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 via email.
    Phone Number: 515-2678
    Email address:


    1.    Introduction to cardiovascular models (steady state) (pdf)
    2.    Cardiovascular models (steady state): notes and exercises
    3.    Cardiovascular models (time-varying) (pdf)
    4.    Cardiovascular models (sensitivities and HW 2) (pdf)
    5.    Time varying cardiovascular model: paper
    6.    Blood pressure data: Data (zip-file)
    7.    New version of "run_periods.m"
    8.    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 3/27)
           1:  Solve 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.
           2:  Solve problems 1.2, 1.3, 1.4, 1.5, and 1.10 from the notes on CV models.

Homework 2 (Due Wednesday 4/3)
           1:    In code enter:
                    load_global.m:    Height, weight, gender
                    modelBasic.m:    Equations for flow and ODE's
           2:    Run the code (DriverBasic) and solve equations. Plot all states (pau, pal, pvl, pvu, Vlv).
           3:    Calculate and plot remaining volumes, qaup, and qalp.
           4:    Compute sensitivities for pau and show ranking.
           5:    Plot sensitivities as a function of time for three parameters
           6:    For 3 parameters change values and re-solve equations, what do you observe for the states. Summarize in Table.

Homework 3 (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 2.
                   In the command window the optimization starts outputting numbers on the form
                    2    2    2
                   1.2583    0.6514         0         0  356.2807
                   1.0327    0.0330         0    1.0000  142.9458

                   This continues until the algorithm has converged and the prompt comes back, these numbers represent
                   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 optimized parameters
                   in load_global (lines XX)

                    %load xopt.mat
                    %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 optimized parameters.

             HW: For this homework, A) show all five states (pau, pal, pvl, pvu, and Vlv) with both nominal parameter values and optimized parameter values.
                      B) Compare values for the parameters (write out values for x0 and x (both found in xopt.mat)) and compare values that differ (those that were estimated)
                      C) What do you observe, how did the parameter values change to make the model match your data?
                      D) Then discuss in a paragraph what you have learned from modeling the CV system, you should put yourself in a situation where you need to
                      advice a clinician how he/she can use modeling to provide more information to the patient.