1 - o = 50 mL/sec 2 Vessels act like circuits(as in the...

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BENG 112B BIOMECHANICS S 2009 Homework #1 Due Tuesday 4/7 before class Suggested Reading: Fung Chapters 2 and 8 Analysis Problems: In 1899 Otto Frank proposed the “Windkessel” theory for blood flow in the aorta based on the diagram on the right. Let Q(t) be the flow rate into the aorta (cm 3 /sec). V(t) is the volume of the system depicted above, such that dV/dt is proportional to dp/dt, with P(t) being the internal pressure of the aorta. p/R is the flow rate out of the aorta and R is the systemic resistance to flow. The differential equation governing pressure P(t) is: Q = K(dp/dt) + p/R. Assuming a vessel stiffness, K, of 5 cm 3 /mmHg and a resistance of R = 1 kdyne-sec/cm 5 , find the arterial pressure if the flow rate into the vessel is Q(t) = Q o sin( ω t), where ω = 2 πν and ν = 1 Hz and Q
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Unformatted text preview: o = 50 mL/sec. 2. Vessels act like circuits (as in the analogy from class; V = IR). Given that relationship and what you should know about the resistance of circuits in series or parallel, describe in mathematical terms how a blockage at point A would change the resistance in the simple arcade arteriole system to the right? Hint: you should compare both the unblocked and blocked cases as you present your answer as well as treating the internal resistance in each vessel (or branch) as R i . Design Problems: 1. Propose a circulatory tree (including both arterial and venule components, separating the twin sides with a dashed line) with similar branching ratios as discussed in class that mimics the arcade arteriole network discussed in the first lecture. P(t) Q(t) R K A...
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This note was uploaded on 09/02/2009 for the course BENG 112B taught by Professor Huang during the Spring '08 term at UCSD.

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