Lecture 7 - Inertance + Oscillatory flow theory

Question 1

What is inertance?

Answer 1

Inertance relates pressure drop with acceleration of flow, symbol L

L = rho * l / A

Inertance plays a bigger role in large vessels than resistance. Opposite for small vessels.

Question 2

Pressure drop using inertance?

Answer 2

deltaP(t) = dQ / dt

Question 3

Explain the inertance effect.

Answer 3

During ventricular ejection flow is first
accelerating and then decelerating;

When accelerating ventricular pressure is
higher then aortic pressure;

When blood is decelerated the pressure
difference reverses;

Pressure difference and time derivative of flow
are almost proportional in systole –> inertance
effect

Question 4

Describe Womersley’s theorum

Answer 4

Womersley’s theory relates an oscillatory, sinusoidal pressure drop to flow in a rigid tube, used due to blood flow being pulsatile

Question 5

Womersley parameter equation? (alpha)

Answer 5

alpha^2 = (r_i^2 * omega * rho) / eta

Question 6

What are the are velocity profiles at different womersley’s numbers?

Answer 6

alpha < 3 - parabolic, viscosity dominates (reduces to effectively poiseuille)

alpha = 7 - balance between inertial and viscous forces, flatter profile

alpha > 10 - inertial effects dominate and profile becomes flat