Arterial Wave Equation Flashcards
Why does Poisseuille’s Law explain the Blood Flow in the Aorta only partially?
1) Blood is not a homogenous fluid
2) Fahraeus-Lindqvist effect:
- red blood cells are becoming concentrated in the middle of a vessel
3) Rouleaux Formation
- red blood cells are stacking together in long chains,
- reduction of membrane shear forces
4) periodic pumping –> blood flow is not stationary laminar but pulsating laminar or in large arterial vessels even turbulent
5) blood vessels ar not rigid tubes –> they have three layers with elastic fibers
Pulse Wave Propagation along the Aorta
–> energy transormations
- based on continous transformation of kinetic energy into potential deformation energy and back
- –> kinetic energy due to blood intertia is transformed into vessel deformation
- –> contraction of stretched vessers transforms potential energy back to kinetic energy
Pulse Wave Velocity
What is its relation to the vessel elastic modulus?
- varying due to a changing vessel wall structure along the arterial tree
- velocity increases as the pulse propagates towards the periphery (pressure gradient enforces acceleration of fluid)
- PWV is proportional to the square root of the vessel elastic modulus
- much faster than the mean blood flow velocity (depends on momentum transfer not mass transfer)
What is the Dicrotic Wave?
- results from the superposition of reflected pulse waves
- backward propagating pulse wave reflected back to the heart
- -> will be reflected again at closed aortic valve
- -> causes second maximum in graph when it reaches the periphery
second maximum = dicrotic wave
Sensitivity of Blood Pressure
on what does it depend?
- mean blood pressure is proportional to c² (c = pulse wave velocity)
–> blood pressure is dependent on blood flow and pulse wave velocity
Determination of PTT with ECG and Peripheral Pulse
PTT: time from R-peak of ECG to begin of peripheral pulse
What is the difference between the electrical cable equation and the arteries?
Arterial elasticity is continuously decreasing along the arterial tree
Arterial tube gets narrower –> like multiple cross sectional jumps in series
Is the pulse wave velocity constant along the arteries?
No
How many layers do the arteries have?
3 layers with different functions
What is the relationship between PTT / pulse wave velocity c and the mean blood pressure?
- mean blood pressure is proportional to 1/PTT²
- mean blood pressure is proportional to c²
Is the pulse wave velocity age dependent?
Yes –> it increases
What does the Compliance describe?
The ability to store volume
What is the reflection coefficient k_e in case of a short circuit? and for a matched impedance?
short circuit: k_e = 1 (Z_last = 0)
matched cable: k_e = 0 (Zi = Z_last)
What kind of differential equation is the undamped wave equation?
2nd order partial differential equation
undamped –> total pressure and flow are given by the forward and backward wave
Is the elasticity of the arteries constant?
No, it changes with the static pressure
