Lecture 12 - Flow modelling

Question 1

Which velocity profiles are seen in arterial flow modelling wrt alpha?

Answer 1

Flat profile: alpha = 16 (large elastic arteries)
Parabolic profile: alpha = 2 (small arteries)

Question 2

How can you simplify the velocity profile

Answer 2

Coriolis’ coefficient

Question 3

what is the electric circuit analogy of blood flow?

Answer 3

Resistance = viscous resistance
Capacitance = vessel compliance
Inductance = inertial effect
Complex velocity profiles can be simulated by adding combinations of inductances and resistances in parallel
Time evolution of pressure and flow in the system
No spatial discretisation

Question 4

Which dimension of model should be used for each vessel in a multiscale vascular model?

Answer 4

long elastic vessel - 1d
Capillary - 0d

Question 5

Womersley Number Equation

Answer 5

alpha = l * sqrt [ (2pirho) / (Tc*mu) ]

Question 6

Womersley Number parameters

Answer 6

alpha - womersley number
rho - density
Tc - period of cardiac cycle
mu - dynamic viscosity
l - characteristic length (but basically radius)

Question 7

Which equations are key for deriving other important simplified equations in 1d and 0d?

Answer 7

Continuity equations (mass, energy, momentum)