Cardiovascular diseases such as heart attacks, stroke and angina comprise some of the most widespread conditions in Sweden. They cause immense suffering, and are the most common cause of death both in Sweden and the rest of the world.
These diseases depend to a large extent on lifestyle – tobacco use, a fat-rich diet and lack of physical activity – but the underlying causes remain largely unknown. Disturbances in the blood flow, however, are believed to play an important role, not least the irregular forces on the inner surfaces of the blood vessel walls that can give rise to, for example, atherosclerosis. Such anatomical barriers can also cause damage to blood cells, and in the long term cause serious harmful changes.
In his doctoral thesis, Turbulence Descriptors in Arterial Flows: Patient-Specific Computational Hemodynamics, Magnus Andersson has developed new ways to calculate and visualise turbulent blood flow in constricted blood vessels. These models are based on data from a patient who has undergone a procedure known as balloon angioplasty. Calculations have been carried out at the National Supercomputer Centre (NSC) at LiU.
“The computing power available at NSC makes it possible to create very accurate and detailed simulations. The most expensive calculation took two months to carry out”, says Magnus Andersson, who has been working on his doctoral thesis since 2012.
The most common methods used to investigate blood flow are ultrasound and magnetic resonance tomography (also known as magnetic resonance imaging, or MRI). These work well when looking at large-scale fluid mechanics, while they cannot reveal small features. This is the reason to use simulations, such as those that Magnus Andersson has worked with.
To appreciate the difference, the MRI images used in the thesis have a spatial resolution that is ten times poorer than the visualisations. The temporal resolution is 1000 times poorer than that of the simulated flow field. The simulations make it possible to analyse flow descriptors in much greater detail and greater accuracy.
A further advantage is that the simulations can be used to predict changes in the blood vessels. Examples of possible predictions are how plaque formation in a blood vessel will develop, and how various procedures (modelled virtually) will affect the blood vessel.
“The magnetic resonance images show the current situation, but do not say anything about the future”, says Magnus Andersson, and points out that the techniques complement each other.
“Indeed. In the best case they can reinforce each other. At the moment, huge amounts of computer power are needed for these calculations, but you can envisage that in the future a ‘Simulate’ button will be incorporated into the magnet resonance camera. And the simulations can already help to increase the resolution of the measurement data.”
Like the weather
This field is known as “computational fluid dynamics”, CFD, and has become a research discipline in its own right. The fundamental problem is the same as that of weather forecasting – how can different flows be estimated and calculated. In principle, there are no differences between blood flows in the body and large-scale air flows in the atmosphere.
The mathematical technique used to solve the problem is to use numerical approximations of differential equations, in which the calculation domain is divided into smaller elements on which the calculations are performed.
“But, of course, the sizes of the elements are extremely different. They are smaller than a millimetre in the aorta, while weather forecasting uses elements that are several kilometres”, says Magnus Andersson.
It is not pure chance that the thesis is being presented at Linköping University. The work has been carried out with the aid of the Center for Medical Image Science and Visualization (CMIV), while LiU offers broad expertise and collaboration within fluid dynamics, image processing and medicine. And supercomputers.
“I’m hoping now that the analysis methods can be tested under conditions closer to clinical practice. It’s a real hope that they can be translated into practical use”, says Magnus Andersson.
Translated by George Farrants