MGC 3143, M. Fenech.
MATLAB
ASSIGNEMENT
The Wormersley equations: blood pulsatil flow in the artery.
Each student should do their own assignment, although you may work together. You may NOT share
electronic copies of the solution. Working together means that you may look at each other’s work,
ask questions, discuss solutions, but please not copy paste!
Objectives
• To apply the Navier&Stocks equations to unsteady flow
• To gain practice using a Fourier coefficients representation to generate a
pressure waveform in Maple.
• To generate a flow waveform from a pulsatile pressure waveform
eθ
er
ez
V
PART 1: Resolution of Navier stocks equations in classe
PART 2: Visualisation: Matlab
MATLAB, 1/3
MGC 3143, M. Fenech.
The diameter of the artery is 2.5 mm. We assume a constant blood viscosity μ = 0.0035 Ns/m2 and
ρ = 1060 kg/m3.
Question 1- The Fourier coefficients shown below describe the pressure-gradient-versus-time
curve in femoral artery. The frequency is 1 Hz (Recall ω=2π/Period). Plot the pressure-gradientversus-time curve.
n
an
coefficient
(Pa/m)
0
-621
1
1250i
2
531
Matlab: You can use i or j for the unit complex number, but be careful to not use the same letter for
another variable. You can take the real part of a number using real( ).
Question 2. Using the Womersley’s Navier-Stokes solution, on 4 different figures, plot the 3
terms of the velocity (n=0, n=1, n=20) and the total velocity as a function of the radius at t=0.5s
With Matlab, the Bessel function command for a zero order Bessel function is BesselJ(0,
argument).
Question 3- On 4 different figures, plot the 3 terms of the velocity (n=0, n=1, n=2) and the total
velocity profile as a function of radius for t=0 to t=1 (20 plots per graph ).
With Matlab use the commands ‘hold on’ ’hold off’.
Question 4- Integrate numerically the velocity V(r,t) over the entire cross-section of the
vessel. The output is flowrate, Q(t). Please show the flowrate in liter/minute.
Question 5- In some dieses the blood viscosity could reach 8 cP. Plot the velocity as a function
of the radius as in question 3 using this hyperviscosity.
Question 6- Discuss the results obtained Question 3 and 5 highlighting α value in each case.
Question 7- To conclude discuss the assumptions made in this model and propose how to
assess the model.
You have to submit a hard copy of your report including an introduction and a conclusion. For each
question mathematical form of equation, extract of matlab code, figures and description of results
are expected.
MATLAB, 2/3
MGC 3143, M. Fenech.
MATLAB, 3/3