Derive differential equation of circuit

Thread Starter

tquiva

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



Eq. (4.71) is:



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



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



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!! :)
 

Attachments

Last edited:

WBahn

Joined Mar 31, 2012
27,868
None of your figures is rendering.

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

t_n_k

Joined Mar 6, 2009
5,455
Presumably with the aortic valve closed there is no flow Q from the heart and the solution would be relatively trivial.
 

Thread Starter

tquiva

Joined Oct 19, 2010
176
Presumably with the aortic valve closed there is no flow Q from the heart and the solution would be relatively trivial.
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.
 

t_n_k

Joined Mar 6, 2009
5,455
I got a first order differential equation, since Q(t) = 0

........

The result is an exponentially decaying curve.
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:
Top