E7 Mondays 12.30 - 15.30:

Class-room: 27.1 room II

    Instructor: Mette S Olufsen
    Office: 27.1 (first floor)
    Office Hours: By appointment via email.
    Phone Number: 4672 2297
    Email address: msolufse@ruc.dk

Documents:

    1.    Syllabus
    2.    Physiology chapter (Larsen, Ottesen, Olufsen)
    3.    Chapter 1
    4.    Pulsatile model
    5.    Heart model (section 4.3.1)
    6.    Fetal circulation
    7.    Smooth function
    8.    Optimization book
    9.    Daun, Rubin et al.
   10.   Code subset and optimization
   11.   Cinton-Arias, Banks et al.

Homework:

14/9: Read Chapter 1 from Hoppenstead and Peskin (Chap1A and 1B)

23/9: Solve equations, do problems 1.2 - 1.5, 1.10, and 1.11
         Read sections 1.9 (autoregulation) and 1.10 (Changes in the circulation occuring at birth), and pages 93-99 in the
         article by Pope et a. (Pulsatile model).
          (NOTE CHANGED DUE DATE)

28/9: Read notes on the heart model and the pulsatile model (a similar model - though without the lungs can be found in
         the paper "Pulsatile model" listed above.
         Develop equations for a pulsatile model including systemic and pulmonary circulation. Include the heart model
         described in section 4.3.1. Include arteries and veins for both the systemic and pulmonary circulations. Also
         include estimates for all model parameters.

       Fetal circulation: show

          Qs/Q = 2 Rp / (Rp + Rs)
          Qp/Q = 2 Rs / (Rp + Rs)

2/10: Complete Homework for 28/9. In particular write up equations for pulsatile model, predict parameter values
and try implementing the model in matlab.

          Compute sensitivities for two parameters with respect to pas, i.e. compute dpas/dpar1 and dpas/dpar2. Note do
          not compute sensitivities for e.g. two resistors or two capacitors. Instead chose one resistor and one capacitor.
          Sketch how many equations must be solved to calculate dpas/dpar for al paraemters.

2/11: Read chapter 1 and 2 (until 2.4.2) in the optimization book (link above).
          Use the code "compilesens" to calculate sensitivities dpas/dpar and dvacp/dpar (sensitivities wrt pressure and
          velocity. Note, velocities are computed as v = 1/A ( pac - pvc )/Racp.

16/11: Read the paper by Daun, Rubin et al. in particular read sections 2.3 - 2.5. In class we will discuss how to
           tease out pairwise correlations from the model.

          Run the "subset" code and vary parameters fixed to understand how subset changes. In class we fixed Aacp, try
          and fix some other parameters of your choice and discuss how that impacts the subset.

          Once you have fixed a subset run the "runopt"code to do an optimization. Importnat information outputted while
          the code is running are (first collumn: Gradient; second column: Cost).

Final HW: Final homework I would like:
        1. Implement and describe (in mathematical terms)
              correlation in your code and use it to predict what parameters are correlated.
          2. Vary the initial guess for the model parameters and see if that impact correlations or subsets.
          3. Use results of 1 and 2 to identify one parameter set.
4. Run optimization with selected parameters.
5. Discuss how initial parameter values impact result.
6. Discuss how the model and results can be used for analysis of data and or design of experiments.
          7. Discuss how to validate the model.

          To complete this homework use paper by Daun et al. and Cintron-Arias et al. (listed above).