent myocardial infarctions, commonly known as heart attacks.
According to a report from the Norwegian heart attack register in 2014, 35 Norwegians suffer a heart attack every day.
By combining electrocardiography (ECG), which records the electrical activity in the heart, with mathematical calculations, this grim statistic can hopefully be reduced.
"The aim is to get to a point where an ordinary ECG reading can be taken at a normal consultation with the doctor, allowing the computer to locate any ischemic heart attacks," says Ole Løseth Elvetun, who recently completed his doctoral thesis at the Norwegian University of Life Sciences (NMBU).
Mathematics to study the cause
Mathematics is currently used within most disciplines. It has become an essential tool for creating models for a long list of phenomena.
"Many of these problems can be described using something called partial differential equations (PDE). This is a mathematical branch in which changes to the unknown also become part of the equation," Elvetun explains.
He compares the use of differential equations to how the size of an ice cream will be crucial to how quickly it will melt.
"We say that the equation can model the effect of the cause. In the case of the ice cream the effect is the melting and the cause is the heat.
“But it is often the case that we cannot observe the cause, only the effect. We are then faced with a mathematical problem that is more complex to solve: a PDE optimisation problem," Elvetun explains.
Even if this may sound rather exotic, it is a relevant issue to a number of disciplines, including medicine. One such optimisation problem within medical research is exactly what Elvetun has studied.
Which area of the heart is affected
In order for the heart to beat it requires an electrical flow that allows it to contract. This flow is the result of a change to the electrical potential in the heart and can therefore be modelled using a partial differential equation.
"If a patient suffers an ischemic heart attack, a compression of a blood vessel that supplies blood to the heart, the electrical potential in the heart will change in this region," says Elvetun.
He explains that ischemia is a precursor to a full-blown heart attack and that it is therefore crucial that this is detected in time. Such ischemia can be detected using mathematics and ECG readings.
"The idea is that since ECG measures electrical potential on the surface of the body we can use a partial differential equation to determine which area of the heart is affected by the ischemic infarction," Elvetun says.
The question is: Where is the ischemia (cause) that results in the electrical potential that can be measured on the surface of the body (effect)?
Elvetun has examined many unsolved issues relating to the use of mathematics and ECG readings to detect ischemia.
Finding the answers more quickly
A minor error in the ECG readings could cause completely wrong results when such issues are to be solved. As such measuring errors are unavoidable in practice it is necessary to make the problem more stable.
As such an optimisation problem often has several million unknowns when represented on a computer, it is crucial to solve it quickly.
"In simple terms I have changed the equations so that the problem became quicker to solve using numerical methods," Elvetun says.
Even if fewer patients die from myocardial infarctions now compared to before, ischemic heart disease remains one of the most common causes of death in Norwegian hospitals, according to the Norwegian heart attack register.
"Plenty of research must still be undertaken, but there are several mathematicians working on this problem. I believe we will reach the stage where the algorithms are good enough for mathematics to be able to tell doctors, within seconds, where the patient's ischemia is located," Elvetun concludes.