Multi-scale haemodynamics of extreme value to research the process of blood flow in cardiac disease

Prof. Dr. Kaxiras addressed the problem and danger of a sudden rupture in a patient's artery because of cholesterol plaque. The diagnosis is called asymptomatic coronary disease which can lead to acute myocardial infarction and sudden death. The problem is challenging because a traditional examination is not always sufficient to predict the status of blood flow in the arteries. A hidden danger in this type of disease is that the artery gets blocked because of plaque behind the artery walls. This causes the death of nearly 2,5 million people in the United States. There is a mortality of 35% for blood flow obstruction in comparison with "only" 25% for cancer, noted Prof. Dr. Kaxiras.

Intravascular ultrasound and tomography provide an accurate reconstruction of the lumen of arteries but the critical issue is to understand the natural history. The role of endothelial shear stress (ESS) is of capital importance in this regard. At a sufficiently low level of ESS, researchers have discovered that there is a build-up of plaque and inflammation as well. How does the flow reshape the endothelium, the inner wall of the artery, is the big question.

When the blood flow is nice and smooth, the inner wall looks like a very tight layer. But when the flow is disturbed, wholes in the inner wall appear. The cells deform and cholesterol enters behind the wall or worse, white blood cells sneak behind the endothelium and the plaque is being formed, showed Prof. Dr. Kaxiras. Therefore, multi-scale haemodynamics is needed to research the process of the blood flow.

Prof. Dr. Kaxiras and his colleagues have designed a model to observe the blood flow using fluid dynamics by cellular automata and the Lattice Boltzmann Equation (LBE). LBE reproduces the distribution with regard to fluid dynamics, fluid density, the momentum of the flow, the stress tensor and the wall stress.

"Particles" such as cells and proteins that enter behind the wall are defined by delta function-like quantities.

The particle dynamics are calculated with Newton equations of acceleration. The fluid-particle coupling forms the momentum exchange with Newton's restitution law where the exchange of momentum information is taking place.

Prof. Dr. Kaxiras showed a movie of red blood cells in motion in which a complicated situation appears with a tumbling motion of red blood cells. The particles are deformable just like cells due to tank treading.

The computation code which the team has used is called MUPHY. It took the team five years of development to create 10.000 lines of code for data preparation modules and 40.000 lines of code for simulations. The code is running on Blue Gene clusters.

Starting from CT patient data, a data segmentation is executed for the HPC data preparation. The segmentation and grid issues are solved with LBE and Navier-Stokes equations. The ESS calculation in a patient-specific arterial tree constitutes a complicated process amounting in a 250 M grid.

For this research the Jugene at the Forschungszentrum in Jülich has also been used. The runtime performance consists of 1 billion of lattice sites, 10 micron of grid resolution, and 10 million particles of red blood cells. A series of red blood cells are called rouleaux. They change the stress on the arterial wall. The

presence of red blood cells affects fluid flow.

As far as current extensions of the computation model are concerned, Prof. Dr. Kaxiras is aiming at modelling a full heart beat, pulsating heart walls, elastic artery walls, white blood cells, endothelium changes versus time, and plaque buildup and rupture processes.

The research has been carried out by Harvard University, the Italian CNR, and EPFL.