Question

Question 1 [25 marks] (a) Derive the Windkessel governing equation for pressure fluctuation in a compliant aorta $\frac{Q}{C} = \frac{dP(t)}{dt} + \frac{P(t)}{RC}$ defining all terms used in the derivation. [3] (b) Using the equation given in Part (a) above, show that the general solution for the aortic pressure is given by $P(t_c) = e^{-t_c/RC} \int_0^{t_c} \frac{Q}{C} e^{t/RC} dt + P(0)e^{-t_c/RC}$ [3]

          Question 1 [25 marks]
(a) Derive the Windkessel governing equation for pressure fluctuation in a compliant
aorta
$\frac{Q}{C} = \frac{dP(t)}{dt} + \frac{P(t)}{RC}$
defining all terms used in the derivation.
[3]
(b) Using the equation given in Part (a) above, show that the general solution for the
aortic pressure is given by
$P(t_c) = e^{-t_c/RC} \int_0^{t_c} \frac{Q}{C} e^{t/RC} dt + P(0)e^{-t_c/RC}$ 
[3]

Question 1 [25 marks]
(a) Derive the Windkessel governing equation for pressure fluctuation in a compliant
aorta
(Q)/(C) = (dP(t))/(dt) + (P(t))/(RC)
defining all terms used in the derivation.
[3]
(b) Using the equation given in Part (a) above, show that the general solution for the
aortic pressure is given by
P(tc) = e^-tc/RC∫0^tc(Q)/(C) e^t/RC dt + P(0)e^-tc/RC
[3]

Added by Jessica P.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

10/01/2023

Step 1

The model is based on the idea that the aorta can be represented as a compliant vessel that can store and release blood. Show more…

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Question 1 [25 marks] (a) Derive the Windkessel governing equation for pressure fluctuation in a compliant aorta $$ \frac{Q}{C} = \frac{dP(t)}{dt} + \frac{P(t)}{RC} $$ defining all terms used in the derivation. [3] (b) Using the equation given in Part (a) above, show that the general solution for the aortic pressure is given by $$ P(t_c) = e^{-t_c/RC} \int_0^{t_c} \frac{Q}{C} e^{t/RC} dt + P(0)e^{-t_c/RC} $$ [3] Q ↑ Qo 0.3 s 0.8 s t Q1 Figure Q1