Week 8 Flashcards
In one-dimensional blood flow modeling, what does U(x, t) represent?
Blood velocity
This is a critical variable in understanding how blood moves through vessels.
What are the key assumptions in the 1-D governing equations?
- Domain decomposition into arterial segments
- Laminar blood flow
- Incompressible and Newtonian fluid
- Constant arterial length
- Thin, deformable, homogeneous, and impermeable arterial walls
- No gravitational effects
These assumptions simplify the modeling process while maintaining accuracy.
State the conservation of mass.
The rate of change
of mass in the control volume must equal the difference between the
mass flux in and the mass flux out of the volume.
What is the tube law derived from Laplace’s law?
Circumferential stress in a thin-walled pressurized cylinder
This law relates the pressure difference across the wall of a vessel to the geometry and material properties of the vessel.
What is the difference in computational cost between 1-D and 3-D blood flow models?
1-D models take seconds, while 3-D models take hours
This highlights the efficiency of 1-D models for certain applications.
What are the three types of blood flow modelling discussed?
0-D, 1-D, and 3-D modeling
0-D modeling is also known as Windkessel modeling.
Why do we need 3D modelling for investigating vascular protheses?
Geometric features affect the risk of occlusion in vascular prostheses.
What equations are used to model the 3-D blood flow problem?
3-D Navier-Stokes equations for an incompressible and Newtonian fluid
What is fluid-structure interaction?
The interaction between the fluid and solid problem in blood flow modeling
What are wall shear stresses important for?
Analyzing blood flow and the risk of vascular occlusion
How is blood flow simulated in 1D modelling?
Each segment in the arterial network is simulated as a thin,
deformable tapered cylindrical tube whose properties can
be described by a single axial coordinate, x.
