SSD Seminar Series with Prof. Ryszard Białecki

Monday, January 8, 2024, 4 to 5pm

On January 8, 2024, we welcome Prof. Ryszard Białecki of the Department of Thermal Technology at the Silesian University of Technology, Poland, as speaker in our SSD Seminar Series. 

The Seminar will take place in Rogowski Building, Room 115, Schinkelstraße 2, 52062 Aachen.

 

Simulation of Blood Flow in Arteries

picture of Prof. Ryszard Białecki Copyright: © Prof. Ryszard Białecki

Simulations of blood flow in the arteries are performed using computational fluid dynamics software. The specific features of this task are:

  • Complex geometry of the cardiovascular system

  • Cyclic character of the flow

  • Deformable vascular walls

  • Blood as a non-Newtonic fluid

  • Non-standard boundary conditions;

The circulatory system consists of arteries and veins connected in a complex network. The complexity of geometry excludes the use of a 3D model to describe blood flow throughout the body. The models used in practice use significantly simplified geometry and 1D formulations Periodicity results from the heart cycle and requires solving transient tasks until repetitive cycle waveforms are obtained.

The deformable walls of the vessel cause the computational area to change its shape (lumen and length) during calculations. To account for these phenomena, the fluid structure interaction option is invoked. However, this requires knowledge of the material properties of the vessel wall that are difficult to measure. Another option is to use imaging of the geometry changes obtained, after proper treatment, from CT, MRI, or similar modalities.

Blood does not behave like a Newtonian fluid; its viscosity depends on the shear stress rate. To account for this, non-Newtonian constitutive equations, available in the literature, can be used. Another approach is to treat blood as a multiphase mixture composed of blood cells immersed in plasma.

In the case of 3D models, due to the very complex geometry of the cardiovascular system. It is necessary to limit the computational domain. As a result, boundary conditions on the so-generated fictitious inflow and outflow openings of the truncated domain. These conditions should take into account the flow resistance of the cutoff part of the circulatory system, but also its ability to accumulate blood, which results from the elasticity of the walls of the blood vessels. The most commonly used model is the 3-element Windkessel which is an analogue of an electrical circuit with two resistances and one capacitor.

The lecture will show the use of blood flow simulations in coronary arteries with a pathological condition called myocardial bridge. This part of the lecture will also discuss the technique of retrieving, from angio-CT images, the changing in time and space geometry vessels. The effect of oscillating shear stress on the vessel wall on the deposition of atherosclerotic plaque will be discussed. Euler-Euler formulation of the multiphase model of blood flow will also be discussed. The resulting separation of red blood cells will be shown.
Stiffening of the walls of blood vessels with age and as a result of past diseases causes dangerous consequences such as hypertension and damage to the soft tissues of the brain, kidneys, and other organs. The use of CFD simulations to determine local wall stiffness will be shown in an example of the carotid artery.
The problem of modeling blood flow through the aortic valve will also be discussed.