MA 325 Mon-Wed-Fri 12.25-1.15 pm:
Class-room: SAS Hall 2225
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
pressure data: Data (zip-file)
7. New version of
Matlab code (zip-file)
9. Cardiovascular models
ver 3: (pdf)
10. Matlab code parameter estimation (zip-file)
11. Cardiovascular models (parameter
estimation and HW 3) (pdf)
Homework 1 (Due Wednesday
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 Wednesday 4/3)
1: In code enter:
load_global.m: Height, weight, gender
modelBasic.m: Equations for flow and ODE's
Run the code (DriverBasic) and solve equations. Plot all states
(pau, pal, pvl, pvu, Vlv).
3: Calculate and plot remaining volumes, qaup, and
4: Compute sensitivities for pau and show ranking.
5: Plot sensitivities as a function of time for
6: For 3 parameters change values and re-solve
equations, what do you observe for the states. Summarize in Table.
(Due Friday 4/12)
1. From the xcel
file (Fina list.xlsx) you will find information that links
people to the data.
2. In load_global.m enter height,
weight, and gender for the subject you use.
3. To run the code with your data in
DriverBasic.m add the data you want to use. For example, line
7 "load data2.mat" loads data from subject 2.
Run model with nominal
parameter values run "DriverBasic" it provides graphs, you may
want to add graphs to plot all states.
4. To run optimization, in
DriverBasic_optimization.m load the data set you want to use.
For example, line 4 "load data2.mat" loads data from subject
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.
5. When your optimization is finished run
DriverBasic again with the optimized parameters. To load
in load_global (lines XX)
%x0 = x;
remove the "%" in front
of these lines, this allows you to load your optimized
parameters. Then run "DriverBasic" again and you
will get graphs with
HW: For this homework, A) show all five states (pau, pal, pvl,
pvu, and Vlv) with both nominal parameter values and optimized
values for the parameters (write out values for x0 and x (both
found in xopt.mat)) and compare values that differ (those that
C) What do
you observe, how did the parameter values change to make the
model match your data?
discuss in a paragraph what you have learned from modeling the
CV system, you should put yourself in a situation where you
clinician how he/she can use modeling to provide more
information to the patient.