Derive differential equation of circuit

Discussion in 'Homework Help' started by tquiva, Sep 30, 2013.

  1. tquiva

    Thread Starter Member

    Oct 19, 2010
    176
    1
    I'm currently working on a biomedical engineering problem that is based on electrical engineering circuits. Below is the following problem:

    [​IMG]

    Eq. (4.71) is:

    [​IMG]

    From this equation, I derived p(t) as follows:

    [​IMG]

    Below is the work I've done so far with what I am provided:

    [​IMG]

    At this point, I have no idea what to do in order to move forward. I know that p1=p-QZo. And this can be substituted into Q, and Q can be substituted back into p(t). But then, this still leaves me with an unknown value of "p" and "Q."

    If I take the integrals on both sides for equation p(t), taking the integral of the derivative will only add a constant to the equation, which is also unknown.

    How would any of you proceed with this problem?
    Any help is greatly appreciated!! :)
     
    Last edited: Sep 30, 2013
  2. WBahn

    Moderator

    Mar 31, 2012
    17,715
    4,788
    None of your figures is rendering.

    Please upload your images to the AAC server so that they will be attached to your post.
     
  3. tquiva

    Thread Starter Member

    Oct 19, 2010
    176
    1
    Sorry about that, just uploaded all the attachments. Any suggestions guys??
     
  4. wayneh

    Expert

    Sep 9, 2010
    12,086
    3,025
    And the parameter values in Table 4.4?
     
  5. tquiva

    Thread Starter Member

    Oct 19, 2010
    176
    1
    Sorry about that, I have the values from Table 4.4 is my derivation.

    [​IMG]
     
  6. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    Presumably with the aortic valve closed there is no flow Q from the heart and the solution would be relatively trivial.
     
  7. tquiva

    Thread Starter Member

    Oct 19, 2010
    176
    1
    I got a first order differential equation, since Q(t) = 0:

    p'(t) = -(1/1.5)p(t)

    How would I go about solving for p with the given information I have? I don't have the values for an initial value problem?

    I put this into MatLab and made up a value for y(1).

    Did I do it correctly?

    p=dsolve('Dp=-(1/1.5)*p','t');
    eqn1='Dp=-(1/1.5)*p';
    p=dsolve(eqn1,'p(1)=1','t');
    ezplot(p), xlabel('t'), ylabel('p(t)'), title('p(t)')

    The result is an exponentially decaying curve.
     
  8. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    Both those statements make sense.

    BTW: Did you realize the electrical analogue you are working with is usually described as the Three-Element Windkessel Model of The Peripheral System? Perhaps of use as a lead if you wanted to look into the origin & derivation of the differential equation 4.71 mentioned in your original post. Perhaps you already know this since you are undertaking a Biomed course.
     
    Last edited: Oct 1, 2013
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