MA 325 Mon-Wed-Fri 12.25-1.15 pm
Class-room: SAS Hall 2229
Instructor: Mette S Olufsen
Office: SAS 3216
Office Hours: By appointment
Phone Number: 515-2678
1. Introduction to
cardiovascular models (steady state) (pdf)
2. Cardiovascular models
(steady state): notes and exercises
3. Cardiovascular models
4. Cardiovascular models
(sensitivities and HW 2) (pdf)
5. Time varying
cardiovascular model: paper
Matlab code (zip-file)
9. Cardiovascular models
lecture 3 (pdf)
10. Cardiovascular models lecture 4 (pdf)
Homework 1 (Due Wed 2/26)
equations displayed on Fig 1.6 for V, P, and Q as a function of
parameters (R's, C's, and K's).
The figure can be found in the powerpoint and
notes on CV models.
problems 1.2, 1.3, 1.4, 1.5, and 1.10 from the notes on CV models.
(Due Wed 2/5)
1: In code enter:
for flows and the right hand side for the ODE's. HAND IN CODE AS
PART OF YOUR HOMEWORK.
Run the code (DriverBasic) and solve equations. Plot all states
(pau, pal, pvl, pvu, Vlv).
3: Calculate and plot all pressures (pau, pal,
pvl, pvu), volumes (Vau, Val, Vvl, Vvu, and Vlv (note this is
a state)) and flows (qaup, qal, qalp, qvl).
4: Derive sensitivity equations as shown on slide
11 for three parameters, you do not have to derive them wrt pau (you
can do one of the other states
e.g. pal, pvl, pvu or Vlv).
5: Compute sensitivities for pau and show ranking
(as shown on Slide 17 - left graph). To compute sensitivities run
6: Plot sensitivities as a function of time for
three parameters, one that is sensitive, one that is medium
sensitive, and one that is insensitive
(make a graph similar to the one on slide 17 right graph - for this
run "DriverBasic_sens" and change figure 1).
7: For the 3 most sensitive parameters change
their values and re-solve equations (run DriverBasic), what do you
observe for the states.
Summarize results in a Table.
8: Discuss results what did you observe?
(Due Wednesday 3/19 -Wednesday after spring break)
CODE: CvCodeOpt.zip Data.zip
1. Subject 1
(height 174 weight 75, Male), Subject 2 (height 160,
weight 52, Female),
Subject 3 (height 170,
weight 63, Female), Subject 4 (height 182, weight 89,
For each of the four subjects:
2. In load_global.m enter height,
weight, and gender
3. With initial parameter values run
DriverBasic plot all states (pau, pal, pvl, pvu, Vlv)
4. Compute sensitivity ranking by running
DriverBasic_sens (show graph with ranked sensitivities and on
the graph note order of parameters)
5. Find a subset for the subject by running
DriverBasic_jacobian (in your homework type up what parameters
are in the subset).
6. Estimate parameters in the subset - to do
so in DriverBasic_optimization edit INDMAP = [ xxx ]
representing the parameters in your subset.
In the command window the
optimization starts outputting numbers on the form
0 1.0000 142.9458
This continues until the
algorithm has converged and the prompt comes back, these
the gradient, the cost, the
iteration number, a second index, and a number indicating how
well the problem is conditioned. The first
two numbers should decrease,
whereas the iteration number goes up.
When the optimization is done you
have a file called xopt.mat this contains your optimized
parameter values in a vector x.
7. When your optimization is finished run
DriverBasic again with the optimized parameters. To load
in DriverBasic.m uncomment
lines 19 and 20 and put a comment ("%") in front of pars = x0
on line 22.
Again plot all states (pau,
pal, pvl, pvu, Vlv), volumes (Vau, Val, Vvl, Vvu), and cardiac
8. In a table note optimized parameters for
each of the three subjects, calculate mean value and standard
deviation for each
9. Discuss what you have learned about the